Hibbeler – Engineering Mechanics – Statics 12th Edition Solution Manual

Hibbeler – Engineering Mechanics – Statics 12th Edition Solution Manual

1. 1
1–1.Round off the following numbers to three significant
figures: (a) 4.65735 m, (b) 55.578 s, (c) 4555 N, and
(d) 2768 kg.
1–2.Represent each of the following combinations of units
in the correct SI form using an appropriate prefix: (a) ,
(b) , (c) , and (d) . kN>msMN>ks
2
N>mm
mMN
1–3.Represent each of the following quantities in the
correct SI form using an appropriate prefix: (a) 0.000431 kg,
(b) , and (c) 0.00532 km.35.3(10
3
) N
*1–4.Represent each of the following combinations of
units in the correct SI form: (a) , (b) , and
(c) .mN>(kg
#
ms)
N>mmMg>ms
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1 Solutions 44918 1/21/09 8:43 AM Page 1

2. 2
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1–5.Represent each of the following combinations of
units in the correct SI form using an appropriate prefix:
(a) , (b) , and (c) . MN>(kg
#
ms)Mg>mNkN>ms
1–7.A rocket has a mass of slugs on earth.
Specify (a) its mass in SI units and (b) its weight in SI units.
If the rocket is on the moon, where the acceleration due to
gravity is , determine to three significant
figures (c) its weight in SI units and (d) its mass in SI units.
g
m=5.30 ft>s
2
250(10
3
)
*1–8.If a car is traveling at , determine its speed in
kilometers per hour and meters per second.
55 mi>h
1–6.Represent each of the following to three significant
figures and express each answer in SI units using an
appropriate prefix: (a) 45 320 kN, (b) , and (c)
0.005 63 mg.
568(10
5
) mm
FPO
FPO
1 Solutions 44918 1/21/09 8:43 AM Page 2

3. 3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
1–9.The pascal(Pa) is actually a very small unit of
pressure. To show this, convert to .
Atmospheric pressure at sea level is in
2
. How many
pascals is this?
14.7 lb>
lb>ft
2
1 Pa=1 N>m
2
FPO
1–10.What is the weight in newtons of an object that has a
mass of: (a) 10 kg, (b) 0.5 g, and (c) 4.50 Mg? Express the
result to three significant figures. Use an appropriate prefix.
1–11.Evaluate each of the following to three significant
figures and express each answer in Sl units using
an appropriate prefix: (a) 354 mg(45 km) (0.0356 kN),
(b) (0.004 53 Mg)(201 ms), and (c) 435 MN 23.2 mm.>
>
*1–12.The specific weight (wt. vol.) of brass is .
Determine its density (mass vol.) in SI units. Use an
appropriate prefix.
>
520 lb>ft
3
>
1 Solutions 44918 1/21/09 8:43 AM Page 3

4. 4
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1–13.Convert each of the following to three significant
figures: (a) to , (b) to , and
(c) 15 ft h to mm s.>>
kN>m
3
450 lb>ft
3
N#
m20 lb#
ft
1–14.The density (mass volume) of aluminum is
. Determine its density in SI units. Use an
appropriate prefix.
5.26 slug>ft
3
>
1–15.Water has a density of . What is the
density expressed in SI units? Express the answer to three
significant figures.
1.94 slug>ft
3
*1–16.Two particles have a mass of 8 kg and 12 kg,
respectively. If they are 800 mm apart, determine the force
of gravity acting between them. Compare this result with
the weight of each particle.
1 Solutions 44918 1/21/09 8:43 AM Page 4

5. 5
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
1–17.Determine the mass in kilograms of an object that
has a weight of (a) 20 mN, (b) 150 kN, and (c) 60 MN.
Express the answer to three significant figures.
1–18.Evaluate each of the following to three significant
figures and express each answer in SI units using an
appropriate prefix: (a) , (b) , and
(c) .(400
m)
3
(0.005 mm)
2
(200 kN)
2
1–19.Using the base units of the SI system, show that
Eq. 1–2 is a dimensionally homogeneous equation which
gives Fin newtons. Determine to three significant figures
the gravitational force acting between two spheres that
are touching each other. The mass of each sphere is 200 kg
and the radius is 300 mm.
1 Solutions 44918 1/21/09 8:43 AM Page 5

6. 6
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*1–20.Evaluate each of the following to three significant
figures and express each answer in SI units using an
appropriate prefix: (a) , and
(b) .(35 mm)
2
(48 kg)
3
(0.631 Mm)>(8.60 kg)
2
1–21.Evaluate (204 mm)(0.00457 kg) (34.6 N) to three
significant figures and express the answer in SI units using
an appropriate prefix.
>
1 Solutions 44918 1/21/09 8:43 AM Page 6

7. 7
•2–1.If and , determine the magnitude
of the resultant force acting on the eyebolt and its direction
measured clockwise from the positive xaxis.
T=6 kNu=30°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8 kN
T
x
y
u
45
2 Solutions 44918 1/21/09 12:01 PM Page 7

8. 8
2–2.If and , determine the magnitude
of the resultant force acting on the eyebolt and its direction
measured clockwise from the positive xaxis.
T=5 kNu=60°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8 kN
T
x
y
u
45
2 Solutions 44918 1/21/09 12:01 PM Page 8

9. 9
2–3.If the magnitude of the resultant force is to be 9 kN
directed along the positive xaxis, determine the magnitude of
force Tacting on the eyebolt and its angle .u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8 kN
T
x
y
u
45
2 Solutions 44918 1/21/09 12:01 PM Page 9

10. 10
*2–4.Determine the magnitude of the resultant force
acting on the bracket and its direction measured
counterclockwise from the positive uaxis.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
u
F
1
200 lb
F
2
150 lb
v
30
30
45
2 Solutions 44918 1/21/09 12:01 PM Page 10

11. 11
•2–5.Resolve F
1
into components along the uand axes,
and determine the magnitudes of these components.
v
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
u
F
1
200 lb
F
2
150 lb
v
30
30
45
2 Solutions 44918 1/21/09 12:01 PM Page 11

12. 12
2–6.Resolve F
2
into components along the uand axes,
and determine the magnitudes of these components.
v
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
u
F
1
200 lb
F
2
150 lb
v
30
30
45
2 Solutions 44918 1/21/09 12:01 PM Page 12

13. 13
2–7.If and the resultant force acts along the
positive uaxis, determine the magnitude of the resultant
force and the angle .u
F
B=2 kN
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
u
B
F
A
3 kN
F
B
A
u30
2 Solutions 44918 1/21/09 12:01 PM Page 13

14. 14
*2–8.If the resultant force is required to act along the
positive uaxis and have a magnitude of 5 kN, determine the
required magnitude of F
B
and its direction .u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
u
B
F
A
3 kN
F
B
A
u30
2 Solutions 44918 1/21/09 12:01 PM Page 14

15. 15
•2–9.The plate is subjected to the two forces at Aand B
as shown. If , determine the magnitude of the
resultant of these two forces and its direction measured
clockwise from the horizontal.
u=60°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
B
F
A
8 kN
F
B
6 kN
40
u
2 Solutions 44918 1/21/09 12:01 PM Page 15

16. 16
2–10.Determine the angle of for connecting member A
to the plate so that the resultant force of F
A
and F
B
is
directed horizontally to the right.Also, what is the magnitude
of the resultant force?
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
B
F
A
8 kN
F
B
6 kN
40
u
2–11.If the tension in the cable is 400 N, determine the
magnitude and direction of the resultant force acting on
the pulley. This angle is the same angle of line ABon the
tailboard block.
u
400 N
30
y
A
B
x
400 N
u
2 Solutions 44918 1/21/09 12:01 PM Page 16

17. 17
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*2–12.The device is used for surgical replacement of the
knee joint. If the force acting along the leg is 360 N,
determine its components along the xand yaxes.¿
60
360 N
10
y
x
y
¿
x¿
2 Solutions 44918 1/21/09 12:01 PM Page 17

18. 18
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•2–13.The device is used for surgical replacement of the
knee joint. If the force acting along the leg is 360 N,
determine its components along the xand yaxes.¿
60
360 N
10
y
x
y
¿
x¿
2 Solutions 44918 1/21/09 12:01 PM Page 18

19. 19
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–14.Determine the design angle for
strut ABso that the 400-lb horizontal force has a
component of 500 lb directed from Atowards C.What is the
component of force acting along member AB? Take
.f=40°
u (0° … u … 90°) A
C
B
400 lb
u
f
2–15.Determine the design angle
between struts ABand ACso that the 400-lb horizontal
force has a component of 600 lb which acts up to the left, in
the same direction as from Btowards A. Take .u=30°
f (0° … f … 90°)
A
C
B
400 lb
u
f
2 Solutions 44918 1/21/09 12:01 PM Page 19

20. 20
*2–16.Resolve F
1
into components along the uand axes
and determine the magnitudes of these components.
v
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
1 250 N
F
2 150 N
u
v
30
30
105
•2–17.Resolve F
2
into components along the uand axes
and determine the magnitudes of these components.
v
F
1 250 N
F
2 150 N
u
v
30
30
105
2 Solutions 44918 1/21/09 12:01 PM Page 20

21. 21
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–18.The truck is to be towed using two ropes. Determine
the magnitudes of forces F
A
and F
B
acting on each rope in
order to develop a resultant force of 950 N directed along
the positive xaxis. Set .u=50°
y
20°
x
A
B
F
A
F
B
u
2–19.The truck is to be towed using two ropes. If the
resultant force is to be 950 N, directed along the positive x
axis, determine the magnitudes of forces F
A
and F
B
acting
on each rope and the angle of F
B
so that the magnitude of
F
B
is a minimum.F
A
acts at 20° from the xaxis as shown.
u
y
20°
x
A
B
F
A
F
B
u
2 Solutions 44918 1/21/09 12:01 PM Page 21

22. 22
*2–20.If , , and the resultant force is
6 kN directed along the positive yaxis, determine the required
magnitude of F
2
and its direction .u
F
1=5 kNf=45°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
1
F
2
x
y
u
f
60
2 Solutions 44918 1/21/09 12:01 PM Page 22

23. 23
•2–21.If and the resultant force is to be 6 kN
directed along the positive yaxis, determine the magnitudes of
F
1
and F
2
and the angle if F
2
is required to be a minimum.u
f=30°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
1
F
2
x
y
u
f
60
2 Solutions 44918 1/21/09 12:01 PM Page 23

24. 24
2–22.If , , and the resultant force is to
be directed along the positive yaxis, determine the
magnitude of the resultant force if F
2
is to be a minimum.
Also, what is F
2
and the angle ?u
F
1=5 kNf=30°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
1
F
2
x
y
u
f
60
2 Solutions 44918 1/21/09 12:01 PM Page 24

25. 25
2–23.If and , determine the magnitude
of the resultant force acting on the plate and its direction
measured clockwise from the positive xaxis.
F
2=6 kNu=30°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
F
3 5 kN
F
1
4 kN
F
2
u
2 Solutions 44918 1/21/09 12:01 PM Page 25

26. 26
*2–24.If the resultant force F
R
is directed along a
line measured 75° clockwise from the positive xaxis and
the magnitude of F
2
is to be a minimum, determine the
magnitudes of F
R
and F
2
and the angle .u…90°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.y
x
F
3
5 kN
F
1
4 kN
F
2
u
2 Solutions 44918 1/21/09 12:01 PM Page 26

27. 27
•2–25.Two forces F
1
and F
2
act on the screw eye. If their
lines of action are at an angle apart and the magnitude
of each force is determine the magnitude of
the resultant force F
R
and the angle between F
R
and F
1
.
F
1=F
2=F,
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
2
F
1
u
2 Solutions 44918 1/21/09 12:01 PM Page 27

28. 28
2–26.The log is being towed by two tractors Aand B.
Determine the magnitudes of the two towing forces F
A
and
F
B
if it is required that the resultant force have a magnitude
and be directed along the xaxis. Set .u=15°F
R=10 kN
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
y
B
A
30
F
A
F
B
u
2–27.The resultant F
R
of the two forces acting on the log is
to be directed along the positive xaxis and have a magnitude
of 10 kN, determine the angle of the cable, attached to Bsuch
that the magnitude of force F
B
in this cable is a minimum.
What is the magnitude of the force in each cable for this
situation?
u
x
y
B
A
30
F
A
F
B
u
2 Solutions 44918 1/21/09 12:01 PM Page 28

29. 29
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*2–28.The beam is to be hoisted using two chains. Deter-
mine the magnitudes of forces F
A
and F
B
acting on each chain
in order to develop a resultant force of 600 N directed along
the positive yaxis. Set .u=45°
F
B F
A
y
x
30
u
2 Solutions 44918 1/21/09 12:01 PM Page 29

30. 30
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•2–29.The beam is to be hoisted using two chains. If the
resultant force is to be 600 N directed along the positive y
axis, determine the magnitudes of forces F
A
and F
B
acting on
each chain and the angle of F
B
so that the magnitude of F
B
is a minimum.F
A
acts at 30° from the yaxis, as shown.
u
F
B F
A
y
x
30
u
2 Solutions 44918 1/21/09 12:01 PM Page 30

31. 31
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–30.Three chains act on the bracket such that they create
a resultant force having a magnitude of 500 lb. If two of the
chains are subjected to known forces, as shown, determine
the angle of the third chain measured clockwise from the
positive xaxis, so that the magnitude of force Fin this chain
is a minimum. All forces lie in the x–yplane. What is the
magnitude of F? Hint: First find the resultant of the two
known forces. Force Facts in this direction.
u
300 lb
200 lb
x
y
F
30
u
2 Solutions 44918 1/21/09 12:01 PM Page 31

32. 32
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–31.Three cables pull on the pipe such that they create a
resultant force having a magnitude of 900 lb. If two of the
cables are subjected to known forces, as shown in the figure,
determine the angle of the third cable so that the
magnitude of force Fin this cable is a minimum. All forces
lie in the x–yplane. What is the magnitude of F? Hint: First
find the resultant of the two known forces.
u
45
30
y
x
400 lb
600 lb
F
u
2 Solutions 44918 1/21/09 12:01 PM Page 32

33. 33
*2–32.Determine the magnitude of the resultant force
acting on the pin and its direction measured clockwise from
the positive xaxis.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
y
F
1 30 lb
F
2 40 lb
F
3 25 lb
15
15
45
2 Solutions 44918 1/21/09 12:01 PM Page 33

34. 34
•2–33.If and , determine the
magnitude of the resultant force acting on the eyebolt and
its direction measured clockwise from the positive xaxis.
f=30°F
1=600 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
3
4
5
F
2
500 N
F
1
F
3
450 N
f
60
2 Solutions 44918 1/21/09 12:01 PM Page 34

35. 35
2–34.If the magnitude of the resultant force acting on
the eyebolt is 600 N and its direction measured clockwise
from the positive xaxis is , determine the magni-
tude of F
1
and the angle .f
u=30°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
3
4
5
F
2
500 N
F
1
F
3
450 N
f
60
2 Solutions 44918 1/21/09 12:01 PM Page 35

36. 36
2–35.The contact point between the femur and tibia
bones of the leg is at A. If a vertical force of 175 lb is applied
at this point, determine the components along the xand y
axes. Note that the ycomponent represents the normal
force on the load-bearing region of the bones. Both the x
and ycomponents of this force cause synovial fluid to be
squeezed out of the bearing space.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
A
175 lb
12
5
13
y
2 Solutions 44918 1/21/09 12:01 PM Page 36

37. 37
*2–36.If and , determine the magnitude
of the resultant force acting on the plate and its direction
measured clockwise from the positive xaxis.
u
F
2=3 kNf=30°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
y
F
2
5
4
3
F
1 4 kN
F
3
5 kN
f
30
2 Solutions 44918 1/21/09 12:01 PM Page 37

38. 38
•2–37.If the magnitude for the resultant force acting on
the plate is required to be 6 kN and its direction measured
clockwise from the positive xaxis is , determine the
magnitude of F
2
and its direction .f
u=30°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
y
F
2
5
4
3
F
1 4 kN
F
3
5 kN
f
30
2 Solutions 44918 1/21/09 12:01 PM Page 38

39. 39
2–38.If and the resultant force acting on the
gusset plate is directed along the positive xaxis, determine
the magnitudes of F
2
and the resultant force.
f=30°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
y
F
2
5
4
3
F
1 4 kN
F
3
5 kN
f
30
2 Solutions 44918 1/21/09 12:01 PM Page 39

40. 40
2–39.Determine the magnitude of F
1
and its direction
so that the resultant force is directed vertically upward and
has a magnitude of 800 N.
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
x
y
F
1
400 N
600 N
3
4
5
30
u
2 Solutions 44918 1/21/09 12:01 PM Page 40

41. 41
*2–40.Determine the magnitude and direction measured
counterclockwise from the positive xaxis of the resultant
force of the three forces acting on the ring A. Take
and .u=20°F
1=500 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
x
y
F
1
400 N
600 N
3
4
5
30
u
2 Solutions 44918 1/21/09 12:01 PM Page 41

42. 42
•2–41.Determine the magnitude and direction of F
B
so
that the resultant force is directed along the positive yaxis
and has a magnitude of 1500 N.
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
B
x
y
B A
30
F
A 700 N
u
2 Solutions 44918 1/21/09 12:01 PM Page 42

43. 43
2–42.Determine the magnitude and angle measured
counterclockwise from the positive yaxis of the resultant
force acting on the bracket if and . u=20°F
B=600 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
B
x
y
B A
30
F
A 700 N
u
2 Solutions 44918 1/21/09 12:01 PM Page 43

44. 44
2–43.If and , determine the
magnitude of the resultant force acting on the bracket and
its direction measured clockwise from the positive xaxis.
F
1=250 lbf=30°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
3
260 lb
F
2
300 lb5
1213
3
4
5
x
y
F
1
f
2 Solutions 44918 1/21/09 12:01 PM Page 44

45. 45
*2–44.If the magnitude of the resultant force acting on
the bracket is 400 lb directed along the positive xaxis,
determine the magnitude of F
1
and its direction .f
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
3
260 lb
F
2
300 lb5
1213
3
4
5
x
y
F
1
f
2 Solutions 44918 1/21/09 12:01 PM Page 45

46. 46
•2–45.If the resultant force acting on the bracket is to be
directed along the positive xaxis and the magnitude of F
1
is
required to be a minimum, determine the magnitudes of the
resultant force and F
1
.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
3
260 lb
F
2
300 lb5
1213
3
4
5
x
y
F
1
f
2 Solutions 44918 1/21/09 12:01 PM Page 46

47. 47
2–46.The three concurrent forces acting on the screw eye
produce a resultant force . If and F
1
is to
be 90° from F
2
as shown, determine the required magnitude
of F
3
expressed in terms of F
1
and the angle .u
F
2=
2
3 F
1F
R=0
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
60
30
F
2
F
3
F
1
u
2–47.Determine the magnitude of F
A
and its direction
so that the resultant force is directed along the positive x
axis and has a magnitude of 1250 N.
u
30
y
x
O
B
A
F
A
F
B 800 N
u
2 Solutions 44918 1/21/09 12:01 PM Page 47

48. 48
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*2–48.Determine the magnitude and direction measured
counterclockwise from the positive xaxis of the resultant
force acting on the ring at Oif and . u=45°F
A=750 N
30
y
x
O
B
A
F
A
F
B 800 N
u
•2–49.Determine the magnitude of the resultant force
and its direction measured counterclockwise from the
positive xaxis.
F
1 = 60 lb
F
2 70 lb
F
3 50 lb
y
x
60
45
1
2
1
2 Solutions 44918 1/21/09 12:01 PM Page 48

49. 49
2–50.The three forces are applied to the bracket.
Determine the range of values for the magnitude of force P
so that the resultant of the three forces does not exceed
2400 N.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3000 N
800 N
P
90
60
2 Solutions 44918 1/21/09 12:01 PM Page 49

50. 50
2–51.If and , det ermine the magnitude
of the resultant force acting on the bracket and its direction
measured clockwise from the positive xaxis.
f=30°F
1=150 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5
12
13
y
x
u
F
3 260 N
F
2
200 N
F
1
f
30
2 Solutions 44918 1/21/09 12:01 PM Page 50

51. 51
*2–52.If the magnitude of the resultant force acting on
the bracket is to be 450 N directed along the positive uaxis,
determine the magnitude of F
1
and its direction .f
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5
12
13
y
x
u
F
3 260 N
F
2
200 N
F
1
f
30
2 Solutions 44918 1/21/09 12:01 PM Page 51

52. 52
•2–53.If the resultant force acting on the bracket is
required to be a minimum, determine the magnitudes of F
1
and the resultant force. Set .f=30°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5
12
13
y
x
u
F
3 260 N
F
2
200 N
F
1
f
30
2 Solutions 44918 1/21/09 12:01 PM Page 52

53. 53
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–54.Three forces act on the bracket. Determine the
magnitude and direction of F
2
so that the resultant force is
directed along the positive uaxis and has a magnitude of 50 lb.
u
x
y
u
12
5
13
F
2
25
F
3 52 lb
F
1 80 lb
u
2 Solutions 44918 1/21/09 12:01 PM Page 53

54. 54
2–55.If and , determine the
magnitude and direction measured clockwise from the
positive xaxis of the resultant force of the three forces
acting on the bracket.
u=55°F
2=150 lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
y
u
12
5
13
F
2
25
F
3 52 lb
F
1 80 lb
u
*2–56.The three concurrent forces acting on the post
produce a resultant force . If , and F
1
is to
be 90° from F
2
as shown, determine the required magnitude
of F
3
expressed in terms of F
1
and the angle .u
F
2=
1
2
F
1F
R=0
x
y
F
1
F
2
F
3
u
2 Solutions 44918 1/21/09 12:01 PM Page 54

55. 55
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•2–57.Determine the magnitude of force Fso that the
resultant force of the three forces is as small as possible.
What is the magnitude of this smallest resultant force? F
8 kN
14 kN
45
30
2 Solutions 44918 1/21/09 12:01 PM Page 55

56. 56
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–58.Express each of the three forces acting on the
bracket in Cartesian vector form with respect to the xand y
axes. Determine the magnitude and direction of F
1
so that
the resultant force is directed along the positive axis and
has a magnitude of .F
R=600 N
x¿
u
F
2 350 N
F
1
F
3 100 N
y
x
x¿
30
30
u
2 Solutions 44918 1/21/09 12:01 PM Page 56

57. 57
2–59.Determine the coordinate angle for F
2
and then
express each force acting on the bracket as a Cartesian
vector.
g
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
z
F
2
600 N
F
1
450 N
45
30
45
60
x
2 Solutions 44918 1/21/09 12:01 PM Page 57

58. 58
*2–60.Determine the magnitude and coordinate direction
angles of the resultant force acting on the bracket.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
z
F
2
600 N
F
1
450 N
45
30
45
60
x
2 Solutions 44918 1/21/09 12:01 PM Page 58

59. 59
•2–61.Express each force acting on the pipe assembly in
Cartesian vector form.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
y
x
5
3
4
F
2
400 lb
F
1
600 lb
120
60
2 Solutions 44918 1/21/09 12:01 PM Page 59

60. 60
2–62.Determine the magnitude and direction of the
resultant force acting on the pipe assembly.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
y
x
5
3
4
F
2
400 lb
F
1
600 lb
120
60
2 Solutions 44918 1/21/09 12:01 PM Page 60

61. 61
2–63.The force Facts on the bracket within the octant
shown. If , , and , determine the
x,y,zcomponents of F.
g=45° b=60°F=400 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
y
z
x
a
b
g
2 Solutions 44918 1/21/09 12:01 PM Page 61

62. 62
*2–64.The force Facts on the bracket within the octant
shown. If the magnitudes of the xand zcomponents of F
are and , respectively, and ,
determine the magnitude of Fand its ycomponent. Also,
find the coordinate direction angles and .ga
b=60°F
z=600 NF
x=300 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
y
z
x
a
b
g
2 Solutions 44918 1/21/09 12:01 PM Page 62

63. 63
•2–65.The two forces F
1
and F
2
acting at Ahave a
resultant force of . Determine the
magnitude and coordinate direction angles of F
2
.
F
R=5-100k6 lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
F
2
A
30
50
F
1 60 lb
z
B
2 Solutions 44918 1/21/09 12:01 PM Page 63

64. 64
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–67.The spur gear is subjected to the two forces caused
by contact with other gears. Express each force as a
Cartesian vector.
135
F
1 50 lb
F
2 180 lb
24
7
25
60
60
z
y
x
*2–68.The spur gear is subjected to the two forces caused
by contact with other gears. Determine the resultant of the
two forces and express the result as a Cartesian vector.
135
F
1 50 lb
F
2 180 lb
24
7
25
60
60
z
y
x
2–66.Determine the coordinate direction angles of the
force F
1
and indicate them on the figure.
y
x
F
2
A
30
50
F
1 60 lb
z
B
2 Solutions 44918 1/21/09 12:01 PM Page 64

65. 65
•2–69.If the resultant force acting on the bracket is
, determine the magnitude
and coordinate direction angles of F.
F
R=5-300i+650j+250k6 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
F
1
750 N
y
z
x
a
b
g
30
45
2 Solutions 44918 1/21/09 12:01 PM Page 65

66. 66
2–70.If the resultant force acting on the bracket is to be
, determine the magnitude and coordinate
direction angles of F.
F
R=5800j6 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
F
1
750 N
y
z
x
a
b
g
30
45
2 Solutions 44918 1/21/09 12:01 PM Page 66

67. 67
2–71.If , , , and ,
determine the magnitude and coordinate direction angles
of the resultant force acting on the hook.
F=400
lbg=60°b690°a=120°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
1 600 lb
F
z
x
y
4
3
5
a
b
g
30
2 Solutions 44918 1/21/09 12:01 PM Page 67

68. 68
*2–72.If the resultant force acting on the hook is
, determine the magnitude
and coordinate direction angles of F.
F
R=5-200i+800j+150k6 lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
1 600 lb
F
z
x
y
4
3
5
a
b
g
30
2 Solutions 44918 1/21/09 12:01 PM Page 68

69. 69
•2–73.The shaft Sexerts three force components on the
die D. Find the magnitude and coordinate direction angles
of the resultant force. Force F
2
acts within the octant shown.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
S
D
z
y
x
3
4
5
F
1 400 N
F
3 200 N
F
2 300 N
g
2 60
a
2 60
2–74.The mast is subjected to the three forces shown.
Determine the coordinate direction angles of
F
1
so that the resultant force acting on the mast is
.
F
R=5350i6 N
a
1, b
1, g
1
F
3 300 N
F
2 200 N
x
z
F
1
y
b
1
a
1
g
1
2 Solutions 44918 1/21/09 12:01 PM Page 69

70. 70
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–75.The mast is subjected to the three forces shown.
Determine the coordinate direction angles of
F
1
so that the resultant force acting on the mast is zero.
a
1, b
1, g
1
F
3 300 N
F
2 200 N
x
z
F
1
y
b
1
a
1
g
1
*2–76.Determine the magnitude and coordinate
direction angles of F
2
so that the resultant of the two forces
acts along the positive xaxis and has a magnitude of 500 N.
y
x
z
F1
180 N
F
2
60
15
b2
a
2
g2
2 Solutions 44918 1/21/09 12:01 PM Page 70

71. 71
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•2–77.Determine the magnitude and coordinate direction
angles of F
2
so that the resultant of the two forces is zero.
y
x
z
F1
180 N
F
2
60
15
b2
a
2
g2
2 Solutions 44918 1/21/09 12:01 PM Page 71

72. 72
2–78.If the resultant force acting on the bracket is directed
along the positive yaxis, determine the magnitude of the
resultant force and the coordinate direction angles of Fso
that .b690°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
y
z
F

500 N
F
1
600 N
a
b
g
30
30
2 Solutions 44918 1/21/09 12:01 PM Page 72

73. 73
2–79.Specify the magnitude of F
3
and its coordinate
direction angles so that the resultant force
.F
R=59j6 kN
a
3, b
3, g
3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
z
5
12
13
y
F
3
30
F
2 10 kN
F
1 12 kN
g
3
b
3
a
3
2 Solutions 44918 1/21/09 12:01 PM Page 73

74. 74
*2–80.If , , and = 45°, determine the
magnitude and coordinate direction angles of the resultant
force acting on the ball-and-socket joint.
fu =30°F
3=9 kN
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4
3
5
F
3
F
2
8 kN
F
1
10 kN
z
y
x
u
f
30
60
2 Solutions 44918 1/21/09 12:01 PM Page 74

75. 75
•2–81.The pole is subjected to the force F, which has
components acting along the x, y, zaxes as shown. If the
magnitude of Fis 3 kN, , and , determine
the magnitudes of its three components.
g=75°b=30°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
F
z
F
y
F
x
F
y
x
a
b
g
2–82.The pole is subjected to the force Fwhich has
components and . If ,
determine the magnitudes of Fand F
y
.
b=75°F
z=1.25 kNF
x=1.5 kN z
F
z
F
y
F
x
F
y
x
a
b
g
2 Solutions 44918 1/21/09 12:01 PM Page 75

76. 76
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–83.Three forces act on the ring. If the resultant force F
R
has a magnitude and direction as shown, determine the
magnitude and the coordinate direction angles of force F
3
.
x
y
z
3
4
5
F
3
45
30
F
1 80 N
F
2 110 N
F
R 120 N
*2–84.Determine the coordinate direction angles of F
1
and F
R
.
x
y
z
3
4
5
F
3
45
30
F
1 80 N
F
2 110 N
F
R 120 N
2 Solutions 44918 1/21/09 12:01 PM Page 76

77. 77
•2–85.Two forces F
1
and F
2
act on the bolt. If the resultant
force F
R
has a magnitude of 50 lb and coordinate direction
angles and , as shown, determine the
magnitude of F
2
and its coordinate direction angles.
b=80°a=110°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
2
80
110
x
y
z
g
F
1 20 lb
F
R 50 lb
2–86.Determine the position vector rdirected from point
Ato point Band the length of cord AB. Take .
z=4 m3 m
2 m
6 m
z
y
z
B
x
A
2 Solutions 44918 1/21/09 12:01 PM Page 77

78. 78
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–87.If the cord ABis 7.5 m long, determine the
coordinate position +zof point B
3 m
2 m
6 m
z
y
z
B
x
A
*2–88.Determine the distance between the end points A
and Bon the wire by first formulating a position vector
from Ato Band then determining its magnitude.
z
x
B
A
y
1 in.
3 in.
8 in.
2 in.
30
60
2 Solutions 44918 1/21/09 12:01 PM Page 78

79. 79
•2–89.Determine the magnitude and coordinate
direction angles of the resultant force acting at A.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2 ft
4 ft
3 ft
3 ft
4 ft
2.5 ft
B
A
x
C
z
F
C
750 lb
F
B
600 lb
2 Solutions 44918 1/21/09 12:01 PM Page 79

80. 80
2–90.Determine the magnitude and coordinate direction
angles of the resultant force.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
z
y
C
B
A
600 N
500 N
8 m
4 m
4 m
2 m
2 Solutions 44918 1/21/09 12:01 PM Page 80

81. 81
2–91.Determine the magnitude and coordinate direction
angles of the resultant force acting at A.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
B
C
A
6 m
3 m
45
4.5 m
6 m
F
B
900 N
F
C
600 N
z
2 Solutions 44918 1/21/09 12:01 PM Page 81

82. 82
*2–92.Determine the magnitude and coordinate direction
angles of the resultant force.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
C
B
4 ft
7 ft
3 ft
x
y
z
F
2
81 lb
F
1
100 l
b
40
4 ft
•2–93.The chandelier is supported by three chains which
are concurrent at point O. If the force in each chain has a
magnitude of 60 lb, express each force as a Cartesian vector
and determine the magnitude and coordinate direction
angles of the resultant force.
120
z
y
120
4 ft
A
B
C
6 ft
O
F
A
F
B
F
C
x
120
2 Solutions 44918 1/21/09 12:01 PM Page 82

83. 83
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–94.The chandelier is supported by three chains which
are concurrent at point O. If the resultant force at Ohas a
magnitude of 130 lb and is directed along the negative zaxis,
determine the force in each chain.
120
z
y
120
4 ft
A
B
C
6 ft
O
F
A
F
B
F
C
x
120
2–95.Express force Fas a Cartesian vector; then
determine its coordinate direction angles.
y
x
z
B
A
10 ft
70
30
7 ft
5 ft
F 135 lb
2 Solutions 44918 1/21/09 12:02 PM Page 83

84. 84
*2–96.The tower is held in place by three cables. If the
force of each cable acting on the tower is shown, determine
the magnitude and coordinate direction angles of
the resultant force. Take , .y=15 mx=20 m
a, b, g
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
z
y
xy
6 m
4 m
18 m
C
A
D
400 N
800 N
600 N
24 m
O
16 m
B
2 Solutions 44918 1/21/09 12:02 PM Page 84

85. 85
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•2–97.The door is held opened by means of two chains. If
the tension in ABand CDis and ,
respectively, express each of these forces in Cartesian
vector form.
F
C=250 NF
A=300 N
x
y
z
2.5 m
1.5 m
0.5 m1 m
30
A
C
B
D
F
A 300 N
F
C 250 N
2–98.The guy wires are used to support the telephone
pole. Represent the force in each wire in Cartesian vector
form. Neglect the diameter of the pole.
y
B
C
D
A
x
z
4 m
4 m
1.5 m
1 m
3 m
2 m
F
A 250 N
F
B 175 N
2 Solutions 44918 1/21/09 12:02 PM Page 85

86. 86
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–99.Two cables are used to secure the overhang boom in
position and support the 1500-N load. If the resultant force
is directed along the boom from point Atowards O,
determine the magnitudes of the resultant force and forces
F
B
and F
C
. Set and . z=2 mx=3 m
z
A
x y
6 m
1500 N
3 m
F
B
F
C
B
C
2 m
x
z
2 Solutions 44918 1/21/09 12:02 PM Page 86

87. 87
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*2–100.Two cables are used to secure the overhang boom
in position and support the 1500-N load. If the resultant
force is directed along the boom from point Atowards O,
determine the values of xand zfor the coordinates of point
Cand the magnitude of the resultant force. Set
and .F
C=2400 NF
B=1610 N
z
A
x y
6 m
1500 N
3 m
F
B
F
C
B
C
2 m
x
z
2 Solutions 44918 1/21/09 12:02 PM Page 87

88. 88
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•2–101.The cable AOexerts a force on the top of the pole
of . If the cable has a length of
34 ft, determine the height zof the pole and the location
(x,y) of its base.
F=5-120i-90j-80k6 lb
y
z
A
z
x
F
x
y
O
2 Solutions 44918 1/21/09 12:02 PM Page 88

89. 89
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–102.If the force in each chain has a magnitude of 450 lb,
determine the magnitude and coordinate direction angles
of the resultant force.
120
120
3 ft
7 ft
120
F
A F
B
F
C
z
C
A
D
B
y
x
2 Solutions 44918 1/21/09 12:02 PM Page 89

90. 90
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–103.If the resultant of the three forces is
, determine the magnitude of the force in
each chain.
F
R=5-900k6 lb
120
120
3 ft
7 ft
120
F
A F
B
F
C
z
C
A
D
B
y
x
2 Solutions 44918 1/21/09 12:02 PM Page 90

91. 91
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*2–104.The antenna tower is supported by three cables. If
the forces of these cables acting on the antenna are
, , and , determine the
magnitude and coordinate direction angles of the resultant
force acting at A.
F
D=560 NF
C=680 NF
B=520 N
24 m
10 m
18 m
8 m
16 m
12 m
18 m
z
x
y
A
O
C
BD
F
B
F
C
F
D
2 Solutions 44918 1/21/09 12:02 PM Page 91

92. 92
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•2–105.If the force in each cable tied to the bin is 70 lb,
determine the magnitude and coordinate direction angles
of the resultant force.
z
B
C
E
D
A
x
y
6 ft
3 ft
3 ft
2 ft
2 ft
F
C
F
D
F
A
F
B
2 Solutions 44918 1/21/09 12:02 PM Page 92

93. 93
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–106.If the resultant of the four forces is
, determine the tension developed in
each cable. Due to symmetry, the tension in the four cables
is the same.
F
R=5-360k6 lb z
B
C
E
D
A
x
y
6 ft
3 ft
3 ft
2 ft
2 ft
F
C
F
D
F
A
F
B
2 Solutions 44918 1/21/09 12:02 PM Page 93

94. 94
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–107.The pipe is supported at its end by a cord AB. If the
cord exerts a force of on the pipe at A, express
this force as a Cartesian vector.
F=12 lb
3 ft
20
yx
A
B
z
5 ft
6 ft
F 12 lb
*2–108.The load at Acreates a force of 200 N in wire AB.
Express this force as a Cartesian vector, acting on Aand
directed towards B.
2 m
1 m
30
120
120
B
A
z
y
x
F 200 N
2 Solutions 44918 1/21/09 12:02 PM Page 94

95. 95
•2–109.The cylindrical plate is subjected to the three cable
forces which are concurrent at point D. Express each force
which the cables exert on the plate as a Cartesian vector,
and determine the magnitude and coordinate direction
angles of the resultant force.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
z
y
D
C
A
B
3 m
30
0.75 m
45
F
B 8 kN
F
C 5 kN
F
A 6 kN
2 Solutions 44918 1/21/09 12:02 PM Page 95

96. 96
2–110.The cable attached to the shear-leg derrick exerts a
force on the derrick of . Express this force as a
Cartesian vector.
F=350 lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
30
50 ft
35 ft
x
y
z
A
B
F 350 lb
2–111.Given the three vectors A, B, and D, show that
.A
#
(B+D)=(A #
B)+(A #
D)
2 Solutions 44918 1/21/09 12:02 PM Page 96

97. 97
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*2–112.Determine the projected component of the force
acting along cable AC. Express the result as a
Cartesian vector.
F
AB=560 N
z
x
y
C
B
A
3 m
1.5 m
1 m
3 m F
AB
560 N
1.5 m
2 Solutions 44918 1/21/09 12:02 PM Page 97

98. 98
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•2–113.Determine the magnitudes of the components of
force acting along and perpendicular to line AO.F=56 N
y
x
z
C
O
D
A
B
3 m
1.5 m
1 m
1 m F

56 N
2 Solutions 44918 1/21/09 12:02 PM Page 98

99. 99
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–114.Determine the length of side BCof the triangular
plate. Solve the problem by finding the magnitude of r
BC
;
then check the result by first finding q,r
AB
, and r
AC
and
then using the cosine law.
y
x
A
C
B
z
1 m
4 m
3 m
3 m
1 m
5 m
u
2 Solutions 44918 1/21/09 12:02 PM Page 99

100. 100
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–115.Determine the magnitudes of the components of
acting along and perpendicular to segment DE
of the pipe assembly.
F=600 N
x y
E
D
C
B
A
z
2 m
2 m
2 m
2 m
3 m
F

600 N
2 Solutions 44918 1/21/09 12:02 PM Page 100

101. 101
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*2–116.Two forces act on the hook. Determine the angle
between them. Also, what are the projections of F
1
and F
2
along the yaxis?
u
x
z
y
45
60
120
F
1
600 N

F
2
{120i + 90j – 80k}N
u
•2–117.Two forces act on the hook. Determine the
magnitude of the projection of F
2
along F
1
.
x
z
y
45
60
120
F
1
600 N

F
2
{120i + 90j – 80k}N
u
2 Solutions 44918 1/21/09 12:02 PM Page 101

102. 102
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–118.Determine the projection of force along
line BC. Express the result as a Cartesian vector.
F=80 N
F

80 N
A
E
B
y
F
C
x
D
z
2 m
2 m
1.5 m
1.5 m
2 m
2 m
2 Solutions 44918 1/21/09 12:02 PM Page 102

103. 103
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–119.The clamp is used on a jig. If the vertical force
acting on the bolt is , determine the
magnitudes of its components F
1
and F
2
which act along the
OAaxis and perpendicular to it.
F={-500k} N
z
O
x
y
40 mm
40 mm
20 mm
F {500 k} N
A
2 Solutions 44918 1/21/09 12:02 PM Page 103

104. 104
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*2–120.Determine the magnitude of the projected
component of force F
AB
acting along the zaxis.
12 ft
18 ft
12 ft
x
B
D
C
A
O
y
z
12 ft
36 ft
F
AB
700 lb
F
AC
600 lb
30
2 Solutions 44918 1/21/09 12:02 PM Page 104

105. 105
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•2–121.Determine the magnitude of the projected
component of force F
AC
acting along the zaxis.
12 ft
18 ft
12 ft
x
B
D
C
A
O
y
z
12 ft
36 ft
F
AB
700 lb
F
AC
600 lb
30
2 Solutions 44918 1/21/09 12:02 PM Page 105

106. 106
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–122.Determine the projection of force
acting along line ACof the pipe assembly. Express the result
as a Cartesian vector.
F=400 N
x
A
B
C
y
z
4 m
3 m
F 400 N
30
45
2 Solutions 44918 1/21/09 12:02 PM Page 106

107. 107
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–123.Determine the magnitudes of the components of
force acting parallel and perpendicular to
segment BCof the pipe assembly.
F=400 N
x
A
B
C
y
z
4 m
3 m
F 400 N
30
45
2 Solutions 44918 1/21/09 12:02 PM Page 107

108. 108
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*2–124.Cable OAis used to support column OB.
Determine the angle it makes with beam OC.u
z
x
C
B
O
D
y
4 m
30
8 m
8 m
A
u
f
•2–125.Cable OAis used to support column OB.
Determine the angle it makes with beam OD.f
z
x
C
B
O
D
y
4 m
30
8 m
8 m
A
u
f
2 Solutions 44918 1/21/09 12:02 PM Page 108

109. 109
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–126.The cables each exert a force of 400 N on the post.
Determine the magnitude of the projected component of F
1
along the line of action of F
2
.
x
z
y
20
35
45
60
120
F
1 400 N
F
2 400 N
u
2–127.Determine the angle between the two cables
attached to the post.
u
x
z
y
20
35
45
60
120
F
1 400 N
F
2 400 N
u
2 Solutions 44918 1/21/09 12:02 PM Page 109

110. 110
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*2–128.A force of is applied to the handle of
the wrench. Determine the angle between the tail of the
force and the handle AB.
u
F=80 N
x
z
B
A
y
300 mm
500 mm
F 80 N
30
45
u
•2–129.Determine the angle between cables ABand AC.u
y
z
x
8 ft
3 ft
12 ft
8 ft
15 ft
A
C
B
F
u
2 Solutions 44918 1/21/09 12:02 PM Page 110

111. 111
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–130.If Fhas a magnitude of 55 lb, determine the
magnitude of its projected components acting along the x
axis and along cable AC.
y
z
x
8 ft
3 ft
12 ft
8 ft
15 ft
A
C
B
F
u
2–131.Determine the magnitudes of the projected
components of the force acting along the xand
yaxes.
F=300 N
z
A
O
x y
300 mm
300 mm
300 mm
F 300 N
30
30
2 Solutions 44918 1/21/09 12:02 PM Page 111

112. 112
*2–132.Determine the magnitude of the projected
component of the force acting along line OA.F=300 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
A
O
x y
300 mm
300 mm
300 mm
F 300 N
30
30
2 Solutions 44918 1/21/09 12:02 PM Page 112

113. 113
•2–133.Two cables exert forces on the pipe. Determine
the magnitude of the projected component of F
1
along the
line of action of F
2
.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
60
y
z
60
30
30
x
F
2 25 lb
F
1 30 lb
u
2–134.Determine the angle between the two cables
attached to the pipe.
u
60
y
z
60
30
30
x
F
2 25 lb
F
1 30 lb
u
2 Solutions 44918 1/21/09 12:02 PM Page 113

114. 114
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–135.Determine the xand ycomponents of the 700-lb
force.
y
x
700 lb
30
60
2 Solutions 44918 1/21/09 12:02 PM Page 114

115. 115
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*2–136.Determine the magnitude of the projected
component of the 100-lb force acting along the axis BCof
the pipe.
y
C
B
A
D
z
8 ft
3 ft
6 ft
2 ft
4 ftx
F 100 lb
u
•2–137.Determine the angle between pipe segments
BAand BC.
u
y
C
B
A
D
z
8 ft
3 ft
6 ft
2 ft
4 ftx
F 100 lb
u
2 Solutions 44918 1/21/09 12:02 PM Page 115

116. 116
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
y
30
30
45
F
1
80 N

F
2
75 N

F
3
50 N

2–138.Determine the magnitude and direction of the
resultant of the three forces by first
finding the resultant and then forming
. Specify its direction measured counter-
clockwise from the positive xaxis.
F
R=F¿+F
2
F¿=F
1+F
3
F
R=F
1+F
2+F
3
2 Solutions 44918 1/21/09 12:02 PM Page 116

117. 117
2–139.Determine the design angle ( < 90°) between
the two struts so that the 500-lb horizontal force has a
component of 600 lb directed from Atoward C. What is the
component of force acting along member BA?
uu
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
500 lb
20
A
B
C
u
2 Solutions 44918 1/21/09 12:02 PM Page 117

118. 118
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*2–140.Determine the magnitude and direction of the
smallestforce F
3
so that the resultant force of all three
forces has a magnitude of 20 lb.
F
2 10 lb
F
3
4
3
5
F
1 5 lb
u
2 Solutions 44918 1/21/09 12:02 PM Page 118

119. 119
•2–141.Resolve the 250-N force into components acting
along the uand axes and determine the magnitudes of
these components.
v
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
u
v
40
20
250 N
2–142.Cable ABexerts a force of 80 N on the end of the
3-m-long boom OA. Determine the magnitude of the
projection of this force along the boom.
O
A
80 N
3 m
B
z
y
x
4 m
60
2 Solutions 44918 1/21/09 12:02 PM Page 119

120. 120
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–143.The three supporting cables exert the forces shown
on the sign. Represent each force as a Cartesian vector.
2 m
z
C
2 m
y
x
A
D
E
B
3 m
3 m
2 m
F
B 400 N
F
C 400 N
F
E 350 N
2 Solutions 44918 1/21/09 12:02 PM Page 120

121. 121
•3–1.Determine the force in each cord for equilibrium of
the 200-kg crate. Cord remains horizontal due to the
roller at , and has a length of . Set .y=0.75 m1.5 mABC
BC
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
C
B
A
2 m
y
3 Solutions 44918 1/21/09 4:25 PM Page 121

122. 122
3–2.If the 1.5-m-long cord can withstand a maximum
force of , determine the force in cord and the
distance yso that the 200-kg crate can be supported.
BC3500 N
AB
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C
B
A
2 m
y
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123. 123
3–3.If the mass of the girder is and its center of mass
is located at point G, determine the tension developed in
cables , , and for equilibrium.BDBCAB
3 Mg
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
AB
A
B
CD
G
30
45
3 Solutions 44918 1/21/09 4:25 PM Page 123

124. 124
*3–4.If cables and can withstand a maximum
tensile force of , determine the maximum mass of the
girder that can be suspended from cable so that neither
cable will fail. The center of mass of the girder is located at
point .G
AB
20 kN
BCBD
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
AB
A
B
CD
G
30
45
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125. 125
•3–5.The members of a truss are connected to the gusset
plate. If the forces are concurrent at point O, determine the
magnitudes of Fand Tfor equilibrium. Take .u=30°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5 kN
A
B
C
D
T
O
45
u
F
8 kN
3–6.The gusset plate is subjected to the forces of four
members. Determine the force in member Band its proper
orientation for equilibrium. The forces are concurrent at
point O. Take .F=12 kN
u
5 kN
A
B
C
D
T
O
45
u
F
8 kN
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126. 126
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–7.The towing pendant ABis subjected to the force of
50 kN exerted by a tugboat. Determine the force in each of
the bridles,BCand BD, if the ship is moving forward with
constant velocity.
30
A
B
C
D
50 kN
20
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127. 127
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*3–8.Members and support the 300-lb crate.
Determine the tensile force developed in each member.
ABAC
A
BC
4 ft
4 ft
3 ft
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128. 128
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•3–9.If members and can support a maximum
tension of and , respectively, determine the
largest weight of the crate that can be safely supported.
250 lb300 lb
ABAC
A
BC
4 ft
4 ft
3 ft
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129. 129
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–10.The members of a truss are connected to the gusset
plate. If the forces are concurrent at point O, determine the
magnitudes of Fand Tfor equilibrium. Take .u=90°
x
y
A
O
F
T
B
9 kN
C
4
5
3
u
3–11.The gusset plate is subjected to the forces of three
members. Determine the tension force in member Cand its
angle for equilibrium. The forces are concurrent at point O.
Take .F=8 kN
u
x
y
A
O
F
T
B
9 kN
C
4
5
3
u
3 Solutions 44918 1/21/09 4:25 PM Page 129

130. 130
*3–12.If block weighs and block weighs ,
determine the required weight of block and the angle
for equilibrium.
uD
100 lbC200 lbB
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
B
D
C
u
30

3 Solutions 44918 1/21/09 4:25 PM Page 130

131. 131
•3–13.If block weighs 300 lb and block weighs 275 lb,
determine the required weight of block and the angle
for equilibrium.
uC
BD
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
B
D
C
u
30

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132. 132
3–14.Determine the stretch in springs ACand ABfor
equilibrium of the 2-kg block. The springs are shown in
the equilibrium position.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3 m
3 m 4 m
k
AC 20 N/m
k
AB 30 N/m
C B
A
D
3–15.The unstretched length of spring ABis 3 m. If the
block is held in the equilibrium position shown, determine
the mass of the block at D.
3 m
3 m 4 m
k
AC 20 N/m
k
AB 30 N/m
C B
A
D
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133. 133
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*3–16.Determine the tension developed in wires and
required for equilibrium of the 10-kg cylinder. Take
.u=40°
CB
CA
30°
A
B
C
u
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134. 134
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•3–17.If cable is subjected to a tension that is twice
that of cable , determine the angle for equilibrium of
the 10-kg cylinder. Also, what are the tensions in wires
and ?CB
CA
uCA
CB
30°
A
B
C
u
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135. 135
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–18.Determine the forces in cables ACand ABneeded
to hold the 20-kg ball Din equilibrium. Take
and .d=1 m
F=300 N
A
C
B
F
D
2 m
1.5 m
d
3 Solutions 44918 1/21/09 4:25 PM Page 135

136. 136
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–19.The ball Dhas a mass of 20 kg. If a force of
is applied horizontally to the ring at A, determine the
dimension dso that the force in cable ACis zero.
F=100 N
A
C
B
F
D
2 m
1.5 m
d
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137. 137
*3–20.Determine the tension developed in each wire
used to support the 50-kg chandelier.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
B
D
C
30

30
45
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138. 138
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•3–21.If the tension developed in each of the four wires is
not allowed to exceed , determine the maximum mass
of the chandelier that can be supported.
600 N
A
B
D
C
30

30
45
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139. 139
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3–22.A vertical force is applied to the ends of
the 2-ft cord ABand spring AC. If the spring has an
unstretched length of 2 ft, determine the angle for
equilibrium. Take k=15 lb>ft.
u
P=10 lb
2 ft
k
2 ft
A
B C
P
u
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140. 140
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–23.Determine the unstretched length of spring ACif a
force causes the angle for equilibrium.
Cord ABis 2 ft long. Take k=50 lb>ft.
u=60°P=80 lb
2 ft
k
2 ft
A
B C
P
u
3 Solutions 44918 1/21/09 4:25 PM Page 140

141. 141
*3–24.If the bucket weighs 50 lb, determine the tension
developed in each of the wires.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
B
E
C
D
4
3
5
30
30
3 Solutions 44918 1/21/09 4:25 PM Page 141

142. 142
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•3–25.Determine the maximum weight of the bucket that
the wire system can support so that no single wire develops
a tension exceeding 100 lb.
A
B
E
C
D
4
3
5
30
30
3 Solutions 44918 1/21/09 4:25 PM Page 142

143. 143
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–26.Determine the tensions developed in wires , ,
and and the angle required for equilibrium of the
30-lb cylinder and the 60-lb cylinder .FE
uBA
CBCD
D A
C
F
E
B
u
30

45
3 Solutions 44918 1/21/09 4:25 PM Page 143

144. 144
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–27.If cylinder weighs 30 lb and , determine
the weight of cylinder .F
u=15°E
D A
C
F
E
B
u
30

45
3 Solutions 44918 1/21/09 4:25 PM Page 144

145. 145
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*3–28.Two spheres Aand Bhave an equal mass and are
electrostatically charged such that the repulsive force acting
between them has a magnitude of 20 mN and is directed
along line AB. Determine the angle the tension in cords
ACand BC, and the mass mof each sphere.
u,
C
30
20 mN
20 mN
30
B
u
A
•3–29.The cords BCAand CDcan each support a
maximum load of 100 lb. Determine the maximum weight
of the crate that can be hoisted at constant velocity and the
angle for equilibrium. Neglect the size of the smooth
pulley at C.
u
12
5
13
B
A
C
D
u
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146. 146
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–30.The springs on the rope assembly are originally
unstretched when . Determine the tension in each
rope when . Neglect the size of the pulleys at B
and D.
F=90 lb
u=0°
F
A
B
C E
D
2 ft 2 ft
k

30 lb/ft k

30 lb/ft
θθ
3 Solutions 44918 1/21/09 4:25 PM Page 146

147. 147
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–31.The springs on the rope assembly are originally
stretched 1 ft when . Determine the vertical force F
that must be applied so that .u=30°
u=0°
F
A
B
C E
D
2 ft 2 ft
k

30 lb/ft k

30 lb/ft
θθ
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148. 148
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*3–32.Determine the magnitude and direction of the
equilibrium force exerted along link ABby the tractive
apparatus shown. The suspended mass is 10 kg. Neglect the
size of the pulley at A.
F
AB
u
45
A
B
75
F
AB
u
3 Solutions 44918 1/21/09 4:25 PM Page 148

149. 149
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•3–33.The wire forms a loop and passes over the small
pulleys at A,B,C, and D. If its end is subjected to a force of
, determine the force in the wire and the
magnitude of the resultant force that the wire exerts on
each of the pulleys.
P=50
N
P
A
B
D
C
30
30
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150. 150
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–34.The wire forms a loop and passes over the small
pulleys at A,B,C, and D. If the maximum resultant forcethat
the wire can exert on each pulley is 120 N, determine the
greatest force Pthat can be applied to the wire as shown.
P
A
B
D
C
30
30
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151. 151
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–35.The picture has a weight of 10 lb and is to be hung
over the smooth pin B. If a string is attached to the frame at
points Aand C, and the maximum force the string can
support is 15 lb, determine the shortest string that can be
safely used.
CA
9 in. 9 in.
B
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152. 152
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*3–36.The 200-lb uniform tank is suspended by means of
a 6-ft-long cable, which is attached to the sides of the tank
and passes over the small pulley located at O. If the cable
can be attached at either points Aand Bor Cand D,
determine which attachment produces the least amount of
tension in the cable. What is this tension?
A
O
C
1 ft
B
2 ft
F
D
2 ft
2 ft
3 Solutions 44918 1/21/09 4:25 PM Page 152

153. 153
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•

3–37.The 10-lb weight is supported by the cord ACand
roller and by the spring that has a stiffness of .
and an unstretched length of 12 in. Determine the distance
dto where the weight is located when it is in equilibrium.
k=10 lb>in
d
A
C
B
12 in.
k
u
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154. 154
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–38.The 10-lb weight is supported by the cord ACand
roller and by a spring. If the spring has an unstretched
length of 8 in. and the weight is in equilibrium when
., determine the stiffness kof the spring.d=4 in
d
A
C
B
12 in.
k
u
3 Solutions 44918 1/21/09 4:25 PM Page 154

155. 155
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•3–39.A “scale” is constructed with a 4-ft-long cord and
the 10-lb block D. The cord is fixed to a pin at Aand passes
over two smallpulleys at Band C. Determine the weight of
the suspended block at Bif the system is in equilibrium.
C
D
B
A
1 ft
1.5 ft
•*3–40.The spring has a stiffness of and an
unstretched length of 200 mm. Determine the force in cables
BCand BDwhen the spring is held in the position shown.
k=800 N>m
A Bk 800 N/m
D
500 mm 400 mm
400 mm
300 mm
C
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156. 156
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•3–41.A continuous cable of total length 4 m is wrapped
around the smallpulleys at A, B, C, and D. If each spring is
stretched 300 mm, determine the mass mof each block.
Neglect the weight of the pulleys and cords. The springs are
unstretched when d=2 m.
B
C
A
k 500 N/m
k 500 N/m
d
D
3–42.Determine the mass of each of the two cylinders if
they cause a sag of when suspended from the
rings at Aand B. Note that when the cylinders are
removed.
s=0
s=0.5 m
1 m 2 m2 m
1.5 m
s
BA
C D
k 100 N/m k 100 N/m
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157. 157
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•3–43.The pail and its contents have a mass of 60 kg. If the
cable BACis 15 m long, determine the distance yto the
pulley at Afor equilibrium. Neglect the size of the pulley. 2 m
y
C
B
A
10 m
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158. 158
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•*3–44.A scale is constructed using the 10-kg mass, the
2-kg pan P, and the pulley and cord arrangement. Cord
BCAis 2 m long. If , determine the mass Din the
pan. Neglect the size of the pulley.
s=0.75 m
1.5 m
0
s
P
D
A C
B
1.5 m
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159. 159
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•3–45.Determine the tension in the cables in order to
support the 100-kg crate in the equilibrium position shown.
2.5 m
2 m
2 m
2 m
1 mA
z
D
y
x
B
C
3 Solutions 44918 1/21/09 4:25 PM Page 159

160. 160
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–46.Determine the maximum mass of the crate so that the
tension developed in any cable does not exceeded 3 kN.
2.5 m
2 m
2 m
2 m
1 mA
z
D
y
x
B
C
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161. 161
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–47.The shear leg derrick is used to haul the 200-kg net of
fish onto the dock. Determine the compressive force along
each of the legs ABand CBand the tension in the winch
cable DB. Assume the force in each leg acts along its axis.
4 m
4 m
2 m
2 m
5.6 m
D
B
C
A
x
y
z
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162. 162
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*3–48.Determine the tension developed in cables , ,
and required for equilibrium of the 300-lb crate.AD
ACAB
A
D
C
x
1 ft
3 ft
2 ft
1 ft
2 ft
2 ft
y
z
2 ft
B
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163. 163
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•3–49.Determine the maximum weight of the crate so that
the tension developed in any cable does not exceed 450 lb.
A
D
C
x
1 ft
3 ft
2 ft
1 ft
2 ft
2 ft
y
z
2 ft
B
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164. 164
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–50.Determine the force in each cable needed to
support the 3500-lb platform. Set .d=2 ft
3 ft d
y
x
C
D
B
A
3500 lb
4 ft
3 ft
10 ft
4 ft
2 ft
z
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165. 165
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–51.Determine the force in each cable needed to
support the 3500-lb platform. Set .d=4 ft
3 ft d
y
x
C
D
B
A
3500 lb
4 ft
3 ft
10 ft
4 ft
2 ft
z
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166. 166
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*3–52.Determine the force in each of the three cables
needed to lift the tractor which has a mass of 8 Mg.
2 m
1.25 m
1.25 m
1 m
3 m
A
D
C
B
y
x
z
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167. 167
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•3–53.Determine the force acting along the axis of each of
the three struts needed to support the 500-kg block.
0.75 m
1.25 m
3 m
2.5 m
z
A
B
C
D
x
y
2 m
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168. 168
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–54.If the mass of the flowerpot is 50 kg, determine the
tension developed in each wire for equilibrium. Set
and .z=2 mx=1.5 m
x
x
A
B
C
y
z
z
6 m
3 m
2 m
D
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–55.If the mass of the flowerpot is 50 kg, determine the
tension developed in each wire for equilibrium. Set
and .z=1.5 m
x=2 m
x
x
A
B
C
y
z
z
6 m
3 m
2 m
D
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*3–56.The ends of the three cables are attached to a ring
at Aand to the edge of a uniform 150-kg plate. Determine
the tension in each of the cables for equilibrium.
z
A
B
x
y
D
C
10 m
6 m 6 m
6 m
4 m
2 m
2 m
12 m
2 m
•3–57.The ends of the three cables are attached to a ring
at Aand to the edge of the uniform plate. Determine the
largest mass the plate can have if each cable can support a
maximum tension of 15 kN.
z
A
B
x
y
D
C
10 m
6 m 6 m
6 m
4 m
2 m
2 m
12 m
2 m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–58.Determine the tension developed in cables , ,
and required for equilibrium of the 75-kg cylinder.
AD
ACAB
1 m
3 m
3 m
4 m
1.5 m
2 m
2 m
1 m
A
C
z
y
x
B
D
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–59.If each cable can withstand a maximum tension of
1000 N, determine the largest mass of the cylinder for
equilibrium.
1 m
3 m
3 m
4 m
1.5 m
2 m
2 m
1 m
A
C
z
y
x
B
D
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*3–60.The 50-kg pot is supported from Aby the three
cables. Determine the force acting in each cable for
equilibrium. Take .
d=2.5 m
A
z
y
x
B
d
2 m 2 m
3 m
6 m
6 m
DC
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•3–61.Determine the height dof cable ABso that the force
in cables ADand ACis one-half as great as the force in
cable AB. What is the force in each cable for this case? The
flower pot has a mass of 50 kg.
A
z
y
x
B
d
2 m 2 m
3 m
6 m
6 m
DC
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–62.A force of holds the 400-lb crate in
equilibrium. Determine the coordinates (0,y,z) of point A
if the tension in cords ACand ABis 700 lb each.F=100 lb
B
C
A
F
y
z
x
4 ft
5 ft
5 ft
z
y
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–63.If the maximum allowable tension in cables ABand
ACis 500 lb, determine the maximum height zto which the
200-lb crate can be lifted. What horizontal force Fmust be
applied? Take .
y=8 ft
B
C
A
F
y
z
x
4 ft
5 ft
5 ft
z
y
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*3–64.The thin ring can be adjusted vertically between
three equally long cables from which the 100-kg chandelier
is suspended. If the ring remains in the horizontal plane and
, determine the tension in each cable.
z=600 mm
x
y
z
z
0.5 m
120
120
120
A
B
C
D
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•3–65.The thin ring can be adjusted vertically between
three equally long cables from which the 100-kg chandelier
is suspended. If the ring remains in the horizontal plane and
the tension in each cable is not allowed to exceed ,
determine the smallest allowable distance required for
equilibrium.
z
1 kN
x
y
z
z
0.5 m
120
120
120
A
B
C
D
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–66.The bucket has a weight of 80 lb and is being hoisted
using three springs, each having an unstretched length of
and stiffness of . Determine the
vertical distance dfrom the rim to point Afor equilibrium.
k=50
lb>ftl
0=1.5 ft
120θ
1.5 ft
80 lb
d
C
A
B
D
120θ
120θ
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–67.Three cables are used to support a 900-lb ring.
Determine the tension in each cable for equilibrium.
A
B
C
D
F
120
120
120
3 ft
y
z
x
4 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*3–68.The three outer blocks each have a mass of 2 kg,
and the central block Ehas a mass of 3 kg. Determine the
sag sfor equilibrium of the system.
s
6030
30
1 m
1 m
A
D
E
B
C
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•3–69.Determine the angle such that an equal force is
developed in legs OBand OC. What is the force in each leg
if the force is directed along the axis of each leg? The force
Flies in the plane. The supports at A,B,Ccan exert
forces in either direction along the attached legs.
x-y
u
120
5 ft
10 ft
120
120
yx
z
O
B
C
A
F = 100 lb
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–70.The 500-lb crate is hoisted using the ropes ABand
AC. Each rope can withstand a maximum tension of 2500 lb
before it breaks. If ABalways remains horizontal,
determine the smallest angle to which the crate can be
hoisted.
u
B
A
C
u
F
3–71.The members of a truss are pin connected at joint O.
Determine the magnitude of and its angle for
equilibrium. Set .F
2=6 kN
uF
1
x
O
y
70
30
5 kN
7 kN
3
4
5
F
2
F
1
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*3–72.The members of a truss are pin connected at joint O.
Determine the magnitudes of and for equilibrium.
Set .u=60°
F
2F
1
x
O
y
70
30
5 kN
7 kN
3
4
5
F
2
F
1
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•3–73.Two electrically charged pith balls, each having a
mass of 0.15 g, are suspended from light threads of equal
length. Determine the magnitude of the horizontal
repulsive force,F, acting on each ball if the measured
distance between them is .r=200 mm
AB
50 mm
150 mm 150 mm
r 200 mm
F–F
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–74.The lamp has a mass of 15 kg and is supported by a
pole AOand cables ABand AC. If the force in the pole acts
along its axis, determine the forces in AO,AB, and ACfor
equilibrium.
x
1.5 m
1.5 m
2 m
4 m
A
z
B
y
6 m
O
C
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–75.Determine the magnitude of Pand the coordinate
direction angles of required for equilibrium of the
particle. Note that acts in the octant shown.F
3
F
3
z
y
x
20
F
3
200 lb
P
(1 ft, 7 ft, 4 ft)
F
4
300 lb
F
1
360 lb
F
2
120 lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*3–76.The ring of negligible size is subjected to a vertical
force of 200 lb. Determine the longest length lof cord AC
such that the tension acting in ACis 160 lb. Also, what is the
force acting in cord AB? Hint:Use the equilibrium
condition to determine the required angle for attachment,
then determine lusing trigonometry applied to .¢ABC
u
40
BC
Al
2 ft
200 lb
u
•3–77.Determine the magnitudes of , , and for
equilibrium of the particle.
F
3F
2F
1 z
P
F
3
F
1
F
2
y
x
3
800 lb
200 lb
4
5
60
60
135
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3–78.Determine the force in each cable needed to
support the 500-lb load.
D
y
x
C
A
B
6 ft
8 ft
2 ft
2 ft
6 ft
z
3–79.The joint of a space frame is subjected to four
member forces. Member OAlies in the plane and
member OBlies in the plane. Determine the forces
acting in each of the members required for equilibrium of
the joint.
y–z
x–y
x
45
A
B
200 lb
F 1
z
y
40

F
2
F
3
O
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–1.If A,B, and Dare given vectors, prove the
distributive law for the vector cross product, i.e.,
.A:(B+D)=(A:B)+(A:D)
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4–2.Prove the triple scalar product identity
.A
#
B:C=A:B #
C
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4–3.Given the three nonzero vectors A,B, and C, show
that if , the three vectors mustlie in the
same plane.
A
#
(B:C)=0
*4–4.Two men exert forces of and on
the ropes. Determine the moment of each force about A.
Which way will the pole rotate, clockwise or counterclockwise?
P=50 lbF=80 lb
A
P
F
B
C
6 ft
45
12 ft
3
4
5
•4–5.If the man at Bexerts a force of on his
rope, determine the magnitude of the force Fthe man at C
must exert to prevent the pole from rotating, i.e., so the
resultant moment about Aof both forces is zero.
P=30 lb
A
P
F
B
C
6 ft
45
12 ft
3
4
5
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–6.If , determine the moment produced by the
4-kN force about point A.
u=45°
3 m
0.45 m
4 kN
A
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–7.If the moment produced by the 4-kN force about
point Ais clockwise, determine the angle , where
.0°…u…90°
u10 kN
#
m
3 m
0.45 m
4 kN
A
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–8.The handle of the hammer is subjected to the force
of Determine the moment of this force about the
point A.
F=20 lb. F
B
A
18 in.
5 in.
30
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–9.In order to pull out the nail at B, the force Fexerted
on the handle of the hammer must produce a clockwise
moment of about point A. Determine the
required magnitude of force F.
500 lb
#
in.
F
B
A
18 in.
5 in.
30
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–10.The hub of the wheel can be attached to the axle
either with negative offset (left) or with positive offset
(right). If the tire is subjected to both a normal and radial
load as shown, determine the resultant moment of these
loads about point Oon the axle for both cases.
4 kN
800 N 800 N
4 kN
Case 1 Case 2
0.4 m
0.05 m
0.05 m
0.4 m
O
O
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4–11.The member is subjected to a force of . If
, determine the moment produced by Fabout
point A.
u=45°
F=6 kN
A
6 m
1.5 m
u
F 6 kN
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–12.Determine the angle of the
force Fso that it produces a maximum moment and a
minimum moment about point A. Also, what are the
magnitudes of these maximum and minimum moments?
u (0°…u…180°)
A
6 m
1.5 m
u
F 6 kN
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–13.Determine the moment produced by the force F
about point Ain terms of the angle . Plot the graph of
versus , where .0°…u…180°u
M
Au
A
6 m
1.5 m
u
F 6 kN
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–14.Serious neck injuries can occur when a football
player is struck in the face guard of his helmet in the
manner shown, giving rise to a guillotine mechanism.
Determine the moment of the knee force about
point A. What would be the magnitude of the neck force F
so that it gives the counterbalancing moment about A?
P=50 lb
2 in.
4 in.
6 in.
30
60
P 50 lb
F
A
4–15.The Achilles tendon force of is
mobilized when the man tries to stand on his toes. As this is
done, each of his feet is subjected to a reactive force of
Determine the resultant moment of and
about the ankle joint A.
N
fF
tN
f=400 N.
F
t=650 N
100 mm
65 mm
200 mm
A
N
f 400 N
F
t
5
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*4–16.The Achilles tendon force is mobilized when the
man tries to stand on his toes. As this is done, each of his feet
is subjected to a reactive force of If the resultant
moment produced by forces and about the ankle joint
Ais required to be zero, determine the magnitude of .F
t
N
tF
t
N
t=400 N.
F
t
100 mm
65 mm
200 mm
A
N
f 400 N
F
t
5
•4–17.The two boys push on the gate with forces of
and as shown. Determine the moment of each
force about C. Which way will the gate rotate, clockwise or
counterclockwise? Neglect the thickness of the gate.
F
A=30 lb
60
6 ft
C
B
A
3 ft
3
4
5
F
B
F
A
4–18.Two boys push on the gate as shown. If the boy at B
exerts a force of , determine the magnitude of
the force the boy at Amust exert in order to prevent the
gate from turning. Neglect the thickness of the gate.
F
A
F
B=30 lb
60
6 ft
C
B
A
3 ft
3
4
5
F
B
F
A
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–19.The tongs are used to grip the ends of the drilling
pipe P. Determine the torque (moment) that the
applied force exerts on the pipe about point P
as a function of . Plot this moment versus for
.0…u…90°
uM
Pu
F=150 lb
M
P
43 in.
6 in.
F
P
M
P
u
*4–20.The tongs are used to grip the ends of the drilling
pipe P. If a torque (moment) of is needed
at Pto turn the pipe, determine the cable force Fthat must
be applied to the tongs. Set .u=30°
M
P=800 lb#
ft
43 in.
6 in.
F
P
M
P
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–21.Determine the direction for of the
force Fso that it produces the maximum moment about
point A. Calculate this moment.
0°…u…180°u F 400 N
3 m
2 m
A
u
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4–22.Determine the moment of the force Fabout point A
as a function of . Plot the results of M(ordinate) versus
(abscissa) for .0°…u…180°
uu
F 400 N
3 m
2 m
A
u
4–23.Determine the minimum moment produced by
the force Fabout point A. Specify the angle
.u…180°)
u (0°…
F 400 N
3 m
2 m
A
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–24.In order to raise the lamp post from the position
shown, force Fis applied to the cable. If
determine the moment produced by Fabout point A.
F=200 lb,
F
75C
A
B
10 ft
20 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–25.In order to raise the lamp post from the position
shown, the force Fon the cable must create a counterclockwise
moment of about point A. Determine the
magnitude of Fthat must be applied to the cable.
1500 lb
#
ftF
75C
A
B
10 ft
20 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–26.The foot segment is subjected to the pull of the two
plantarflexor muscles. Determine the moment of each force
about the point of contact Aon the ground.
60
30
4 in.
A
1 in.
3.5 in.
70
F
2 30 lb
F
1 20 lb
4–27.The 70-N force acts on the end of the pipe at B.
Determine (a) the moment of this force about point A, and
(b) the magnitude and direction of a horizontal force, applied
at C, which produces the same moment. Take u=60°.
A
C
0.3 m 0.7 m
0.9 m
B
70 N
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–28.The 70-N force acts on the end of the pipe at B.
Determine the angles of the force that
will produce maximum and minimum moments about
pointA. What are the magnitudes of these moments?
u 10°…u…180°2
A
C
0.3 m 0.7 m
0.9 m
B
70 N
u
•4–29.Determine the moment of each force about the
bolt located at A. Take F
B=40 lb, F
C=50 lb.
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4–30.If and determine the resultant
moment about the bolt located at A.
F
C=45 lb,F
B=30 lb
4–31.The rod on the power control mechanism for a
business jet is subjected to a force of 80 N. Determine the
moment of this force about the bearing at A.
20
60
A
80 N
150 mm
*4–32.The towline exerts a force of at the end
of the 20-m-long crane boom. If determine the
placement xof the hook at Aso that this force creates a
maximum moment about point O. What is this moment?
u=30°,
P=4 kN
1.5 m
O
20 m
A
B
P 4 kN
x
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–33.The towline exerts a force of at the end
of the 20-m-long crane boom. If determine the
position of the boom so that this force creates a maximum
moment about point O. What is this moment?
u
x=25 m,
P=4 kN
1.5 m
O
20 m
A
B
P 4 kN
x
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–34.In order to hold the wheelbarrow in the position
shown, force Fmust produce a counterclockwise moment
of about the axle at A. Determine the required
magnitude of force F.
200 N
#
m
B
0.65 m
0.5 m
1.2 m
30

0.3 m
F
G
A
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–35.The wheelbarrow and its contents have a mass of
50 kg and a center of mass at G. If the resultant moment
produced by force Fand the weight about point Ais to be
zero, determine the required magnitude of force F.
B
0.65 m
0.5 m
1.2 m
30

0.3 m
F
G
A
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–36.The wheelbarrow and its contents have a center of
mass at G. If and the resultant moment produced
by force Fand the weight about the axle at Ais zero,
determine the mass of the wheelbarrow and its contents.
F=100 NB
0.65 m
0.5 m
1.2 m
30

0.3 m
F
G
A
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–37.Determine the moment produced by about
pointO. Express the result as a Cartesian vector.
F
1
y
x
z
1 ft
2 ft
2 ft
A
O
3 ft
F
2 {10i 30j 50k} lb
F
1 {20i 10j 30k} lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–38.Determine the moment produced by about
pointO. Express the result as a Cartesian vector.
F
2
y
x
z
1 ft
2 ft
2 ft
A
O
3 ft
F
2 {10i 30j 50k} lb
F
1 {20i 10j 30k} lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–39.Determine the resultant moment produced by the two
forces about point O. Express the result as a Cartesian vector.
y
x
z
1 ft
2 ft
2 ft
A
O
3 ft
F
2 {10i 30j 50k} lb
F
1 {20i 10j 30k} lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–40.Determine the moment produced by force
about point O. Express the result as a Cartesian vector.
F
B
y
x
z
C
O
B
A
6 m
3 m
2 m
2.5 m
F
C 420 N
F
B 780 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–41.Determine the moment produced by force
about point O. Express the result as a Cartesian vector.
F
C
y
x
z
C
O
B
A
6 m
3 m
2 m
2.5 m
F
C 420 N
F
B 780 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–42.Determine the resultant moment produced by
forces and about point O. Express the result as a
Cartesian vector.
F
CF
B
y
x
z
C
O
B
A
6 m
3 m
2 m
2.5 m
F
C 420 N
F
B 780 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–43.Determine the moment produced by each force
about point Olocated on the drill bit. Express the results as
Cartesian vectors.
x
z
A B
O
y
150 mm
600 mm
300 mm
150 mm
F
A {40i 100j 60k} N
F
B {50i 120j 60k} N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–44.A force of produces a
moment of about the origin
of coordinates, point O. If the force acts at a point having an
xcoordinate of determine the yand zcoordinates.x=1 m,
M
O=54i+5j-14k6 kN #
m
F=56i-2j+1k6 kN
•4–45.The pipe assembly is subjected to the 80-N force.
Determine the moment of this force about point A.
400 mm
y300 mm
200 mm
250 mm
x
z
30
40
F 80 N
B
C
A
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–47.The force creates a
moment about point Oof .
If the force passes through a point having an xcoordinate of
1 m, determine the yand zcoordinates of the point. Also,
realizing that , determine the perpendicular
distance dfrom point Oto the line of action of F.
M
O=Fd
M
O=5-14i+8j+2k6 N#
m
F=56i+8j+10k6 N
d
z
x
y
O
y
1 m
z
P
F
M
O
4–46.The pipe assembly is subjected to the 80-N force.
Determine the moment of this force about point B.
400 mm
y300 mm
200 mm
250 mm
x
z
30
40
F 80 N
B
C
A
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–48.Force Facts perpendicular to the inclined plane.
Determine the moment produced by Fabout point A.
Express the result as a Cartesian vector.
z
x y
3 m
3 m
4 m
A
B
C
F 400 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–49.Force Facts perpendicular to the inclined plane.
Determine the moment produced by Fabout point B.
Express the result as a Cartesian vector.
z
x y
3 m
3 m
4 m
A
B
C
F 400 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–50.A 20-N horizontal force is applied perpendicular to
the handle of the socket wrench. Determine the magnitude
and the coordinate direction angles of the moment created
by this force about point O.
15
200 mm
75 mm
20 N
A
O
x
y
z
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–51.Determine the moment produced by force Fabout
the diagonal AFof the rectangular block. Express the result
as a Cartesian vector.
3 m
1.5 m
3 m
x
C
A
B
G
F
y
z
O
D
F {6i 3j 10k} N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–52.Determine the moment produced by force Fabout
the diagonal ODof the rectangular block. Express the
result as a Cartesian vector.
3 m
1.5 m
3 m
x
C
A
B
G
F
y
z
O
D
F {6i 3j 10k} N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–53.The tool is used to shut off gas valves that are
difficult to access. If the force Fis applied to the handle,
determine the component of the moment created about the
zaxis of the valve.
x
y
0.4 m
F {60i 20j 15k} N
30
z
0.25 m
4–54.Determine the magnitude of the moments of the
forceFabout the x,y, and zaxes. Solve the problem (a) using
a Cartesian vector approach and (b) using a scalar approach.
4 ft
3 ft
2 ft
y
z
C
A
B
F {4i 12j 3k} lb
x
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–55.Determine the moment of the force Fabout an axis
extending between Aand C. Express the result as a
Cartesian vector.
4 ft
3 ft
2 ft
y
z
C
A
B
F {4i 12j 3k} lb
x
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–56.Determine the moment produced by force Fabout
segment ABof the pipe assembly. Express the result as a
Cartesian vector.
y
x
z
4 m
4 m
3 m
A
B
C
F {20i 10j 15k} N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–57.Determine the magnitude of the moment that the
force Fexerts about the yaxis of the shaft. Solve the
problem using a Cartesian vector approach and using a
scalar approach.
200 mm
250 mm
45
B
x
yz
A
O
30
50 mm
16 NF
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–58.If , determine the magnitude of the
moment produced by this force about the xaxis.
F=450 N
300 mmx
y
z
A
B
60
60
45
F
100 mm
150 mm
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–59.The friction at sleeve Acan provide a maximum
resisting moment of about the xaxis. Determine
the largest magnitude of force Fthat can be applied to the
bracket so that the bracket will not turn.
125 N
#
m
300 mmx
y
z
A
B
60
60
45
F
100 mm
150 mm
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–60.Determine the magnitude of the moment
produced by the force of about the hinged axis
(the xaxis) of the door.
F=200 N
y
x
z
15
A
B
2.5 m
2 m
F 200 N
0.5 m
1 m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–61.If the tension in the cable is , determine
the magnitude of the moment produced by this force about
the hinged axis,CD, of the panel.
F=140 lb
6 ft
4 ft
4 ft
6 ft
y
z
A
C
F
D
B
6 ft
x
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–62.Determine the magnitude of force Fin cable ABin
order to produce a moment of about the hinged
axis CD, which is needed to hold the panel in the position
shown.
500 lb
#
ft
6 ft
4 ft
4 ft
6 ft
y
z
A
C
F
D
B
6 ft
x
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–63.The A-frame is being hoisted into an upright
position by the vertical force of . Determine the
moment of this force about the axis passing through
points Aand Bwhen the frame is in the position shown.
y¿
F=80 lb
30
15
6 ft
y
y¿
x¿
C
A
B
F
x
z
3 ft
3 ft
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239. 239
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–64.The A-frame is being hoisted into an upright
position by the vertical force of . Determine the
moment of this force about the xaxis when the frame is in
the position shown.
F=80 lb
30
15
6 ft
y
y¿
x¿
C
A
B
F
x
z
3 ft
3 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–65.The A-frame is being hoisted into an upright
position by the vertical force of . Determine the
moment of this force about the yaxis when the frame is in
the position shown.
F=80 lb
30
15
6 ft
y
y¿
x¿
C
A
B
F
x
z
3 ft
3 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–66.The flex-headed ratchet wrench is subjected to a
force of applied perpendicular to the handle as
shown. Determine the moment or torque this imparts along
the vertical axis of the bolt at A.
P=16 lb,
60
A
10 in.
0.75 in.
P
4–67.If a torque or moment of is required to
loosen the bolt at A, determine the force Pthat must be
applied perpendicular to the handle of the flex-headed ratchet
wrench.
80 lb #
in.
60
A
10 in.
0.75 in.
P
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242. 242
*4–68.The pipe assembly is secured on the wall by the
two brackets. If the flower pot has a weight of 50 lb,
determine the magnitude of the moment produced by the
weight about the OAaxis.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
O
z
x
y
4 ft
3 ft
3 ft
4 ft
60
30
B
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243. 243
•4–69.The pipe assembly is secured on the wall by the two
brackets. If the frictional force of both brackets can resist a
maximum moment of , determine the largest
weight of the flower pot that can be supported by the
assembly without causing it to rotate about the OAaxis.
150 lb
#
ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
O
z
x
y
4 ft
3 ft
3 ft
4 ft
60
30
B
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244. 244
4–70.A vertical force of is applied to the
handle of the pipe wrench. Determine the moment that this
force exerts along the axis AB(xaxis) of the pipe assembly.
Both the wrench and pipe assembly ABClie in the
plane.Suggestion:Use a scalar analysis.
x-y
F=60 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
45
z
y
A
C
B
500 mm
200 mm
150 mm
F
x
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245. 245
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–71.Determine the magnitude of the vertical force F
acting on the handle of the wrench so that this force
produces a component of moment along the ABaxis (xaxis)
of the pipe assembly of . Both the pipe
assembly ABCand the wrench lie in the plane.
Suggestion:Use a scalar analysis.
x-y
(M
A)
x=5-5i6 N #
m
45
z
y
A
C
B
500 mm
200 mm
150 mm
F
x
*4–72.The frictional effects of the air on the blades of the
standing fan creates a couple moment of on
the blades. Determine the magnitude of the couple forces
at the base of the fan so that the resultant couple moment
on the fan is zero.
M
O=6 N#
m
0.15 m 0.15 m
FF
M
O
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–73.Determine the required magnitude of the couple
moments and so that the resultant couple moment
is zero.
M
3M
2
M
3
M
2
45
M
1 300 Nm
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247. 247
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–74.The caster wheel is subjected to the two couples.
Determine the forces Fthat the bearings exert on the shaft
so that the resultant couple moment on the caster is zero.
40 mm
45 mm
100 mm
500 N
500 N
50 mm
F
F
A
B
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248. 248
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–75.If , determine the resultant couple
moment.
F=200 lb
A
B
F
F
2 ft
2 ft
2 ft
2 ft
150 lb
150 lb
3
3
4
4
5
5
2 ft
30
30
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249. 249
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–76.Determine the required magnitude of force Fif the
resultant couple moment on the frame is ,
clockwise.
200 lb
#
ft
A
B
F
F
2 ft
2 ft
2 ft
2 ft
150 lb
150 lb
3
3
4
4
5
5
2 ft
30
30
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–78.If , determine the magnitude of force Fso that
the resultant couple moment is , clockwise.100 N
#
m
u=30°
30
15
15
F
F
300 N
300 N
300 mm
30
u
u
•4–77.The floor causes a couple moment of
and on the brushes of the
polishing machine. Determine the magnitude of the couple
forces that must be developed by the operator on the
handles so that the resultant couple moment on the polisher
is zero. What is the magnitude of these forces if the brush
at Bsuddenly stops so that M
B=0?
M
B=30 N#
mM
A=40 N#
m
0.3 m
M
B
M
A
F
F
A
B
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251. 251
4–79.If , determine the required angle so that
the resultant couple moment is zero.
uF=200 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
30
15
15
F
F
300 N
300 N
300 mm
30
u
u
*4–80.Two couples act on the beam. Determine the
magnitude of Fso that the resultant couple moment is
counterclockwise. Where on the beam does the
resultant couple moment act?
450 lb
#
ft,
200 lb
200 lb
2 ft
1.5 ft 1.25 ft
30
30
F
F
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252. 252
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–82.The cord passing over the two small pegs Aand Bof
the board is subjected to a tension of 100 N. Determine the
minimumtension Pand the orientation of the cord
passing over pegs Cand D, so that the resultant couple
moment produced by the two cords is , clockwise.20 N
#
m
u
100 N
100 N
P
P
CB
30
300 mm
300 mm
30
AD
45
u
u
•4–81.The cord passing over the two small pegs Aand Bof
the square board is subjected to a tension of 100 N.
Determine the required tension Pacting on the cord that
passes over pegs Cand Dso that the resultant couple
produced by the two couples is acting clockwise.
Take .u=15°
15 N
#
m
100 N
100 N
P
P
CB
30
300 mm
300 mm
30
AD
45
u
u
4–83.A device called a rolamite is used in various ways to
replace slipping motion with rolling motion. If the belt,
which wraps between the rollers, is subjected to a tension of
15 N, determine the reactive forces Nof the top and bottom
plates on the rollers so that the resultant couple acting on
the rollers is equal to zero.
N
N
30
25 mm
A
B
25 mm
T 15 N
T 15 N
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253. 253
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–84.Two couples act on the beam as shown. Determine
the magnitude of Fso that the resultant couple moment is
counterclockwise. Where on the beam does the
resultant couple act?
300 lb
#
ft
200 lb
200 lb
1.5 ft
•4–85.Determine the resultant couple moment acting on
the beam. Solve the problem two ways: (a) sum moments
about point O; and (b) sum moments about point A. 1.5 m 1.8 m
45
45
30
30
A
2 kN
2 kN
8 kN
B
0.3 m
8 kN
O
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254. 254
4–86.Two couples act on the cantilever beam. If
, determine the resultant couple moment.F=6 kN
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
F 5 kN
5 kN
0.5 m
0.5 m
30
30
4
4
3
3
5
5
3 m
A
B
3 m
4 Solutions 44918 1/23/09 12:03 PM Page 254

255. 255
4–87.Determine the required magnitude of force F, if the
resultant couple moment on the beam is to be zero.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
F 5 kN
5 kN
0.5 m
0.5 m
30
30
4
4
3
3
5
5
3 m
A
B
3 m
4 Solutions 44918 1/23/09 12:03 PM Page 255

256. 256
*4–88.Two couples act on the frame. If the resultant
couple moment is to be zero, determine the distance d
between the 40-lb couple forces.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3 ft
60 lb
40 lb
40 lb
30
d
y
x
A
B
1 ft30
3
45
4 ft
2 ft
3
4
5
60 lb
•4–89.Two couples act on the frame. If , determine
the resultant couple moment. Compute the result by resolving
each force into xand ycomponents and (a) finding the
moment of each couple (Eq. 4–13) and (b) summing the
moments of all the force components about point A.
d=4 ft
3 ft
60 lb
40 lb
40 lb
30
d
y
x
A
B
1 ft30
3
45
4 ft
2 ft
3
4
5
60 lb
4–90.Two couples act on the frame. If , determine
the resultant couple moment. Compute the result by
resolving each force into xand ycomponents and (a) finding
the moment of each couple (Eq. 4–13) and (b) summing the
moments of all the force components about point B.
d=4 ft
3 ft
60 lb
40 lb
40 lb
30
d
y
x
A
B
1 ft30
3
45
4 ft
2 ft
3
4
5
60 lb
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257. 257
4–91.If , , and ,
determine the magnitude and coordinate direction angles
of the resultant couple moment.
M
3 =450 N#
mM
2=600 N#
mM
1=500 N#
m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
30
x
z
y
M
1
M
2
M
3
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258. 258
*4–92.Determine the required magnitude of couple
moments so that the resultant couple
moment is .M
R=5-300i+450j-600k6 N #
m
M
1, M
2, and M
3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
30
x
z
y
M
1
M
2
M
3
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259. 259
•4–93.If , determine the magnitude and
coordinate direction angles of the couple moment. The pipe
assembly lies in the x–yplane.
F=80 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
z
y
300 mm
200 mm
200 mm
300 mm
300 mm
F
F
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260. 260
4–94.If the magnitude of the couple moment acting on
the pipe assembly is , determine the magnitude of
the couple forces applied to each wrench. The pipe
assembly lies in the x–yplane.
50 N
#
m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
z
y
300 mm
200 mm
200 mm
300 mm
300 mm
F
F
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261. 261
4–95.From load calculations it is determined that the
wing is subjected to couple moments and
. Determine the resultant couple moments
created about the and axes. The axes all lie in the same
horizontal plane.
y¿x¿
M
y=25 kip#
ft
M
x=17 kip#
ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
y
x¿
x
¿
25
M
y
M
x
*4–96.Express the moment of the couple acting on the
frame in Cartesian vector form. The forces are applied
perpendicular to the frame. What is the magnitude of the
couple moment? Take .F=50 N
F
x
y
z
O
1.5 m
3 m
30
F
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262. 262
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–97.In order to turn over the frame, a couple moment is
applied as shown. If the component of this couple moment
along the xaxis is , determine the
magnitude Fof the couple forces.
M
x=5-20i6 N #
m
F
x
y
z
O
1.5 m
3 m
30
F
4–98.Determine the resultant couple moment of the two
couples that act on the pipe assembly. The distance from Ato
Bis . Express the result as a Cartesian vector.d=400
mm
x
30
y
z
350 mm
250 mm
{35k} N
{35k} N
{50i} N
{50i} N
A
B
d
C
4 Solutions 44918 1/23/09 12:03 PM Page 262

263. 263
4–99.Determine the distance dbetween Aand Bso that the
resultant couple moment has a magnitude of .M
R=20 N#
m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
30
y
z
350 mm
250 mm
{35k} N
{35k} N
{50i} N
{50i} N
A
B
d
C
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264. 264
*4–100.If , , and ,
determine the magnitude and coordinate direction angles
of the resultant couple moment.
M
3=120 lb#
ftM
2=90 lb#
ftM
1=180 lb#
ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
z
y
2 ft
2 ft
2 ft
3 ft
150 lbft
1 ft
45
45
M
1
M
2
M
3
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265. 265
•4–101.Determine the magnitudes of couple moments
so that the resultant couple moment is zero.M
1, M
2, and M
3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
z
y
2 ft
2 ft
2 ft
3 ft
150 lbft
1 ft
45
45
M
1
M
2
M
3
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266. 266
4–102.If , determine the
magnitude and coordinate direction angles of the resultant
couple moment.
F
1=100 lb and F
2=200 lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2 ft
3 ft
4 ft
z
y
x
F
2
F
1
F
2
250 lb
250 lb
F
1
4 Solutions 44918 1/23/09 12:03 PM Page 266

267. 267
4–103.Determine the magnitude of couple forces and
so that the resultant couple moment acting on the block
is zero.
F
2
F
1
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2 ft
3 ft
4 ft
z
y
x
F
2
F
1
F
2
250 lb
250 lb
F
1
4 Solutions 44918 1/23/09 12:03 PM Page 267

268. 268
*4–104.Replace the force system acting on the truss by a
resultant force and couple moment at point C.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
BA
C
2 ft
6 ft
2 ft
200 lb
150 lb
100 lb
2 ft 2 ft
500 lb
3
4
5
4 Solutions 44918 1/23/09 12:03 PM Page 268

269. 269
•4–105.Replace the force system acting on the beam by
an equivalent force and couple moment at point A.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2.5 kN1.5 kN
3 kN
A
B
4 m
3
4
5
2 m 2 m
30
4–106.Replace the force system acting on the beam by an
equivalent force and couple moment at point B.
2.5 kN1.5 kN
3 kN
A
B
4 m
3
4
5
2 m 2 m
30
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270. 270
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4 Solutions 44918 1/23/09 12:03 PM Page 270

271. 271
4–107.Replace the two forces by an equivalent resultant
force and couple moment at point O. Set .F=20 lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 in.
30
4
3
5
1.5 in.
F
20 lb
2 in.
x
y
O
40
4 Solutions 44918 1/23/09 12:03 PM Page 271

272. 272
*4–108.Replace the two forces by an equivalent resultant
force and couple moment at point O. Set .F=15
lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 in.
30
4
3
5
1.5 in.
F
20 lb
2 in.
x
y
O
40
4 Solutions 44918 1/23/09 12:03 PM Page 272

273. 273
•4–109.Replace the force system acting on the post by a
resultant force and couple moment at point A.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
250 N
500 N
0.2 m
0.5 m
3
4
5
300 N
1 m
1 m
1 m
A
B
30
4 Solutions 44918 1/23/09 12:03 PM Page 273

274. 274
4–110.Replace the force and couple moment system
acting on the overhang beam by a resultant force and
couple moment at point A.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
B
A
5
1213
30 kN
45 kNm
26 kN
0.3 m
0.3 m
2 m2 m
1 m 1 m
30
4 Solutions 44918 1/23/09 12:04 PM Page 274

275. 275
4–111.Replace the force system by a resultant force and
couple moment at point O.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
200 N
200 N
500 N
4
3
5
O
750 N
1.25 m 1.25 m
1 m
4 Solutions 44918 1/23/09 12:04 PM Page 275

276. 276
*4–112.Replace the two forces acting on the grinder by a
resultant force and couple moment at point O. Express the
results in Cartesian vector form.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
250 mm
y
x
z
25 mm
40 mm
150 mm
100 mm
O
A
B
F
2 {15i 20j 30k} N
F
1 {10i 15j 40k} N
4 Solutions 44918 1/23/09 12:04 PM Page 276

277. 277
•4–113.Replace the two forces acting on the post by a
resultant force and couple moment at point O. Express the
results in Cartesian vector form.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
A
D
B
C
O
x y
8 m
6 m
6 m
3 m
2 m
F
B 5 kN
F
D 7 kN
4 Solutions 44918 1/23/09 12:04 PM Page 277

278. 278
4–114.The three forces act on the pipe assembly. If
and replace this force system by an
equivalent resultant force and couple moment acting at O.
Express the results in Cartesian vector form.
F
2=80 N,F
1=50 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
O
z
x
1.25 m
180 N
0.75 m
0.5 m
F
2
F
1
4–115.Handle forces and are applied to the electric
drill. Replace this force system by an equivalent resultant
force and couple moment acting at point O. Express the
results in Cartesian vector form.
F
2F
1
x y
z
0.25 m
0.3 m
O
F
1 {6i 3j 10k} N
F
2 {2j 4k} N
0.15 m
4 Solutions 44918 1/23/09 12:04 PM Page 278

279. 279
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–116.Replace the force system acting on the pipe
assembly by a resultant force and couple moment at point O.
Express the results in Cartesian vector form.
x
z
2 ft
1.5 ft
2 ft
2 ft
O
x
F
1 {20i 10j 25k}lb
F
2 {10i 25j 20k} lb
4 Solutions 44918 1/23/09 12:04 PM Page 279

280. 280
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–117.The slab is to be hoisted using the three slings
shown. Replace the system of forces acting on slings by an
equivalent force and couple moment at point O. The force
is vertical.F
1
y
x
z
45
60
60
45
30
6 m 2 m
2 m
F
2 5 kN

F
3 4 kN

O
F
1 6 kN
4–118.The weights of the various components of the truck
are shown. Replace this system of forces by an equivalent
resultant force and specify its location measured from B.
14 ft 6 ft
2 ft3 ft
AB
3500 lb
5500 lb
1750 lb
4 Solutions 44918 1/23/09 12:04 PM Page 280

281. 281
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–119.The weights of the various components of the
truck are shown. Replace this system of forces by an
equivalent resultant force and specify its location
measured from point A.
14 ft 6 ft
2 ft3 ft
AB
3500 lb
5500 lb
1750 lb
*4–120.The system of parallel forces acts on the top of the
Warren truss.Determine the equivalent resultant force of the
system and specify its location measured from point A.
A
500 N 500 N 500 N
1 kN
2 kN
1 m 1 m 1 m 1 m
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282. 282
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–121.The system of four forces acts on the roof truss.
Determine the equivalent resultant force and specify its
location along AB, measured from point A.
4 ft150 lb
B
A
300 lb
30
30
275 lb
200 lb
4 ft
4 ft
4 Solutions 44918 1/23/09 12:04 PM Page 282

283. 283
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–122.Replace the force and couple system acting on the
frame by an equivalent resultant force and specify where
the resultant’s line of action intersects member AB,
measured from A.
3 ft
30

4 ft
3
5
4
2 ft
150 lb
50 lb
500 lb ft
C B
A
4 Solutions 44918 1/23/09 12:04 PM Page 283

284. 284
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–123.Replace the force and couple system acting on the
frame by an equivalent resultant force and specify where
the resultant’s line of action intersects member BC,
measured from B.
3 ft
30

4 ft
3
5
4
2 ft
150 lb
50 lb
500 lb ft
C B
A
4 Solutions 44918 1/23/09 12:04 PM Page 284

285. 285
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–124.Replace the force and couple moment system
acting on the overhang beam by a resultant force, and
specify its location along ABmeasured from point A.
B
A
5
1213
30 kN
45 kNm
26 kN
0.3 m
0.3 m
2 m2 m
1 m 1 m
30
4 Solutions 44918 1/23/09 12:04 PM Page 285

286. 286
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–125.Replace the force system acting on the frame by
an equivalent resultant force and specify where the
resultant’s line of action intersects member AB, measured
from point A.
2 ft
4 ft
3 ft
25 lb
2 ft
20 lb
A B
C
30
35 lb
4 Solutions 44918 1/23/09 12:04 PM Page 286

287. 287
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–126.Replace the force system acting on the frame by
an equivalent resultant force and specify where the
resultant’s line of action intersects member BC, measured
from point B.
2 ft
4 ft
3 ft
25 lb
2 ft
20 lb
A B
C
30
35 lb
4 Solutions 44918 1/23/09 12:04 PM Page 287

288. 288
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–127.Replace the force system acting on the post by a
resultant force, and specify where its line of action
intersects the post ABmeasured from point A.
250 N
500 N
0.2 m
0.5 m
3
4
5
300 N
1 m
30
1 m
1 m
A
B
4 Solutions 44918 1/23/09 12:04 PM Page 288

289. 289
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–128.Replace the force system acting on the post by a
resultant force, and specify where its line of action
intersects the post ABmeasured from point B.
250 N
500 N
0.2 m
0.5 m
3
4
5
300 N
1 m
30
1 m
1 m
A
B
•4–129.The building slab is subjected to four parallel
column loadings. Determine the equivalent resultant force
and specify its location (x, y) on the slab. Take
F
2=40 kN.
F
1=30 kN,
y
x
20 kN
3 m
2 m
8 m
6 m
4 m
50 kN F
1
F
2
z
4 Solutions 44918 1/23/09 12:04 PM Page 289

290. 290
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–130.The building slab is subjected to four parallel
column loadings. Determine the equivalent resultant force
and specify its location (x, y) on the slab. Take
F
2=50 kN.
F
1=20 kN,
y
x
20 kN
3 m
2 m
8 m
6 m
4 m
50 kN F
1
F
2
z
4–131.The tube supports the four parallel forces.
Determine the magnitudes of forces and acting at C
and Dso that the equivalent resultant force of the force
system acts through the midpoint Oof the tube.
F
DF
C
x
z
A
D
C
y
zB
O
400 mm
400 mm
500 N
200 mm
200 mm
600 N
F
C
F
D
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*4–132.Three parallel bolting forces act on the circular
plate. Determine the resultant force, and specify its
location (x,z) on the plate. , , and
.F
C=400 lb
F
B=100 lbF
A=200 lb
45
30
1.5 ft
z
x
yA
B
C
F
B
F
A
F
C
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–133.The three parallel bolting forces act on the circular
plate. If the force at Ahas a magnitude of ,
determine the magnitudes of and so that the resultant
force of the system has a line of action that coincides with
the yaxis.Hint:This requires and . ©M
z=0©M
x=0
F
R
F
CF
B
F
A=200 lb
45
30
1.5 ft
z
x
yA
B
C
F
B
F
A
F
C
4–134.If , determine the
magnitude of the resultant force and specify the location of
its point of application (x, y) on the slab.
F
A=40 kN and F
B=35 kN
2.5 m
2.5 m
0.75 m
0.75 m
0.75 m
3 m
3 m
0.75 m 90 kN
30 kN
20 kN
x
y
z
F
A
F
B
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4–135.If the resultant force is required to act at the center
of the slab, determine the magnitude of the column loadings
and and the magnitude of the resultant force.F
BF
A
2.5 m
2.5 m
0.75 m
0.75 m
0.75 m
3 m
3 m
0.75 m 90 kN
30 kN
20 kN
x
y
z
F
A
F
B
*4–136.Replace the parallel force system acting on
the plate by a resultant force and specify its location on the
x–zplane.
1 m
1 m
1 m
0.5 m
0.5 m
5 kN
3 kN
x
y
z
2 kN
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–137.If , represent the force
system acting on the corbels by a resultant force, and
specify its location on the x–yplane.
F
A=7 kN and F
B=5 kN
750 mm
z
x
y
650 mm
100 mm
150 mm
600 mm
700 mm
100 mm
150 mm
8kN
6 kN
F
A
F
B
O
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–138.Determine the magnitudes of and so that
the resultant force passes through point Oof the column.
F
BF
A
750 mm
z
x
y
650 mm
100 mm
150 mm
600 mm
700 mm
100 mm
150 mm
8kN
6 kN
F
A
F
B
O
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–139.Replace the force and couple moment system
acting on the rectangular block by a wrench. Specify the
magnitude of the force and couple moment of the wrench
and where its line of action intersects the x–yplane.
y
x
z
300 lb
450 lb 600 lb
2 ft
4 ft
3 ft
600 lbft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–140.Replace the three forces acting on the plate by a
wrench. Specify the magnitude of the force and couple
moment for the wrench and the point P(y,z) where its line
of action intersects the plate.
y
y
x
z
P
A
C
B
z
F
B {60j} lb
F
C {40i} lb
F
A {80k}lb
12 ft
12 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–141.Replace the three forces acting on the plate by a
wrench. Specify the magnitude of the force and couple
moment for the wrench and the point P(x, y) where its line
of action intersects the plate.
4 m
6 m
y
y
x
x
P
A
C
B
z
F
A {500i} N
F
C {300j} N
F
B {800k} N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–142.Replace the distributed loading with an equivalent
resultant force, and specify its location on the beam
measured from point A.
A
B
3 m 3 m
15 kN/m
10 kN/m
3 m
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4–143.Replace the distributed loading with an equivalent
resultant force, and specify its location on the beam
measured from point A.
B
A
8 kN/m
4 kN/m
3 m 3 m
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*4–144.Replace the distributed loading by an equivalent
resultant force and specify its location, measured from
point A.
3 m2 m
A
B
800 N/m
200 N/m
•4–145.Replace the distributed loading with an
equivalent resultant force, and specify its location on the
beam measured from point A.
A
B
L
––
2
L
––
2
w
0 w
0
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–146.The distribution of soil loading on the bottom of
a building slab is shown. Replace this loading by an
equivalent resultant force and specify its location, measured
from point O.
12 ft 9 ft
100 lb/ft
50 lb/ft
300 lb/ft
O
4–147.Determine the intensities and of the
distributed loading acting on the bottom of the slab so that
this loading has an equivalent resultant force that is equal
but opposite to the resultant of the distributed loading
acting on the top of the plate.
w
2w
1
300 lb/ft
AB
3 ft 6 ft
1.5 ft
w
2
w
1
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*4–148.The bricks on top of the beam and the supports
at the bottom create the distributed loading shown in the
second figure. Determine the required intensity wand
dimension dof the right support so that the resultant force
and couple moment about point Aof the system are
both zero.
3 m
0.5 m
d
3 m
75 N/m
A
200 N/m
0.5 m
d
w
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–149.The wind pressure acting on a triangular sign is
uniform. Replace this loading by an equivalent resultant
force and couple moment at point O.
1.2 m
1 m
O
1.2 m 0.1 m
150 Pa
y
x
z
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–150.The beam is subjected to the distributed loading.
Determine the length bof the uniform load and its position
aon the beam such that the resultant force and couple
moment acting on the beam are zero.
6 ft10 ft
b
a
60 lb/ft
40 lb/ft
4–151.Currently eighty-five percent of all neck injuries
are caused by rear-end car collisions. To alleviate this
problem, an automobile seat restraint has been developed
that provides additional pressure contact with the cranium.
During dynamic tests the distribution of load on the
cranium has been plotted and shown to be parabolic.
Determine the equivalent resultant force and its location,
measured from point A.
A
w
B
x
w 12(1 2x
2
) lb/ft
0.5 ft
12 lb/ft
18 lb/ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–152.Wind has blown sand over a platform such that
the intensity of the load can be approximated by the
function Simplify this distributed loading
to an equivalent resultant force and specify its magnitude
and location measured from A.
w=10.5x
3
2 N>m.
x
w
A
10 m
500 N/m
w (0.5x
3
) N/m
•4–153.Wet concrete exerts a pressure distribution along
the wall of the form. Determine the resultant force of this
distribution and specify the height hwhere the bracing strut
should be placed so that it lies through the line of action of
the resultant force. The wall has a width of 5 m.
4 m
h
(4 ) kPap
1
/
2
z
8 kPa
z
p
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–154.Replace the distributed loading with an equivalent
resultant force, and specify its location on the beam
measured from point A.
w
x
A
B
4 m
8 kN/m
w (4 x)
21
––
2
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4–155.Replace the loading by an equivalent resultant
force and couple moment at point A.
60
6 ft
50 lb/ft
50 lb/ft
100 lb/ft
4 ft
A
B
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–156.Replace the loading by an equivalent resultant
force and couple moment acting at point B.
60
6 ft
50 lb/ft
50 lb/ft
100 lb/ft
4 ft
A
B
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–157.The lifting force along the wing of a jet aircraft
consists of a uniform distribution along AB, and a
semiparabolic distribution along BCwith origin at B.
Replace this loading by a single resultant force and specify
its location measured from point A.
x
w
24 ft12 ft
w (2880 5x
2
) lb/ft
2880 lb/ft
A B
C
4–158.The distributed load acts on the beam as shown.
Determine the magnitude of the equivalent resultant force
and specify where it acts, measured from point A.
w (2x
2
4x

16) lb/ft
x
B
A
w
4 ft
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4–159.The distributed load acts on the beam as shown.
Determine the maximum intensity . What is the
magnitude of the equivalent resultant force? Specify where
it acts, measured from point B.
w
max
w (2x
2
4x

16) lb/ft
x
B
A
w
4 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*4–160.The distributed load acts on the beam as shown.
Determine the magnitude of the equivalent resultant force
and specify its location, measured from point A.
w ( x
2
x

4) lb/ft
x
BA
w
10 ft
2 lb/ft
4 lb/ft
2
15
17
15
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•4–161.If the distribution of the ground reaction on the
pipe per foot of length can be approximated as shown,
determine the magnitude of the resultant force due to this
loading.
2.5 ft
50 lb/ft
25 lb/ft
w 25 (1 cos u) lb/ft
u
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4–162.The beam is subjected to the parabolic loading.
Determine an equivalent force and couple system at
pointA.
w (25 x
2
)lb/ft
4 ft
400 lb
/ft
x
w
A
O
4–163.Two couples act on the frame. If the resultant
couple moment is to be zero, determine the distance d
between the 100-lb couple forces.
d3 ft
4 ft
A
B
3 ft
30°
100 lb
150 lb
150 lb
100 lb
3
4
5
3
4
5
30°
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*4–164.Determine the coordinate direction angles , ,
of F, which is applied to the end of the pipe assembly, so
that the moment of Fabout Ois zero.
gba
x
10 in.
F 20 lb
6 in.
6 in.8 in.
z
O y
•4–165.Determine the moment of the force Fabout point
O. The force has coordinate direction angles of ,
, . Express the result as a Cartesian vector.g=45°b=120°
a=60°
x
10 in.
F 20 lb
6 in.
6 in.8 in.
z
O y
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–166.The snorkel boom lift is extended into the position
shown. If the worker weighs 160 lb, determine the moment
of this force about the connection at A.
25 ft
50
A
2 ft
4–167.Determine the moment of the force about the
door hinge at A. Express the result as a Cartesian vector.
F
C
0.5 m
1 m
30
2.5 m 1.5 m
z
C
A
B
a
a
x
y
F
C 250 N
*4–168.Determine the magnitude of the moment of the
force about the hinged axis aaof the door.F
C
0.5 m
1 m
30
2.5 m 1.5 m
z
C
A
B
a
a
x
y
F
C 250 N
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z
y
x
O
B
F
200 mm
A
–F
300 mm
400 mm
150 mm
200 mm
•4–169.Express the moment of the couple acting on the
pipe assembly in Cartesian vector form. Solve the problem
(a) using Eq. 4–13 and (b) summing the moment of each
force about pointO. Take .F=525k6
N
z
y
x
O
B
F
200 mm
A
–F
300 mm
400 mm
150 mm
200 mm
4–170.If the couple moment acting on the pipe has a
magnitude of , determine the magnitude Fof the
vertical force applied to each wrench.
400 N
#
m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4–171.Replace the force at Aby an equivalent resultant
force and couple moment at point P. Express the results in
Cartesian vector form.
z
A
F 120 lb
y
x
P
4 ft
10 ft
8 ft
8 ft
6 ft
6 ft
*4–172.The horizontal 30-N force acts on the handle of
the wrench. Determine the moment of this force about
point O. Specify the coordinate direction angles , , of
the moment axis.
gba
O
z
x
B
y
50 mm
200 mm
10 mm
30 N
45
45
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•4–173.The horizontal 30-N force acts on the handle of
the wrench. What is the magnitude of the moment of this
force about the zaxis?
O
z
x
B
y
50 mm
200 mm
10 mm
30 N
45
45
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•5–1.Draw the free-body diagram of the 50-kg paper roll
which has a center of mass at Gand rests on the smooth
blade of the paper hauler. Explain the significance of each
force acting on the diagram. (See Fig. 5–7b.)
B
30
35 mm
A
G
5–2.Draw the free-body diagram of member AB, which is
supported by a roller at Aand a pin at B. Explain the
significance of each force on the diagram. (See Fig. 5–7b.)
A
B
8 ft
30
4 ft3 ft
1312
5
800 lb ft
390 lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–3.Draw the free-body diagram of the dumpster Dof the
truck, which has a weight of 5000 lb and a center of gravity
at G. It is supported by a pin at Aand a pin-connected
hydraulic cylinder BC(short link). Explain the significance
of each force on the diagram. (See Fig. 5–7b.)
1.5 m
3 m
1 m
20
30
B
A
D
G
C
*5–4.Draw the free-body diagram of the beam which
supports the 80-kg load and is supported by the pin at Aand
a cable which wraps around the pulley at D. Explain the
significance of each force on the diagram. (See Fig. 5–7b.)
2 m 2 m
4
3
5
1.5 m
BA
C
E
D
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•5–5.Draw the free-body diagram of the truss that is
supported by the cable ABand pin C. Explain the significance
of each force acting on the diagram. (See Fig. 5–7b.)
A
B
C
2 m 2 m 2 m
2 m
30
3 kN
4 kN
5–6.Draw the free-body diagram of the crane boom AB
which has a weight of 650 lb and center of gravity at G.The
boom is supported by a pin at Aand cable BC. The load of
1250 lb is suspended from a cable attached at B. Explain
the significance of each force acting on the diagram. (See
Fig. 5–7b.)
12
13
5
G
C
A
B
30
18 ft
12 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–7.Draw the free-body diagram of the “spanner
wrench” subjected to the 20-lb force. The support at Acan
be considered a pin, and the surface of contact at Bis
smooth. Explain the significance of each force on the
diagram. (See Fig. 5–7b.)
A
B
6 in.
20 lb
1 in.
*5–8.Draw the free-body diagram of member ABCwhich
is supported by a smooth collar at A, roller at B, and short
link CD. Explain the significance of each force acting on the
diagram. (See Fig. 5–7b.)
6 m
2.5 kN
60
3 m
4 kN m
4 m
45
A
B
C
D
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•5–9.Draw the free-body diagram of the bar, which has a
negligible thickness and smooth points of contact at A,B,
and C. Explain the significance of each force on the
diagram. (See Fig. 5–7b.)
3 in.
5 in.
8 in.
A
30
10 lb
30
BC
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–10.Draw the free-body diagram of the winch, which
consists of a drum of radius 4 in. It is pin-connected at its
center C, and at its outer rim is a ratchet gear having a mean
radius of 6 in. The pawl ABserves as a two-force member
(short link) and prevents the drum from rotating. Explain
the significance of each force on the diagram. (See
Fig. 5–7b.) 3 in.
2 in.
6 in.
B
A
500 lb
C
4 in.
5–11.Determine the normal reactions at Aand Bin
Prob. 5–1.
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*5–12.Determine the tension in the cord and the
horizontal and vertical components of reaction at support A
of the beam in Prob. 5–4.
•5–13.Determine the horizontal and vertical components
of reaction at Cand the tension in the cable ABfor the
truss in Prob. 5–5.
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5–14.Determine the horizontal and vertical components
of reaction at Aand the tension in cable BCon the boom in
Prob. 5–6.
5–15.Determine the horizontal and vertical components
of reaction at Aand the normal reaction at Bon the
spanner wrench in Prob. 5–7.
*5–16.Determine the normal reactions at Aand Band the
force in link CDacting on the member in Prob. 5–8.
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328. 328
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•5–17.Determine the normal reactions at the points of
contact at A,B, and Cof the bar in Prob. 5–9.
5–18.Determine the horizontal and vertical components
of reaction at pin Cand the force in the pawl of the winch in
Prob. 5–10.
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329. 329
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–19.Compare the force exerted on the toe and heel of a
120-lb woman when she is wearing regular shoes and
stiletto heels. Assume all her weight is placed on one foot
and the reactions occur at points Aand Bas shown.
A AB B
5.75 in.
3.75 in.0.75 in.
1.25 in.
120 lb
120 lb
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330. 330
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*5–20.The train car has a weight of 24 000 lb and a center
of gravity at G. It is suspended from its front and rear on the
track by six tires located at A,B, and C. Determine the
normal reactions on these tires if the track is assumed to be
a smooth surface and an equal portion of the load is
supported at both the front and rear tires.
5 ft
A
C
B
G
4 ft
6 ft
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331. 331
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•5–21.Determine the horizontal and vertical components
of reaction at the pin Aand the tension developed in cable
BCused to support the steel frame.
A
B
C
30 kN m
60 kN
1 m
3 m
1 m 1 m
5
4
3
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332. 332
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–22.The articulated crane boom has a weight of 125 lb and
center of gravity at G. If it supports a load of 600 lb, determine
the force acting at the pin Aand the force in the hydraulic
cylinder BCwhen the boom is in the position shown.
C
40
B
G
A
1 ft
4 ft
1 ft
8 ft
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333. 333
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–23.The airstroke actuator at Dis used to apply a force of
F= 200 N on the member at B. Determine the horizontal
and vertical components of reaction at the pin Aand the
force of the smooth shaft at Con the member.
A
C
B
D
60
600 mm
600 mm
15
200 mm
F

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334. 334
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*5–24.The airstroke actuator at Dis used to apply a force
of Fon the member at B. The normal reaction of the
smooth shaft at Con the member is 300 N. Determine the
magnitude of Fand the horizontal and vertical components
of reaction at pin A.
A
C
B
D
60
600 mm
600 mm
15
200 mm
F

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335. 335
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•5–25.The 300-lb electrical transformer with center of gravity
at Gis supported by a pin at Aand a smooth pad at B.
Determine the horizontal and vertical components of reaction
at the pin Aand the reaction of the pad Bon the transformer.
B
A
1.5 ft
3 ft
G
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336. 336
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–26.A skeletal diagram of a hand holding a load is shown
in the upper figure. If the load and the forearm have masses
of 2 kg and 1.2 kg, respectively, and their centers of mass are
located at and , determine the force developed in the
biceps CDand the horizontal and vertical components of
reaction at the elbow joint B. The forearm supporting
system can be modeled as the structural system shown in
the lower figure.
G
2G
1
B
B
C
C
D
D
G
2
G
2
G
1
G
1
A
A
135 mm
65 mm
75
100 mm
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337. 337
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–27.As an airplane’s brakes are applied, the nose wheel
exerts two forces on the end of the landing gear as shown.
Determine the horizontal and vertical components of
reaction at the pin Cand the force in strut AB.
20
30
2 kN
6 kN
B
A
600 mm
400 mm
C
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338. 338
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*5–28.The 1.4-Mg drainpipe is held in the tines of the fork
lift. Determine the normal forces at Aand Bas functions of
the blade angle and plot the results of force (vertical axis)
versus (horizontal axis) for 0…u…90°.u
u
0.4 m
A
B
u
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339. 339
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•5–29.The mass of 700 kg is suspended from a trolley
which moves along the crane rail from to
. Determine the force along the pin-connected
knee strut BC(short link) and the magnitude of force at pin
Aas a function of position d. Plot these results of and
(vertical axis) versus d(horizontal axis).
F
AF
BC
d=3.5 m
d=1.7
m
A
B
C
2 m
1.5 m
d
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340. 340
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–30.If the force of F =100 lb is applied to the handle of
the bar bender, determine the horizontal and vertical
components of reaction at pin Aand the reaction of the
roller Bon the smooth bar.
60
F
40 in.
5 in.
B
A
C
5 Solutions 44918 1/23/09 5:11 PM Page 340

341. 341
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–31.If the force of the smooth roller at Bon the bar
bender is required to be 1.5 kip, determine the horizontal
and vertical components of reaction at pin Aand the
required magnitude of force Fapplied to the handle.
60
F
40 in.
5 in.
B
A
C
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342. 342
*5–32.The jib crane is supported by a pin at Cand rod AB.
If the load has a mass of 2 Mg with its center of mass located
at G, determine the horizontal and vertical components of
reaction at the pin Cand the force developed in rod ABon
the crane when x= 5 m.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
G
D
4 m
0.2 m
3.2 m
B
C
A
x
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343. 343
•5–33.The jib crane is supported by a pin at Cand rod AB.
The rod can withstand a maximum tension of 40 kN. If the
load has a mass of 2 Mg, with its center of mass located at G,
determine its maximum allowable distance xand the
corresponding horizontal and vertical components of
reaction at C.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
G
D
4 m
0.2 m
3.2 m
B
C
A
x
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344. 344
5–34.Determine the horizontal and vertical components
of reaction at the pin Aand the normal force at the smooth
peg Bon the member.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
C
F 600 N
B
30
0.4 m
0.4 m
30
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345. 345
5–35.The framework is supported by the member AB
which rests on the smooth floor. When loaded, the pressure
distribution on ABis linear as shown. Determine the length d
of member ABand the intensity wfor this case.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4 ft
800 lb
d
w
7 ft
A
B
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346. 346
*5–36.Outriggers Aand Bare used to stabilize the crane
from overturning when lifting large loads. If the load to be
lifted is 3 Mg, determine the maximumboom angle so that
the crane does not overturn. The crane has a mass of 5 Mg
and center of mass at , whereas the boom has a mass of
0.6 Mg and center of mass at .G
B
G
C
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2.8 m
4.5 m
AB
5 m
0.7 m
2.3 m
G
B
G
C
u
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347. 347
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•5–37.The wooden plank resting between the buildings
deflects slightly when it supports the 50-kg boy. This
deflection causes a triangular distribution of load at its ends,
having maximum intensities of and . Determine
and , each measured in , when the boy is standing
3 m from one end as shown. Neglect the mass of the plank.
N>mw
B
w
Aw
Bw
A
3 m
0.45 m 0.3 m
6 m
AB
w
A
w
B
5 Solutions 44918 1/23/09 5:11 PM Page 347

348. 348
5–38.Spring CDremains in the horizontal position at all
times due to the roller at D. If the spring is unstretched
when and the bracket achieves its equilibrium
position when , determine the stiffness kof the
spring and the horizontal and vertical components of
reaction at pin A.
u=30°
u=0°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
0.45 m
0.6 m
k
D C
B
A
F 300 N
u
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349. 349
5–39.Spring CDremains in the horizontal position at all
times due to the roller at D. If the spring is unstretched
when and the stiffness is , determine
the smallest angle for equilibrium and the horizontal and
vertical components of reaction at pin A.
u
k=1.5 kN>mu=0°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
0.45 m
0.6 m
k
D C
B
A
F 300 N
u
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350. 350
*5–40.The platform assembly has a weight of 250 lb and
center of gravity at If it is intended to support a
maximum load of 400 lb placed at point determine the
smallest counterweight Wthat should be placed at Bin
order to prevent the platform from tipping over.
G
2,
G
1.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 ft
8 ft
1 ft1 ft
C
B
G
1
D
2 ft
6 ft
G
2
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351. 351
•5–41.Determine the horizontal and vertical components
of reaction at the pin Aand the reaction of the smooth
collar Bon the rod.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
B
D
C
2 ft
300 lb
4 ft
1 ft 1 ft
30
450 lb
5 Solutions 44918 1/23/09 5:11 PM Page 351

352. 352
5–42.Determine the support reactions of roller Aand the
smooth collar Bon the rod. The collar is fixed to the rod
AB, but is allowed to slide along rod CD.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
1 m
2 m
600 N m
1 m
B
D
C
900 N
45
45
5 Solutions 44918 1/23/09 5:11 PM Page 352

353. 353
5–43.The uniform rod ABhas a weight of 15 lb. Determine
the force in the cable when the rod is in the position shown.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
10
30
5 ft
C
B
T
*5–44.Determine the horizontal and vertical components
of force at the pin Aand the reaction at the rocker Bof the
curved beam.
AB
500 N
200 N
1015
2 m
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354. 354
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•5–45.The floor crane and the driver have a total weight
of 2500 lb with a center of gravity at G. If the crane is
required to lift the 500-lb drum, determine the normal
reaction on boththe wheels at Aand boththe wheels at B
when the boom is in the position shown.
12 ft
30
3 ft
6 ft
8.4 ft
2.2 ft
1.4 ft
A B
D
E
F
C
G
5 Solutions 44918 1/23/09 5:11 PM Page 354

355. 355
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–46.The floor crane and the driver have a total weight of
2500 lb with a center of gravity at G. Determine the largest
weight of the drum that can be lifted without causing the
crane to overturn when its boom is in the position shown.
12 ft
30
3 ft
6 ft
8.4 ft
2.2 ft
1.4 ft
A B
D
E
F
C
G
5 Solutions 44918 1/23/09 5:11 PM Page 355

356. 356
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–47.The motor has a weight of 850 lb. Determine the
force that each of the chains exerts on the supporting hooks
at A, B, and C. Neglect the size of the hooks and the
thickness of the beam.
1.5 ft1 ft
0.5 ft
CA
B
30
1010
850 lb
*5–48.Determine the force Pneeded to pull the 50-kg roller
over the smooth step. Take u=60°.
20
A
B
P
0.6 m
0.1 m
u
5 Solutions 44918 1/23/09 5:11 PM Page 356

357. 357
•5–49.Determine the magnitude and direction of the
minimum force Pneeded to pull the 50-kg roller over the
smooth step.
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
20
A
B
P
0.6 m
0.1 m
u
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358. 358
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–50.The winch cable on a tow truck is subjected to a
force of when the cable is directed at .
Determine the magnitudes of the total brake frictional
force Ffor the rear set of wheels Band the total normal
forces at bothfront wheels Aand both rear wheels Bfor
equilibrium. The truck has a total mass of 4 Mg and mass
center at G.
u=60°T=6 kN
1.25 m
3 m
A
G
B F
T
1.5 m
2 m 2.5 m
u
5 Solutions 44918 1/23/09 5:11 PM Page 358

359. 359
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–51.Determine the minimum cable force Tand critical
angle which will cause the tow truck to start tipping, i.e., for
the normal reaction at Ato be zero. Assume that the truck is
braked and will not slip at B. The truck has a total mass of
4 Mg and mass center at G.x
u
1.25 m
3 m
A
G
B F
T
1.5 m
2 m 2.5 m
u
*5–52.Three uniform books, each having a weight Wand
length a, are stacked as shown. Determine the maximum
distance dthat the top book can extend out from the
bottom one so the stack does not topple over.
ad
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360. 360
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•5–53.Determine the angle at which the link ABCis
held in equilibrium if member BDmoves 2 in. to the right.
The springs are originally unstretched when . Each
spring has the stiffness shown. The springs remain
horizontal since they are attached to roller guides.
u=0°
u
k
CF 100 lb/ft
k
AE
500 lb/ft
E
F
C
A
B
D
F
6 in.
6 in.
u
5 Solutions 44918 1/23/09 5:11 PM Page 360

361. 361
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–54.The uniform rod ABhas a weight of 15 lb and the
spring is unstretched when . If , determine
the stiffness kof the spring.
u=30°u=0°
6 ft
u
B
A
3 ftk
5–55.The horizontal beam is supported by springs at its
ends. Each spring has a stiffness of and is
originally unstretched so that the beam is in the horizontal
position. Determine the angle of tilt of the beam if a load of
800 N is applied at point Cas shown.
k=5 kN>m
800 N
B
C
A
3 m
1 m
5 Solutions 44918 1/23/09 5:11 PM Page 361

362. 362
*5–56.The horizontal beam is supported by springs at its
ends. If the stiffness of the spring at Ais ,
determine the required stiffness of the spring at Bso that if
the beam is loaded with the 800 N it remains in the
horizontal position. The springs are originally constructed
so that the beam is in the horizontal position when it is
unloaded.
k
A=5 kN>m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
800 N
B
C
A
3 m
1 m
5 Solutions 44918 1/23/09 5:11 PM Page 362

363. 363
•5–57.The smooth disks Dand Ehave a weight of 200 lb
and 100 lb, respectively. If a horizontal force of
is applied to the center of disk E, determine the normal
reactions at the points of contact with the ground at A,B,
and C.
P=200
lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
P
1.5 ft
A
B
D
E
C
3
5
4
1 ft
5 Solutions 44918 1/23/09 5:11 PM Page 363

364. 364
5–58.The smooth disks Dand Ehave a weight of 200 lb
and 100 lb, respectively. Determine the largest horizontal
force Pthat can be applied to the center of disk Ewithout
causing the disk Dto move up the incline.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
P
1.5 ft
A
B
D
E
C
3
5
4
1 ft
5 Solutions 44918 1/23/09 5:11 PM Page 364

365. 365
5–59.A man stands out at the end of the diving board,
which is supported by two springs Aand B, each having a
stiffness of . In the position shown the board
is horizontal. If the man has a mass of 40 kg, determine the
angle of tilt which the board makes with the horizontal after
he jumps off. Neglect the weight of the board and assume it
is rigid.
k=15
kN>m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
BA
1 m 3 m
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366. 366
*5–60.The uniform rod has a length land weight W. It is
supported at one end Aby a smooth wall and the other end
by a cord of length swhich is attached to the wall as
shown. Show that for equilibrium it is required that
.h=[(s
2
-l
2
)>3]
1>2
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
h
s
C
B
A
l
5 Solutions 44918 1/23/09 5:11 PM Page 366

367. 367
•5–61.If spring BCis unstretched with and the bell
crank achieves its equilibrium position when ,
determine the force Fapplied perpendicular to segment
ADand the horizontal and vertical components of reaction
at pin A. Spring BCremains in the horizontal postion at all
times due to the roller at C.
u=15°
u=0°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
300 mm
400 mm
B
k 2 kN/m
D
C
A
150
F
u
5 Solutions 44918 1/23/09 5:11 PM Page 367

368. 368
5–62.The thin rod of length lis supported by the smooth
tube. Determine the distance aneeded for equilibrium if
the applied load is P.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
P
B
A
2r
a
l
5 Solutions 44918 1/23/09 5:11 PM Page 368

369. 369
5–63.The cart supports the uniform crate having a mass of
85 kg. Determine the vertical reactions on the three casters
at A,B, and C. The caster at Bis not shown. Neglect the
mass of the cart.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
B
A
C
0.2 m
0.5 m
0.6 m 0.35 m
0.1 m
0.4 m
0.2 m
0.35 m
5 Solutions 44918 1/23/09 5:11 PM Page 369

370. 370
*5–64.The pole for a power line is subjected to the two
cable forces of 60 lb, each force lying in a plane parallel to
the plane. If the tension in the guy wire ABis 80 lb,
determine the x,y,zcomponents of reaction at the fixed
base of the pole,O.
x-y
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
45
60 lb
60 lb
80 lb
1 ft
10 ft
4 ft
45
3 ft
y
B
A
O
x
5 Solutions 44918 1/23/09 5:11 PM Page 370

371. 371
•5–65.If and , determine
the tension developed in cables AB, CD,and EF. Neglect
the weight of the plate.
y=1 mP=6 kN, x=0.75 m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
F
B
D
A
y
x
x
y
E
C
P
2 m
2 m
5 Solutions 44918 1/23/09 5:11 PM Page 371

372. 372
5–66.Determine the location xand yof the point of
application of force Pso that the tension developed in
cables AB, CD, and EFis the same. Neglect the weight of
the plate.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.z
F
B
D
A
y
x
x
y
E
C
P
2 m
2 m
5 Solutions 44918 1/23/09 5:11 PM Page 372

373. 373
5–67.Due to an unequal distribution of fuel in the wing
tanks, the centers of gravity for the airplane fuselage A
and wings Band Care located as shown. If these
components have weights
and determine the normal reactions of the
wheels D, E, and Fon the ground.
W
C=6000 lb,
W
B=8000 lb,W
A=45 000 lb,
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8 ft
20 ft
A
B
D
E
F
8 ft
6 ft
6 ft
4 ft
3 ft
z
x
y
C
5 Solutions 44918 1/23/09 5:11 PM Page 373

374. 374
*5–68.Determine the magnitude of force Fthat must be
exerted on the handle at Cto hold the 75-kg crate in the
position shown. Also, determine the components of reaction
at the thrust bearing Aand smooth journal bearing B.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F
0.1 m
0.2 m
0.5 m
0.6 m
0.1 m
z
x
y
A
B
C
5 Solutions 44918 1/23/09 5:11 PM Page 374

375. 375
•5–69.The shaft is supported by three smooth journal
bearings at A, B, and C. Determine the components of
reaction at these bearings.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
0.6 m
x
B
C
A
z
0.9 m
0.6 m
0.9 m y
0.9 m
0.9 m
0.9 m
900 N
500 N
450 N600 N
5 Solutions 44918 1/23/09 5:11 PM Page 375

376. 376
5–70.Determine the tension in cables BDand CDand
the x, y, zcomponents of reaction at the ball-and-socket
joint at A.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
y
x
C
B A
3 m
300 N
D
1 m
0.5 m
1.5 m
5 Solutions 44918 1/23/09 5:11 PM Page 376

377. 377
5–71.The rod assembly is used to support the 250-lb cylinder.
Determine the components of reaction at the ball-and-
socket joint A, the smooth journal bearing E,and the force
developed along rod CD. The connections at Cand Dare
ball-and-socket joints.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x y
z
D
A
C
E
F
1 ft
1 ft
1 ft
1.5 ft
1 ft
5 Solutions 44918 1/23/09 5:11 PM Page 377

378. 378
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5 Solutions 44918 1/23/09 5:11 PM Page 378

379. 379
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*5–72.Determine the components of reaction acting at the
smooth journal bearings A,B, and C.
0.6 m
45
x y
C
z
B
A
0.4 m
0.8 m
0.4 m
450 N
300 N m
5 Solutions 44918 1/23/09 5:11 PM Page 379

380. 380
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•5–73.Determine the force components acting on the ball-
and-socket at A, the reaction at the roller Band the tension
on the cord CD needed for equilibrium of the quarter
circular plate.
z
x
350 N
1 m
2 m
60
3 m
200 N
200 N
y
B
A
C
D
5 Solutions 44918 1/23/09 5:11 PM Page 380

381. 381
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–74.If the load has a weight of 200 lb, determine the x, y,
zcomponents of reaction at the ball-and-socket joint Aand
the tension in each of the wires.
y
x
z
C
A
D
E
F
GB
2 ft
2 ft
2 ft
2 ft
3 ft
2 ft
4 ft
5 Solutions 44918 1/23/09 5:11 PM Page 381

382. 382
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5 Solutions 44918 1/23/09 5:11 PM Page 382

383. 383
5–75.If the cable can be subjected to a maximum tension
of 300 lb, determine the maximum force Fwhich may be
applied to the plate. Compute the x, y, zcomponents of
reaction at the hinge Afor this loading.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9 ft
F
3 ft
z
x
y
A
B
2 ft
3 ft
1 ft
C
*5–76.The member is supported by a pin at Aand a cable
BC. If the load at Dis 300 lb, determine the x, y, z
components of reaction at the pin Aand the tension in
cableB C.
C
1 ft
z
A
B
D
x
6 ft
2 ft
2 ft
2 ft
2 ft
y
5 Solutions 44918 1/23/09 5:11 PM Page 383

384. 384
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•5–77.The plate has a weight of Wwith center of gravity at
G. Determine the distance dalong line GHwhere the
vertical force P= 0.75Wwill cause the tension in wire CDto
become zero.
z
F
B
D
A
H
y
x
G
d
E
C
P
L
––
2
L
––
2
L
––
2
L
––
2
5 Solutions 44918 1/23/09 5:11 PM Page 384

385. 385
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–78.The plate has a weight of Wwith center of gravity at
G. Determine the tension developed in wires AB,CD, and
EFif the force P= 0.75Wis applied at d = L/2.
z
F
B
D
A
H
y
x
G
d
E
C
P
L
––
2
L
––
2
L
––
2
L
––
2
5 Solutions 44918 1/23/09 5:11 PM Page 385

386. 386
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–79.The boom is supported by a ball-and-socket joint at A
and a guy wire at B. If the 5-kN loads lie in a plane which is
parallel to the x–yplane, determine the x,y,zcomponents of
reaction at Aand the tension in the cable at B.
z
5 kN
5 kN
y
x
3 m
2 m
1.5 m
30
30
B
A
5 Solutions 44918 1/23/09 5:12 PM Page 386

387. 387
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*5–80.The circular door has a weight of 55 lb and a center
of gravity at G. Determine the x,y,zcomponents of
reaction at the hinge Aand the force acting along strut CB
needed to hold the door in equilibrium. Set .u=45°
C
z
x
y
B
G
A
3 ft
3 ft
u
5 Solutions 44918 1/23/09 5:12 PM Page 387

388. 388
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•5–81.The circular door has a weight of 55 lb and a center
of gravity at G. Determine the x,y,zcomponents of
reaction at the hinge Aand the force acting along strut CB
needed to hold the door in equilibrium. Set .u=90°
C
z
x
y
B
G
A
3 ft
3 ft
u
5 Solutions 44918 1/23/09 5:12 PM Page 388

389. 389
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–82.Member ABis supported at Bby a cable and at Aby
a smooth fixed squarerod which fits loosely through the
square hole of the collar. If ,
determine the x,y,zcomponents of reaction at Aand the
tension in the cable.
F=520i-40j-75k6 lb
8 ft C
z
6 ft
12 ft
4 ft
F
B
x
A
y
5 Solutions 44918 1/23/09 5:12 PM Page 389

390. 390
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–83.Member ABis supported at Bby a cable and at Aby
a smooth fixed squarerod which fits loosely through the
square hole of the collar. Determine the tension in cable BC
if the force .F=5-45k6 lb
8 ft C
z
6 ft
12 ft
4 ft
F
B
x
A
y
5 Solutions 44918 1/23/09 5:12 PM Page 390

391. 391
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*5–84.Determine the largest weight of the oil drum that
the floor crane can support without overturning. Also, what
are the vertical reactions at the smooth wheels A, B,and C
for this case. The floor crane has a weight of 300 lb, with its
center of gravity located at G.
x
z
C
G
B
A
y
3 ft
1.5ft
10 ft
4 ft
2 ft
2.5 ft
2.5 ft
1 ft
30
5 Solutions 44918 1/23/09 5:12 PM Page 391

392. 392
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•5–85.The circular plate has a weight Wand center of
gravity at its center. If it is supported by three vertical cords
tied to its edge, determine the largest distance dfrom the
center to where any vertical force Pcan be applied so as not
to cause the force in any one of the cables to become zero.
A
d
120
120
120
C
r
P
B
5 Solutions 44918 1/23/09 5:12 PM Page 392

393. 393
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–86.Solve Prob. 5–85 if the plate’s weight Wis neglected.
A
d
120
120
120
C
r
P
B
5 Solutions 44918 1/23/09 5:12 PM Page 393

394. 394
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
5–87.A uniform square table having a weight Wand sides
ais supported by three vertical legs. Determine the smallest
vertical force Pthat can be applied to its top that will cause
it to tip over.
a/2
a/2
a
5 Solutions 44918 1/23/09 5:12 PM Page 394

395. 395
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*5–88.Determine the horizontal and vertical components
of reaction at the pin Aand the force in the cable BC.
Neglect the thickness of the members. B
C
A
4.5 m
4 m
100 N
3 m
200 N/m
30
5 Solutions 44918 1/23/09 5:12 PM Page 395

396. 396
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•5–89.Determine the horizontal and vertical components
of reaction at the pin Aand the reaction at the roller B
required to support the truss. Set .F=600 N
A
B
2 m 2 m 2 m
45
2 m
FFF
5–90.If the roller at Bcan sustain a maximum load of
3 kN, determine the largest magnitude of each of the three
forces Fthat can be supported by the truss.
A
B
2 m 2 m 2 m
45
2 m
FFF
5 Solutions 44918 1/23/09 5:12 PM Page 396

397. 397
5–91.Determine the normal reaction at the roller Aand
horizontal and vertical components at pin Bfor equilibrium
of the member.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
0.4 m
60
0.8 m
10 kN
0.6 m0.6 m
6 kN
A
B
5 Solutions 44918 1/23/09 5:12 PM Page 397

398. 398
*5–92.The shaft assembly is supported by two smooth
journal bearings Aand Band a short link DC. If a couple
moment is applied to the shaft as shown, determine the
components of force reaction at the journal bearings and the
force in the link. The link lies in a plane parallel to the y–z
plane and the bearings are properly aligned on the shaft.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
250 mm
300 mm
400 mm
250 N m
y
A
x
20
120 mm
30
D
B
z
C
5 Solutions 44918 1/23/09 5:12 PM Page 398

399. 399
•5–93.Determine the reactions at the supports Aand Bof
the frame.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
B
8 ft 6 ft
8 ft
6 ft
0.5 kip
2 kip
10 kip
7 kip
5 kip
6 ft
5 Solutions 44918 1/23/09 5:12 PM Page 399

400. 400
5–94.A skeletal diagram of the lower leg is shown in the
lower figure. Here it can be noted that this portion of the leg
is lifted by the quadriceps muscle attached to the hip at A
and to the patella bone at B. This bone slides freely over
cartilage at the knee joint. The quadriceps is further
extended and attached to the tibia at C. Using the
mechanical system shown in the upper figure to model the
lower leg, determine the tension in the quadriceps at Cand
the magnitude of the resultant force at the femur (pin),D,
in order to hold the lower leg in the position shown. The
lower leg has a mass of 3.2 kg and a mass center at ; the
foot has a mass of 1.6 kg and a mass center at .G
2
G
1
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
A
B
C
D
D
C
B
350 mm
300 mm
75 mm
75
25 mm
G
1
G
2
5 Solutions 44918 1/23/09 5:12 PM Page 400

401. 401
5–95.A vertical force of 80 lb acts on the crankshaft.
Determine the horizontal equilibrium force Pthat must be
applied to the handle and the x, y, zcomponents of force at
the smooth journal bearing Aand the thrust bearing B.The
bearings are properly aligned and exert only force reactions
on the shaft.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
P
B
z
x
y80 lb
14 in.
10 in.
14 in.
6 in.
4 in.
8 in.
5 Solutions 44918 1/23/09 5:12 PM Page 401

402. 402
*5–96.The symmetrical shelf is subjected to a uniform
load of 4 kPa. Support is provided by a bolt (or pin) located
at each end Aand and by the symmetrical brace arms,
which bear against the smooth wall on both sides at Band
. Determine the force resisted by each bolt at the wall
and the normal force at Bfor equilibrium.
B¿
A¿
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
0.2 m
0.15 m
4 kPa
1.5 m
A
A¿
B
B¿
5 Solutions 44918 1/23/09 5:12 PM Page 402

403. 403
•6–1.Determine the force in each member of the truss,
and state if the members are in tension or compression.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
600 N
900 N
2 m
2 m
2 m
A
C
E
D
B
6 Solutions 44918 1/26/09 1:45 PM Page 403

404. 404
6–2.The truss, used to support a balcony, is subjected to
the loading shown. Approximate each joint as a pin and
determine the force in each member. State whether the
members are in tension or compression. Set
P
2=400 lb.
P
1=600 lb,
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
45
4 ft 4 ft
45
D
E
CB
P
2
A
4 ft
P
1
6 Solutions 44918 1/26/09 1:45 PM Page 404

405. 405
6–3.The truss, used to support a balcony, is subjected to
the loading shown. Approximate each joint as a pin and
determine the force in each member. State whether the
members are in tension or compression. Set
P
2=0.
P
1=800 lb,
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
45
4 ft 4 ft
45
D
E
CB
P
2
A
4 ft
P
1
6 Solutions 44918 1/26/09 1:45 PM Page 405

406. 406
*6–4.Determine the force in each member of the truss
and state if the members are in tension or compression.
Assume each joint as a pin. Set P= 4 kN.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
E
D
CB
PP
2P
4 m
4 m 4 m
6 Solutions 44918 1/26/09 1:45 PM Page 406

407. 407
•6–5.Assume that each member of the truss is made of steel
having a mass per length of 4 kg/m. Set , determine the
force in each member, and indicate if the members are in
tension or compression. Neglect the weight of the gusset plates
and assume each joint is a pin. Solve the problem by assuming
the weight of each member can be represented as a vertical
force, half of which is applied at the end of each member.
P=0
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
E
D
CB
PP
2P
4 m
4 m 4 m
6 Solutions 44918 1/26/09 1:45 PM Page 407

408. 408
6–6.Determine the force in each member of the truss and
state if the members are in tension or compression. Set
and .P
2=1.5 kNP
1=2 kN
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
E D
30 30
B
C
3 m 3 m
P
2P
1
6 Solutions 44918 1/26/09 1:45 PM Page 408

409. 409
6–7.Determine the force in each member of the truss and
state if the members are in tension or compression. Set
.P
1=P
2=4 kN
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
E D
30 30
B
C
3 m 3 m
P
2P
1
6 Solutions 44918 1/26/09 1:45 PM Page 409

410. 410
*6–8.Determine the force in each member of the truss,
and state if the members are in tension or compression. Set
.P= 800 lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3 ft
3 ft
3 ft
P
3 ft
500 lb
A
CB
D
F
E
6 Solutions 44918 1/26/09 1:45 PM Page 410

411. 411
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–9.Remove the 500-lb force and then determine the
greatest force Pthat can be applied to the truss so that none
of the members are subjected to a force exceeding either
800 lb in tension or in compression.600 lb
3 ft
3 ft
3 ft
P
3 ft
500 lb
A
CB
D
F
E
6 Solutions 44918 1/26/09 1:45 PM Page 411

412. 412
6–10.Determine the force in each member of the truss
and state if the members are in tension or compression. Set
,.P
2=0P
1=800 lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 ft
A
G
B
C
F
D
E
P
1
P
2
4 ft 4 ft 4 ft 4 ft
6 Solutions 44918 1/26/09 1:45 PM Page 412

413. 413
6–11.Determine the force in each member of the truss
and state if the members are in tension or compression. Set
,.P
2=400 lbP
1=600 lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 ft
A
G
B
C
F
D
E
P
1
P
2
4 ft 4 ft 4 ft 4 ft
6 Solutions 44918 1/26/09 1:45 PM Page 413

414. 414
*6–12.Determine the force in each member of the truss
and state if the members are in tension or compression. Set
,.P
2=100 lbP
1=240 lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
B
C D
A
12 ft
5 ft
P
1
P
2
6 Solutions 44918 1/26/09 1:45 PM Page 414

415. 415
•6–13.Determine the largest load that can be applied
to the truss so that the force in any member does not exceed
500 lb (T) or 350 lb (C). Take .P
1=0
P
2
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
B
C D
A
12 ft
5 ft
P
1
P
2
6 Solutions 44918 1/26/09 1:45 PM Page 415

416. 416
6–14.Determine the force in each member of the truss,
and state if the members are in tension or compression. Set
.P=2500 lb
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4 ft
4 ft
1200 lb 1200 lb
P
4 ft 4 ft 4 ft
A B
F
EDC
G
30 30
6 Solutions 44918 1/26/09 1:45 PM Page 416

417. 417
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–15.Remove the 1200-lb forces and determine the
greatest force Pthat can be applied to the truss so that none
of the members are subjected to a force exceeding either
2000 lb in tension or 1500 lb in compression.
4 ft
4 ft
1200 lb 1200 lb
P
4 ft 4 ft 4 ft
A B
F
EDC
G
30 30
6 Solutions 44918 1/26/09 1:45 PM Page 417

418. 418
*6–16.Determine the force in each member of the truss,
and state if the members are in tension or compression. Set
.P=5 kN
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
C
B
D
E
P
1.5 m
1.5 m
2 m2 m
1.5 m
6 Solutions 44918 1/26/09 1:45 PM Page 418

419. 419
•6–17.Determine the greatest force Pthat can be applied
to the truss so that none of the members are subjected to a
force exceeding either in tension or in
compression.
2 kN2.5 kN
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
C
B
D
E
P
1.5 m
1.5 m
2 m2 m
1.5 m
6 Solutions 44918 1/26/09 1:46 PM Page 419

420. 420
6–18.Determine the force in each member of the truss,
and state if the members are in tension or compression.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3 ft
4 ft
900 lb
600 lb
4 ft 4 ft
A
B
C
DE
F
6 Solutions 44918 1/26/09 1:46 PM Page 420

421. 421
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–19.The truss is fabricated using members having a
weight of . Remove the external forces from the
truss, and determine the force in each member due to the
weight of the members. State whether the members are in
tension or compression. Assume that the total force acting
on a joint is the sum of half of the weight of every member
connected to the joint.
10 lb>ft
3 ft
4 ft
900 lb
600 lb
4 ft 4 ft
A
B
C
DE
F
6 Solutions 44918 1/26/09 1:46 PM Page 421

422. 422
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 Solutions 44918 1/26/09 1:46 PM Page 422

423. 423
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–20.Determine the force in each member of the truss
and state if the members are in tension or compression. The
load has a mass of 40 kg.
G
A
B
F
C
E
D
0.1 m
6 m
2.5 m
3.5 m
6 Solutions 44918 1/26/09 1:46 PM Page 423

424. 424
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–21.Determine the largest massmof the suspended
block so that the force in any member does not exceed
30 kN (T) or 25 kN (C).
G
A
B
F
C
E
D
0.1 m
6 m
2.5 m
3.5 m
6 Solutions 44918 1/26/09 1:46 PM Page 424

425. 425
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–22.Determine the force in each member of the truss,
and state if the members are in tension or compression.
A
E D
B
C
2 m
400 N
45 4545 45
2 m
600 N
6 Solutions 44918 1/26/09 1:46 PM Page 425

426. 426
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–23.The truss is fabricated using uniform members
having a mass of . Remove the external forces from
the truss, and determine the force in each member due to
the weight of the truss. State whether the members are in
tension or compression. Assume that the total force acting
on a joint is the sum of half of the weight of every member
connected to the joint.
5 kg>m
A
E D
B
C
2 m
400 N
45 4545 45
2 m
600 N
6 Solutions 44918 1/26/09 1:46 PM Page 426

427. 427
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–24.Determine the force in each member of the truss,
and state if the members are in tension or compression. Set
.P=4 kN
P
3 m
A CB
E
D
F
P
3 m 3 m3 m
6 Solutions 44918 1/26/09 1:46 PM Page 427

428. 428
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–25.Determine the greatest force Pthat can be applied
to the truss so that none of the members are subjected to a
force exceeding either in tension or in
compression.
1 kN1.5 kN
P
3 m
A CB
E
D
F
P
3 m 3 m3 m
6 Solutions 44918 1/26/09 1:46 PM Page 428

429. 429
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–26.A sign is subjected to a wind loading that exerts
horizontal forces of 300 lb on joints Band Cof one of the
side supporting trusses. Determine the force in each
member of the truss and state if the members are in tension
or compression.
A
C
B
D
E
13 ft
13 ft
12 ft
5 ft
300 lb
300 lb
12 ft
45
6 Solutions 44918 1/26/09 1:46 PM Page 429

430. 430
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–27.Determine the force in each member of the double
scissors truss in terms of the load Pand state if the members
are in tension or compression.
A
DFE
PP
B C
L/3
L/3L/3L/3
6 Solutions 44918 1/26/09 1:46 PM Page 430

431. 431
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–28.Determine the force in each member of the truss in
terms of the load P, and indicate whether the members are
in tension or compression.
A
B
C
DF
E
P
d
d
dd /2d/2 d
6 Solutions 44918 1/26/09 1:46 PM Page 431

432. 432
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–29.If the maximum force that any member can support
is 4 kN in tension and 3 kN in compression, determine the
maximum force Pthat can be applied at joint B. Take
.d=1 m
A
B
C
DF
E
P
d
d
dd /2d/2 d
6 Solutions 44918 1/26/09 1:46 PM Page 432

433. 433
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–30.The two-member truss is subjected to the force of
300 lb. Determine the range of for application of the load so
that the force in either member does not exceed 400 lb (T) or
200 lb (C).
u
B
CA
4 ft
3 ft
300 lb
u
6 Solutions 44918 1/26/09 1:46 PM Page 433

434. 434
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 Solutions 44918 1/26/09 1:46 PM Page 434

435. 435
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–31.The internal drag truss for the wing of a light
airplane is subjected to the forces shown. Determine the
force in members BC,BH, and HC, and state if the
members are in tension or compression.
2 ft
AB CD
J IHG
E
F
2 ft 2 ft 2 ft 1.5 ft
80 lb 80 lb
60 lb
40 lb
6 Solutions 44918 1/26/09 1:46 PM Page 435

436. 436
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–32.The Howe bridge trussis subjected to the loading
shown. Determine the force in members HD,CD, and GD,
and state if the members are in tension or compression.
AE
B CD
IJ
30 kN
20 kN 20 kN
40 kN
HG F
4 m
16 m, 4@4m
6 Solutions 44918 1/26/09 1:46 PM Page 436

437. 437
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–33.The Howe bridge trussis subjected to the loading
shown. Determine the force in members HI,HB, and BC,
and state if the members are in tension or compression.
AE
B CD
IJ
30 kN
20 kN 20 kN
40 kN
HG F
4 m
16 m, 4@4m
6 Solutions 44918 1/26/09 1:46 PM Page 437

438. 438
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–34.Determine the force in members JK,CJ, and CDof
the truss, and state if the members are in tension or
compression.
A
B C D FE
G
H
IJ
L
K
6 kN
8 kN
5 kN
4 kN
3 m
2 m2 m 2 m 2 m 2 m 2 m
6 Solutions 44918 1/26/09 1:46 PM Page 438

439. 439
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–35.Determine the force in members HI,FI, and EFof
the truss, and state if the members are in tension or
compression.
A
B C D FE
G
H
IJ
L
K
6 kN
8 kN
5 kN
4 kN
3 m
2 m2 m 2 m 2 m 2 m 2 m
6 Solutions 44918 1/26/09 1:46 PM Page 439

440. 440
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–36.Determine the force in members BC,CG, and GF
of the Warrentruss. Indicate if the members are in tension
or compression.
A E
B CD
6 kN
8 kN
G F
3 m
3 m 3 m 3 m
3 m
3 m3 m
•6–37.Determine the force in members CD,CF, and FG
of the Warren truss. Indicate if the members are in tension
or compression.
A E
B CD
6 kN
8 kN
G F
3 m
3 m 3 m 3 m
3 m
3 m3 m
6 Solutions 44918 1/26/09 1:46 PM Page 440

441. 441
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–38.Determine the force in members DC,HC, and HIof
the truss, and state if the members are in tension or
compression.
A
C
G
E D
H
F
I
B
2 m 2 m 2 m
1.5 m
50 kN
40 kN
40 kN
30 kN
1.5 m
1.5 m
6 Solutions 44918 1/26/09 1:46 PM Page 441

442. 442
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–39.Determine the force in members ED,EH, and GH
of the truss, and state if the members are in tension or
compression.
A
C
G
E D
H
F
I
B
2 m 2 m 2 m
1.5 m
50 kN
40 kN
40 kN
30 kN
1.5 m
1.5 m
6 Solutions 44918 1/26/09 1:46 PM Page 442

443. 443
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–40.Determine the force in members GF,GD, and CD
of the truss and state if the members are in tension or
compression.
260 lb
4 ft 4 ft
4 ft
3 ft 3 ft
4 ft 4 ft
5
12
13
A
H G F
B
C
D
E
•6–41.Determine the force in members BG,BC, and HG
of the truss and state if the members are in tension or
compression.
260 lb
4 ft 4 ft
4 ft
3 ft 3 ft
4 ft 4 ft
5
12
13
A
H G F
B
C
D
E
6 Solutions 44918 1/26/09 1:46 PM Page 443

444. 444
6–42.Determine the force in members ICand CGof the
truss and state if these members are in tension or
compression. Also, indicate all zero-force members.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
1.5 m 1.5 m 1.5 m
A
H
B CD
JI
GF
E
1.5 m
2 m
2 m
6 kN 6 kN
6–43.Determine the force in members JEand GFof the
truss and state if these members are in tension or
compression. Also, indicate all zero-force members.
1.5 m 1.5 m 1.5 m
A
H
B CD
JI
GF
E
1.5 m
2 m
2 m
6 kN 6 kN
6 Solutions 44918 1/26/09 1:46 PM Page 444

445. 445
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–44.Determine the force in members JI,EF,EI, and JE
of the truss, and state if the members are in tension or
compression.
8 ft
8 ft
8 ft
900 lb
1500 lb
1000 lb1000 lb
A
G
N B
H
F
M
CDE
I
JL K
8 ft 8 ft 8 ft 8 ft 8 ft 8 ft
6 Solutions 44918 1/26/09 1:46 PM Page 445

446. 446
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–45.Determine the force in members CD,LD, and KL
of the truss, and state if the members are in tension or
compression.
8 ft
8 ft
8 ft
900 lb
1500 lb
1000 lb1000 lb
A
G
N B
H
F
M
CDE
I
JL K
8 ft 8 ft 8 ft 8 ft 8 ft 8 ft
6 Solutions 44918 1/26/09 1:46 PM Page 446

447. 447
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–46.Determine the force developed in members BCand
CHof the roof truss and state if the members are in tension
or compression.
1.5 m
2 m2 m
1 m 1 m
0.8 m
2 kN
1.5 kN
A
H
B
D
G
C
F
E
6 Solutions 44918 1/26/09 1:46 PM Page 447

448. 448
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–47.Determine the force in members CDand GFof the
truss and state if the members are in tension or
compression. Also indicate all zero-force members.
1.5 m
2 m2 m
1 m 1 m
0.8 m
2 kN
1.5 kN
A
H
B
D
G
C
F
E
6 Solutions 44918 1/26/09 1:46 PM Page 448

449. 449
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–48.Determine the force in members IJ,EJ, and CDof
the Howetruss, and state if the members are in tension or
compression.
2 kN
3 kN
4 kN
5 kN
4 kN
6 kN
5 kN
B
A
C D E F
G
H
I
J
K
L
2 m
4 m
2 m 2 m 2 m 2 m 2 m
6 Solutions 44918 1/26/09 1:46 PM Page 449

450. 450
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–49.Determine the force in members KJ,KC, and BC
of the Howetruss, and state if the members are in tension or
compression.
2 kN
3 kN
4 kN
5 kN
4 kN
6 kN
5 kN
B
A
C D E F
G
H
I
J
K
L
2 m
4 m
2 m 2 m 2 m 2 m 2 m
6 Solutions 44918 1/26/09 1:46 PM Page 450

451. 451
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–50.Determine the force in each member of the truss
and state if the members are in tension or compression. Set
,.P
2=10 kNP
1=20 kN
A
GF
E
DCB
P
2P
1
1.5 m 1.5 m 1.5 m 1.5 m
2 m
6 Solutions 44918 1/26/09 1:46 PM Page 451

452. 452
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 Solutions 44918 1/26/09 1:46 PM Page 452

453. 453
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–51.Determine the force in each member of the truss
and state if the members are in tension or compression. Set
,.P
2=20 kNP
1=40 kN
A
GF
E
DCB
P
2P
1
1.5 m 1.5 m 1.5 m 1.5 m
2 m
6 Solutions 44918 1/26/09 1:46 PM Page 453

454. 454
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 Solutions 44918 1/26/09 1:46 PM Page 454

455. 455
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–52.Determine the force in members KJ,NJ,ND, and
CDof the K truss. Indicate if the members are in tension or
compression.Hint:Use sections aaand bb.
1800 lb
15 ft
15 ft
20 ft 20 ft 20 ft 20 ft 20 ft
A
B
IH
20 ft
L
M
N O P
G
FEDC
1500 lb
1200 lb
ab
JK
ab
6 Solutions 44918 1/26/09 1:46 PM Page 455

456. 456
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–53.Determine the force in members JIand DEof
the K truss. Indicate if the members are in tension or
compression.
1800 lb
15 ft
15 ft
20 ft 20 ft 20 ft 20 ft 20 ft
A
B
IH
20 ft
L
M
N O P
G
FEDC
1500 lb
1200 lb
ab
JK
ab
6 Solutions 44918 1/26/09 1:46 PM Page 456

457. 457
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–54.The space truss supports a force
. Determine the force in
each member, and state if the members are in tension or
compression.
F=5-500i+600j+400k6 lb
A
B
C
D
x
y
z
F
8 ft
6 ft
6 ft
6 ft
6 ft
6 Solutions 44918 1/26/09 1:46 PM Page 457

458. 458
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 Solutions 44918 1/26/09 1:46 PM Page 458

459. 459
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–55.The space truss supports a force
. Determine the force in each
member, and state if the members are in tension or
compression.
F=5600i+450j-750k6 lb
A
B
C
D
x
y
z
F
8 ft
6 ft
6 ft
6 ft
6 ft
6 Solutions 44918 1/26/09 1:46 PM Page 459

460. 460
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 Solutions 44918 1/26/09 1:46 PM Page 460

461. 461
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–56.Determine the force in each member of the space
truss and state if the members are in tension or
compression. The truss is supported by ball-and-socket
joints at A,B, and E. Set . Hint:The support
reaction at Eacts along member EC. Why?
F=5800j6
N
F
D
A
z
2 m
x
y
B
C
E
5 m
1 m
2 m
1.5 m
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462. 462
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•6–57.Determine the force in each member of the space
truss and state if the members are in tension or
compression. The truss is supported by ball-and-socket
joints at A,B, and E. Set . Hint:The
support reaction at Eacts along member EC. Why?
F=5-200i+400j6 N
F
D
A
z
2 m
x
y
B
C
E
5 m
1 m
2 m
1.5 m
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463. 463
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–58.Determine the force in members BE,DF, and BCof
the space truss and state if the members are in tension or
compression.
2 m
2 m
2 m
E
A
3 m
F
D
C
B
{2k} kN
{2k} kN
2 m
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464. 464
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–59.Determine the force in members AB,CD,ED, and
CFof the space truss and state if the members are in tension
or compression.
2 m
2 m
2 m
E
A
3 m
F
D
C
B
{2k} kN
{2k} kN
2 m
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465. 465
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–60.Determine the force in the members AB,AE,BC,
BF,BD, and BEof the space truss, and state if the members
are in tension or compression.
F
E
D
x
z
y
C
B
A
4 ft
4 ft
2 ft
2 ft
300 lb
600 lb
400 lb
4 ft
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466. 466
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 Solutions 44918 1/26/09 1:46 PM Page 466

467. 467
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–61.Determine the force in the members EF,DF,CF,
and CDof the space truss, and state if the members are in
tension or compression.
F
E
D
x
z
y
C
B
A
4 ft
4 ft
2 ft
2 ft
300 lb
600 lb
400 lb
4 ft
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468. 468
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 Solutions 44918 1/26/09 1:46 PM Page 468

469. 469
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–62.If the truss supports a force of ,
determine the force in each member and state if the
members are in tension or compression.
F=200 N
y
D
E
F
x
z
C
B
A
200 mm
200 mm
200 mm
200 mm
500 mm
300 mm
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470. 470
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–63.If each member of the space truss can support a
maximum force of 600 N in compression and 800 N in
tension, determine the greatest force Fthe truss can
support.
y
D
E
F
x
z
C
B
A
200 mm
200 mm
200 mm
200 mm
500 mm
300 mm
6 Solutions 44918 1/26/09 1:46 PM Page 470

471. 471
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–64.Determine the force developed in each member of
the space truss and state if the members are in tension or
compression. The crate has a weight of 150 lb.
x
y
z
A
B
C
D
6 ft
6 ft
6 ft
6 ft
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472. 472
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•6–65.Determine the force in members FEand EDof the
space truss and state if the members are in tension or
compression. The truss is supported by a ball-and-socket
joint at Cand short links at Aand B. z
x
y
{500k} lb
G
{200j} lb
6 ft
6 ft
F
E
D
C
4 ft
2 ft
3 ft
3 ft
A
B
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473. 473
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–66.Determine the force in members GD,GE, and FD
of the space truss and state if the members are in tension or
compression. z
x
y
{500k} lb
G
{200j} lb
6 ft
6 ft
F
E
D
C
4 ft
2 ft
3 ft
3 ft
A
B
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474. 474
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–67.Determine the force required to hold the
100-lb weight in equilibrium.
P
P
A
B
C
D
6 Solutions 44918 1/26/09 1:47 PM Page 474

475. 475
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–68.Determine the force required to hold the
150-kg crate in equilibrium.
P
P
A
B
C
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476. 476
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–69.Determine the force required to hold the 50-kg
mass in equilibrium.
P
P
A
B
C
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477. 477
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6–70.Determine the force needed to hold the 20-lb block
in equilibrium.
P
C
B
A
P
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478. 478
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–71.Determine the force needed to support the 100-lb
weight. Each pulley has a weight of 10 lb. Also, what are the
cord reactions at Aand B?
P
P
2 in.
2 in.
2 in.
C
A
B
6 Solutions 44918 1/26/09 1:47 PM Page 478

479. 479
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–72.The cable and pulleys are used to lift the 600-lb
stone. Determine the force that must be exerted on the cable
at Aand the corresponding magnitude of the resultant force
the pulley at Cexerts on pin Bwhen the cables are in the
position shown.
P
A
C
B
D
30
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480. 480
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•6–73.If the peg at Bis smooth, determine the
components of reaction at the pin Aand fixed support C.
A
B C
600 mm
800 mm
900 Nm
600 mm
500 N
45
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481. 481
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6–74.Determine the horizontal and vertical components
of reaction at pins Aand C.
B
A
C
2 ft3 ft
150 lb
100 lb
2 ft
45
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482. 482
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6–75.The compound beam is fixed at Aand supported by
rockers at Band C. There are hinges (pins) at Dand E.
Determine the components of reaction at the supports.
6 m
2 m
6 m
30 kN m
2 m 2 m
15 kN
A D BE
C
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483. 483
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*6–76.The compound beam is pin-supported at Cand
supported by rollers at Aand B. There is a hinge (pin) at D.
Determine the components of reaction at the supports.
Neglect the thickness of the beam.
A DB C
8 ft
3
4
5
8 ft
12 kip
15 kip ft
4 kip
30
8 kip
8 ft
4 ft 2 ft
6 ft
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484. 484
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–77.The compound beam is supported by a rocker at B
and is fixed to the wall at A. If it is hinged (pinned) together
at C, determine the components of reaction at the supports.
Neglect the thickness of the beam.
4 ft 4 ft
500 lb
200 lb
4000 lb ft
4 ft8 ft
A C
B
12
13
5 60
6 Solutions 44918 1/26/09 1:47 PM Page 484

485. 485
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6–78.Determine the horizontal and vertical components
of reaction at pins Aand Cof the two-member frame.
3 m
3 m
200 N
/ m
A
B
C
6 Solutions 44918 1/26/09 1:47 PM Page 485

486. 486
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–79.If a force of acts on the rope, determine
the cutting force on the smooth tree limb at Dand the
horizontal and vertical components of force acting on pin A.
The rope passes through a small pulley at Cand a smooth
ring at E.
F=50 N
F 50 N
B
C
E
30 mm
100 mm
A
D
6 Solutions 44918 1/26/09 1:47 PM Page 486

487. 487
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–80.Two beams are connected together by the short
link BC. Determine the components of reaction at the fixed
support Aand at pin D.
A
B
C
D
10 kN
12 kN
3 m
1.5 m1 m 1.5 m
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488. 488
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•6–81.The bridge frame consists of three segments which
can be considered pinned at A,D, and E, rocker supported
at Cand F, and roller supported at B. Determine the
horizontal and vertical components of reaction at all these
supports due to the loading shown.
15 ft
20 ft
5 ft 5 ft
15 ft
2 kip/ft
30 ft
A
B
C F
D
E
6 Solutions 44918 1/26/09 1:47 PM Page 488

489. 489
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6–82.If the 300-kg drum has a center of mass at point G,
determine the horizontal and vertical components of force
acting at pin Aand the reactions on the smooth pads C
andD. The grip at Bon member DABresists both
horizontal and vertical components of force at the rim of
the drum.
P
390 mm
100 mm
60 mm
60 mm
600 mm
30
B
A
C
D G
E
6 Solutions 44918 1/26/09 1:47 PM Page 489

490. 490
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6–83.Determine the horizontal and vertical components
of reaction that pins Aand Cexert on the two-member arch.
1 m
1.5 m
2 kN
1.5 kN
0.5 m
A
B
C
6 Solutions 44918 1/26/09 1:47 PM Page 490

491. 491
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*6–84.The truck and the tanker have weights of 8000 lb
and 20 000 lb respectively. Their respective centers of
gravity are located at points and . If the truck is at
rest, determine the reactions on both wheels at A, at B, and
at C. The tanker is connected to the truck at the turntable
Dwhich acts as a pin.
G
2G
1
G
1
15 ft 10 ft 9 ft
5 ft
A B
D
C
G
2
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492. 492
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•6–85.The platform scale consists of a combination of
third and first class levers so that the load on one lever
becomes the effort that moves the next lever. Through this
arrangement, a small weight can balance a massive object.
If , determine the required mass of the
counterweight Srequired to balance a 90-kg load,L.
x=450 mm
350 mm
150 mm
150 mm100 mm
250 mm
B
A
CD
E F
H
G
x
L
S
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493. 493
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6–86.The platform scale consists of a combination of
third and first class levers so that the load on one lever
becomes the effort that moves the next lever. Through this
arrangement, a small weight can balance a massive object. If
and, the mass of the counterweight Sis 2 kg,
determine the mass of the load Lrequired to maintain the
balance.
x=450 mm
350 mm
150 mm
150 mm100 mm
250 mm
B
A
CD
E F
H
G
x
L
S
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494. 494
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6–87.The hoist supports the 125-kg engine. Determine
the force the load creates in member DBand in member
FB, which contains the hydraulic cylinder H.
C
D
E
F
G
H
2 m
1 m
1 m
2 m1 m
2 m
A B
6 Solutions 44918 1/26/09 1:47 PM Page 494

495. 495
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–88.The frame is used to support the 100-kg cylinder E.
Determine the horizontal and vertical components of
reaction at Aand D.
A
CD
E
0.6 m
1.2 m
r 0.1 m
6 Solutions 44918 1/26/09 1:47 PM Page 495

496. 496
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–89.Determine the horizontal and vertical components
of reaction which the pins exert on member ABof the frame.
A
E
B
C
D
500 lb
300 lb
3 ft 3 ft
4 ft
60
6 Solutions 44918 1/26/09 1:47 PM Page 496

497. 497
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–90.Determine the horizontal and vertical components of
reaction which the pins exert on member EDCof the frame.
A
E
B
C
D
500 lb
300 lb
3 ft 3 ft
4 ft
60
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498. 498
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–91.The clamping hooks are used to lift the uniform
smooth 500-kg plate. Determine the resultant compressive
force that the hook exerts on the plate at Aand B, and the
pin reaction at C.
A
B
80 mm
P
PP
150 mm
C
6 Solutions 44918 1/26/09 1:47 PM Page 498

499. 499
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–92.The wall crane supports a load of 700 lb. Determine
the horizontal and vertical components of reaction at the pins
Aand D. Also, what is the force in the cable at the winch W?
4 ft
D
AB
C
E
W
4 ft
700 lb
60
4 ft
6 Solutions 44918 1/26/09 1:47 PM Page 499

500. 500
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–93.The wall crane supports a load of 700 lb.
Determine the horizontal and vertical components of
reaction at the pins Aand D. Also, what is the force in the
cable at the winch W? The jib ABChas a weight of 100 lb
and member BDhas a weight of 40 lb. Each member is
uniform and has a center of gravity at its center.
4 ft
D
AB
C
E
W
4 ft
700 lb
60
4 ft
6 Solutions 44918 1/26/09 1:47 PM Page 500

501. 501
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–94.The lever-actuated scale consists of a series of
compound levers. If a load of weight is placed
on the platform, determine the required weight of the
counterweight Sto balance the load. Is it necessary to place
the load symmetrically on the platform? Explain.
W=150 lb
BA
C
DE
F
G H
I
J
K
S
M
W
L
1.5 in.
1.5 in.
7.5 in. 7.5 in.
4.5 in.
4 in.
1.25 in.
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502. 502
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–95.If , determine the force Fthat the toggle
clamp exerts on the wooden block.
P=75 N 85 mm
140 mm
50 mm
50 mm
20 mm
140 mm
P
P F
A
B
C
D
E
6 Solutions 44918 1/26/09 1:47 PM Page 502

503. 503
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–96.If the wooden block exerts a force of
on the toggle clamp, determine the force Papplied to the
handle.
F=600 N 85 mm
140 mm
50 mm
50 mm
20 mm
140 mm
P
P F
A
B
C
D
E
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504. 504
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–97.The pipe cutter is clamped around the pipe P.If
the wheel at Aexerts a normal force of on the
pipe, determine the normal forces of wheels Band Con
the pipe. The three wheels each have a radius of 7 mm and
the pipe has an outer radius of 10 mm.
F
A=80 N
10 mm
10 mm
P
C
B
A
6 Solutions 44918 1/26/09 1:47 PM Page 504

505. 505
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–98.A 300-kg counterweight, with center of mass at G,is
mounted on the pitman crank ABof the oil-pumping unit.
If a force of is to be developed in the fixed cable
attached to the end of the walking beam DEF, determine
the torque Mthat must be supplied by the motor.
F=5 kN
A
B
M
D E
F
F0.5 m
30
30
1.75 m 2.50 m
G
0.65 m
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506. 506
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–99.A 300-kg counterweight, with center of mass at G,is
mounted on the pitman crank ABof the oil-pumping unit.
If the motor supplies a torque of , determine
the force Fdeveloped in the fixed cable attached to the end
of the walking beam DEF.
M=2500 N
#
m
A
B
M
D E
F
F0.5 m
30
30
1.75 m 2.50 m
G
0.65 m
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507. 507
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–100.The two-member structure is connected at Cby a
pin, which is fixed to BDEand passes through the smooth
slot in member AC. Determine the horizontal and vertical
components of reaction at the supports.
3 ft 3 ft 2 ft
4 ft
A
B
CD
E
600 lb ft
500 lb
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508. 508
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–101.The frame is used to support the 50-kg cylinder.
Determine the horizontal and vertical components of
reaction at Aand D.
A B
C
D
1.2 m
0.8 m 0.8 m
100 mm
100 mm
6 Solutions 44918 1/26/09 1:47 PM Page 508

509. 509
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–102.The frame is used to support the 50-kg cylinder.
Determine the force of the pin at Con member ABCand
on member CD.
A B
C
D
1.2 m
0.8 m 0.8 m
100 mm
100 mm
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510. 510
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6–103.Determine the reactions at the fixed support Eand
the smooth support A. The pin, attached to member BD,
passes through a smooth slot at D.
B
C
D
E
0.3 m 0.3 m 0.3 m 0.3 m
0.4 m
0.4 m
600 N
A
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511. 511
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–104.The compound arrangement of the pan scale is
shown. If the mass on the pan is 4 kg, determine the
horizontal and vertical components at pins A,B, and Cand
the distance xof the 25-g mass to keep the scale in balance.
50 mm
G
100 mm 75 mm
300 mm 350 mm
x
FE
D
B
A
4 kg
C
6 Solutions 44918 1/26/09 1:47 PM Page 511

512. 512
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–105.Determine the horizontal and vertical components
of reaction that the pins at A,B, and Cexert on the frame.
The cylinder has a mass of 80 kg.
A
B
C
1 m
0.7 m
0.5 m
D
100 mm
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513. 513
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–106.The bucket of the backhoe and its contents have a
weight of 1200 lb and a center of gravity at G. Determine
the forces of the hydraulic cylinder ABand in links ACand
ADin order to hold the load in the position shown. The
bucket is pinned at E.
120
45
1.5 ft
1 ft
B
G
E
A D
C
0.25 ft
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514. 514
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–107.A man having a weight of 175 lb attempts to hold
himself using one of the two methods shown. Determine the
total force he must exert on bar ABin each case and
the normal reaction he exerts on the platform at C. Neglect
the weight of the platform.
CC
AB
AB
(a) (b)
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515. 515
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–108.A man having a weight of 175 lb attempts to hold
himself using one of the two methods shown. Determine the
total force he must exert on bar ABin each case and the
normal reaction he exerts on the platform at C.The platform
has a weight of 30 lb.
CC
AB
AB
(a) (b)
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516. 516
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–109.If a clamping force of is required at A,
determine the amount of force Fthat must be applied to the
handle of the toggle clamp.
300 N
275 mm30
30
235 mm
30 mm
30 mm
70 mm
F
C
E
B
D
A
6 Solutions 44918 1/26/09 1:47 PM Page 516

517. 517
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–110.If a force of is applied to the handle of
the toggle clamp, determine the resulting clamping force at A.
F=350 N
275 mm30
30
235 mm
30 mm
30 mm
70 mm
F
C
E
B
D
A
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518. 518
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–111.Two smooth tubes Aand B, each having the same
weight,W, are suspended from a common point Oby means
of equal-length cords. A third tube,C, is placed between A
and B. Determine the greatest weight of Cwithout
upsetting equilibrium.
r/2
r
B
C
3r 3r
O
r
A
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519. 519
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–112.The handle of the sector press is fixed to gear G,
which in turn is in mesh with the sector gear C. Note that
ABis pinned at its ends to gear Cand the underside of the
table EF, which is allowed to move vertically due to the
smooth guides at Eand F. If the gears only exert tangential
forces between them, determine the compressive force
developed on the cylinder Swhen a vertical force of 40 N is
applied to the handle of the press.
1.2 m
EF
A
B C
G
D
S
0.5 m
0.2 m
0.35 m
0.65 m
40 N
H
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520. 520
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–113.Show that the weight of the counterweight at
Hrequired for equilibrium is , and so it is
independent of the placement of the load Won the
platform.
W
1=(b>a)W
W
1
A
B
W
C
E
G
H
D
F
c
b
3b a
c
4
6 Solutions 44918 1/26/09 1:47 PM Page 520

521. 521
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–114.The tractor shovel carries a 500-kg load of soil,
having a center of mass at G. Compute the forces developed
in the hydraulic cylinders IJand BCdue to this loading.
100 mm
300 mm
300 mm
30
A
C
E
G
D
F
H
J
B
30
50 mm
400 mm200 mm
200 mm
200 mm
I350 mm
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522. 522
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–115.If a force of is applied to the handle of
the toggle clamp, determine the horizontal clamping force
N
E
that the clamp exerts on the smooth wooden block at E.
P=100 N
B
C
D
160 mm
50 mm
75 mm
60 mm
30
45
A
E
P
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523. 523
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–116.If the horizontal clamping force that the toggle
clamp exerts on the smooth wooden block at Eis
, determine the force applied to the handle of
the clamp.
PN
E=200 N
B
C
D
160 mm
50 mm
75 mm
60 mm
30
45
A
E
P
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524. 524
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–117.The engine hoist is used to support the 200-kg
engine. Determine the force acting in the hydraulic cylinder
AB, the horizontal and vertical components of force at the
pin C, and the reactions at the fixed support D.
C
D
A
G
1250 mm
350 mm
850 mm
550 mm
10

B
6 Solutions 44918 1/26/09 1:48 PM Page 524

525. 525
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–118.Determine the force that the smooth roller C
exerts on member AB. Also, what are the horizontal and
vertical components of reaction at pin A? Neglect the
weight of the frame and roller.
C
0.5 ft
3 ft
A
60 lb ft
4 ft
B
D
6–119.Determine the horizontal and vertical components
of reaction which the pins exert on member ABC.
3 ft
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526. 526
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–120.Determine the couple moment Mthat must be
applied to member DCfor equilibrium of the quick-return
mechanism. Express the result in terms of the angles
and , dimension L, and the applied vertical forceP.The
block at Cis confined to slide within the slot of member AB.
u
f
C
M
DA
B
4 L
L
P
u
f
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527. 527
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–121.Determine the couple moment Mthat must be
applied to member DCfor equilibrium of the quick-return
mechanism. Express the result in terms of the angles
and , dimension L, and the applied force P,which should
be changed in the figure and instead directed horizontally
to the right. The block at Cis confined to slide within the
slot of member AB.
u
f
C
M
DA
B
4 L
L
P
u
f
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528. 528
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–122.The kinetic sculpture requires that each of the
three pinned beams be in perfect balance at all times during
its slow motion. If each member has a uniform weight
of 2 and length of 3 ft, determine the necessary
counterweights and which must be added to the
ends of each member to keep the system in balance for any
position. Neglect the size of the counterweights.
W
3W
1, W
2,
lb>ft
W
6 Solutions 44918 1/26/09 1:48 PM Page 528

529. 529
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–123.The four-member “A” frame is supported at Aand
Eby smooth collars and at Gby a pin. All the other joints
are ball-and-sockets. If the pin at Gwill fail when the
resultant force there is 800 N, determine the largest vertical
force Pthat can be supported by the frame. Also, what are
thex, y, zforce components which member BDexerts on
members EDCand ABC? The collars at Aand Eand the
pin at Gonly exert force components on the frame.
x
y
C
D
B
F
G
E
A
P Pk
z
300 mm
300 mm
600 mm
600 mm
600 mm
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530. 530
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–124.The structure is subjected to the loading shown.
Member ADis supported by a cable ABand roller at Cand
fits through a smooth circular hole at D. Member EDis
supported by a roller at Dand a pole that fits in a smooth
snug circular hole at E. Determine the x, y, zcomponents of
reaction at Eand the tension in cable AB.
z
C
A
D
B
E
0.3 m
y
0.3 m
0.5 m
0.4 m
F {2.5k} kN
x
0.8 m
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531. 531
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–125.The three-member frame is connected at its ends
using ball-and-socket joints. Determine the x, y, zcomponents
of reaction at Band the tension in member ED. The force
acting at Dis F=5135i+200j-180k6 lb.
y
6 ft
2 ft
1ft
3 ft
6 ft
3 ft
4 ft
x
A
D
F
B
C
E
z
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532. 532
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–126.The structure is subjected to the loadings shown.
Member ABis supported by a ball-and-socket at Aand
smooth collar at B. Member CDis supported by a pin at C.
Determine the x, y, zcomponents of reaction at Aand C.
2 m 3 m
y
4 m
1.5 m
B
800 N m
A
250 N
D
45
60
60
z
x
C
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533. 533
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–127.Determine the clamping force exerted on the
smooth pipe atBif a force of 20 lb is applied to the handles
of the pliers. The pliers are pinned together at A.
A
20 lb
20 lb
10 in. 40
1.5 in.
0.5 in.
B
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534. 534
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–128.Determine the forces which the pins at Aand
Bexert on the two-member frame which supports the
100-kg crate.
A
C
B
D
0.6 m
0.8 m 0.6 m
0.4 m
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535. 535
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–129.Determine the force in each member of the truss
and state if the members are in tension or compression.
D
A
E
3 m 3 m
3 m
8 kN
B
0.1 m
C
6 Solutions 44918 1/26/09 1:48 PM Page 535

536. 536
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–130.The space truss is supported by a ball-and-socket
joint at Dand short links at Cand E. Determine the force in
each member and state if the members are in tension or
compression. Take and . F
2=5400j6 lbF
1=5-500k6 lb
3 ft
4 ft
3 ft
x
y
z
C
D
E
A
B
F
F
2
F
1
6 Solutions 44918 1/26/09 1:48 PM Page 536

537. 537
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 Solutions 44918 1/26/09 1:48 PM Page 537

538. 538
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–131.The space truss is supported by a ball-and-socket
joint at Dand short links at Cand E. Determine the force
in each member and state if the members are in tension
or compression. Take and
.F
2=5400j6 lb
F
1=5200i+300j-500k6 lb
3 ft
4 ft
3 ft
x
y
z
C
D
E
A
B
F
F
2
F
1
6 Solutions 44918 1/26/09 1:48 PM Page 538

539. 539
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 Solutions 44918 1/26/09 1:48 PM Page 539

540. 540
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–132.Determine the horizontal and vertical components
of reaction that the pins Aand Bexert on the two-member
frame. Set .F=0
1.5 m
400 N/m
60
1 m
1 m
B
C
A
F
6 Solutions 44918 1/26/09 1:48 PM Page 540

541. 541
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•6–133.Determine the horizontal and vertical components
of reaction that pins Aand Bexert on the two-member
frame. Set .F=500 N
1.5 m
400 N/m
60
1 m
1 m
B
C
A
F
6 Solutions 44918 1/26/09 1:48 PM Page 541

542. 542
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–134.The two-bar mechanism consists of a lever arm AB
and smooth link CD, which has a fixed smooth collar at its
end Cand a roller at the other end D. Determine the force P
needed to hold the lever in the position . The spring has a
stiffness kand unstretched length 2L. The roller contacts
either the top or bottom portion of the horizontal guide.
u
2 L
L
k
C
A
B
D
P
u
6 Solutions 44918 1/26/09 1:48 PM Page 542

543. 543
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6–135.Determine the horizontal and vertical components
of reaction at the pin supports Aand Eof the compound
beam assembly. 2 ft
2 kip/ft
1 ft
3 ft 6 ft2 ft
1 ft
A
C
E
DB
6 Solutions 44918 1/26/09 1:48 PM Page 543

544. 544
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*6–136.Determine the force in members AB,AD, and AC
of the space truss and state if the members are in tension or
compression.
1.5 ft
1.5 ft
2 ft
F {600k} lb
8 ft
x
y
z
B
A
C
D
6 Solutions 44918 1/26/09 1:48 PM Page 544

545. 545
•7–1.Determine the internal normal force and shear
force, and the bending moment in the beam at points Cand
D.Assume the support at Bis a roller. Point Cis located just
to the right of the 8-kip load.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
40 kip ft
8 ft8 ft 8 ft
8 kip
A
BCD
7 Solutions 44918 1/27/09 10:38 AM Page 545

546. 546
7–2.Determine the shear force and moment at points C
and D.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 ft
A
CD
E
B
6 ft
2 ft
4 ft 4 ft
300 lb
200 lb
500 lb
7 Solutions 44918 1/27/09 10:38 AM Page 546

547. 547
7–3.Determine the internal normal force, shear force, and
moment at point Cin the simply supported beam. Point Cis
located just to the right of the 1500-lb ft couple moment.–
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
BA
C
500 lb/ft
1500 lb ft
6 ft
30
6 ft
7 Solutions 44918 1/27/09 10:38 AM Page 547

548. 548
*7–4.Determine the internal normal force, shear force,
and moment at points Eand Fin the beam.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
D BA
E F
1.5 m
300 N/m
45
1.5 m 1.5 m 1.5 m
C
7 Solutions 44918 1/27/09 10:38 AM Page 548

549. 549
•7–5.Determine the internal normal force, shear force,
and moment at point C.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3 m 2 m
1.5 m
1 m
0.2 m
400 N
A
C
B
7 Solutions 44918 1/27/09 10:38 AM Page 549

550. 550
7–6.Determine the internal normal force, shear force, and
moment at point Cin the simply supported beam.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
C
B
A
3 m
4 kN/m
3 m
7 Solutions 44918 1/27/09 10:38 AM Page 550

551. 551
7–7.Determine the internal normal force, shear force, and
moment at point Cin the cantilever beam.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
B
C
w
0
L
––
2
L
––
2
7 Solutions 44918 1/27/09 10:38 AM Page 551

552. 552
*7–8.Determine the internal normal force, shear force,
and moment at points Cand Din the simply supported
beam. Point Dis located just to the left of the 5-kN force.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
C D
B
3 kN/m
5 kN
3 m1.5 m 1.5 m
7 Solutions 44918 1/27/09 10:38 AM Page 552

553. 553
•7–9.The bolt shank is subjected to a tension of 80 lb.
Determine the internal normal force, shear force, and
moment at point C.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
AB
C
90
6 in.
7 Solutions 44918 1/27/09 10:38 AM Page 553

554. 554
7–10.Determine the internal normal force, shear force,
and moment at point Cin the double-overhang beam.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
C
B
1.5 m
3 kN/m
1.5 m 1.5 m 1.5 m
7 Solutions 44918 1/27/09 10:38 AM Page 554

555. 555
7–11.Determine the internal normal force, shear force,
and moment at points Cand Din the simply supported
beam. Point Dis located just to the left of the 10-kN
concentrated load.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
C D
B
1.5 m
6 kN/m
10 kN
1.5 m 1.5 m 1.5 m
7 Solutions 44918 1/27/09 10:38 AM Page 555

556. 556
*7–12.Determine the internal normal force, shear force,
and moment in the beam at points Cand D. Point Dis just
to the right of the 5-kip load.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
6 ft 6 ft 6 ft 6 ft
5 kip
0.5 kip/ft
A
C D
B
7 Solutions 44918 1/27/09 10:38 AM Page 556

557. 557
•7–13.Determine the internal normal force, shear force,
and moment at point Dof the two-member frame.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2 m
1.5 m
250 N/m
300 N/m
4 m
A
C
D
E
B
7 Solutions 44918 1/27/09 10:38 AM Page 557

558. 558
7–14.Determine the internal normal force, shear force,
and moment at point Eof the two-member frame.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2 m
1.5 m
250 N/m
300 N/m
4 m
A
C
D
E
B
7 Solutions 44918 1/27/09 10:38 AM Page 558

559. 559
7–15.Determine the internal normal force, shear force,
and moment acting at point Cand at point D, which is
located just to the right of the roller support at B.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
200 lb/ft200 lb/ft
300 lb/ft
4 ft
A
FE
CB
D
4 ft4 ft4 ft
*7–16.Determine the internal normal force, shear force,
and moment in the cantilever beam at point B.
A
6 kip/ft
B
12 ft3 ft
7 Solutions 44918 1/27/09 10:38 AM Page 559

560. 560
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–17.Determine the ratio of for which the shear force
will be zero at the midpoint Cof the double-overhang beam.
a>b
BC
ab /2 b/2
w
0
a
AB C
7 Solutions 44918 1/27/09 10:38 AM Page 560

561. 561
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–18.Determine the internal normal force, shear force,
and moment at points Dand Ein the overhang beam. Point
Dis located just to the left of the roller support at B, where
the couple moment acts.
2 kN/m
5 kN
3 m 1.5 m
3
4
5
A
D
B
E
C
6 kN m
1.5 m
7 Solutions 44918 1/27/09 10:38 AM Page 561

562. 562
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–19.Determine the distance ain terms of the beam’s
length Lbetween the symmetrically placed supports A
and Bso that the internal moment at the center of the
beam is zero.
w
0 w
0
A B
L
a
––
2
a
––
2
7 Solutions 44918 1/27/09 10:38 AM Page 562

563. 563
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–20.Determine the internal normal force, shear force,
and moment at points Dand Ein the compound beam.
Point Eis located just to the left of the 10-kN concentrated
load.Assume the support at Ais fixed and the connection at
Bis a pin.
10 kN
2 kN/m
D
B
E
C
A
1.5 m 1.5 m 1.5 m 1.5 m
7 Solutions 44918 1/27/09 10:38 AM Page 563

564. 564
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–21.Determine the internal normal force, shear force,
and moment at points Fand Gin the compound beam. Point
Fis located just to the right of the 500-lb force, while point G
is located just to the right of the 600-lb force.
A
F
G
E
B
D
C
2 ft 2 ft 2 ft
2 ft
1.5 ft
2 ft
500 lb
600 lb
7 Solutions 44918 1/27/09 10:38 AM Page 564

565. 565
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–22.The stacker crane supports a 1.5-Mg boat with the
center of mass at G. Determine the internal normal force,
shear force, and moment at point Din the girder. The trolley
is free to roll along the girder rail and is located at the
position shown. Only vertical reactions occur at Aand B.
3.5 m
D
G
C
BA
5 m
7.5 m
1 m1 m
2 m
2 m
7 Solutions 44918 1/27/09 10:38 AM Page 565

566. 566
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–23.Determine the internal normal force, shear force,
and moment at points Dand Ein the two members.
2 m
1 m
0.75 m
0.75 m
60 N
D
E
B
CA
6030
7 Solutions 44918 1/27/09 10:38 AM Page 566

567. 567
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–24.Determine the internal normal force, shear force,
and moment at points Fand Ein the frame. The crate
weighs 300 lb.
1.5 ft 1.5 ft 1.5 ft 1.5 ft
0.4 ft
4 ft
A
B
F C E
D
7 Solutions 44918 1/27/09 10:38 AM Page 567

568. 568
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–25.Determine the internal normal force, shear force,
and moment at points Dand Eof the frame which supports
the 200-lb crate. Neglect the size of the smooth peg at C. C
B
E
A
D
4 ft
4.5 ft
2 ft
1.5 ft
1.5 ft
7 Solutions 44918 1/27/09 10:38 AM Page 568

569. 569
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–26.The beam has a weight wper unit length. Determine
the internal normal force, shear force, and moment at point
Cdue to its weight.
B
A
C
L
––
2
L
––
2
u
7 Solutions 44918 1/27/09 10:38 AM Page 569

570. 570
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–27.Determine the internal normal force, shear force,
and moment acting at point C. The cooling unit has a total
mass of 225 kg with a center of mass at G.
3 m
F
3 m
30 30
0.2 m
G
A B
E
D
C
7 Solutions 44918 1/27/09 10:39 AM Page 570

571. 571
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–28.The jack ABis used to straighten the bent beam
DEusing the arrangement shown. If the axial compressive
force in the jack is 5000 lb, determine the internal moment
developed at point Cof the top beam. Neglect the weight of
the beams.
10 ft
10 ft
2 ft
2 ft
A
B
C
D
E
7 Solutions 44918 1/27/09 10:39 AM Page 571

572. 572
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–29.Solve Prob. 7–28 assuming that each beam has a
uniform weight of .150 lb>ft
10 ft
10 ft
2 ft
2 ft
A
B
C
D
E
7 Solutions 44918 1/27/09 10:39 AM Page 572

573. 573
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–30.The jib crane supports a load of 750 lb from the
trolley which rides on the top of the jib. Determine the
internal normal force, shear force, and moment in the jib at
point Cwhen the trolley is at the position shown. The crane
members are pinned together at B,Eand Fand supported
by a short link BH.
1 ft
1 ft 3 ft 5 ft
1 ft
3 ft
750 lb
2 ft
3 ft
G
F
CB
H
D
E
A
7 Solutions 44918 1/27/09 10:39 AM Page 573

574. 574
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–31.The jib crane supports a load of 750 lb from the
trolley which rides on the top of the jib. Determine
the internal normal force, shear force, and moment in the
column at point Dwhen the trolley is at the position shown.
The crane members are pinned together at B,Eand Fand
supported by a short link BH.
1 ft
1 ft 3 ft 5 ft
1 ft
3 ft
750 lb
2 ft
3 ft
G
F
CB
H
D
E
A
7 Solutions 44918 1/27/09 10:39 AM Page 574

575. 575
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–32.Determine the internal normal force, shear force,
and moment acting at points Band Con the curved rod.
45
30
2 ft
B
C
A
3
4
5
500 lb
7 Solutions 44918 1/27/09 10:39 AM Page 575

576. 576
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–33.Determine the internal normal force, shear force,
and moment at point Dwhich is located just to the right of
the 50-N force.
50 N
50 N
50 N
50 N
600 mm
D
C
B
A
30

30
3030
30
7 Solutions 44918 1/27/09 10:39 AM Page 576

577. 577
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–34.Determine the x,y,zcomponents of internal loading
at point Cin the pipe assembly. Neglect the weight of the
pipe. The load is , ,
and .M
= 5-30k6 lb#
ft
F
2=5-80i6 lbF
1=5-24i -10k6 lb
F
1
F
2
2 ft
x
z
y
3 ft
C
B
A
M
1.5 ft
7–35.Determine the x, y, zcomponents of internal loading
at a section passing through point Cin the pipe assembly.
Neglect the weight of the pipe. Take
and F
2=5150i-300k6 lb.
F
1=5350j-400k6 lb
x
z
y
C
1.5 ft
2 ft
F
1
F
2
3 ft
7 Solutions 44918 1/27/09 10:39 AM Page 577

578. 578
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–36.Determine the x, y, zcomponents of internal loading at
a section passing through point Cin the pipe assembly. Neglect
the weight of the pipe. Take
andF
2=5250i-150j-200k6 lb.
F
1=5-80i+200j-300k6 lb
x
z
y
C
1.5 ft
2 ft
F
1
F
2
3 ft
7 Solutions 44918 1/27/09 10:39 AM Page 578

579. 579
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–37.The shaft is supported by a thrust bearing at Aand
a journal bearing at B. Determine the x,y,zcomponents of
internal loading at point C.
1 m
1 m
0.5 m0.2 m
0.2 m
1 m
750 N
750 N
600 N
z
C
y
x
900 N
A
B
7 Solutions 44918 1/27/09 10:39 AM Page 579

580. 580
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–38.Determine the x, y, zcomponents of internal loading
in the rod at point D. There are journal bearings at A,B,
andC. Take F=57i-12j-5k6 kN.
0.75 m
0.2 m
0.2 m
0.5 m
0.5 m
A
3 kN m
C
z
x
B
D
E
F
y
0.6 m
7 Solutions 44918 1/27/09 10:39 AM Page 580

581. 581
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–39.Determine the x, y, zcomponents of internal loading
in the rod at point E. Take F=57i-12j-5k6 kN.
0.75 m
0.2 m
0.2 m
0.5 m
0.5 m
A
3 kN m
C
z
x
B
D
E
F
y
0.6 m
7 Solutions 44918 1/27/09 10:39 AM Page 581

582. 582
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–40.Draw the shear and moment diagrams for the
beam (a) in terms of the parameters shown; (b) set
L=12 ft.a=5 ft,P=800 lb,
aa
L
P P
7 Solutions 44918 1/27/09 10:39 AM Page 582

583. 583
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–41.Draw the shear and moment diagrams for the
simply supported beam.
4 m 2 m
9 kN
A
B
7 Solutions 44918 1/27/09 10:39 AM Page 583

584. 584
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:39 AM Page 584

585. 585
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–42.Draw the shear and moment diagrams for the beam
ABCDE. All pulleys have a radius of 1 ft. Neglect the weight
of the beam and pulley arrangement.The load weighs 500 lb.
A
B CD
E
8 ft
2 ft
2 ft
2 ft
3 ft
2 ft
3 ft
7 Solutions 44918 1/27/09 10:39 AM Page 585

586. 586
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–43.Draw the shear and moment diagrams for the
cantilever beam.
2 kN/m
6 kN m
2 m
A
7 Solutions 44918 1/27/09 10:39 AM Page 586

587. 587
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–44.Draw the shear and moment diagrams for the
beam (a) in terms of the parameters shown; (b) set
,.L=8 mM
0=500 N#
m
L/2 L/2
M
0
A B
7 Solutions 44918 1/27/09 10:39 AM Page 587

588. 588
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–45.If , the beam will fail when the maximum
shear force is or the maximum bending
moment is . Determine the largest couple
moment the beam will support.M
0
M
max=22 kN#
m
V
max=5 kN
L=9 m
L/2 L/2
M
0
A B
7 Solutions 44918 1/27/09 10:39 AM Page 588

589. 589
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–46.Draw the shear and moment diagrams for the
simply supported beam.
A
B
w
0
L
––
2
L
––
2
7 Solutions 44918 1/27/09 10:39 AM Page 589

590. 590
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:39 AM Page 590

591. 591
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–47.Draw the shear and moment diagrams for the
simply supported beam.
300 N/m
4 m
300 N m
A
B
7 Solutions 44918 1/27/09 10:39 AM Page 591

592. 592
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:39 AM Page 592

593. 593
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–48.Draw the shear and moment diagrams for the
overhang beam.
A
B
C
4 m 2 m
8 kN/m
7 Solutions 44918 1/27/09 10:39 AM Page 593

594. 594
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–49.Draw the shear and moment diagrams for the
beam.
5 m 5 m
2 kN/m
50 kN m
A
B
C
7 Solutions 44918 1/27/09 10:39 AM Page 594

595. 595
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–50.Draw the shear and moment diagrams for the beam. 250 lb/ft
150 lb ft150 lb ft
AB
20 ft
7 Solutions 44918 1/27/09 10:39 AM Page 595

596. 596
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–51.Draw the shear and moment diagrams for the beam.
A
B
3 m
1.5 kN/m
7 Solutions 44918 1/27/09 10:39 AM Page 596

597. 597
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–52.Draw the shear and moment diagrams for the
simply supported beam.
A
B
150 lb/ft
12 ft
300 lb ft
7 Solutions 44918 1/27/09 10:39 AM Page 597

598. 598
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:39 AM Page 598

599. 599
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–53.Draw the shear and moment diagrams for the beam.
A
B C
9 ft 4.5 ft
30 lb/ft
180 lb ft
7 Solutions 44918 1/27/09 10:39 AM Page 599

600. 600
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–54.If the beam will fail when the maximum
shear force is or the maximum moment is
Determine the largest intensity of
the distributed loading it will support.
wM
max=1200 lb#
ft.
V
max=800 lb,
L=18 ft,
L
w
A
B
7 Solutions 44918 1/27/09 10:39 AM Page 600

601. 601
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–55.Draw the shear and moment diagrams for the beam.
12 ft
A
12 ft
4 kip/ft
7 Solutions 44918 1/27/09 10:39 AM Page 601

602. 602
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–56.Draw the shear and moment diagrams for the
cantilevered beam.
300 lb
200 lb/ft
A
6 ft
7 Solutions 44918 1/27/09 10:39 AM Page 602

603. 603
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:39 AM Page 603

604. 604
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–57.Draw the shear and moment diagrams for the
overhang beam.
4 kN/m
3 m 3 m
A
B
7 Solutions 44918 1/27/09 10:39 AM Page 604

605. 605
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–58.Determine the largest intensity of the distributed
load that the beam can support if the beam can withstand a
maximum shear force of and a maximum
bending moment of .M
max=600 lb #
ft
V
max=1200 lb
w
0
w
0
2w
0
6 ft 6 ft
A B
7 Solutions 44918 1/27/09 10:39 AM Page 605

606. 606
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:39 AM Page 606

607. 607
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–59.Determine the largest intensity of the distributed
load that the beam can support if the beam can withstand a
maximum bending moment of and a
maximum shear force of .V
max=80 kN
M
max=20 kN#
m
w
0
w
0
4.5 m 1.5 m
A
B
C
7 Solutions 44918 1/27/09 10:39 AM Page 607

608. 608
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:39 AM Page 608

609. 609
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–60.Determine the placement aof the roller support B
so that the maximum moment within the span ABis
equivalent to the moment at the support B.
L
a
A
B
w
0
7 Solutions 44918 1/27/09 10:39 AM Page 609

610. 610
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–61.The compound beam is fix supported at A, pin
connected at Band supported by a roller at C. Draw the
shear and moment diagrams for the beam.
A B
C
500 lb/ft
6 ft3 ft
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611. 611
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:39 AM Page 611

612. 612
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–62.The frustum of the cone is cantilevered from point
A. If the cone is made from a material having a specific
weight of , determine the internal shear force and moment
in the cone as a function of x.
g
A
L x
2 r
0
r
0
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613. 613
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–63.Express the internal shear and moment components
acting in the rod as a function of y,where 0…y…4 ft.
y
z
x
y
4 ft
2 ft
4 lb/ft
7 Solutions 44918 1/27/09 10:39 AM Page 613

614. 614
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–64.Determine the normal force, shear force, and
moment in the curved rod as a function of u.
r
w
u
7 Solutions 44918 1/27/09 10:39 AM Page 614

615. 615
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–65.The shaft is supported by a smooth thrust bearing
at Aand a smooth journal bearing at B. Draw the shear and
moment diagrams for the shaft.
300 lb
600 lb
400 lb
B
A
2 ft 2 ft2 ft 2 ft
7 Solutions 44918 1/27/09 10:39 AM Page 615

616. 616
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
AB
5 kN
10 kN
5 kN
2 m2 m2 m2 m
7–66.Draw the shear and moment diagrams for the
double overhang beam.
7 Solutions 44918 1/27/09 10:39 AM Page 616

617. 617
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–67.Draw the shear and moment diagrams for the
overhang beam.
A
B
M = 10 kN m
2 m 2 m 2 m
6 kN
18 kN
7 Solutions 44918 1/27/09 10:39 AM Page 617

618. 618
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
B
M 2 kN m
4 kN
2 m 2 m 2 m
*7–68.Draw the shear and moment diagrams for the
simply supported beam.
7 Solutions 44918 1/27/09 10:39 AM Page 618

619. 619
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–69.Draw the shear and moment diagrams for the
simply supported beam.
A
B
2 m 2 m 2 m
10 kN 10 kN
15 kN m
7 Solutions 44918 1/27/09 10:39 AM Page 619

620. 620
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–70.Draw the shear and moment diagrams for the beam.
The support at Aoffers no resistance to vertical load.
P
L
––
3
L
––
3
L
––
3
A B
P
7 Solutions 44918 1/27/09 10:39 AM Page 620

621. 621
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–71.Draw the shear and moment diagrams for the lathe
shaft if it is subjected to the loads shown.The bearing at Ais
a journal bearing, and Bis a thrust bearing.
200 mm
100 mm 50 mm
50 mm
50 mm50 mm
200 mm
40 N
80 N
60 N 100 N
50 N
40 N
50 N
A B
7 Solutions 44918 1/27/09 10:39 AM Page 621

622. 622
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–72.Draw the shear and moment diagrams for the beam.
6 m
10 kN
3 kN/m
A B
•7–73.Draw the shear and moment diagrams for the
shaft. The support at Ais a thrust bearing and at Bit is a
journal bearing. AB
2 kN/m
4 kN
0.8 m
0.2 m
7 Solutions 44918 1/27/09 10:39 AM Page 622

623. 623
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–74.Draw the shear and moment diagrams for the beam. 8 kN
15 kN/m
20 kN m
8 kN
1 m 1 m 1 m0.75 m
0.25 m
A
B CD
7 Solutions 44918 1/27/09 10:39 AM Page 623

624. 624
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–75.The shaft is supported by a smooth thrust bearing at
Aand a smooth journal bearing at B. Draw the shear and
moment diagrams for the shaft.
500 N
BA
1.5 m 1.5 m
300 N/m
7 Solutions 44918 1/27/09 10:39 AM Page 624

625. 625
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–76.Draw the shear and moment diagrams for the beam. 10 kN
2 kN/m
5 m 3 m 2 m
A
B
•7–77.Draw the shear and moment diagrams for the
shaft. The support at Ais a journal bearing and at Bit is a
thrust bearing.
1 ft 4 ft 1 ft
100 lb/ft
A
300 lb ft
200 lb
B
7 Solutions 44918 1/27/09 10:39 AM Page 625

626. 626
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–78.The beam consists of two segments pin connected at
B. Draw the shear and moment diagrams for the beam.
8 ft 4 ft 6 ft
700 lb
150 lb/ft
800 lb ft
A B
C
7 Solutions 44918 1/27/09 10:39 AM Page 626

627. 627
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–79.Draw the shear and moment diagrams for the
cantilever beam.
300 lb
200 lb/ft
A
6 ft
7 Solutions 44918 1/27/09 10:39 AM Page 627

628. 628
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–80.Draw the shear and moment diagrams for the
simply supported beam.
10 kN
10 kN/m
A
B
3 m 3 m
7 Solutions 44918 1/27/09 10:39 AM Page 628

629. 629
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–81.Draw the shear and moment diagrams for the
beam.
A
B
2000 lb
500 lb/ft
9 ft 9 ft
7–82.Draw the shear and moment diagrams for the beam. w
0
A
B
LL
7 Solutions 44918 1/27/09 10:39 AM Page 629

630. 630
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–83.Draw the shear and moment diagrams for the beam.
3 m
8 kN/m
8 kN/m
3 m
A
7 Solutions 44918 1/27/09 10:39 AM Page 630

631. 631
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
40 kN/m
20 kN
150 kN m
A
B
8 m 3 m
*7–84.Draw the shear and moment diagrams for the beam.
7 Solutions 44918 1/27/09 10:39 AM Page 631

632. 632
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–85.The beam will fail when the maximum moment
is or the maximum shear is
Determine the largest intensity wof the distributed load the
beam will support.
V
max=8 kip.M
max=30 kip#
ft w
6 ft 6 ft
A
B
7 Solutions 44918 1/27/09 10:39 AM Page 632

633. 633
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–86.Draw the shear and moment diagrams for the
compound beam.
5 kN
3 kN/m
A
B C
D
3 m 3 m 1.5 m 1.5 m
7 Solutions 44918 1/27/09 10:39 AM Page 633

634. 634
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–87.Draw the shear and moment diagrams for the shaft.
The supports at Aand Bare journal bearings.
A B
2 kN/m
300 mm
450 mm600 mm
7 Solutions 44918 1/27/09 10:39 AM Page 634

635. 635
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
6 ft 10 ft 6 ft
5 kip/ft
B
15 kip ft15 kip ft
*7–88.Draw the shear and moment diagrams for the beam.
7 Solutions 44918 1/27/09 10:39 AM Page 635

636. 636
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–89.Determine the tension in each segment of the
cable and the cable’s total length. Set .P=80
lb
P
A
B
C
D
2 ft
3 ft
50 lb
5 ft
4 ft3 ft
7 Solutions 44918 1/27/09 10:39 AM Page 636

637. 637
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–90.If each cable segment can support a maximum tension
of 75 lb, determine the largest load Pthat can be applied.
P
A
B
C
D
2 ft
3 ft
50 lb
5 ft
4 ft3 ft
7 Solutions 44918 1/27/09 10:39 AM Page 637

638. 638
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–91.The cable segments support the loading shown.
Determine the horizontal distance from the force at Bto
point A. Set .P=40 lb
x
B
5 ft
2 ft
3 ft
60 lb
D
C
B
A
x
B
8 ft
P
7 Solutions 44918 1/27/09 10:39 AM Page 638

639. 639
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–92.The cable segments support the loading shown.
Determine the magnitude of the horizontal force Pso that
.x
B=6 ft
5 ft
2 ft
3 ft
60 lb
D
C
B
A
x
B
8 ft
P
7 Solutions 44918 1/27/09 10:39 AM Page 639

640. 640
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–93.Determine the force Pneeded to hold the cable
in the position shown, i.e., so segment BCremains
horizontal. Also, compute the sag and the maximum
tension in the cable.
y
B
4 m 3 m 2 m6 m
4 kN P
6 kN
y
B
3 m
A
B C
D
E
7 Solutions 44918 1/27/09 10:39 AM Page 640

641. 641
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–94.Cable ABCDsupports the 10-kg lamp Eand the
15-kg lamp F. Determine the maximum tension in the cable
and the sag of point B.y
B
3 m1 m
0.5 m
y
B 2 m
A D
B
C
E
F
7 Solutions 44918 1/27/09 10:39 AM Page 641

642. 642
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–95.The cable supports the three loads shown. Determine
the sags and of points Band D. Take
P
2=250 lb.
P
1=400 lb,y
Dy
B
4 ft
12 ft 20 ft 15 ft 12 ft
A
E
B
C
D
y
B
y
D
14 ft
P
2
P
2
P
1
7 Solutions 44918 1/27/09 10:39 AM Page 642

643. 643
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–96.The cable supports the three loads shown.
Determine the magnitude of if and
Also find the sag y
D.y
B=8 ft.
P
2=300 lbP
1
4 ft
12 ft 20 ft 15 ft 12 ft
A
E
B
C
D
y
B
y
D
14 ft
P
2
P
2
P
1
7 Solutions 44918 1/27/09 10:39 AM Page 643

644. 644
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–97.The cable supports the loading shown. Determine
the horizontal distance the force at point Bacts from A.
Set P=40 lb.
x
B
5 ft
2 ft
3 ft
30 lb
D
C
B
A
x
B
5
4
3
8 ft
P
7–98.The cable supports the loading shown. Determine
the magnitude of the horizontal force Pso that x
B=6 ft.
5 ft
2 ft
3 ft
30 lb
D
C
B
A
x
B
5
4
3
8 ft
P
7 Solutions 44918 1/27/09 10:39 AM Page 644

645. 645
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–99.Determine the maximum uniform distributed
loading N/m that the cable can support if it is capable of
sustaining a maximum tension of 60 kN.
w
0 60 m
7 m
w
0
7 Solutions 44918 1/27/09 10:39 AM Page 645

646. 646
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–100.The cable supports the uniform distributed load
of . Determine the tension in the cable at
each support Aand B.
w
0=600 lb>ft
A
w
0
B
25 ft
10 ft
15 ft
7 Solutions 44918 1/27/09 10:39 AM Page 646

647. 647
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–101.Determine the maximum uniform distributed
load the cable can support if the maximum tension the
cable can sustain is 4000 lb.
w
0
A
w
0
B
25 ft
10 ft
15 ft
7 Solutions 44918 1/27/09 10:39 AM Page 647

648. 648
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–102.The cable is subjected to the triangular loading. If
the slope of the cable at point Ois zero, determine the
equation of the curve which defines the cable
shape OB, and the maximum tension developed in the cable.
y=f1x2
15 ft 15 ft
500 lb/ft 500 lb /ft
8 ft
y
x
A
O
B
7 Solutions 44918 1/27/09 10:39 AM Page 648

649. 649
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–103.If cylinders Cand Deach weigh 900 lb, determine
the maximum sag h, and the length of the cable between the
smooth pulleys at Aand B. The beam has a weight per unit
length of .100 lb>ft
12 ft
h
B
D
A
C
7 Solutions 44918 1/27/09 10:39 AM Page 649

650. 650
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:39 AM Page 650

651. 651
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–104.The bridge deck has a weight per unit length of
. It is supported on each side by a cable. Determine
the tension in each cable at the piers Aand B.
80 kN>m A
B
1000 m
150 m
75 m
7 Solutions 44918 1/27/09 10:39 AM Page 651

652. 652
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:39 AM Page 652

653. 653
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–105.If each of the two side cables that support the
bridge deck can sustain a maximum tension of 50 MN,
determine the allowable uniform distributed load caused
by the weight of the bridge deck.
w
0
A
B
1000 m
150 m
75 m
7 Solutions 44918 1/27/09 10:39 AM Page 653

654. 654
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:39 AM Page 654

655. 655
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–106.If the slope of the cable at support Ais 10°,
determine the deflection curve y= f(x) of the cable and the
maximum tension developed in the cable.
10 ft
500 lb/ft
10
A
B
x
y
40 ft
7 Solutions 44918 1/27/09 10:39 AM Page 655

656. 656
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–107.If h= 5 m, determine the maximum tension
developed in the chain and its length. The chain has a mass
per unit length of .8 kg>m
AB
50 m
h 5 m
7 Solutions 44918 1/27/09 10:40 AM Page 656

657. 657
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:40 AM Page 657

658. 658
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–108.A cable having a weight per unit length of
is suspended between supports Aand B. Determine the
equation of the catenary curve of the cable and the cable’s
length.
5 lb>ft
AB
150 ft
30 30
7 Solutions 44918 1/27/09 10:40 AM Page 658

659. 659
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:40 AM Page 659

660. 660
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–109.If the 45-m-long cable has a mass per unit length
of , determine the equation of the catenary curve of
the cable and the maximum tension developed in the cable.
5 kg>m
A B
40 m
7 Solutions 44918 1/27/09 10:40 AM Page 660

661. 661
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:40 AM Page 661

662. 662
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–110.Show that the deflection curve of the cable discussed
in Example 7–13 reduces to Eq. 4 in Example 7–12 when the
hyperbolic cosine functionis expanded in terms of a series
and only the first two terms are retained. (The answer
indicates that the catenarymay be replaced by a parabola
in the analysis of problems in which the sag is small. In this
case, the cable weight is assumed to be uniformly distributed
along the horizontal.)
7 Solutions 44918 1/27/09 10:40 AM Page 662

663. 663
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–111.The cable has a mass per unit length of .
Determine the shortest total length Lof the cable that can
be suspended in equilibrium.
10 kg>m
A B
8 m
7 Solutions 44918 1/27/09 10:40 AM Page 663

664. 664
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:40 AM Page 664

665. 665
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:40 AM Page 665

666. 666
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–112.The power transmission cable has a weight per
unit length of . If the lowest point of the cable must
be at least 90 ft above the ground, determine the maximum
tension developed in the cable and the cable’s length
between Aand B.
15 lb>ft
A
B
180 ft
90 ft
120 ft
300 ft
7 Solutions 44918 1/27/09 10:40 AM Page 666

667. 667
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:40 AM Page 667

668. 668
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7 Solutions 44918 1/27/09 10:40 AM Page 668

669. 669
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–113.If the horizontal towing force is T = 20 kN and the
chain has a mass per unit length of , determine the
maximum sag h. Neglect the buoyancy effect of the water
on the chain. The boats are stationary.
15 kg>m
40 m
hT
T
7 Solutions 44918 1/27/09 10:40 AM Page 669

670. 670
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–114.A 100-lb cable is attached between two points at a
distance 50 ft apart having equal elevations. If the maximum
tension developed in the cable is 75 lb, determine the length
of the cable and the sag.
7 Solutions 44918 1/27/09 10:40 AM Page 670

671. 671
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–115.Draw the shear and moment diagrams for beam CD.
4 kip · ft
10 kip
A
C
B
D
3 ft
3 ft
2 ft
2 ft 2 ft
7 Solutions 44918 1/27/09 10:40 AM Page 671

672. 672
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–116.Determine the internal normal force, shear force,
and moment at points Band Cof the beam.
5 m5 m 3 m
2 kN/m
1 kN/m
7.5 kN
40 kN m
6 kN
1 m
A
B
C
7 Solutions 44918 1/27/09 10:40 AM Page 672

673. 673
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–117.Determine the internal normal force, shear force
and moment at points Dand Eof the frame.
60
A
D
E
C
B
1 m
0.75 m
0.75 m
0.75 m
0.25 m
400 N/m
7 Solutions 44918 1/27/09 10:40 AM Page 673

674. 674
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–118.Determine the distance abetween the supports in
terms of the beam’s length Lso that the moment in the
symmetricbeam is zero at the beam’s center.
L
a
w
7 Solutions 44918 1/27/09 10:40 AM Page 674

675. 675
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–119.A chain is suspended between points at the same
elevation and spaced a distance of 60 ft apart. If it has a
weight per unit length of and the sag is 3 ft,
determine the maximum tension in the chain.
0.5 lb>ft
7 Solutions 44918 1/27/09 10:40 AM Page 675

676. 676
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–120.Draw the shear and moment diagrams for the beam.
5 m 5 m
2 kN/m
A
50 kN m
B
C
•7–121.Determine the internal shear and moment in
member ABCas a function of x, where the origin for xis at A.
A C
D
B
3 m 1.5 m
1.5 m
1.5 m
6 kN
45
7 Solutions 44918 1/27/09 10:40 AM Page 676

677. 677
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–122.The traveling crane consists of a 5-m-long beam
having a uniform mass per unit length of 20 kg/m. The chain
hoist and its supported load exert a force of 8 kN on the
beam when . Draw the shear and moment diagrams
for the beam. The guide wheels at the ends Aand Bexert
only vertical reactions on the beam. Neglect the size of the
trolley at C.
x=2 m
x 2 m
A
C
5 m
8 kN
B
7 Solutions 44918 1/27/09 10:40 AM Page 677

678. 678
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–123.Determine the internal normal force, shear force,
and the moment as a function of and
for the member loaded as shown.0…y…2 ft
0°…u…180°
2 ft
1 ft
150 lb
200 lb
y
A
B C
u
7 Solutions 44918 1/27/09 10:40 AM Page 678

679. 679
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*7–124.The yacht is anchored with a chain that has a total
length of 40 m and a mass per unit length of and the
tension in the chain at Ais 7 kN. Determine the length of
chain which is lying at the bottom of the sea. What is the
distance d? Assume that buoyancy effects of the water on
the chain are negligible.Hint:Establish the origin of the
coordinate system at Bas shown in order to find the chain
length BA.
l
d
18 kg/m,
d
A
B
s
x
y
60
d
l
7 Solutions 44918 1/27/09 10:40 AM Page 679

680. 680
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•7–125.Determine the internal normal force, shear force,
and moment at points Dand Eof the frame.
E
4 ft
1 ft
8 ft
3 ft
D
F
C
A
30
150 lb
B
7 Solutions 44918 1/27/09 10:40 AM Page 680

681. 681
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–126.The uniform beam weighs 500 lb and is held in the
horizontal position by means of cable AB, which has a
weight of 5 lb/ft. If the slope of the cable at Ais 30°,
determine the length of the cable.
A
B
C
15 ft
30
7 Solutions 44918 1/27/09 10:40 AM Page 681

682. 682
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
7–127.The balloon is held in place using a 400-ft cord that
weighs 0.8 lb/ft and makes a 60° angle with the horizontal. If
the tension in the cord at point Ais 150 lb, determine the
length of the cord,l, that is lying on the ground and the
height h.Hint: Establish the coordinate system at Bas
shown.
60
A
l
x
y h
s
B
7 Solutions 44918 1/27/09 10:40 AM Page 682

683. 683
•8–1.Determine the minimum horizontal force P
required to hold the crate from sliding down the plane. The
crate has a mass of 50 kg and the coefficient of static friction
between the crate and the plane is .m
s=0.25
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
P
30
8 Solutions 44918 1/27/09 1:51 PM Page 683

684. 684
8–2.Determine the minimum force Prequired to push
the crate up the plane. The crate has a mass of 50 kg and the
coefficient of static friction between the crate and the plane
is .m
s=0.25
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
P
30
8 Solutions 44918 1/27/09 1:51 PM Page 684

685. 685
8–3.A horizontal force of is just sufficient to
hold the crate from sliding down the plane, and a horizontal
force of is required to just push the crate up the
plane. Determine the coefficient of static friction between
the plane and the crate, and find the mass of the crate.
P=350 N
P=100 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
P
30
8 Solutions 44918 1/27/09 1:51 PM Page 685

686. 686
*8–4.If the coefficient of static friction at Ais
and the collar at Bis smooth so it only exerts a horizontal
force on the pipe, determine the minimum distance so
that the bracket can support the cylinder of any mass
without slipping. Neglect the mass of the bracket.
x
m
s=0.4
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
200 mm
x
100 mm
B
A
C
8 Solutions 44918 1/27/09 1:51 PM Page 686

687. 687
•8–5.The 180-lb man climbs up the ladder and stops at the
position shown after he senses that the ladder is on the verge
of slipping. Determine the inclination of the ladder if the
coefficient of static friction between the friction pad Aand the
ground is .Assume the wall at Bis smooth.The center
of gravity for the man is at G. Neglect the weight of the ladder.
m
s=0.4
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
G
A
B
10 ft
3 ft
u
8 Solutions 44918 1/27/09 1:51 PM Page 687

688. 688
8–6.The 180-lb man climbs up the ladder and stops at the
position shown after he senses that the ladder is on the verge
of slipping. Determine the coefficient of static friction between
the friction pad at Aand ground if the inclination of the ladder
is and the wall at Bis smooth.The center of gravity for
the man is at G. Neglect the weight of the ladder.
u=60°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
G
A
B
10 ft
3 ft
u
8 Solutions 44918 1/27/09 1:51 PM Page 688

689. 689
8–7.The uniform thin pole has a weight of 30 lb and a
length of 26 ft. If it is placed against the smooth wall and on
the rough floor in the position , will it remain in
this position when it is released? The coefficient of static
friction is .m
s=0.3
d=10 ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
d
B
26 ft
8 Solutions 44918 1/27/09 1:51 PM Page 689

690. 690
*8–8.The uniform pole has a weight of 30 lb and a length
of 26 ft. Determine the maximum distance dit can be placed
from the smooth wall and not slip. The coefficient of static
friction between the floor and the pole is .m
s=0.3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
d
B
26 ft
8 Solutions 44918 1/27/09 1:52 PM Page 690

691. 691
•8–9.If the coefficient of static friction at all contacting
surfaces is , determine the inclination at which the
identical blocks, each of weight W, begin to slide.
um
s
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
B
u
8 Solutions 44918 1/27/09 1:52 PM Page 691

692. 692
8–10.The uniform 20-lb ladder rests on the rough floor
for which the coefficient of static friction is and
against the smooth wall at B. Determine the horizontal
force Pthe man must exert on the ladder in order to cause
it to move.
m
s=0.8
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
B
8 ft
5 ft
5 ft
6 ft
P
8 Solutions 44918 1/27/09 1:52 PM Page 692

693. 693
8–11.The uniform 20-lb ladder rests on the rough floor
for which the coefficient of static friction is and
against the smooth wall at B. Determine the horizontal
force Pthe man must exert on the ladder in order to cause
it to move.
m
s=0.4
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
B
8 ft
5 ft
5 ft
6 ft
P
8 Solutions 44918 1/27/09 1:52 PM Page 693

694. 694
*8–12.The coefficients of static and kinetic friction
between the drum and brake bar are and ,
respectively. If and determine the
horizontal and vertical components of reaction at the pin O.
Neglect the weight and thickness of the brake. The drum has
a mass of 25 kg.
P=85 NM=50 N
#
m
m
k=0.3m
s=0.4
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
M
P
B
O 125 mm
700 mm
500 mm
300 mm
8 Solutions 44918 1/27/09 1:52 PM Page 694

695. 695
•8–13.The coefficient of static friction between the drum
and brake bar is . If the moment ,
determine the smallest force Pthat needs to be applied to
the brake bar in order to prevent the drum from rotating.
Also determine the corresponding horizontal and vertical
components of reaction at pin O. Neglect the weight and
thickness of the brake bar. The drum has a mass of 25 kg.
M=35 N
#
mm
s=0.4
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
M
P
B
O 125 mm
700 mm
500 mm
300 mm
8 Solutions 44918 1/27/09 1:52 PM Page 695

696. 696
8–14.Determine the minimum coefficient of static
friction between the uniform 50-kg spool and the wall so
that the spool does not slip.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
B
0.6 m
0.3 m
60
8 Solutions 44918 1/27/09 1:52 PM Page 696

697. 697
8–15.The spool has a mass of 200 kg and rests against the
wall and on the floor. If the coefficient of static friction at B
is , the coefficient of kinetic friction is
, and the wall is smooth, determine the friction
force developed at Bwhen the vertical force applied to the
cable is .P=800 N
(m
k)
B=0.2
(m
s)
B=0.3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
0.1 m
G
A
B
0.4 m
P
8 Solutions 44918 1/27/09 1:52 PM Page 697

698. 698
*8–16.The 80-lb boy stands on the beam and pulls on the
cord with a force large enough to just cause him to slip. If
the coefficient of static friction between his shoes and the
beam is , determine the reactions at Aand B.
The beam is uniform and has a weight of 100 lb. Neglect the
size of the pulleys and the thickness of the beam.
(m
s)
D=0.4
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
D A
C
B
5 ft
60
3 ft
12
13
5
4 ft
1 ft
8 Solutions 44918 1/27/09 1:52 PM Page 698

699. 699
•8–17.The 80-lb boy stands on the beam and pulls with a
force of 40 lb. If , determine the frictional force
between his shoes and the beam and the reactions at Aand
B. The beam is uniform and has a weight of 100 lb. Neglect
the size of the pulleys and the thickness of the beam.
(m
s)
D=0.4
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
D A
C
B
5 ft
60
3 ft
12
13
5
4 ft
1 ft
8 Solutions 44918 1/27/09 1:52 PM Page 699

700. 700
8–18.The tongs are used to lift the 150-kg crate, whose
center of mass is at G. Determine the least coefficient of
static friction at the pivot blocks so that the crate can be
lifted.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
275 mm
300 mm
30
500 mm
500 mm
A
C D
F
H
E
B
P
G
8 Solutions 44918 1/27/09 1:52 PM Page 700

701. 701
8–19.Two blocks Aand Bhave a weight of 10 lb and 6 lb,
respectively. They are resting on the incline for which the
coefficients of static friction are and .
Determine the incline angle for which both blocks begin
to slide. Also find the required stretch or compression in the
connecting spring for this to occur. The spring has a stiffness
of .k=2 lb>ft
u
m
B=0.25m
A=0.15
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
u
Bk 2 lb/ft
8 Solutions 44918 1/27/09 1:52 PM Page 701

702. 702
*8–20.Two blocks Aand Bhave a weight of 10 lb and 6 lb,
respectively. They are resting on the incline for which the
coefficients of static friction are and .
Determine the angle which will cause motion of one of
the blocks. What is the friction force under each of the
blocks when this occurs? The spring has a stiffness of
and is originally unstretched.k=2 lb>ft
u
m
B=0.25m
A=0.15
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
u
Bk 2 lb/ft
8 Solutions 44918 1/27/09 1:52 PM Page 702

703. 703
•8–21.Crates Aand Bweigh 200 lb and 150 lb,
respectively. They are connected together with a cable and
placed on the inclined plane. If the angle is gradually
increased, determine when the crates begin to slide. The
coefficients of static friction between the crates and the
plane are and . m
B=0.35m
A=0.25
u
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
B
A C
D
u
8 Solutions 44918 1/27/09 1:52 PM Page 703

704. 704
8–22.A man attempts to support a stack of books
horizontally by applying a compressive force of
to the ends of the stack with his hands. If each book has a
mass of 0.95 kg, determine the greatest number of books
that can be supported in the stack. The coefficient of static
friction between the man’s hands and a book is
and between any two books .(m
s)
b=0.4
(m
s)
h=0.6
F=120 N
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
F 120 NF 120 N
8 Solutions 44918 1/27/09 1:52 PM Page 704

705. 705
8–23.The paper towel dispenser carries two rolls of paper.
The one in use is called the stub roll Aand the other is the
fresh roll B. They weigh 2 lb and 5 lb, respectively. If the
coefficients of static friction at the points of contact Cand D
are and , determine the initial
vertical force Pthat must be applied to the paper on the stub
roll in order to pull down a sheet.The stub roll is pinned in the
center, whereas the fresh roll is not. Neglect friction at the pin.
(m
s)
D=0.5(m
s)
C=0.2
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
P
60
3 in.
4 in.
45
A
B
C
D
8 Solutions 44918 1/27/09 1:52 PM Page 705

706. 706
*8–24.The drum has a weight of 100 lb and rests on the
floor for which the coefficient of static friction is . If
ft and ft, determine the smallest magnitude of
the force Pthat will cause impending motion of the drum.
b=3a=2
m
s=0.6
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
b
a
P
3
4
5
•8–25.The drum has a weight of 100 lb and rests on the
floor for which the coefficient of static friction is . If
ft and ft, determine the smallest magnitude of
the force Pthat will cause impending motion of the drum.
b=4a=3
m
s=0.5
b
a
P
3
4
5
8 Solutions 44918 1/27/09 1:52 PM Page 706

707. 707
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–26.The refrigerator has a weight of 180 lb and rests on a
tile floor for which . If the man pushes
horizontally on the refrigerator in the direction shown,
determine the smallest magnitude of horizontal force
needed to move it. Also, if the man has a weight of 150 lb,
determine the smallest coefficient of friction between his
shoes and the floor so that he does not slip.
m
s=0.25
3 ft
3 ft
1.5 ft
G
A
4 ft
8 Solutions 44918 1/27/09 1:52 PM Page 707

708. 708
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–27.The refrigerator has a weight of 180 lb and rests on a
tile floor for which . Also, the man has a weight of
150 lb and the coefficient of static friction between the floor
and his shoes is . If he pushes horizontally on the
refrigerator, determine if he can move it. If so, does the
refrigerator slip or tip?
m
s=0.6
m
s=0.25
3 ft
3 ft
1.5 ft
G
A
4 ft
8 Solutions 44918 1/27/09 1:52 PM Page 708

709. 709
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–28.Determine the minimum force Pneeded to push
the two 75-kg cylinders up the incline. The force acts
parallel to the plane and the coefficients of static friction of
the contacting surfaces are , , and
. Each cylinder has a radius of 150 mm.m
C=0.4
m
B=0.25m
A=0.3
P
A
B
C
30
8 Solutions 44918 1/27/09 1:52 PM Page 709

710. 710
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–29.If the center of gravity of the stacked tables is at G,
and the stack weighs 100 lb, determine the smallest force P
the boy must push on the stack in order to cause movement.
The coefficient of static friction at Aand Bis . The
tables are locked together.
m
s=0.3
G
AB
30
3.5 ft
3 ft
2 ft
P
2 ft
8 Solutions 44918 1/27/09 1:52 PM Page 710

711. 711
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–30.The tractor has a weight of 8000 lb with center of
gravity at G. Determine if it can push the 550-lb log up the
incline. The coefficient of static friction between the log and
the ground is , and between the rear wheels of the
tractor and the ground . The front wheels are free
to roll. Assume the engine can develop enough torque to
cause the rear wheels to slip.
m
œ
s
=0.8
m
s=0.5
7 ft
3 ft
1.25 ft
2.5 ft
10
A
B
G
C
8 Solutions 44918 1/27/09 1:52 PM Page 711

712. 712
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–31.The tractor has a weight of 8000 lb with center of
gravity at G. Determine the greatest weight of the log that
can be pushed up the incline. The coefficient of static
friction between the log and the ground is , and
between the rear wheels of the tractor and the ground
. The front wheels are free to roll. Assume the
engine can develop enough torque to cause the rear wheels
to slip.
m
s
œ=0.7
m
s=0.5
7 ft
3 ft
1.25 ft
2.5 ft
10
A
B
G
C
8 Solutions 44918 1/27/09 1:52 PM Page 712

713. 713
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–32.The 50-kg uniform pole is on the verge of slipping
at Awhen . Determine the coefficient of static
friction at A.
u=45°
A
B
C
8 m
5 m
u
8 Solutions 44918 1/27/09 1:52 PM Page 713

714. 714
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–33.A force of is applied perpendicular to
the handle of the gooseneck wrecking bar as shown. If the
coefficient of static friction between the bar and the wood is
, determine the normal force of the tines at Aon
the upper board. Assume the surface at Cis smooth.
m
s=0.5
P=20
lb
20 in.
3 in.3 in.
1 in.
A
C
P
30
8 Solutions 44918 1/27/09 1:52 PM Page 714

715. 715
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–34.The thin rod has a weight Wand rests against the
floor and wall for which the coefficients of static friction are
and , respectively. Determine the smallest value of
for which the rod will not move.
um
Bm
A
L
A
B
u
8–35.A roll of paper has a uniform weight of 0.75 lb and
is suspended from the wire hanger so that it rests against
the wall. If the hanger has a negligible weight and the
bearing at Ocan be considered frictionless, determine the
force Pneeded to start turning the roll if . The
coefficient of static friction between the wall and the paper
is .m
s=0.25
u=30°
30
P
A
3 in.
O
u
8 Solutions 44918 1/27/09 1:52 PM Page 715

716. 716
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–36.A roll of paper has a uniform weight of 0.75 lb and
is suspended from the wire hanger so that it rests against
the wall. If the hanger has a negligible weight and the
bearing at Ocan be considered frictionless, determine the
minimum force Pand the associated angle needed to start
turning the roll. The coefficient of static friction between
the wall and the paper is m
s=0.25.
u
30
P
A
3 in.
O
u
8 Solutions 44918 1/27/09 1:52 PM Page 716

717. 717
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–37.If the coefficient of static friction between the
chain and the inclined plane is , determine the
overhang length bso that the chain is on the verge of
slipping up the plane. The chain weighs wper unit length.
m
s=tan u
b
a
u
8 Solutions 44918 1/27/09 1:52 PM Page 717

718. 718
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–38.Determine the maximum height hin meters to
which the girl can walk up the slide without supporting
herself by the rails or by her left leg. The coefficient of static
friction between the girl’s shoes and the slide is .m
s=0.8
y
h
x
y

x
21
––
3
8 Solutions 44918 1/27/09 1:52 PM Page 718

719. 719
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–39.If the coefficient of static friction at Bis ,
determine the largest angle and the minimum coefficient
of static friction at Aso that the roller remains self-locking,
regardless of the magnitude of force Papplied to the belt.
Neglect the weight of the roller and neglect friction
between the belt and the vertical surface.
u
m
s=0.3
P
A
B
30 mm
u
8 Solutions 44918 1/27/09 1:52 PM Page 719

720. 720
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–40.If , determine the minimum coefficient of
static friction at Aand Bso that the roller remains self-
locking, regardless of the magnitude of force Papplied to
the belt. Neglect the weight of the roller and neglect friction
between the belt and the vertical surface.
u=30°
P
A
B
30 mm
u
8 Solutions 44918 1/27/09 1:52 PM Page 720

721. 721
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–41.The clamp is used to tighten the connection
between two concrete drain pipes. Determine the least
coefficient of static friction at Aor Bso that the clamp does
not slip regardless of the force in the shaft CD.
B
C D
A
100 mm
250 mm
8 Solutions 44918 1/27/09 1:52 PM Page 721

722. 722
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–42.The coefficient of static friction between the 150-kg
crate and the ground is , while the coefficient of
static friction between the 80-kg man’s shoes and the
ground is . Determine if the man can move the
crate.
m
s
œ=0.4
m
s=0.3
30
8 Solutions 44918 1/27/09 1:52 PM Page 722

723. 723
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–43.If the coefficient of static friction between the crate
and the ground is , determine the minimum
coefficient of static friction between the man’s shoes and
the ground so that the man can move the crate.
m
s=0.3
30
8 Solutions 44918 1/27/09 1:52 PM Page 723

724. 724
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–44.The 3-Mg rear-wheel-drive skid loader has a center
of mass at G. Determine the largest number of crates that
can be pushed by the loader if each crate has a mass of
500 kg. The coefficient of static friction between a crate and
the ground is , and the coefficient of static friction
between the rear wheels of the loader and the ground is
. The front wheels are free to roll. Assume that the
engine of the loader is powerful enough to generate a
torque that will cause the rear wheels to slip.
m
s
œ=0.5
m
s=0.3
0.75 m
0.25 m
G
0.3 m
BA
8 Solutions 44918 1/27/09 1:52 PM Page 724

725. 725
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–45.The 45-kg disk rests on the surface for which the
coefficient of static friction is Determine the
largest couple moment Mthat can be applied to the bar
without causing motion.
m
A=0.2.
400 mm
125 mm
300 mm
B
A
C
M
8–46.The 45-kg disk rests on the surface for which the
coefficient of static friction is If
determine the friction force at A.
M=50 N
#
m,m
A=0.15.
400 mm
125 mm
300 mm
B
A
C
M
8 Solutions 44918 1/27/09 1:52 PM Page 725

726. 726
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–47.Block Chas a mass of 50 kg and is confined between
two walls by smooth rollers. If the block rests on top of the
40-kg spool, determine the minimum cable force Pneeded
to move the spool. The cable is wrapped around the spool’s
inner core. The coefficients of static friction at Aand Bare
and .m
B=0.6m
A=0.3
C
A
B
O
0.4 m
0.2 m
P
*8–48.Block Chas a mass of 50 kg and is confined
between two walls by smooth rollers. If the block rests on
top of the 40-kg spool, determine the required coefficients
of static friction at Aand Bso that the spool slips at Aand
Bwhen the magnitude of the applied force is increased to
.P=300 N C
A
B
O
0.4 m
0.2 m
P
8 Solutions 44918 1/27/09 1:52 PM Page 726

727. 727
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–49.The 3-Mg four-wheel-drive truck (SUV) has a
center of mass at G. Determine the maximum mass of the
log that can be towed by the truck. The coefficient of static
friction between the log and the ground is , and the
coefficient of static friction between the wheels of the truck
and the ground is . Assume that the engine of the
truck is powerful enough to generate a torque that will
cause all the wheels to slip.
m
s
œ=0.4
m
s=0.8
1.2 m1.6 m0.5 m
G
AB
8 Solutions 44918 1/27/09 1:52 PM Page 727

728. 728
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–50.A 3-Mg front-wheel-drive truck (SUV) has a center
of mass at G. Determine the maximum mass of the log that
can be towed by the truck. The coefficient of static friction
between the log and the ground is , and the
coefficient of static friction between the front wheels of the
truck and the ground is . The rear wheels are free to
roll. Assume that the engine of the truck is powerful enough
to generate a torque that will cause the front wheels to slip.
m
s
œ=0.4
m
s=0.8
1.2 m1.6 m0.5 m
G
AB
8 Solutions 44918 1/27/09 1:52 PM Page 728

729. 729
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–51.If the coefficients of static friction at contact points
Aand Bare and respectively, determine
the smallest force Pthat will cause the 150-kg spool to have
impending motion.
m
s
œ=0.4m
s=0.3 P
400 mm
200 mm
150 mm
B
A
8 Solutions 44918 1/27/09 1:52 PM Page 729

730. 730
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–52.If the coefficients of static friction at contact points
Aand Bare and respectively, determine
the smallest force Pthat will cause the 150-kg spool to have
impending motion.
m
s
œ=0.2m
s=0.4 P
400 mm
200 mm
150 mm
B
A
8 Solutions 44918 1/27/09 1:52 PM Page 730

731. 731
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–53.The carpenter slowly pushes the uniform board
horizontally over the top of the saw horse. The board has a
uniform weight of and the saw horse has a weight
of 15 lb and a center of gravity at G. Determine if the saw
horse will stay in position, slip, or tip if the board is pushed
forward when The coefficients of static friction
are shown in the figure.
d=10 ft.
3 lb>ft,
d
G
18 ft
1 ft1 ft
3 ft
m 0.5
m¿ 0.3 m¿ 0.3
8 Solutions 44918 1/27/09 1:52 PM Page 731

732. 732
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–54.The carpenter slowly pushes the uniform board
horizontally over the top of the saw horse. The board has a
uniform weight of and the saw horse has a weight of
15 lb and a center of gravity at G. Determine if the saw
horse will stay in position, slip, or tip if the board is pushed
forward when The coefficients of static friction
are shown in the figure.
d=14 ft.
3 lb>ft,
d
G
18 ft
1 ft1 ft
3 ft
m 0.5
m¿ 0.3 m¿ 0.3
8 Solutions 44918 1/27/09 1:52 PM Page 732

733. 733
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–55.If the 75-lb girl is at position d= 4 ft, determine the
minimum coefficient of static friction at contact points A
and Bso that the plank does not slip. Neglect the weight of
the plank.
m
s
A
G
d
B
12 ft
4560
8 Solutions 44918 1/27/09 1:52 PM Page 733

734. 734
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–56.If the coefficient of static friction at the contact
points Aand Bis , determine the minimum distance
dwhere a 75-lb girl can stand on the plank without causing it
to slip. Neglect the weight of the plank.
m
s=0.4
A
G
d
B
12 ft
4560
8 Solutions 44918 1/27/09 1:52 PM Page 734

735. 735
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–57.If each box weighs 150 lb, determine the least
horizontal force Pthat the man must exert on the top box in
order to cause motion. The coefficient of static friction
between the boxes is , and the coefficient of static
friction between the box and the floor is .m
s
œ=0.2
m
s=0.5
3 ft
4.5 ft
5 ft
P
4.5 ft
AB
8 Solutions 44918 1/27/09 1:52 PM Page 735

736. 736
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–58.If each box weighs 150 lb, determine the least
horizontal force Pthat the man must exert on the top box in
order to cause motion. The coefficient of static friction
between the boxes is , and the coefficient of static
friction between the box and the floor is .m
s
œ=0.35
m
s=0.65
3 ft
4.5 ft
5 ft
P
4.5 ft
AB
8 Solutions 44918 1/27/09 1:52 PM Page 736

737. 737
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–59.If the coefficient of static friction between the collars
Aand B and the rod is , determine the maximum
angle for the system to remain in equilibrium, regardless of
the weight of cylinder D. Links ACand BChave negligible
weight and are connected together at Cby a pin.
u
m
s=0.6
D
C
A B
uu
1515
8 Solutions 44918 1/27/09 1:52 PM Page 737

738. 738
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–60.If , determine the minimum coefficient of
static friction between the collars Aand B and the rod
required for the system to remain in equilibrium, regardless
of the weight of cylinder D. Links ACand BChave
negligible weight and are connected together at Cby a pin.
u=15°
D
C
A B
uu
1515
8 Solutions 44918 1/27/09 1:52 PM Page 738

739. 739
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–61.Each of the cylinders has a mass of 50 kg. If the
coefficients of static friction at the points of contact are
, , , and , determine the
smallest couple moment Mneeded to rotate cylinder E.
m
D=0.6m
C=0.5m
B=0.5m
A=0.5
300 mm
A D
300 mm
E
M
BC
8 Solutions 44918 1/27/09 1:52 PM Page 739

740. 740
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–62.Blocks A,B, and Chave weights of 50 lb, 25 lb, and
15 lb, respectively. Determine the smallest horizontal force P
that will cause impending motion. The coefficient of static
friction between Aand Bis , between Band
C, , and between block Cand the ground,
.m¿
œ
s
=0.35
m
s
œ=0.4
m
s=0.3
P
A
B
C
D
8 Solutions 44918 1/27/09 1:52 PM Page 740

741. 741
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–63.Determine the smallest force Pthat will cause
impending motion. The crate and wheel have a mass of
50 kg and 25 kg, respectively. The coefficient of static
friction between the crate and the ground is , and
between the wheel and the ground .m
s
œ=0.5
m
s=0.2
300 mm
P
B
C A
8 Solutions 44918 1/27/09 1:52 PM Page 741

742. 742
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–64.Determine the smallest force Pthat will cause
impending motion. The crate and wheel have a mass of
50 kg and 25 kg, respectively. The coefficient of static
friction between the crate and the ground is , and
between the wheel and the ground .m
s
œ=0.3
m
s=0.5
300 mm
P
B
C A
8 Solutions 44918 1/27/09 1:52 PM Page 742

743. 743
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–65.Determine the smallest horizontal force Prequired
to pull out wedge A. The crate has a weight of 300 lb and the
coefficient of static friction at all contacting surfaces is
. Neglect the weight of the wedge.m
s=0.3
AP
B
B
15
8 Solutions 44918 1/27/09 1:52 PM Page 743

744. 744
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–66.Determine the smallest horizontal force Prequired
to lift the 200-kg crate. The coefficient of static friction at
all contacting surfaces is . Neglect the mass of
the wedge.
m
s=0.3
P
A
B
15
8 Solutions 44918 1/27/09 1:52 PM Page 744

745. 745
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–67.Determine the smallest horizontal force Prequired
to lift the 100-kg cylinder. The coefficients of static friction
at the contact points Aand Bare and
, respectively; and the coefficient of static
friction between the wedge and the ground is .m
s=0.3
(m
s)
B=0.2
(m
s)
A=0.6
P
10
A
C
B
0.5 m
8 Solutions 44918 1/27/09 1:52 PM Page 745

746. 746
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–68.The wedge has a negligible weight and a coefficient
of static friction with all contacting surfaces.
Determine the largest angle so that it is “self-locking.”
This requires no slipping for any magnitude of the force P
applied to the joint.
u
m
s=0.35
––
2
––
2
P
uu
P
8 Solutions 44918 1/27/09 1:52 PM Page 746

747. 747
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–69.Determine the smallest horizontal force P
required to just move block Ato the right if the spring force
is and the coefficient of static friction at all contacting
surfaces on Ais .The sleeve at Cis smooth. Neglect
the mass of Aand B.
m
s=0.3
600 N
AP
BC
4545
8 Solutions 44918 1/27/09 1:52 PM Page 747

748. 748
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–70.The three stone blocks have weights of
, and Determine
the smallest horizontal force Pthat must be applied to
block Cin order to move this block. The coefficient of static
friction between the blocks is and between the
floor and each block m
s
œ=0.5.
m
s=0.3,
W
C=500 lb.W
B=150 lb,W
A=600 lb
A
B
C
45
P
8 Solutions 44918 1/27/09 1:52 PM Page 748

749. 749
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–71.Determine the smallest horizontal force Prequired
to move the wedge to the right. The coefficient of static
friction at all contacting surfaces is . Set
and . Neglect the weight of the wedge.F=400 N
u=15°m
s=0.3
P
300 mm
450 mm
20 mm
A
B
C
F
u
8 Solutions 44918 1/27/09 1:52 PM Page 749

750. 750
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–72.If the horizontal force Pis removed, determine the
largest angle that will cause the wedge to be self-locking
regardless of the magnitude of force Fapplied to the
handle. The coefficient of static friction at all contacting
surfaces is .m
s=0.3
u
P
300 mm
450 mm
20 mm
A
B
C
F
u
8 Solutions 44918 1/27/09 1:52 PM Page 750

751. 751
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–73.Determine the smallest vertical force Prequired to
hold the wedge between the two identical cylinders, each
having a weight of W. The coefficient of static friction at all
contacting surfaces is .m
s=0.1
P
3030
15
8 Solutions 44918 1/27/09 1:52 PM Page 751

752. 752
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–74.Determine the smallest vertical force Prequired to
push the wedge between the two identical cylinders, each
having a weight of W. The coefficient of static friction at all
contacting surfaces is .m
s=0.3
P
3030
15
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753. 753
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–75.If the uniform concrete block has a mass of 500 kg,
determine the smallest horizontal force Pneeded to move
the wedge to the left. The coefficient of static friction
between the wedge and the concrete and the wedge and the
floor is . The coefficient of static friction between
the concrete and floor is .m
s
œ=0.5
m
s=0.3
A
3 m
P
150 mm
B
7.5
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754. 754
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–76.The wedge blocks are used to hold the specimen
in a tension testing machine. Determine the largest design
angle of the wedges so that the specimen will not slip
regardless of the applied load. The coefficients of static
friction are at Aand at B. Neglect the
weight of the blocks.
m
B=0.6m
A=0.1
u
P
AB
uu
•8–77.The square threaded screw of the clamp has a
mean diameter of 14 mm and a lead of 6 mm. If for
the threads, and the torque applied to the handle is
, determine the compressive force Fon the block.1.5 N
#
m
m
s=0.2
1.5 N m
F
F
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755. 755
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–78.The device is used to pull the battery cable terminal
Cfrom the post of a battery. If the required pulling force is
85 lb, determine the torque Mthat must be applied to the
handle on the screw to tighten it. The screw has square
threads, a mean diameter of 0.2 in., a lead of 0.08 in., and the
coefficient of static friction is .m
s=0.5
C
A
B
M
8–79.The jacking mechanism consists of a link that has a
square-threaded screw with a mean diameter of 0.5 in. and a
lead of 0.20 in., and the coefficient of static friction is
. Determine the torque Mthat should be applied to
the screw to start lifting the 6000-lb load acting at the end of
member ABC.
m
s=0.4
D
B
C
A
7.5 in.
10 in.
15 in.20 in. 10 in.
6000 lb
M
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© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–80.Determine the magnitude of the horizontal force P
that must be applied to the handle of the bench vise in order
to produce a clamping force of 600 N on the block. The
single square-threaded screw has a mean diameter of
25 mm and a lead of 7.5 mm. The coefficient of static
friction is .m
s=0.25
•8–81.Determine the clamping force exerted on the
block if a force of P= 30 N is applied to the lever of the
bench vise. The single square-threaded screw has a mean
diameter of 25 mm and a lead of 7.5 mm. The coefficient of
static friction is .m
s=0.25
100 mm
P
100 mm
P
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757. 757
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–82.Determine the required horizontal force that must
be applied perpendicular to the handle in order to develop
a 900-N clamping force on the pipe. The single square-
threaded screw has a mean diameter of 25 mm and a lead of
5 mm. The coefficient of static friction is .Note:The
screw is a two-force member since it is contained within
pinned collars at Aand B.
m
s=0.4
B
D
E
C
A
150 mm
200 mm
200 mm
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758. 758
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–83.If the clamping force on the pipe is 900 N,
determine the horizontal force that must be applied
perpendicular to the handle in order to loosen the screw.
The single square-threaded screw has a mean diameter of
25 mm and a lead of 5 mm. The coefficient of static friction
is . Note:The screw is a two-force member since it
is contained within pinned collars at Aand B.
m
s=0.4
B
D
E
C
A
150 mm
200 mm
200 mm
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759. 759
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–84.The clamp provides pressure from several directions
on the edges of the board. If the square-threaded screw has a
lead of 3 mm, mean radius of 10 mm, and the coefficient of
static friction is determine the horizontal force
developed on the board at Aand the vertical forces
developed at Band Cif a torque of is applied
to the handle to tighten it further. The blocks at Band Care
pin connected to the board.
M=1.5 N
#
m
m
s=0.4,
45
A
B
C
D
45
M
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760. 760
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–85.If the jack supports the 200-kg crate, determine the
horizontal force that must be applied perpendicular to the
handle at Eto lower the crate. Each single square-threaded
screw has a mean diameter of 25 mm and a lead of 7.5 mm.
The coefficient of static friction is .m
s=0.25
C
AB
D
E
100 mm
45
45
45
45
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761. 761
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–86.If the jack is required to lift the 200-kg crate,
determine the horizontal force that must be applied
perpendicular to the handle at E. Each single square-
threaded screw has a mean diameter of 25 mm and a lead of
7.5 mm. The coefficient of static friction is .m
s=0.25
C
AB
D
E
100 mm
45
45
45
45
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762. 762
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–87.The machine part is held in place using the
double-end clamp. The bolt at Bhas square threads with a
mean radius of 4 mm and a lead of 2 mm, and the
coefficient of static friction with the nut is If a
torque of is applied to the nut to tighten it,
determine the normal force of the clamp at the smooth
contacts Aand C.
M=0.4 N
#
m
m
s=0.5.
260 mm
AC
B
90 mm
*8–88.Blocks Aand Bweigh 50 lb and 30 lb, respectively.
Using the coefficients of static friction indicated, determine
the greatest weight of block Dwithout causing motion.
A
B
C
D
m 0.5
m
BA 0.6
m
AC 0.4
20
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© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–89.Blocks Aand Bweigh 75 lb each, and Dweighs
30 lb. Using the coefficients of static friction indicated,
determine the frictional force between blocks Aand Band
between block Aand the floor C.
A
B
C
D
m 0.5
m
BA 0.6
m
AC 0.4
20
8–90.A cylinder having a mass of 250 kg is to be
supported by the cord which wraps over the pipe.
Determine the smallest vertical force Fneeded to support
the load if the cord passes (a) once over the pipe, ,
and (b) two times over the pipe, . Take .m
s=0.2b=540°
b=180°
F
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764. 764
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–91.A cylinder having a mass of 250 kg is to be
supported by the cord which wraps over the pipe.
Determine the largest vertical force Fthat can be applied
to the cord without moving the cylinder. The cord passes
(a) once over the pipe, , and (b) two times over the
pipe, . Take . m
s=0.2b=540°
b=180°
F
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765. 765
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–92.The boat has a weight of 500 lb and is held in
position off the side of a ship by the spars at Aand B. A man
having a weight of 130 lb gets in the boat, wraps a rope
around an overhead boom at C, and ties it to the end of the
boat as shown. If the boat is disconnected from the spars,
determine the minimum number of half turnsthe rope must
make around the boom so that the boat can be safely
lowered into the water at constant velocity. Also, what is the
normal force between the boat and the man? The coefficient
of kinetic friction between the rope and the boom is
.Hint: The problem requires that the normal force
between the man’s feet and the boat be as small as possible.
m
s=0.15
A
C
B
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766. 766
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–93.The 100-lb boy at Ais suspended from the cable
that passes over the quarter circular cliff rock. Determine if
it is possible for the 185-lb woman to hoist him up; and if
this is possible, what smallest force must she exert on the
horizontal cable? The coefficient of static friction between
the cable and the rock is , and between the shoes of
the woman and the ground .m
s
œ=0.8
m
s=0.2
A
8–94.The 100-lb boy at Ais suspended from the cable
that passes over the quarter circular cliff rock. What
horizontal force must the woman at Aexert on the cable in
order to let the boy descend at constant velocity? The
coefficients of static and kinetic friction between the cable
and the rock are and , respectively.m
k=0.35m
s=0.4
A
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© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–95.A 10-kg cylinder D, which is attached to a small
pulley B, is placed on the cord as shown. Determine the
smallest angle so that the cord does not slip over the peg at
C. The cylinder at Ehas a mass of 10 kg, and the coefficient
of static friction between the cord and the peg is .m
s=0.1
u
A
B
D
E
C
uu
*8–96.A 10-kg cylinder D, which is attached to a small
pulley B, is placed on the cord as shown. Determine the
largest angle so that the cord does not slip over the peg at
C. The cylinder at Ehas a mass of 10 kg, and the coefficient
of static friction between the cord and the peg is .m
s=0.1
u
A
B
D
E
C
uu
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768. 768
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–97.Determine the smallest lever force Pneeded to
prevent the wheel from rotating if it is subjected to a torque
of The coefficient of static friction between
the belt and the wheel is The wheel is pin
connected at its center,B.
m
s=0.3.
M=250 N
#
m.
400 mm
200 mm
750 mm
P
M
B
A
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769. 769
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–98.If a force of is applied to the handle of
the bell crank, determine the maximum torque Mthat can
be resisted so that the flywheel is not on the verge of
rotating clockwise. The coefficient of static friction between
the brake band and the rim of the wheel is .m
s=0.3
P=200 N
P
900 mm
400 mm
100 mm
300 mm
M
O
A
B
C
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770. 770
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–99.Show that the frictional relationship between the
belt tensions, the coefficient of friction , and the angular
contacts and for the V-belt is .T
2=T
1e
mb>sin(a>2)
ba
m
T
2 T
1
Impending
motion
b
a
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771. 771
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–100.Determine the force developed in spring ABin
order to hold the wheel from rotating when it is subjected
to a couple moment of . The coefficient of
static friction between the belt and the rim of the wheel is
, and between the belt and peg C,.The
pulley at Bis free to rotate.
m
s
œ=0.4m
s=0.2
M=200 N
#
m
C
A
200 mm
B
M
45
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772. 772
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–101.If the tension in the spring is ,
determine the largest couple moment that can be applied to
the wheel without causing it to rotate. The coefficient of
static friction between the belt and the wheel is ,
and between the belt the peg . The pulley Bfree to
rotate.
m
s
œ=0.4
m
s=0.2
F
AB=2.5 kN
C
A
200 mm
B
M
45
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773. 773
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–102.The simple band brake is constructed so that the
ends of the friction strap are connected to the pin at Aand
the lever arm at B. If the wheel is subjected to a torque of
determine the smallest force Papplied to the
lever that is required to hold the wheel stationary. The
coefficient of static friction between the strap and wheel is
m
s=0.5.
M=80 lb
#
ft,
1.5 ft 3 ft
45
M 80 lb ft
20
1.25 ft
A
B
P
O
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774. 774
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–103.A 180-lb farmer tries to restrain the cow from
escaping by wrapping the rope two turns around the tree
trunk as shown. If the cow exerts a force of 250 lb on the
rope, determine if the farmer can successfully restrain the
cow. The coefficient of static friction between the rope and
the tree trunk is , and between the farmer’s shoes
and the ground .m
s
œ=0.3
m
s=0.15
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775. 775
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–104.The uniform 50-lb beam is supported by the rope
which is attached to the end of the beam, wraps over the
rough peg, and is then connected to the 100-lb block. If
the coefficient of static friction between the beam and the
block, and between the rope and the peg, is
determine the maximum distance that the block can be
placed from Aand still remain in equilibrium. Assume the
block will not tip.
m
s=0.4,
10 ft
1 ft
d
A
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776. 776
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–105.The 80-kg man tries to lower the 150-kg crate
using a rope that passes over the rough peg. Determine the
least number of full turns in addition to the basic wrap
(165°) around the peg to do the job. The coefficients of
static friction between the rope and the peg and between
the man’s shoes and the ground are and ,
respectively.
m
s
œ=0.4m
s=0.1
15
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777. 777
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–106.If the rope wraps three full turns plus the basic
wrap (165°) around the peg, determine if the 80-kg man can
keep the 300-kg crate from moving. The coefficients of
static friction between the rope and the peg and between
the man’s shoes and the ground are and ,
respectively.
m
s
œ=0.4m
s=0.1
15
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778. 778
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–107.The drive pulley Bin a video tape recorder is on
the verge of slipping when it is subjected to a torque of
. If the coefficient of static friction between
the tape and the drive wheel and between the tape and the
fixed shafts Aand Cis , determine the tensions
and developed in the tape for equilibrium.T
2
T
1m
s=0.1
M=0.005 N
#
m
T
1
T
2
A
C
B
M 5 mN m
10 mm
10 mm
10 mm
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779. 779
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–108.Determine the maximum number of 50-lb packages
that can be placed on the belt without causing the belt to
slip at the drive wheel Awhich is rotating with a constant
angular velocity. Wheel Bis free to rotate. Also, find the
corresponding torsional moment Mthat must be supplied
to wheel A. The conveyor belt is pre-tensioned with the
300-lb horizontal force. The coefficient of kinetic friction
between the belt and platform Pis , and the
coefficient of static friction between the belt and the rim of
each wheel is .m
s=0.35
m
k=0.2
P 300 lb
A
P
B
M
0.5 ft
0.5 ft
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780. 780
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–109.Blocks Aand Bhave a mass of 7 kg and 10 kg,
respectively. Using the coefficients of static friction
indicated, determine the largest vertical force Pwhich can
be applied to the cord without causing motion.
P
300 mm
400 mm
A
C
D
B
m
D
0.1
m
C
0.4
m
B
0.4
m
A
0.3
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781. 781
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–110.Blocks Aand Bhave a mass of 100 kg and 150 kg,
respectively. If the coefficient of static friction between A
and Band between Band Cis and between the
ropes and the pegs Dand E , determine the
smallest force Fneeded to cause motion of block Bif
P=30 N.
m
s
œ=0.5
m
s=0.25,
P
F
D
A
B
E
C
45
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782. 782
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–111.Block Ahas a weight of 100 lb and rests on a
surface for which . If the coefficient of static
friction between the cord and the fixed peg at Cis ,
determine the greatest weight of the suspended cylinder B
without causing motion.
m
s=0.3
m
s=0.25
B
4 ft
2 ft
C
30
A
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783. 783
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–112.Block Ahas a mass of 50 kg and rests on surface
Bfor which . If the coefficient of static friction
between the cord and the fixed peg at Cis ,
determine the greatest mass of the suspended cylinder D
without causing motion.
m
s
œ=0.3
m
s=0.25
C
D
A
0.3 m
0.25 m
3
4
5
0.4 m
B
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784. 784
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–113.Block Ahas a mass of 50 kg and rests on surface
Bfor which . If the mass of the suspended cylinder
Dis 4 kg, determine the frictional force acting on Aand
check if motion occurs. The coefficient of static friction
between the cord and the fixed peg at Cis .m
s
œ=0.3
m
s=0.25
C
D
A
0.3 m
0.25 m
3
4
5
0.4 m
B
8–114.The collar bearing uniformly supports an axial
force of If the coefficient of static friction is
determine the torque Mrequired to overcome
friction.
m
s=0.3,
P=800 lb.
3 in. 2 in. P
M
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785. 785
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–115.The collar bearing uniformly supports an axial
force of If a torque of is applied to
the shaft and causes it to rotate at constant velocity,
determine the coefficient of kinetic friction at the surface of
contact.
M=3 lb
#
ftP=500 lb.
3 in. 2 in. P
M
*8–116.If the spring exerts a force of 900 lb on the block,
determine the torque Mrequired to rotate the shaft. The
coefficient of static friction at all contacting surfaces is
.m
s=0.3
6 in.
2 in.
M
•8–117.The disk clutchis used in standard transmissions
of automobiles. If four springs are used to force the two
plates Aand Btogether, determine the force in each spring
required to transmit a moment of across the
plates. The coefficient of static friction between Aand Bis
.m
s=0.3
M=600
lb#
ft
F
s
M
5 in.
B
2 in.
A
M
F
s
F
s
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786. 786
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–118.If is applied to the handle of the bell
crank, determine the maximum torque Mthe cone clutch
can transmit. The coefficient of static friction at the
contacting surface is .m
s=0.3
P=900 N
375 mm
200 mm
300 mm
250 mm
P
M
A
B
C
15
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787. 787
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–119.Because of wearing at the edges, the pivot bearing
is subjected to a conical pressure distribution at its surface
of contact. Determine the torque Mrequired to overcome
friction and turn the shaft, which supports an axial force P.
The coefficient of static friction is . For the solution, it is
necessary to determine the peak pressure in terms of P
and the bearing radius R.
p
0
m
s
P
M
R
p
0
8 Solutions 44918 1/27/09 1:53 PM Page 787

788. 788
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–120.The pivot bearing is subjected to a parabolic
pressure distribution at its surface of contact. If the
coefficient of static friction is , determine the torque M
required to overcome friction and turn the shaft if it
supports an axial force P.
m
s P
p
0
p p
0
(1 )
r
2
––
R
2
R
r
M
8 Solutions 44918 1/27/09 1:53 PM Page 788

789. 789
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–121.The shaft is subjected to an axial force P. If the
reactive pressure on the conical bearing is uniform,
determine the torque Mthat is just sufficient to rotate the
shaft. The coefficient of static friction at the contacting
surface is .m
s
P
M
d
1
d
2
uu
8 Solutions 44918 1/27/09 1:53 PM Page 789

790. 790
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–122.The tractor is used to push the 1500-lb pipe. To do
this it must overcome the frictional forces at the ground,
caused by sand.Assuming that the sand exerts a pressure on
the bottom of the pipe as shown, and the coefficient of static
friction between the pipe and the sand is
determine the horizontal force required to push the pipe
forward. Also, determine the peak pressure p
0.
m
s=0.3,
15 in.
12 ft
p p
0 cos u
p
0
u
8 Solutions 44918 1/27/09 1:53 PM Page 790

791. 791
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–123.The conical bearing is subjected to a constant
pressure distribution at its surface of contact. If the
coefficient of static friction is determine the torque M
required to overcome friction if the shaft supports an axial
force P.
m
s, P
M
R
u
8 Solutions 44918 1/27/09 1:53 PM Page 791

792. 792
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–124.Assuming that the variation of pressure at the
bottom of the pivot bearing is defined as ,
determine the torque Mneeded to overcome friction if the
shaft is subjected to an axial force P.The coefficient of static
friction is . For the solution, it is necessary to determine
in terms of Pand the bearing dimensions and .R
2R
1p
0
m
s
p=p
01R
2>r2
P
M
R
2
R
1
p
0
p p
0
R
2
r
r
8 Solutions 44918 1/27/09 1:53 PM Page 792

793. 793
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–125.The shaft of radius rfits loosely on the journal
bearing. If the shaft transmits a vertical force Pto the
bearing and the coefficient of kinetic friction between the
shaft and the bearing is , determine the torque M
required to turn the shaft with constant velocity.
m
k
r
P
M
8 Solutions 44918 1/27/09 1:53 PM Page 793

794. 794
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–126.The pulley is supported by a 25-mm-diameter pin.
If the pulley fits loosely on the pin, determine the smallest
force Prequired to raise the bucket. The bucket has a mass
of 20 kg and the coefficient of static friction between the
pulley and the pin is . Neglect the mass of the
pulley and assume that the cable does not slip on the pulley.
m
s=0.3
75 mm
P
z 60
8 Solutions 44918 1/27/09 1:53 PM Page 794

795. 795
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–127.The pulley is supported by a 25-mm-diameter pin.
If the pulley fits loosely on the pin, determine the largest
force Pthat can be applied to the rope and yet lower the
bucket. The bucket has a mass of 20 kg and the coefficient
of static friction between the pulley and the pin is .
Neglect the mass of the pulley and assume that the cable
does not slip on the pulley.
m
s=0.3
75 mm
P
z 60
8 Solutions 44918 1/27/09 1:53 PM Page 795

796. 796
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–128.The cylinders are suspended from the end of the
bar which fits loosely into a 40-mm-diameter pin. If Ahas a
mass of 10 kg, determine the required mass of Bwhich is
just sufficient to keep the bar from rotating clockwise. The
coefficient of static friction between the bar and the pin is
. Neglect the mass of the bar.m
s=0.3
A
B
800 mm 600 mm
•8–129.The cylinders are suspended from the end of the
bar which fits loosely into a 40-mm-diameter pin. If Ahas a
mass of 10 kg, determine the required mass of Bwhich is just
sufficient to keep the bar from rotating counterclockwise.
The coefficient of static friction between the bar and the pin
is . Neglect the mass of the bar.m
s=0.3
A
B
800 mm 600 mm
8–130.The connecting rod is attached to the piston by
a 0.75-in.-diameter pin at Band to the crank shaft by a
2-in.-diameter bearing A. If the piston is moving
downwards, and the coefficient of static friction at the
contact points is , determine the radius of the
friction circle at each connection.
m
s=0.2
A
B
8 Solutions 44918 1/27/09 1:53 PM Page 796

797. 797
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–131.The connecting rod is attached to the piston by a
20-mm-diameter pin at Band to the crank shaft by a
50-mm-diameter bearing A. If the piston is moving
upwards, and the coefficient of static friction at the contact
points is , determine the radius of the friction circle
at each connection.
m
s=0.3
A
B
*8–132.The 5-kg pulley has a diameter of 240 mm and the
axle has a diameter of 40 mm. If the coefficient of kinetic
friction between the axle and the pulley is
determine the vertical force Pon the rope required to lift
the 80-kg block at constant velocity.
m
k=0.15,
120 mm
P
8 Solutions 44918 1/27/09 1:53 PM Page 797

798. 798
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–133.Solve Prob. 8–132 if the force Pis applied
horizontally to the right.
120 mm
P
8–134.The bell crank fits loosely into a 0.5-in-diameter
pin. Determine the required force Pwhich is just sufficient
to rotate the bell crank clockwise. The coefficient of static
friction between the pin and the bell crank is .m
s=0.3
P
10 in.
12 in.50 lb
45
8 Solutions 44918 1/27/09 1:53 PM Page 798

799. 799
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–135.The bell crank fits loosely into a 0.5-in-diameter
pin. If P= 41 lb, the bell crank is then on the verge of
rotating counterclockwise. Determine the coefficient of
static friction between the pin and the bell crank.
P
10 in.
12 in.50 lb
45
8 Solutions 44918 1/27/09 1:53 PM Page 799

800. 800
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–136.The wagon together with the load weighs 150 lb.
If the coefficient of rolling resistance is a= 0.03 in.,
determine the force Prequired to pull the wagon with
constant velocity.
P
3 in.3 in.
45
8 Solutions 44918 1/27/09 1:53 PM Page 800

801. 801
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•8–137.The lawn roller has a mass of 80 kg. If the arm BA
is held at an angle of 30° from the horizontal and the
coefficient of rolling resistance for the roller is 25 mm,
determine the force Pneeded to push the roller at constant
speed. Neglect friction developed at the axle,A, and assume
that the resultant force Pacting on the handle is applied
along arm BA.
P
250 mm
B
A
30
8 Solutions 44918 1/27/09 1:53 PM Page 801

802. 802
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–138.Determine the force Prequired to overcome
rolling resistance and pull the 50-kg roller up the inclined
plane with constant velocity. The coefficient of rolling
resistance is .a=15 mm
300 mm
P
30
30
8 Solutions 44918 1/27/09 1:53 PM Page 802

803. 803
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–139.Determine the force Prequired to overcome
rolling resistance and support the 50-kg roller if it rolls
down the inclined plane with constant velocity. The
coefficient of rolling resistance is .a=15 mm
300 mm
P
30
30
8 Solutions 44918 1/27/09 1:53 PM Page 803

804. 804
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–140.The cylinder is subjected to a load that has a
weight W. If the coefficients of rolling resistance for the
cylinder’s top and bottom surfaces are and ,
respectively, show that a horizontal force having a
magnitude of is required to move the
load and thereby roll the cylinder forward. Neglect the
weight of the cylinder.
P=[W(a
A+a
B)]>2r
a
Ba
A
W
P
r
A
B
•8–141.The 1.2-Mg steel beam is moved over a level
surface using a series of 30-mm-diameter rollers for which
the coefficient of rolling resistance is 0.4 mm at the ground
and 0.2 mm at the bottom surface of the beam. Determine
the horizontal force Pneeded to push the beam forward at
a constant speed.Hint:Use the result of Prob. 8–140.
P
8 Solutions 44918 1/27/09 1:53 PM Page 804

805. 805
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8–142.Determine the smallest horizontal force Pthat
must be exerted on the 200-lb block to move it forward. The
rollers each weigh 50 lb, and the coefficient of rolling
resistance at the top and bottom surfaces is .a=0.2 in
1.25 ft
P
1.25 ft
8–143.A single force Pis applied to the handle of the
drawer. If friction is neglected at the bottom and the
coefficient of static friction along the sides is ,
determine the largest spacing sbetween the symmetrically
placed handles so that the drawer does not bind at the
corners Aand Bwhen the force Pis applied to one of
the handles.
m
s=0.4
P
s
B
Drawer
1.25 m
0.3 mChest
A
8 Solutions 44918 1/27/09 1:53 PM Page 805

806. 806
*8–144.The semicircular thin hoop of weight Wand
center of gravity at Gis suspended by the small peg at A.A
horizontal force Pis slowly applied at B. If the hoop begins
to slip at Awhen , determine the coefficient of static
friction between the hoop and the peg.
u=30°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
P
R
A
B
G
2R
––
u
p
8 Solutions 44918 1/27/09 1:53 PM Page 806

807. 807
•8–145.The truck has a mass of 1.25 Mg and a center of
mass at G. Determine the greatest load it can pull if (a) the
truck has rear-wheel drive while the front wheels are free to
roll, and (b) the truck has four-wheel drive. The coefficient of
static friction between the wheels and the ground is ,
and between the crate and the ground, it is .m
s
œ=0.4
m
s=0.5
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
1.5 m 1 m
G
AB
600 mm
800 mm
8 Solutions 44918 1/27/09 1:53 PM Page 807

808. 808
8–146.Solve Prob. 8–145 if the truck and crate are
traveling up a 10° incline.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
1.5 m 1 m
G
AB
600 mm
800 mm
8 Solutions 44918 1/27/09 1:53 PM Page 808

809. 809
8–147.If block Ahas a mass of 1.5 kg, determine the
largest mass of block Bwithout causing motion of the
system. The coefficient of static friction between the blocks
and inclined planes is .m
s=0.2
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
45
60
A
B
8 Solutions 44918 1/27/09 1:53 PM Page 809

810. 810
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*8–148.The cone has a weight Wand center of gravity at
G. If a horizontal force Pis gradually applied to the string
attached to its vertex, determine the maximum coefficient
of static friction for slipping to occur.
G
P
h
3
4
h
1
4
h
1
4 h
1
4
8 Solutions 44918 1/27/09 1:53 PM Page 810

811. 811
•8–149.The tractor pulls on the fixed tree stump.
Determine the torque that must be applied by the engine to
the rear wheels to cause them to slip. The front wheels are
free to roll. The tractor weighs 3500 lb and has a center of
gravity at G. The coefficient of static friction between the
rear wheels and the ground is .m
s=0.5
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2 ft
5 ft 3 ft
BA
G
2 ft
O
8 Solutions 44918 1/27/09 1:53 PM Page 811

812. 812
8–150.The tractor pulls on the fixed tree stump. If the
coefficient of static friction between the rear wheels and
the ground is , determine if the rear wheels slip or
the front wheels lift off the ground as the engine provides
torque to the rear wheels. What is the torque needed to
cause this motion? The front wheels are free to roll. The
tractor weighs 2500 lb and has a center of gravity at G.
m
s=0.6
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2 ft
5 ft 3 ft
BA
G
2 ft
O
8 Solutions 44918 1/27/09 1:53 PM Page 812

813. 813
8–151.A roofer, having a mass of 70 kg, walks slowly in an
upright position down along the surface of a dome that has
a radius of curvature of If the coefficient of static
friction between his shoes and the dome is
determine the angle at which he first begins to slip.u
m
s=0.7,
r=20 m.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
60
20 m
u
*8–152.Column Dis subjected to a vertical load of
8000 lb. It is supported on two identical wedges Aand Bfor
which the coefficient of static friction at the contacting
surfaces between Aand Band between Band Cis
Determine the force Pneeded to raise the column and the
equilibrium force needed to hold wedge Astationary.
The contacting surface between Aand Dis smooth.
P¿
m
s=0.4.
D
10
10
C
B
A
P
P¿
8000 lb
8 Solutions 44918 1/27/09 1:53 PM Page 813

814. 814
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
D
10
10
C
B
A
P
P¿
8000 lb•8–153.Column Dis subjected to a vertical load of 8000 lb.
It is supported on two identical wedges Aand Bfor which
the coefficient of static friction at the contacting surfaces
between Aand Band between Band Cis If the
forces Pand are removed, are the wedges self-locking?
The contacting surface between Aand Dis smooth.
P¿
m
s=0.4.
8 Solutions 44918 1/27/09 1:53 PM Page 814

815. 815
•9–1.Determine the mass and the location of the center of
mass of the uniform parabolic-shaped rod. The mass
per unit length of the rod is .2 kg>m
(x
, y)
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
4 m
4 m
y
2
4x
9 Solutions 44918 1/28/09 2:34 PM Page 815

816. 816
9–2.The uniform rod is bent into the shape of a parabola
and has a weight per unit length of . Determine the
reactions at the fixed support A.
6 lb>ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
3 ft
3 ft
A
y
2
3x
9 Solutions 44918 1/28/09 2:34 PM Page 816

817. 817
9–3.Determine the distance to the center of mass of the
homogeneous rod bent into the shape shown. If the rod has
a mass per unit length of , determine the reactions
at the fixed support O.
0.5 kg>m
x
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
1 m
1 m
y
x
y
2
x
3
O
9 Solutions 44918 1/28/09 2:34 PM Page 817

818. 818
*9–4.Determine the mass and locate the center of mass
of the uniform rod. The mass per unit length of the
rod is .3 kg>m
(x, y)
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
2 m
4 m
y 4 x
2
9 Solutions 44918 1/28/09 2:34 PM Page 818

819. 819
•9–5.Determine the mass and the location of the center of
mass of the rod if its mass per unit length is
.m=m
0(1+x>L)
x
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
L
9 Solutions 44918 1/28/09 2:34 PM Page 819

820. 820
9–6.Determine the location ( , ) of the centroid of the wire.yx
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
y x

2
2 ft
4 ft
9–7.Locate the centroid of the circular rod. Express the
answer in terms of the radius rand semiarc angle .a
x y
x
C
r
r
–
x
a
a
9 Solutions 44918 1/28/09 2:34 PM Page 820

821. 821
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*9–8.Determine the area and the centroid of the area.(x, y) y
x
4 m
4 m
y
2
4x
9 Solutions 44918 1/28/09 2:34 PM Page 821

822. 822
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•9–9.Determine the area and the centroid of the area.(x, y) y
1 m
1 m
y
2
x
3
x
9 Solutions 44918 1/28/09 2:34 PM Page 822

823. 823
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–10.Determine the area and the centroid of the area.(x, y) y
x
3 ft
3 ft
y x
3

1
––
9
9 Solutions 44918 1/28/09 2:34 PM Page 823

824. 824
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–11.Determine the area and the centroid of the area.(x, y) y
x
2 ab
b
y
2
4ax
9 Solutions 44918 1/28/09 2:34 PM Page 824

825. 825
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*

9–12.Locate the centroid of the area.x
y
x
2 ft
x
1/2
2x
5/3
y
9 Solutions 44918 1/28/09 2:34 PM Page 825

826. 826
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•

9–13.Locate the centroid of the area.y y
x
2 ft
x
1/2
2x
5/3
y
9 Solutions 44918 1/28/09 2:34 PM Page 826

827. 827
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–14.Determine the area and the centroid of the area.(x, y) y
x
a
b
xy c
2

9 Solutions 44918 1/28/09 2:34 PM Page 827

828. 828
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–15.Determine the area and the centroid of the area.(x, y) y
x
a
h y x
2

h
––
a
2
9 Solutions 44918 1/28/09 2:34 PM Page 828

829. 829
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*9–16.Locate the centroid ( , ) of the area.yx y
x
2 m
1 m
y 1 – x
2
1
–
4
9 Solutions 44918 1/28/09 2:34 PM Page 829

830. 830
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•9–17.Determine the area and the centroid of the area.(x, y)
x
h
a
y x
2

h
––
a
2
y
9 Solutions 44918 1/28/09 2:34 PM Page 830

831. 831
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–18.The plate is made of steel having a density of
. If the thickness of the plate is 10 mm, determine
the horizontal and vertical components of reaction at the pin
Aand the tension in cable BC.
7850 kg>m
3
y
A
B
C
x
2 m
4 m
y
3
2x
9 Solutions 44918 1/28/09 2:34 PM Page 831

832. 832
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–19.Determine the location to the centroid Cof the
upper portion of the cardioid, .r=a(1-cos u)
x
r
r a (1 cos u)
C
_
x
x
y
u
9 Solutions 44918 1/28/09 2:34 PM Page 832

833. 833
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*9–20.The plate has a thickness of 0.5 in. and is made of
steel having a specific weight of . Determine the
horizontal and vertical components of reaction at the pin A
and the force in the cord at B.
490 lb>ft
3
y
A
B
x
3 ft
3 ft
y
x
2
––
3
9 Solutions 44918 1/28/09 2:34 PM Page 833

834. 834
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•9–21.Locate the centroid of the shaded area.x y
x
a
ka
y 2k(x
)
x
2
—
2a
9–22.Locate the centroid of the area.x y
x
2 in.
2 in.
y
1

0.5 in.
0.5 in.
x
9 Solutions 44918 1/28/09 2:34 PM Page 834

835. 835
9–23.Locate the centroid of the area.y
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
2 in.
2 in.
y
1

0.5 in.
0.5 in.
x
*9–24.Locate the centroid ( , ) of the area.yx y
x
9 ft
3 ft
y 9 x
2
9 Solutions 44918 1/28/09 2:34 PM Page 835

836. 836
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•9–25.Determine the area and the centroid of the
area.
(x, y) y
x
y
y x
3 ft
3 ft
x
3
––
9
9 Solutions 44918 1/28/09 2:34 PM Page 836

837. 837
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–26.Locate the centroid of the area.x y
x
1 m
y x
2

1 m
y
2
x
9–27.Locate the centroid of the area.y y
x
1 m
y x
2

1 m
y
2
x
9 Solutions 44918 1/28/09 2:34 PM Page 837

838. 838
*9–28.Locate the centroid of the area.x
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
h
a
y x
nh
––
a
n
•9–29.Locate the centroid of the area.y y
x
h
a
y x
nh
––
a
n
9 Solutions 44918 1/28/09 2:34 PM Page 838

839. 839
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–30.The steel plate is 0.3 m thick and has a density of
. Determine the location of its center of mass.
Also determine the horizontal and vertical reactions at the
pin and the reaction at the roller support.Hint:The normal
force at Bis perpendicular to the tangent at B, which is
found from tan .u=dy>dx
7850 kg>m
3
y
A
B
x
2 m
2 m
2 m
y
2
2x
9 Solutions 44918 1/28/09 2:34 PM Page 839

840. 840
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–31.Locate the centroid of the area.Hint:Choose
elements of thickness dyand length .[(2-y)-y
2
]
y
x
1 m
1 m
1 m
y x 2
y
2
x
9 Solutions 44918 1/28/09 2:34 PM Page 840

841. 841
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*9–32.Locate the centroid of the area.x y
x
1 ft
y 2x
2 ft
y
2
4x
•9–33.Locate the centroid of the area.y y
x
1 ft
y 2x
2 ft
y
2
4x
9 Solutions 44918 1/28/09 2:34 PM Page 841

842. 842
9–34.If the density at any point in the rectangular plate is
defined by , where is a constant,
determine the mass and locate the center of mass of the
plate. The plate has a thickness t.
x
r
0r=r
0(1+x>a)
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
a
x
b
––
2
b
––
2
9 Solutions 44918 1/28/09 2:34 PM Page 842

843. 843
9–35.Locate the centroid of the homogeneous solid
formed by revolving the shaded area about the yaxis.
y
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
z
y
2
(z a)
2
a
2
a
9 Solutions 44918 1/28/09 2:34 PM Page 843

844. 844
*9–36.Locate the centroid of the solid.z
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
z
x
a
z
a
1
a
a y()
2
9 Solutions 44918 1/28/09 2:34 PM Page 844

845. 845
•9–37.Locate the centroid of the homogeneous solid
formed by revolving the shaded area about the yaxis.
y
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
y
x
z
2
y
31
––
16
2 m
4 m
9 Solutions 44918 1/28/09 2:34 PM Page 845

846. 846
9–38.Locate the centroid of the homogeneous solid
frustum of the paraboloid formed by revolving the shaded
area about the zaxis.
z
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
a
z (a
2
y
2
)
h
–
a
2
h
–
2
h
–
2
z
x
y
9 Solutions 44918 1/28/09 2:34 PM Page 846

847. 847
9–39.Locate the centroid of the homogeneous solid
formed by revolving the shaded area about the yaxis.
y
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
z
z
2
y
2
9
3 ft
5 ft
4 ft
9 Solutions 44918 1/28/09 2:34 PM Page 847

848. 848
*9–40.Locate the center of mass of the circular cone
formed by revolving the shaded area about the yaxis. The
density at any point in the cone is defined by ,
where is a constant.r
0
r=(r
0 >h)y
y
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
z
h
a
z y a
a
––
h
9 Solutions 44918 1/28/09 2:34 PM Page 848

849. 849
•9–41.Determine the mass and locate the center of mass
of the hemisphere formed by revolving the shaded area
about the yaxis. The density at any point in the hemisphere
can be defined by , where is a constant.r
0r=r
0(1+y>a)
y
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
z
y
2
z
2
a
2
r
9 Solutions 44918 1/28/09 2:34 PM Page 849

850. 850
9–42.Determine the volume and locate the centroid
of the homogeneous conical wedge.
(y, z)
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
x
y
a
z y
a
––
h

h
9 Solutions 44918 1/28/09 2:34 PM Page 850

851. 851
9–43.The hemisphere of radius ris made from a stack of
very thin plates such that the density varies with height,
, where kis a constant. Determine its mass and the
distance to the center of mass G.z
r=kz
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
y
z
G
x
_
r
9 Solutions 44918 1/28/09 2:34 PM Page 851

852. 852
*9–44.Locate the centroid ( , ) of the uniform wire bent
in the shape shown.
yx
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
y
50 mm
150 mm
100 mm
20 mm
9 Solutions 44918 1/28/09 2:34 PM Page 852

853. 853
•9–45.Locate the centroid of the wire.(x, y, z)
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
z
400 mm
200 mm
y
9 Solutions 44918 1/28/09 2:34 PM Page 853

854. 854
9–46.Locate the centroid ( , , ) of the wire.zyx
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
z
6 in.
4 in.
y
x
9 Solutions 44918 1/28/09 2:34 PM Page 854

855. 855
9–47.Locate the centroid ( , , ) of the wire which is bent
in the shape shown.
zyx
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
y
z
4 in.
2 in.
2 in.
9 Solutions 44918 1/28/09 2:34 PM Page 855

856. 856
*9–48.The truss is made from seven members, each having
a mass per unit length of 6 kg/m. Locate the position ( , )
of the center of mass. Neglect the mass of the gusset plates
at the joints.
y
x
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
3 m
3 m
C
D
BA
E
y
x
3 m
9 Solutions 44918 1/28/09 2:34 PM Page 856

857. 857
•9–49.Locate the centroid of the wire. If the wire is
suspended from A, determine the angle segment ABmakes
with the vertical when the wire is in equilibrium.
(x, y)
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
A
CB
200 mm200 mm
60
9 Solutions 44918 1/28/09 2:34 PM Page 857

858. 858
9–50.Each of the three members of the frame has a mass
per unit length of 6 kg/m. Locate the position ( , ) of the
center of mass. Neglect the size of the pins at the joints and
the thickness of the members. Also, calculate the reactions
at the pin Aand roller E.
y
x
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
A
B
C D
E
4 m
6 m
7 m
4 m
9 Solutions 44918 1/28/09 2:34 PM Page 858

859. 859
9–51.Locate the centroid of the cross-sectional area
of the channel.
(x, y)
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
y
9 in.1 in.
1 in.
22 in.
1 in.
9 Solutions 44918 1/28/09 2:34 PM Page 859

860. 860
*9–52.Locate the centroid of the cross-sectional area of
the concrete beam.
y
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
y
3 in.
6 in.
3 in.
27 in.
3 in.
12 in.12 in.
9 Solutions 44918 1/28/09 2:34 PM Page 860

861. 861
•9–53.Locate the centroid of the cross-sectional area of
the built-up beam.
y
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
6 in.
1 in.
1 in.
1 in.1 in.
3 in.3 in.
6 in.
9 Solutions 44918 1/28/09 2:34 PM Page 861

862. 862
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–55.Locate the distance to the centroid of the
member’s cross-sectional area.
y
x
y
0.5 in.
6 in.
0.5 in.
1.5 in.
1 in.
3 in. 3 in.
9–54.Locate the centroid of the channel’s cross-
sectional area.
y
2 in.
4 in.
2 in.
12 in.
2 in.
C
y
9 Solutions 44918 1/28/09 2:34 PM Page 862

863. 863
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*9–56.Locate the centroid of the cross-sectional area of
the built-up beam.
y y
x
1.5 in.
1.5 in.
11.5 in.
1.5 in.
3.5 in.
4in.
1.5 in.
4 in.
9 Solutions 44918 1/28/09 2:34 PM Page 863

864. 864
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•9–57.The gravity wall is made of concrete. Determine the
location ( , ) of the center of mass Gfor the wall.yx
y
1.2 m
x
_
x
_
y
0.6 m 0.6 m
2.4 m
3 mG
0.4 m
9 Solutions 44918 1/28/09 2:34 PM Page 864

865. 865
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–58.Locate the centroid of the composite area.x
x
y
r
i
r
0
9 Solutions 44918 1/28/09 2:34 PM Page 865

866. 866
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–59.Locate the centroid of the composite area.(x, y)
x
y
4 in.
3 in.
3 in.
3 in.
9 Solutions 44918 1/28/09 2:34 PM Page 866

867. 867
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*9–60.Locate the centroid of the composite area.(x, y)
3 ft3 ft
1.5 ft
1 ft
y
x
9 Solutions 44918 1/28/09 2:34 PM Page 867

868. 868
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•9–61.Divide the plate into parts, and using the grid for
measurement, determine approximately the location ( , )
of the centroid of the plate.
y
x
y
x
200 mm
200 mm
9 Solutions 44918 1/28/09 2:34 PM Page 868

869. 869
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–62.To determine the location of the center of gravity of
the automobile it is first placed in a level position, with the
two wheels on one side resting on the scale platform P.In
this position the scale records a reading of . Then, one
side is elevated to a convenient height cas shown. The new
reading on the scale is . If the automobile has a total
weight of W, determine the location of its center of gravity
G .(x
, y)
W
2
W
1
b
P
c
G–
y
–
x
W
2
9 Solutions 44918 1/28/09 2:34 PM Page 869

870. 870
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–63.Locate the centroid of the cross-sectional area of
the built-up beam.
y y
x
450 mm
150 mm
150 mm
200 mm
20 mm
20 mm
9 Solutions 44918 1/28/09 2:34 PM Page 870

871. 871
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*9–64.Locate the centroid of the cross-sectional area of
the built-up beam.
y
200 mm
20 mm
50 mm
150 mm
y
x
200 mm
300 mm
10 mm
20 mm 20 mm
10 mm
9 Solutions 44918 1/28/09 2:34 PM Page 871

872. 872
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•9–65.The composite plate is made from both steel (A)
and brass (B) segments. Determine the mass and location
of its mass center G. Take and
r
br=8.74 Mg>m
3
.
r
st=7.85 Mg>m
3
1x
, y, z2
y
x
z
G
B
A
225 mm
150 mm
150 mm
30 mm
9 Solutions 44918 1/28/09 2:34 PM Page 872

873. 873
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–66.The car rests on four scales and in this position the
scale readings of both the front and rear tires are shown by
and . When the rear wheels are elevated to a height of
3 ft above the front scales, the new readings of the front
wheels are also recorded. Use this data to compute the
location and to the center of gravity Gof the car. The
tires each have a diameter of 1.98 ft.
y
x
F
BF
A
F
A 1129 lb 1168 lb 2297 lb
F
A 1269 lb 1307 lb 2576 lb
F
B 975 lb 984 lb 1959 lb
A
_
x
B
9.40 ft
3.0 ft
G
_
y
B
G
A
9 Solutions 44918 1/28/09 2:34 PM Page 873

874. 874
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–67.Uniform blocks having a length Land mass mare
stacked one on top of the other, with each block overhanging
the other by a distance d, as shown. If the blocks are glued
together, so that they will not topple over, determine the
location of the center of mass of a pile of nblocks.x
L
d
2d
y
x
9 Solutions 44918 1/28/09 2:34 PM Page 874

875. 875
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*9–68.Uniform blocks having a length Land mass mare
stacked one on top of the other, with each block
overhanging the other by a distance d, as shown. Show that
the maximum number of blocks which can be stacked in
this manner is .n6L>d
L
d
2d
y
x
9 Solutions 44918 1/28/09 2:34 PM Page 875

876. 876
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•9–69.Locate the center of gravity ( , ) of the sheet-
metal bracket if the material is homogeneous and has a
constant thickness. If the bracket is resting on the horizontal
x–yplane shown, determine the maximum angle of tilt
which it can have before it falls over, i.e., begins to rotate
about the yaxis.
u
z
x z
y
x
60 mm
60 mm
20 mm
20 mm
20 mm
20 mm
60 mm
10 mm dia. holes
80 mm
u
9 Solutions 44918 1/28/09 2:34 PM Page 876

877. 877
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–70.Locate the center of mass for the compressor
assembly. The locations of the centers of mass of the various
components and their masses are indicated and tabulated in
the figure. What are the vertical reactions at blocks Aand B
needed to support the platform?
x
y
1
2
3
4
Instrument panel
Filter system
Piping assembly
Liquid storage
Structural framework
230 kg
183 kg
120 kg
85 kg
468 kg
1
2
3
4
5
5
2.30 m
1.80 m
3.15 m
4.83 m
3.26 m
A B
2.42 m 2.87 m
1.64 m1.19 m
1.20 m
3.68 m
9 Solutions 44918 1/28/09 2:34 PM Page 877

878. 878
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–71.Major floor loadings in a shop are caused by the
weights of the objects shown. Each force acts through its
respective center of gravity G. Locate the center of gravity
( , ) of all these components.y
x
z
y
G
2
G
4G
3
G
1
x
600 lb
9 ft
7 ft
12 ft
6 ft
8 ft
4 ft 3 ft
5 ft
1500 lb
450 lb
280 lb
9 Solutions 44918 1/28/09 2:34 PM Page 878

879. 879
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*9–72.Locate the center of mass of the
homogeneous block assembly.
(x, y, z)
y
z
x 150 mm
250 mm
200 mm
150 mm
150 mm
100 mm
9 Solutions 44918 1/28/09 2:34 PM Page 879

880. 880
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•9–73.Locate the center of mass of the assembly. The
hemisphere and the cone are made from materials having
densities of and , respectively.4 Mg>m
3
8 Mg>m
3
z
y
z
x
100 mm
300 mm
9 Solutions 44918 1/28/09 2:34 PM Page 880

881. 881
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–74.Locate the center of mass of the assembly. The
cylinder and the cone are made from materials having
densities of and , respectively.9 Mg>m
3
5 Mg>m
3
z z
x
0.8 m
0.6 m0.4 m
0.2 m
y
9 Solutions 44918 1/28/09 2:34 PM Page 881

882. 882
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–75.Locate the center of gravity of the
homogeneous block assembly having a hemispherical hole.
(x, y, z)
y
z
x
1 in.
3 in.
2.25 in.
2.25 in.
2.5 in.
2.5 in.
1 in.
3 in.
9 Solutions 44918 1/28/09 2:34 PM Page 882

883. 883
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*9–76.Locate the center of gravity of the
assembly. The triangular and the rectangular blocks are
made from materials having specific weights of
and , respectively.0.1 lb>in
3
0.25 lb>in
3
(x
, y, z)
y
z
x
1 in.
3 in.
2.25 in.
2.25 in.
2.5 in.
2.5 in.
1 in.
3 in.
9 Solutions 44918 1/28/09 2:34 PM Page 883

884. 884
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•9–77.Determine the distance to the centroid of the
solid which consists of a cylinder with a hole of length
bored into its base.h=50 mm
x y
x
h
120 mm
40 mm
20 mm
9 Solutions 44918 1/28/09 2:34 PM Page 884

885. 885
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–78.Determine the distance hto which a hole must be
bored into the cylinder so that the center of mass of the
assembly is located at . The material has a
density of .8 Mg>m
3
x
=64 mm
y
x
h
120 mm
40 mm
20 mm
9 Solutions 44918 1/28/09 2:34 PM Page 885

886. 886
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–79.The assembly is made from a steel hemisphere,
, and an aluminum cylinder,
. Determine the mass center of the
assembly if the height of the cylinder is .h=200 mm
r
al=2.70 Mg>m
3
r
st=7.80 Mg>m
3
160 mm
h
z
y
x
80 mm
z
G
_
9 Solutions 44918 1/28/09 2:34 PM Page 886

887. 887
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*9–80.The assembly is made from a steel hemisphere,
, and an aluminum cylinder,
. Determine the height hof the cylinder
so that the mass center of the assembly is located at
.z=160 mm
r
al=2.70 Mg>m
3
r
st=7.80 Mg>m
3
160 mm
h
z
y
x
80 mm
z
G
_
9 Solutions 44918 1/28/09 2:35 PM Page 887

888. 888
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•9–81.The elevated water storage tank has a conical top
and hemispherical bottom and is fabricated using thin steel
plate. Determine how many square feet of plate is needed
to fabricate the tank.
6 ft
8 ft
8 ft
10 ft
9 Solutions 44918 1/28/09 2:35 PM Page 888

889. 889
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–82.The elevated water storage tank has a conical top
and hemispherical bottom and is fabricated using thin steel
plate. Determine the volume within the tank.
6 ft
8 ft
8 ft
10 ft
9 Solutions 44918 1/28/09 2:35 PM Page 889

890. 890
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–83.Determine the volume of the solid formed by
revolving the shaded area about the xaxis using the second
theorem of Pappus–Guldinus.The area and centroid of the
shaded area should first be obtained by using integration.
y
x
y
4 ft
4 ft
y
2
4x
9 Solutions 44918 1/28/09 2:35 PM Page 890

891. 891
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*9–84.Determine the surface area from Ato Bof the tank.
A
1 m
z
B
1.5 m
3 m
•9–85.Determine the volume within the thin-walled tank
from Ato B.
A
1 m
z
B
1.5 m
3 m
9 Solutions 44918 1/28/09 2:35 PM Page 891

892. 892
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–86.Determine the surface area of the roof of the
structure if it is formed by rotating the parabola about the
yaxis.
16 m
y
x
16 m
y 16 (x
2
/16)
9 Solutions 44918 1/28/09 2:35 PM Page 892

893. 893
9–87.Determine the surface area of the solid formed by
revolving the shaded area about the zaxis.360°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2 in.
3 in.
z
0.75 in.
0.75 in.
1 in.
0.5 in.
9 Solutions 44918 1/28/09 2:35 PM Page 893

894. 894
*9–88.Determine the volume of the solid formed by
revolving the shaded area about the zaxis.360°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2 in.
3 in.
z
0.75 in.
0.75 in.
1 in.
0.5 in.
•9–89.Determine the volume of the solid formed by
revolving the shaded area about the zaxis.360°
75 mm
75 mm
75 mm
75 mm
250 mm
z
300 mm
9 Solutions 44918 1/28/09 2:35 PM Page 894

895. 895
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–90.Determine the surface area and volume of the solid
formed by revolving the shaded area about the zaxis.360°
1 in.
z
2 in.
1 in.
9 Solutions 44918 1/28/09 2:35 PM Page 895

896. 896
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–91.Determine the surface area and volume of the solid
formed by revolving the shaded area about the zaxis.360°
z
75 mm 50 mm
400 mm
300 mm
50 mm
75 mm
*9–92.The process tank is used to store liquids during
manufacturing. Estimate both the volume of the tank and
its surface area. The tank has a flat top and a thin wall. 3 m 3 m
6 m
4 m
9 Solutions 44918 1/28/09 2:35 PM Page 896

897. 897
•9–93.The hopper is filled to its top with coal. Estimate
the volume of coal if the voids (air space) are 35 percent of
the volume of the hopper.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
0.2 m
4 m
z
1.2 m
1.5 m
9–94.The thin-wall tank is fabricated from a hemisphere
and cylindrical shell. Determine the vertical reactions that
each of the four symmetrically placed legs exerts on the
floor if the tank contains water which is 12 ft deep in
the tank. The specific gravity of water is . Neglect
the weight of the tank.
62.4 lb>ft
3
water
surface
8 ft
4 ft
6 ft
8 ft
9 Solutions 44918 1/28/09 2:35 PM Page 897

898. 898
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–95.Determine the approximate amount of paint needed
to cover the outside surface of the open tank. Assume that a
gallon of paint covers .400 ft
2
water
surface
8 ft
4 ft
6 ft
8 ft
*9–96.Determine the surface area of the tank, which
consists of a cylinder and hemispherical cap.
8 m
4 m
9 Solutions 44918 1/28/09 2:35 PM Page 898

899. 899
•9–97.Determine the volume of the thin-wall tank, which
consists of a cylinder and hemispherical cap.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
8 m
4 m
9 Solutions 44918 1/28/09 2:35 PM Page 899

900. 900
9–98.The water tank ABhas a hemispherical top and is
fabricated from thin steel plate. Determine the volume
within the tank.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
1.5 m
1.6 m
0.2 m
B
A
1.6 m
9 Solutions 44918 1/28/09 2:35 PM Page 900

901. 901
9–99.The water tank ABhas a hemispherical roof and is
fabricated from thin steel plate. If a liter of paint can cover
of the tank’s surface, determine how many liters are
required to coat the surface of the tank from Ato B.
3 m
2
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
1.5 m
1.6 m
0.2 m
B
A
1.6 m
9 Solutions 44918 1/28/09 2:35 PM Page 901

902. 902
*9–100.Determine the surface area and volume of the
wheel formed by revolving the cross-sectional area
about the zaxis.
360°
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4 in.
2 in.
1 in.
1 in.
1.5 in.
z
9 Solutions 44918 1/28/09 2:35 PM Page 902

903. 903
•9–101.Determine the outside surface area of the
storage tank.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
15 ft
4 ft
30 ft
9–102.Determine the volume of the thin-wall storage tank. 15 ft
4 ft
30 ft
9 Solutions 44918 1/28/09 2:35 PM Page 903

904. 904
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–103.Determine the height hto which liquid should be
poured into the conical paper cup so that it contacts half the
surface area on the inside of the cup.
100 mm
h
150 mm
*9–104.The tank is used to store a liquid having a specific
weight of . If it is filled to the top, determine the
magnitude of the force the liquid exerts on each of its two
sides ABDCand BDFE.
80 lb>ft
3
A
B
E
C
D
F
12 ft
8 ft
4 ft
6 ft
6 ft
9 Solutions 44918 1/28/09 2:35 PM Page 904

905. 905
•9–105.The concrete “gravity” dam is held in place by its
own weight. If the density of concrete is ,
and water has a density of , determine the
smallest dimension dthat will prevent the dam from
overturning about its end A.
r
w=1.0 Mg>m
3
r
c=2.5 Mg>m
3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
6 m
d
9 Solutions 44918 1/28/09 2:35 PM Page 905

906. 906
9–106.The symmetric concrete “gravity” dam is held in
place by its own weight. If the density of concrete is
, and water has a density of
, determine the smallest distance dat its
base that will prevent the dam from overturning about its
end A. The dam has a width of 8 m.
r
w=1.0 Mg>m
3
r
c=2.5 Mg>m
3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
d
1.5 m
9 m
9 Solutions 44918 1/28/09 2:35 PM Page 906

907. 907
9–107.The tank is used to store a liquid having a specific
weight of . If the tank is full, determine the
magnitude of the hydrostatic force on plates CDEFand
ABDC.
60 lb>ft
3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
B
A
D
E
y
z
5 ft
2 ft
2 ft
1.5 ft
1.5 ft
1.5 ft
1.5 ft
C
F
9 Solutions 44918 1/28/09 2:35 PM Page 907

908. 908
*9–108.The circular steel plate Ais used to seal the
opening on the water storage tank. Determine the
magnitude of the resultant hydrostatic force that acts on it.
The density of water is .r
w=1 Mg>m
3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
45
1 m
2 m
0.5 m
0.5 m
1 m
A
B
1 m
9 Solutions 44918 1/28/09 2:35 PM Page 908

909. 909
•9–109.The elliptical steel plate Bis used to seal the
opening on the water storage tank. Determine the
magnitude of the resultant hydrostatic force that acts on it.
The density of water is .r
w=1 Mg>m
3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
45
1 m
2 m
0.5 m
0.5 m
1 m
A
B
1 m
9 Solutions 44918 1/28/09 2:35 PM Page 909

910. 910
9–110.Determine the magnitude of the hydrostatic force
acting on the glass window if it is circular,A. The specific
weight of seawater is .g
w=63.6 lb>ft
3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4 ft
0.5 ft
0.5 ft
1 ft 1 ft
1 ft
A B
9 Solutions 44918 1/28/09 2:35 PM Page 910

911. 911
9–111.Determine the magnitude and location of the
resultant hydrostatic force acting on the glass window if it is
elliptical,B. The specific weight of seawater is
.g
w=63.6 lb>ft
3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4 ft
0.5 ft
0.5 ft
1 ft 1 ft
1 ft
A B
9 Solutions 44918 1/28/09 2:35 PM Page 911

912. 912
*9–112.Determine the magnitude of the hydrostatic force
acting per foot of length on the seawall. .g
w=62.4 lb>ft
3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
y
8 ft
2 ft
y 2x
2
9 Solutions 44918 1/28/09 2:35 PM Page 912

913. 913
•9–113.If segment ABof gate ABCis long enough, the
gate will be on the verge of opening. Determine the length
Lof this segment in order for this to occur. The gate is
hinged at Band has a width of 1 m. The density of water is
.r
w=1 Mg>m
3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
C
B
A
L
2 m
4 m
9 Solutions 44918 1/28/09 2:35 PM Page 913

914. 914
9–114.If L =2 m, determine the force the gate ABCexerts
on the smooth stopper at C. The gate is hinged at B, free at
A, and is 1 m wide. The density of water is .r
w=1 Mg>m
3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
C
B
A
L
2 m
4 m
9 Solutions 44918 1/28/09 2:35 PM Page 914

915. 915
9–115.Determine the mass of the counterweight Aif the
1-m-wide gate is on the verge of opening when the water is
at the level shown. The gate is hinged at Band held by the
smooth stop at C. The density of water is .r
w=1 Mg>m
3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
B
C
1 m
45
2 m
2 m
9 Solutions 44918 1/28/09 2:35 PM Page 915

916. 916
*9–116.If the mass of the counterweight at Ais 6500 kg,
determine the force the gate exerts on the smooth stop at C.
The gate is hinged at Band is 1-m wide. The density of
water is .r
w=1 Mg>m
3
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
A
B
C
1 m
45
2 m
2 m
9 Solutions 44918 1/28/09 2:35 PM Page 916

917. 917
•9–117.The concrete gravity dam is designed so that it is held
in position by its own weight. Determine the factor of safety
against overturning about point Aif . The factor of
safety is defined as the ratio of the stabilizing moment divided
by the overturning moment. The densities of concrete
and water are and ,
respectively. Assume that the dam does not slide.
r
w=1 Mg>m
3
r
conc=2.40 Mg>m
3
x=2 m
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
x
3
––
2
y x
2
6 m
2 m
A
9 Solutions 44918 1/28/09 2:35 PM Page 917

918. 918
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9 Solutions 44918 1/28/09 2:35 PM Page 918

919. 919
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
x
3
––
2
y x
2
6 m
2 m
A
9–118.The concrete gravity dam is designed so that it is
held in position by its own weight. Determine the minimum
dimension xso that the factor of safety against overturning
about point Aof the dam is 2. The factor of safety is defined
as the ratio of the stabilizing moment divided by the
overturning moment. The densities of concrete and water
are and , respectively.
Assume that the dam does not slide.
r
w=1 Mg>m
3
r
conc=2.40 Mg>m
3
9 Solutions 44918 1/28/09 2:35 PM Page 919

920. 920
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9 Solutions 44918 1/28/09 2:35 PM Page 920

921. 921
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–119.The underwater tunnel in the aquatic center is
fabricated from a transparent polycarbonate material
formed in the shape of a parabola. Determine the magnitude
of the hydrostatic force that acts per meter length along the
surface ABof the tunnel. The density of the water is
.r
w=1000 kg/m
3
y
x
2 m 2 m
2 m
4 m
y 4 x
2A
B
9 Solutions 44918 1/28/09 2:35 PM Page 921

922. 922
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*9–120.Locate the centroid of the shaded area.x
y
x
1 in. 1 in.
4 in.
1 in.
y x
2
•9–121.Locate the centroid of the shaded area.y y
x
1 in. 1 in.
4 in.
1 in.
y x
2
9 Solutions 44918 1/28/09 2:35 PM Page 922

923. 923
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–122.Locate the centroid of the beam’s cross-sectional
area.
y
100 mm
25 mm
25 mm
x
25 mm
y
50 mm 50 mm
y
75 mm75 mm
C
9–123.Locate the centroid of the solid.z z
x
2a
y
y
2
a a –
z
–
2
a
9 Solutions 44918 1/28/09 2:35 PM Page 923

924. 924
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*9–124.The steel plate is 0.3 m thick and has a density of
Determine the location of its center of mass. Also
compute the reactions at the pin and roller support.
7850 kg>m
3
.
A
B
x
y
y
2
2x
y x
2 m
2 m
2 m
•9–125.Locate the centroid ( , ) of the area.yx y
x
3 in.
1 in.
3 in.6 in.
9 Solutions 44918 1/28/09 2:35 PM Page 924

925. 925
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
9–126.Determine the location ( , ) of the centroid for
the structural shape. Neglect the thickness of the member.
yx
1.5 in. 1.5 in. 1.5 in. 1.5 in.
1 in.1 in.
3 in.
x
y
9–127.Locate the centroid of the shaded area.y
x
y
a
—
2
a
—
2
a
aa
9 Solutions 44918 1/28/09 2:35 PM Page 925

926. 926
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*9–128.The load over the plate varies linearly along the
sides of the plate such that . Determine
the resultant force and its position ( , ) on the plate.y
x
p=
2
3
[x(4-y)] kPa
p
3 m
4 m
y
x
8 kPa
•9–129.The pressure loading on the plate is described by
the function . Determine
the magnitude of the resultant force and coordinates of the
point where the line of action of the force intersects
the plate.
p=5-240>(x+1)+3406 Pa
p
x
y
6 m
5 m
100 Pa
300 Pa
9 Solutions 44918 1/28/09 2:35 PM Page 926

927. 927
•10–1.Determine the moment of inertia of the area about
the axis.x
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
2 m
2 m
y 0.25 x
3
10 Solutions 44918 1/28/09 4:21 PM Page 927

928. 928
10–2.Determine the moment of inertia of the area about
the axis.y
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
2 m
2 m
y 0.25 x
3
10 Solutions 44918 1/28/09 4:21 PM Page 928

929. 929
10–3.Determine the moment of inertia of the area about
the axis.x
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
y
2
x
3

1 m
1 m
10 Solutions 44918 1/28/09 4:21 PM Page 929

930. 930
*10–4.Determine the moment of inertia of the area about
the axis.y
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
y
2
x
3

1 m
1 m
10 Solutions 44918 1/28/09 4:21 PM Page 930

931. 931
•10–5.Determine the moment of inertia of the area about
the axis.x
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
y
2
2x
2 m
2 m
10 Solutions 44918 1/28/09 4:21 PM Page 931

932. 932
10–6.Determine the moment of inertia of the area about
the axis.y
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
y
2
2x
2 m
2 m
10 Solutions 44918 1/28/09 4:21 PM Page 932

933. 933
10–7.Determine the moment of inertia of the area about
the axis.x
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
O
y 2x
4
2 m
1 m
10 Solutions 44918 1/28/09 4:21 PM Page 933

934. 934
*10–8.Determine the moment of inertia of the area about
the axis.y
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
O
y 2x
4
2 m
1 m
10 Solutions 44918 1/28/09 4:21 PM Page 934

935. 935
•10–9.Determine the polar moment of inertia of the area
about the axis passing through point .Oz
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
O
y 2x
4
2 m
1 m
10 Solutions 44918 1/28/09 4:21 PM Page 935

936. 936
10–10.Determine the moment of inertia of the area about
the xaxis.
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
2 in.
8 in.
y x
3
10–11.Determine the moment of inertia of the area about
the yaxis.
y
x
2 in.
8 in.
y x
3
10 Solutions 44918 1/28/09 4:21 PM Page 936

937. 937
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•10–13.Determine the moment of inertia of the area
about the yaxis.
x
y
1 in.
2 in.

y

2 – 2 x
3
*10–12.Determine the moment of inertia of the area
about the xaxis.
x
y
1 in.
2 in.

y

2 – 2 x
3
10 Solutions 44918 1/28/09 4:21 PM Page 937

938. 938
10–14.Determine the moment of inertia of the area about
the xaxis. Solve the problem in two ways, using rectangular
differential elements: (a) having a thickness of dx, and
(b) having a thickness of dy.
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
1 in. 1 in.
4 in.
y 4 – 4x
2
x
y
10 Solutions 44918 1/28/09 4:21 PM Page 938

939. 939
10–15.Determine the moment of inertia of the area about
the yaxis. Solve the problem in two ways, using rectangular
differential elements: (a) having a thickness of dx, and
(b) having a thickness of dy.
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
1 in. 1 in.
4 in.
y 4 – 4x
2
x
y
10 Solutions 44918 1/28/09 4:21 PM Page 939

940. 940
*10–16.Determine the moment of inertia of the triangular
area about the xaxis.
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y (b x)
h
––
b
y
x
b
h
•10–17.Determine the moment of inertia of the triangular
area about the yaxis.
y (b x)
h
––
b
y
x
b
h
10 Solutions 44918 1/28/09 4:21 PM Page 940

941. 941
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–19.Determine the moment of inertia of the area about
the yaxis.
x
y
b
h
y

x
2

h
—
b
2
10–18.Determine the moment of inertia of the area about
the xaxis.
x
y
b
h
y

x
2

h
—
b
2
10 Solutions 44918 1/28/09 4:21 PM Page 941

942. 942
*10–20.Determine the moment of inertia of the area
about the xaxis.
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
y
3
x
2 in.
8 in.
10 Solutions 44918 1/28/09 4:21 PM Page 942

943. 943
•10–21.Determine the moment of inertia of the area
about the yaxis.
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
y
3
x
2 in.
8 in.
10 Solutions 44918 1/28/09 4:21 PM Page 943

944. 944
10–22.Determine the moment of inertia of the area about
the xaxis.
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
y π 2 cos ( x)––
8
2 in.
4 in.4 in.
π
10–23.Determine the moment of inertia of the area about
the yaxis.
y
x
y π 2 cos ( x)––
8
2 in.
4 in.4 in.
π
10 Solutions 44918 1/28/09 4:21 PM Page 944

945. 945
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*10–24.Determine the moment of inertia of the area
about the axis.x
y
x
x
2
y
2
r
2

r
0
0
10 Solutions 44918 1/28/09 4:21 PM Page 945

946. 946
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•10–25.Determine the moment of inertia of the area
about the axis.y
y
x
x
2
y
2
r
2

r
0
0
10 Solutions 44918 1/28/09 4:21 PM Page 946

947. 947
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–26.Determine the polar moment of inertia of the area
about the axis passing through point O.z
y
x
x
2
y
2
r
2

r
0
0
10–27.Determine the distance to the centroid of the
beam’s cross-sectional area; then find the moment of inertia
about the axis.x¿
y
2 in.
4 in.
1 in.1 in.
C
x¿
x
y
y
6 in.
10 Solutions 44918 1/28/09 4:21 PM Page 947

948. 948
*10–28.Determine the moment of inertia of the beam’s
cross-sectional area about the xaxis.
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2 in.
4 in.
1 in.1 in.
C
x¿
x
y
y
6 in.
•10–29.Determine the moment of inertia of the beam’s
cross-sectional area about the yaxis.
2 in.
4 in.
1 in.1 in.
C
x¿
x
y
y
6 in.
10 Solutions 44918 1/28/09 4:21 PM Page 948

949. 949
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–30.Determine the moment of inertia of the beam’s
cross-sectional area about the axis.x
y
x
15 mm15 mm
60 mm60 mm
100 mm
100 mm
50 mm
50 mm
15 mm
15 mm
10 Solutions 44918 1/28/09 4:22 PM Page 949

950. 950
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–31.Determine the moment of inertia of the beam’s
cross-sectional area about the axis.y
y
x
15 mm15 mm
60 mm60 mm
100 mm
100 mm
50 mm
50 mm
15 mm
15 mm
10 Solutions 44918 1/28/09 4:22 PM Page 950

951. 951
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*10–32.Determine the moment of inertia of the
composite area about the axis.x
y
x
150 mm
300 mm
150 mm
100 mm
100 mm
75 mm
10 Solutions 44918 1/28/09 4:22 PM Page 951

952. 952
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•10–33.Determine the moment of inertia of the
composite area about the axis.y
y
x
150 mm
300 mm
150 mm
100 mm
100 mm
75 mm
10 Solutions 44918 1/28/09 4:22 PM Page 952

953. 953
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–34.Determine the distance to the centroid of the
beam’s cross-sectional area; then determine the moment of
inertia about the axis.x¿
y
x
x¿
C
y
50 mm 50 mm
75 mm
25 mm
25 mm
75 mm
100 mm
_
y
25 mm
25 mm
100 mm
10 Solutions 44918 1/28/09 4:22 PM Page 953

954. 954
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–35.Determine the moment of inertia of the beam’s
cross-sectional area about the yaxis.
x
x¿
C
y
50 mm 50 mm
75 mm
25 mm
25 mm
75 mm
100 mm
_
y
25 mm
25 mm
100 mm
*10–36.Locate the centroid of the composite area, then
determine the moment of inertia of this area about the
centroidal axis.x¿
y
y
1 in.1 in.
2 in.
3 in.
5 in.
x¿
x
y
3 in.
C
10 Solutions 44918 1/28/09 4:22 PM Page 954

955. 955
•10–37.Determine the moment of inertia of the
composite area about the centroidal axis.y
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
1 in.1 in.
2 in.
3 in.
5 in.
x¿
x
y
3 in.
C
10–38.Determine the distance to the centroid of the
beam’s cross-sectional area; then find the moment of inertia
about the axis.x¿
y
300 mm
100 mm
200 mm
50 mm50 mm
y
C
x
y
x¿
10 Solutions 44918 1/28/09 4:22 PM Page 955

956. 956
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–39.Determine the moment of inertia of the beam’s
cross-sectional area about the xaxis.
300 mm
100 mm
200 mm
50 mm50 mm
y
C
x
y
x¿
10 Solutions 44918 1/28/09 4:22 PM Page 956

957. 957
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*10–40.Determine the moment of inertia of the beam’s
cross-sectional area about the yaxis.
300 mm
100 mm
200 mm
50 mm50 mm
y
C
x
y
x¿
10 Solutions 44918 1/28/09 4:22 PM Page 957

958. 958
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•10–41.Determine the moment of inertia of the beam’s
cross-sectional area about the axis.x
y
50 mm 50 mm
15 mm
115 mm
115 mm
7.5 mm
x
15 mm
10 Solutions 44918 1/28/09 4:22 PM Page 958

959. 959
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–42.Determine the moment of inertia of the beam’s
cross-sectional area about the axis.y
y
50 mm 50 mm
15 mm
115 mm
115 mm
7.5 mm
x
15 mm
10 Solutions 44918 1/28/09 4:22 PM Page 959

960. 960
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–43.Locate the centroid of the cross-sectional area
for the angle. Then find the moment of inertia about the
centroidal axis.x¿
I
x¿
y
6 in.
2 in.
6 in.
x
2 in.
C x¿
y¿y
–
x
–
y
*10–44.Locate the centroid of the cross-sectional area
for the angle. Then find the moment of inertia about the
centroidal axis.y¿
I
y¿
x
6 in.
2 in.
6 in.
x
2 in.
C x¿
y¿y
–
x
–
y
10 Solutions 44918 1/28/09 4:22 PM Page 960

961. 961
•10–45.Determine the moment of inertia of the
composite area about the axis.x
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
150 mm 150 mm
150 mm
150 mm
10 Solutions 44918 1/28/09 4:22 PM Page 961

962. 962
10–46.Determine the moment of inertia of the composite
area about the axis.y
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
150 mm 150 mm
150 mm
150 mm
10 Solutions 44918 1/28/09 4:22 PM Page 962

963. 963
10–47.Determine the moment of inertia of the composite
area about the centroidal axis.y
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
x¿
y
C
400 mm
240 mm
50 mm
150 mm 150 mm
50 mm
50 mm
y
10 Solutions 44918 1/28/09 4:22 PM Page 963

964. 964
*10–48.Locate the centroid of the composite area, then
determine the moment of inertia of this area about the
axis.x¿
y
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
x¿
y
C
400 mm
240 mm
50 mm
150 mm 150 mm
50 mm
50 mm
y
10 Solutions 44918 1/28/09 4:22 PM Page 964

965. 965
•10–49.Determine the moment of inertia of the
section. The origin of coordinates is at the centroid C.
I
x¿
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
200 mm
600 mm
20 mm
C
y¿
x¿
200 mm
20 mm
20 mm
10–50.Determine the moment of inertia of the section.
The origin of coordinates is at the centroid C.
I
y¿
200 mm
600 mm
20 mm
C
y¿
x¿
200 mm
20 mm
20 mm
10 Solutions 44918 1/28/09 4:22 PM Page 965

966. 966
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–51.Determine the beam’s moment of inertia about
the centroidal axis.x
I
xy
x
50 mm
50 mm
100 mm
15 mm
15 mm
10 mm
100 mm
C
10 Solutions 44918 1/28/09 4:22 PM Page 966

967. 967
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*10–52.Determine the beam’s moment of inertia about
the centroidal axis.y
I
y
y
x
50 mm
50 mm
100 mm
15 mm
15 mm
10 mm
100 mm
C
10 Solutions 44918 1/28/09 4:22 PM Page 967

968. 968
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•10–53.Locate the centroid of the channel’s cross-
sectional area, then determine the moment of inertia of the
area about the centroidal axis.x¿
y
6 in.
0.5 in.
0.5 in.
0.5 in.
6.5 in. 6.5 in.
y
C
x¿
x
y
10 Solutions 44918 1/28/09 4:22 PM Page 968

969. 969
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–54.Determine the moment of inertia of the area of the
channel about the axis.y
6 in.
0.5 in.
0.5 in.
0.5 in.
6.5 in. 6.5 in.
y
C
x¿
x
y
10 Solutions 44918 1/28/09 4:22 PM Page 969

970. 970
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–55.Determine the moment of inertia of the cross-
sectional area about the axis.x
100 mm10 mm
10 mm
180 mm
x
y¿y
C
100 mm
10 mm
x
10 Solutions 44918 1/28/09 4:22 PM Page 970

971. 971
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*10–56.Locate the centroid of the beam’s cross-
sectional area, and then determine the moment of inertia of
the area about the centroidal axis.y¿
x
100 mm10 mm
10 mm
180 mm
x
y¿y
C
100 mm
10 mm
x
10 Solutions 44918 1/28/09 4:22 PM Page 971

972. 972
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•10–57.Determine the moment of inertia of the beam’s
cross-sectional area about the axis.x
y
100 mm
12 mm
125 mm
75 mm12 mm
75 mm
x
12 mm
25 mm
125 mm
12 mm
10 Solutions 44918 1/28/09 4:22 PM Page 972

973. 973
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–58.Determine the moment of inertia of the beam’s
cross-sectional area about the axis.y
y
100 mm
12 mm
125 mm
75 mm12 mm
75 mm
x
12 mm
25 mm
125 mm
12 mm
10 Solutions 44918 1/28/09 4:22 PM Page 973

974. 974
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–59.Determine the moment of inertia of the beam’s
cross-sectional area with respect to the axis passing
through the centroid Cof the cross section. .y
=104.3 mm
x¿
x¿
C
A
B
–
y
150 mm
15 mm
35 mm
50 mm
*10–60.Determine the product of inertia of the parabolic
area with respect to the xand yaxes.
y
x
y 2x
2
2 in.
1 in.
10 Solutions 44918 1/28/09 4:22 PM Page 974

975. 975
•10–61.Determine the product of inertia of the right
half of the parabolic area in Prob. 10–60, bounded by the
lines . and .x=0y=2 in
I
xy
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
y 2x
2
2 in.
1 in.
10 Solutions 44918 1/28/09 4:22 PM Page 975

976. 976
10–62.Determine the product of inertia of the quarter
elliptical area with respect to the and axes.yx
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
a
b
x
1
x
2
––
a
2
y
2
––
b
2
10 Solutions 44918 1/28/09 4:22 PM Page 976

977. 977
10–63.Determine the product of inertia for the area with
respect to the xand yaxes.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
8 in.
2 in.
y
3
x
10 Solutions 44918 1/28/09 4:22 PM Page 977

978. 978
*10–64.Determine the product of inertia of the area with
respect to the and axes.yx
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
y
x
––
4
4 in.
4 in.
(x 8)
10 Solutions 44918 1/28/09 4:22 PM Page 978

979. 979
•10–65.Determine the product of inertia of the area with
respect to the and axes.yx
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
2 m
3 m
8y x
3
2x
2
4x
10 Solutions 44918 1/28/09 4:22 PM Page 979

980. 980
10–66.Determine the product of inertia for the area with
respect to the xand yaxes.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
2 m
1 m
y
2
1 0.5x
10 Solutions 44918 1/28/09 4:22 PM Page 980

981. 981
10–67.Determine the product of inertia for the area with
respect to the xand yaxes.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
y
3
x
b
h
3
h
b
10 Solutions 44918 1/28/09 4:22 PM Page 981

982. 982
*10–68.Determine the product of inertia for the area of
the ellipse with respect to the xand yaxes.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
4 in.
2 in.
x
2
4y
2
16
•10–69.Determine the product of inertia for the parabolic
area with respect to the xand yaxes.
y
4 in.
2 in.
x
y
2
x
10 Solutions 44918 1/28/09 4:22 PM Page 982

983. 983
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–70.Determine the product of inertia of the composite
area with respect to the and axes.yx
1.5 in.
y
x
2 in.
2 in.
2 in. 2 in.
10 Solutions 44918 1/28/09 4:22 PM Page 983

984. 984
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–71.Determine the product of inertia of the cross-
sectional area with respect to the xand yaxes that have
their origin located at the centroid C.
4 in.
4 in.
x
y
5 in.
1 in.
1 in.
3.5 in.
0.5 in.
C
*10–72.Determine the product of inertia for the beam’s
cross-sectional area with respect to the xand yaxes that
have their origin located at the centroid C.
x
y
5 mm
30 mm
5 mm
50 mm
7.5 mm
C
17.5 mm
10 Solutions 44918 1/28/09 4:22 PM Page 984

985. 985
•10–73.Determine the product of inertia of the beam’s
cross-sectional area with respect to the xand yaxes.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
x
y
300 mm
100 mm
10 mm
10 mm
10 mm
10–74.Determine the product of inertia for the beam’s
cross-sectional area with respect to the xand yaxes that
have their origin located at the centroid C.
1 in.
5 in.5 in.
5 in.
1 in.
C
5 in.
x
y
1 in.
0.5 in.
10 Solutions 44918 1/28/09 4:22 PM Page 985

986. 986
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–75.Locate the centroid of the beam’s cross-sectional
area and then determine the moments of inertia and the
product of inertia of this area with respect to the and
axes. The axes have their origin at the centroid C.v
u
x
y
x
u
x
200 mm
200 mm
175 mm
20 mm
20 mm
20 mm
C
60
v
10 Solutions 44918 1/28/09 4:22 PM Page 986

987. 987
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*10–76.Locate the centroid ( , ) of the beam’s cross-
sectional area, and then determine the product of inertia of
this area with respect to the centroidal and axes.y¿x¿
y
x
x¿
y¿
x
y
300 mm
200 mm
10 mm
10 mm
C
y
x
10 mm
100 mm
10 Solutions 44918 1/28/09 4:22 PM Page 987

988. 988
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•10–77.Determine the product of inertia of the beam’s
cross-sectional area with respect to the centroidal and
axes.y
x
x
C
150 mm
100 mm
100 mm
10 mm
10 mm
10 mm
y
150 mm
5 mm
10 Solutions 44918 1/28/09 4:22 PM Page 988

989. 989
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–78.Determine the moments of inertia and the product
of inertia of the beam’s cross-sectional area with respect to
the and axes.vu
3 in.
1.5 in.
3 in.
y
u
x
1.5 in.
C
v
30
10 Solutions 44918 1/28/09 4:22 PM Page 989

990. 990
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–79.Locate the centroid of the beam’s cross-sectional
area and then determine the moments of inertia and the
product of inertia of this area with respect to the and
axes.v
u
y
y
x
u
8 in.
4 in.
0.5 in.
0.5 in.
4.5 in.
0.5 in.
y
4.5 in.
C
v
60
10 Solutions 44918 1/28/09 4:22 PM Page 990

991. 991
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10 Solutions 44918 1/28/09 4:22 PM Page 991

992. 992
*10–80.Locate the centroid and of the cross-sectional
area and then determine the orientation of the principal
axes, which have their origin at the centroid Cof the area.
Also, find the principal moments of inertia.
y
x
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
y
x
6 in.
0.5 in.
6 in.
y
x
0.5 in.
C
10 Solutions 44918 1/28/09 4:22 PM Page 992

993. 993
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10 Solutions 44918 1/28/09 4:22 PM Page 993

994. 994
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•10–81.Determine the orientation of the principal axes,
which have their origin at centroid Cof the beam’s cross-
sectional area. Also, find the principal moments of inertia.
y
C
x
100 mm
100 mm
20 mm
20 mm
20 mm
150 mm
150 mm
10 Solutions 44918 1/28/09 4:22 PM Page 994

995. 995
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10 Solutions 44918 1/28/09 4:22 PM Page 995

996. 996
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–82.Locate the centroid of the beam’s cross-sectional
area and then determine the moments of inertia of this area
and the product of inertia with respect to the and axes.
The axes have their origin at the centroid C.
vu
y
200 mm
25 mm
y
u
C
x
y
60
75 mm75 mm
25 mm25 mm v
10 Solutions 44918 1/28/09 4:22 PM Page 996

997. 997
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10 Solutions 44918 1/28/09 4:22 PM Page 997

998. 998
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–83.Solve Prob. 10–75 using Mohr’s circle.
10 Solutions 44918 1/28/09 4:22 PM Page 998

999. 999
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*10–84.Solve Prob. 10–78 using Mohr’s circle.
10 Solutions 44918 1/28/09 4:22 PM Page 999

1000. 1000
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•10–85.Solve Prob. 10–79 using Mohr’s circle.
10 Solutions 44918 1/28/09 4:22 PM Page 1000

1001. 1001
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–86.Solve Prob. 10–80 using Mohr’s circle.
10 Solutions 44918 1/28/09 4:22 PM Page 1001

1002. 1002
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–87.Solve Prob. 10–81 using Mohr’s circle.
10 Solutions 44918 1/28/09 4:22 PM Page 1002

1003. 1003
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*10–88.Solve Prob. 10–82 using Mohr’s circle.
10 Solutions 44918 1/28/09 4:22 PM Page 1003

1004. 1004
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•10–89.Determine the mass moment of inertia of the
cone formed by revolving the shaded area around the axis.
The density of the material is . Express the result in terms
of the mass of the cone.m
r
z
I
z
z
z (r
0 y)
h
––
y
h
x
r
0
r
0
10 Solutions 44918 1/28/09 4:22 PM Page 1004

1005. 1005
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–90.Determine the mass moment of inertia of the
right circular cone and express the result in terms of the
total mass mof the cone. The cone has a constant density .r
I
x
h
y
x
r
r
–
h
xy
10 Solutions 44918 1/28/09 4:22 PM Page 1005

1006. 1006
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–91.Determine the mass moment of inertia of the
slender rod. The rod is made of material having a variable
density , where is constant. The cross-
sectional area of the rod is . Express the result in terms of
the mass mof the rod.
A
r
0r=r
0(1+x>l)
I
y
x
y
l
z
10 Solutions 44918 1/28/09 4:22 PM Page 1006

1007. 1007
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*10–92.Determine the mass moment of inertia of the
solid formed by revolving the shaded area around the
axis. The density of the material is . Express the result in
terms of the mass of the solid.m
r
y
I
y
z

y
2
x
y
z
1
4
2 m
1 m
10 Solutions 44918 1/28/09 4:22 PM Page 1007

1008. 1008
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•10–93.The paraboloid is formed by revolving the shaded
area around the xaxis. Determine the radius of gyration .
The density of the material is .r=5 Mg>m
3
k
x
y
x
100 mm
y
2
50 x
200 mm
10 Solutions 44918 1/28/09 4:22 PM Page 1008

1009. 1009
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–94.Determine the mass moment of inertia of the
solid formed by revolving the shaded area around the axis.
The density of the material is . Express the result in terms
of the mass of the semi-ellipsoid.m
r
y
I
y
y
a
b
z
x
1
y
2
––
a
2
z
2
––
b
2
10 Solutions 44918 1/28/09 4:22 PM Page 1009

1010. 1010
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–95.The frustum is formed by rotating the shaded area
around the xaxis. Determine the moment of inertia and
express the result in terms of the total mass mof the
frustum. The material has a constant density .r
I
x
y
x
2b
b
–
a
x by
a
b
10 Solutions 44918 1/28/09 4:22 PM Page 1010

1011. 1011
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*10–96.The solid is formed by revolving the shaded area
around the yaxis. Determine the radius of gyration The
specific weight of the material is g=380 lb>ft
3
.
k
y.
y
3
9x
3 in.
x
3 in.
y
10 Solutions 44918 1/28/09 4:22 PM Page 1011

1012. 1012
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•10–97.Determine the mass moment of inertia of the
solid formed by revolving the shaded area around the axis.
The density of the material is .r=7.85 Mg>m
3
z
I
z
2 m
4 m
z
2
8y
z
y
x
10 Solutions 44918 1/28/09 4:22 PM Page 1012

1013. 1013
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–98.Determine the mass moment of inertia of the
solid formed by revolving the shaded area around the axis.
The solid is made of a homogeneous material that weighs
400 lb.
z
I
z
4 ft
8 ft
y
x
z y
3
––
2
z
10 Solutions 44918 1/28/09 4:22 PM Page 1013

1014. 1014
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–99.Determine the mass moment of inertia of the
solid formed by revolving the shaded area around the axis.
The total mass of the solid is .1500 kg
y
I
y
y
x
z
4 m
2 m
z
2
y
31
––
16
O
10 Solutions 44918 1/28/09 4:22 PM Page 1014

1015. 1015
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*10–100.Determine the mass moment of inertia of the
pendulum about an axis perpendicular to the page and
passing through point O. The slender rod has a mass of 10 kg
and the sphere has a mass of 15 kg.
450 mm
A
O
B
100 mm
10 Solutions 44918 1/28/09 4:22 PM Page 1015

1016. 1016
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•10–101.The pendulum consists of a disk having a mass of
6 kg and slender rods ABand DCwhich have a mass per unit
length of . Determine the length Lof DCso that the
center of mass is at the bearing O. What is the moment of
inertia of the assembly about an axis perpendicular to the
page and passing through point O?
2 kg>m
O
0.2 m
L
A B
C
D
0.8 m 0.5 m
10 Solutions 44918 1/28/09 4:22 PM Page 1016

1017. 1017
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–102.Determine the mass moment of inertia of the
2-kg bent rod about the zaxis.
300 mm
300 mm
z
y
x
10 Solutions 44918 1/28/09 4:22 PM Page 1017

1018. 1018
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–103.The thin plate has a mass per unit area of
. Determine its mass moment of inertia about the
yaxis.
10 kg>m
2
200 mm
200 mm
200 mm
200 mm
200 mm
200 mm
200 mm
200 mm
z
y
x
100 mm
100 mm
10 Solutions 44918 1/28/09 4:22 PM Page 1018

1019. 1019
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*10–104.The thin plate has a mass per unit area of
. Determine its mass moment of inertia about the
zaxis.
10 kg>m
2
200 mm
200 mm
200 mm
200 mm
200 mm
200 mm
200 mm
200 mm
z
y
x
100 mm
100 mm
10 Solutions 44918 1/28/09 4:22 PM Page 1019

1020. 1020
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•10–105.The pendulum consists of the 3-kg slender rod
and the 5-kg thin plate. Determine the location of the
center of mass Gof the pendulum; then find the mass
moment of inertia of the pendulum about an axis
perpendicular to the page and passing through G.
y
G
2 m
1 m
0.5 m
y
O
10 Solutions 44918 1/28/09 4:22 PM Page 1020

1021. 1021
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–106.The cone and cylinder assembly is made of
homogeneous material having a density of .
Determine its mass moment of inertia about the axis.z
7.85 Mg>m
3
300 mm
300 mm
z
x
y
150 mm
150 mm
10 Solutions 44918 1/28/09 4:22 PM Page 1021

1022. 1022
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–107.Determine the mass moment of inertia of the
overhung crank about the xaxis. The material is steel
having a density of .r=7.85 Mg>m
3
90 mm
50 mm
20 mm
20 mm
20 mm
x
x¿
50 mm
30 mm
30 mm
30 mm
180 mm
10 Solutions 44918 1/28/09 4:22 PM Page 1022

1023. 1023
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*10–108.Determine the mass moment of inertia of the
overhung crank about the axis. The material is steel
having a density of .r=7.85 Mg>m
3
x¿
90 mm
50 mm
20 mm
20 mm
20 mm
x
x¿
50 mm
30 mm
30 mm
30 mm
180 mm
10 Solutions 44918 1/28/09 4:22 PM Page 1023

1024. 1024
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•10–109.If the large ring, small ring and each of the spokes
weigh 100 lb, 15 lb, and 20 lb, respectively, determine the mass
moment of inertia of the wheel about an axis perpendicular
to the page and passing through point A.
A
O
1 ft
4 ft
10 Solutions 44918 1/28/09 4:22 PM Page 1024

1025. 1025
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–110.Determine the mass moment of inertia of the thin
plate about an axis perpendicular to the page and passing
through point O. The material has a mass per unit area of
.20 kg>m
2
400 mm
150 mm
400 mm
O
50 mm
50 mm
150 mm
150 mm 150 mm
10 Solutions 44918 1/28/09 4:22 PM Page 1025

1026. 1026
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–111.Determine the mass moment of inertia of the thin
plate about an axis perpendicular to the page and passing
through point O. The material has a mass per unit area of
.20 kg>m
2
200 mm
200 mm
O
200 mm
10 Solutions 44918 1/28/09 4:22 PM Page 1026

1027. 1027
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*10–112.Determine the moment of inertia of the beam’s
cross-sectional area about the xaxis which passes through
the centroid C.
C
x
y
d
2
d
2
d
2
d
2 60
60
•10–113.Determine the moment of inertia of the beam’s
cross-sectional area about the yaxis which passes through
the centroid C.
C
x
y
d
2
d
2
d
2
d
2 60
60
10 Solutions 44918 1/28/09 4:22 PM Page 1027

1028. 1028
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–114.Determine the moment of inertia of the beam’s
cross-sectional area about the xaxis.
aa
aa
a
––
2
y

– x
y
x
10 Solutions 44918 1/28/09 4:22 PM Page 1028

1029. 1029
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–115.Determine the moment of inertia of the beam’s
cross-sectional area with respect to the axis passing
through the centroid C.
x¿
0.5 in.
0.5 in.
4 in.
2.5 in.
C
x¿
0.5 in.
_
y
*10–116.Determine the product of inertia for the angle’s
cross-sectional area with respect to the and axes
having their origin located at the centroid C.Assume all
corners to be right angles.
y¿x¿
C
57.37 mm
x¿
y¿
200 mm
20 mm
57.37 mm
200 mm
20 mm
10 Solutions 44918 1/28/09 4:22 PM Page 1029

1030. 1030
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–118.Determine the moment of inertia of the area
about the xaxis.
y
4y 4 –

x
2
1 ft
x
2 ft
•10–117.Determine the moment of inertia of the area
about the yaxis.
y
4y 4 –

x
2
1 ft
x
2 ft
10 Solutions 44918 1/28/09 4:22 PM Page 1030

1031. 1031
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
10–119.Determine the moment of inertia of the area
about the xaxis. Then, using the parallel-axis theorem, find
the moment of inertia about the axis that passes through
the centroid Cof the area. .y
=120 mm
x¿
1
–––
200
200 mm
200 mm
y
x
x¿
–
y
C
y x
2
10 Solutions 44918 1/28/09 4:22 PM Page 1031

1032. 1032
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*10–120.The pendulum consists of the slender rod OA,
which has a mass per unit length of . The thin disk
has a mass per unit area of .Determine the
distance to the center of mass Gof the pendulum; then
calculate the moment of inertia of the pendulum about an
axis perpendicular to the page and passing through G.
y
12 kg>m
2
3 kg>m
G
1.5 m
A
y
O
0.3 m
0.1 m
10 Solutions 44918 1/28/09 4:22 PM Page 1032

1033. 1033
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•10–121.Determine the product of inertia of the area
with respect to the xand yaxes.
y x
3
y
1 m
1 m
x
10 Solutions 44918 1/28/09 4:22 PM Page 1033

1034. 1034
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•11–1.The 200-kg crate is on the lift table at the position
. Determine the force in the hydraulic cylinder AD
for equilibrium. Neglect the mass of the lift table’s
components.
u=30°
A
B
C
D E
HI
F
1.2 m
1.2 m
u
11 Solutions 44918 1/29/09 12:42 PM Page 1034

1035. 11–2.The uniform rod OAhas a weight of 10 lb. When the
rod is in a vertical position, , the spring is unstretched.
Determine the angle for equilibrium if the end of the spring
wraps around the periphery of the disk as the disk turns.
u
u
= 0°
O
u
A
k 30 lb/ft
2 ft
0.5 ft
1035
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11 Solutions 44918 1/29/09 12:42 PM Page 1035

1036. 1036
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–3.The “Nuremberg scissors” is subjected to a
horizontal force of . Determine the angle for
equilibrium. The spring has a stiffness of and
is unstretched when .u=15°
k=15 kN>m
uP=600 N
P
200 mm
200 mm
A
C
D
E
B
k
u
11 Solutions 44918 1/29/09 12:42 PM Page 1036

1037. 1037
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*11–4.The “Nuremberg scissors” is subjected to a
horizontal force of . Determine the stiffness kof
the spring for equilibrium when . The spring is
unstretched when .u=15°
u=60°
P=600 N
P
200 mm
200 mm
A
C
D
E
B
k
u
11 Solutions 44918 1/29/09 12:42 PM Page 1037

1038. 1038
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•11–5.Determine the force developed in the spring
required to keep the 10 lb uniform rod ABin equilibrium
when .u=35°
A
u
B
k 15 lb/ft
6 ft
M = 10 lb
ft
11 Solutions 44918 1/29/09 12:42 PM Page 1038

1039. 1039
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–6.If a force of is applied to the handle of the
mechanism, determine the force the screw exerts on the cork
of the bottle.The screw is attached to the pin at Aand passes
through the collar that is attached to the bottle neck at B.
P=5 lb
3 in.
D
B
A
u 30°
P 5 lb
11 Solutions 44918 1/29/09 12:42 PM Page 1039

1040. 1040
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–7.The pin-connected mechanism is constrained at Aby
a pin and at Bby a roller. If , determine the angle
for equilibrium. The spring is unstretched when .
Neglect the weight of the members.
u=45°u
P=10 lb
0.5 ft
B PA
u
0.5 ft0.5 ft
k 50 lb/ft
11 Solutions 44918 1/29/09 12:42 PM Page 1040

1041. 1041
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*11–8.The pin-connected mechanism is constrained by a
pin at Aand a roller at B. Determine the force Pthat must
be applied to the roller to hold the mechanism in
equilibrium when . The spring is unstretched when
. Neglect the weight of the members.u=45°
u=30°
0.5 ft
B PA
u
0.5 ft0.5 ft
k 50 lb/ft
11 Solutions 44918 1/29/09 12:42 PM Page 1041

1042. 1042
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•11–9.If a force is applied to the lever arm of
the toggle press, determine the clamping force developed in
the block when . Neglect the weight of the block.u=45°
P=100 N
200 mm
200 mm
500 mm
B
C
D
E
F
A
P
u
u
11 Solutions 44918 1/29/09 12:42 PM Page 1042

1043. 1043
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–10.When the forces are applied to the handles of the
bottle opener, determine the pulling force developed on
the cork.
A C
B D
E
F
90 mm 90 mm
15 mm
15 mm
5 N 5 NP P
11 Solutions 44918 1/29/09 12:42 PM Page 1043

1044. 1044
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–11.If the spring has a stiffness kand an unstretched
length , determine the force Pwhen the mechanism is in
the position shown. Neglect the weight of the members.
l
0
P
l
k
B
u
C
A
l
*11–12.Solve Prob. 11–11 if the force Pis applied
vertically downward at B.
P
l
k
B
u
C
A
l
11 Solutions 44918 1/29/09 12:42 PM Page 1044

1045. 1045
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•11–13.Determine the angles for equilibrium of the
4-lb disk using the principle of virtual work. Neglect the
weight of the rod. The spring is unstretched when and
always remains in the vertical position due to the roller guide.
u=0°
u
k 50 lb/ft
A
B
C
u
3 ft
1 ft
11 Solutions 44918 1/29/09 12:42 PM Page 1045

1046. 1046
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–14.The truck is weighed on the highway inspection
scale. If a known mass mis placed a distance sfrom the
fulcrum Bof the scale, determine the mass of the truck if
its center of gravity is located at a distance dfrom point C.
When the scale is empty, the weight of the lever ABC
balances the scale CDE.
m
t
sa
C
B
D
E
A
m
a
d
11 Solutions 44918 1/29/09 12:42 PM Page 1046

1047. 1047
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–15.The assembly is used for exercise. It consists of four
pin-connected bars, each of length L, and a spring of
stiffness kand unstretched length . If horizontal
forces are applied to the handles so that is slowly
decreased, determine the angle at which the magnitude of
Pbecomes a maximum.
u
u
a (62L)
LL
uu
LL
D
–
P
k
P
B
C
A
11 Solutions 44918 1/29/09 12:42 PM Page 1047

1048. 1048
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*11–16.A 5-kg uniform serving table is supported on each
side by pairs of two identical links, and , and springs
. If the bowl has a mass of , determine the angle
where the table is in equilibrium. The springs each have a
stiffness of and are unstretched when .
Neglect the mass of the links.
u=90°k=200 N>m
u1 kgCE
CDAB
A
C k
250 mm
250 mm 150 mm
150 mm
B
D
E
u u
11 Solutions 44918 1/29/09 12:42 PM Page 1048

1049. 1049
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•11–17.A 5-kg uniform serving table is supported on each
side by two pairs of identical links, and , and springs
. If the bowl has a mass of and is in equilibrium when
, determine the stiffness of each spring. The springs
are unstretched when . Neglect the mass of the links.u=90°
ku=45°
1 kgCE
CDAB
A
C k
250 mm
250 mm 150 mm
150 mm
B
D
E
u u
11 Solutions 44918 1/29/09 12:42 PM Page 1049

1050. 1050
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–18.If a vertical force of is applied to the
handle of the toggle clamp, determine the clamping force
exerted on the pipe.
P=50 N
A
B
C
P 50 N
D
300 mm 500 mm
100 mm
150 mm
u 45
11 Solutions 44918 1/29/09 12:42 PM Page 1050

1051. 1051
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–19.The spring is unstretched when and has a
stiffness of . Determine the angle for
equilibrium if each of the cylinders weighs 50 lb. Neglect the
weight of the members. The spring remains horizontal at all
times due to the roller.
uk=1000 lb>ft
u=45°
D
E
k
A
B C
4 ft
4 ft
2 ft
2 ft
uu
11 Solutions 44918 1/29/09 12:42 PM Page 1051

1052. 1052
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*11–20.The machine shown is used for forming metal
plates. It consists of two toggles ABCand DEF, which are
operated by the hydraulic cylinder. The toggles push the
moveable bar Gforward, pressing the plate into the cavity.
If the force which the plate exerts on the head is ,
determine the force Fin the hydraulic cylinder when
.u=30°
P=8 kN
200 mm 200 mm
200 mm 200 mm
A
B
H
E
u
uD F
F
–F
C
G
P
30 plate
11 Solutions 44918 1/29/09 12:42 PM Page 1052

1053. 1053
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•11–21.The vent plate is supported at Bby a pin. If it weighs
15 lb and has a center of gravity at G, determine the stiffness
kof the spring so that the plate remains in equilibrium at
. The spring is unstretched when .u=0°u=30°
0.5 ft
1 ft
A
k
u
B
G
C
4 ft
11 Solutions 44918 1/29/09 12:42 PM Page 1053

1054. 1054
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–22.Determine the weight of block required to
balance the differential lever when the 20-lb load Fis
placed on the pan. The lever is in balance when the load and
block are not on the lever. Take .x=12 in
G
4 in.4 in. x
A
B
C G
ED
2 in.
F
11 Solutions 44918 1/29/09 12:42 PM Page 1054

1055. 1055
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–23.If the load weighs 20 lb and the block weighs
2 lb, determine its position for equilibrium of the
differential lever. The lever is in balance when the load and
block are not on the lever.
x
GF
4 in.4 in. x
A
B
C G
ED
2 in.
F
11 Solutions 44918 1/29/09 12:42 PM Page 1055

1056. 1056
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*11–24.Determine the magnitude of the couple moment
required to support the 20-kg cylinder in the
configuration shown. The smooth peg at can slide freely
within the slot. Neglect the mass of the members.
B
M
2.5 m
1 m
1 m
A
B
C
D
E
M
u 30
11 Solutions 44918 1/29/09 12:42 PM Page 1056

1057. 1057
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•11–25.The crankshaft is subjected to a torque of
. Determine the vertical compressive force F
applied to the piston for equilibrium when .u=60°
M=50 lb
#
ft
A
u
B
M
3 in.
5 in.
F
11 Solutions 44918 1/29/09 12:42 PM Page 1057

1058. 1058
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–26.If the potential energy for a conservative one-
degree-of-freedom system is expressed by the relation
, where xis given in feet,
determine the equilibrium positions and investigate the
stability at each position.
V=(4x
3
-x
2
-3x+10) ft #
lb
11–27.If the potential energy for a conservative one-
degree-of-freedom system is expressed by the relation
, , determine
the equilibrium positions and investigate the stability at
each position.
0°…u…90°V=(24 sin u+10 cos 2u) ft
#
lb
11 Solutions 44918 1/29/09 12:42 PM Page 1058

1059. 1059
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*11–28.If the potential energy for a conservative one-
degree-of-freedom system is expressed by the relation
, where yis given in meters,
determine the equilibrium positions and investigate the
stability at each position.
V=(3y
3
+2y
2
-4y+50) J
11 Solutions 44918 1/29/09 12:42 PM Page 1059

1060. 1060
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•11–29.The 2-Mg bridge, with center of mass at point G,is
lifted by two beams CD, located at each side of the bridge.
If the 2-Mg counterweight Eis attached to the beams as
shown, determine the angle for equilibrium. Neglect the
weight of the beams and the tie rods.
u
D
A G
C
B
E
2.5 m
2.5 m
2 m
5 m
0.3 m
2 m
u
u
11 Solutions 44918 1/29/09 12:42 PM Page 1060

1061. 1061
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–30.The spring has a stiffness and is
unstretched when . If the mechanism is in equilibrium
when determine the weight of cylinder D. Neglect
the weight of the members. Rod ABremains horizontal at all
times since the collar can slide freely along the vertical guide.
u=60°,
u=45°
k=600 lb>ft
A
k
B
C
D5 ftu
11 Solutions 44918 1/29/09 12:42 PM Page 1061

1062. 1062
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–31.If the springs at Aand Chave an unstretched
length of 10 in. while the spring at Bhas an unstretched
length of 12 in., determine the height hof the platform
when the system is in equilibrium. Investigate the stability
of this equilibrium configuration. The package and the
platform have a total weight of 150 lb.
h
ABC
k
1
20 lb/in.
k
1
20 lb/in.k
2
30 lb/in.
11 Solutions 44918 1/29/09 12:42 PM Page 1062

1063. 1063
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*11–32.The spring is unstretched when and has a
stiffness of . Determine the angle for
equilibrium if each of the cylinders weighs 50 lb. Neglect the
weight of the members.
uk= 1000 lb>ft
u=45°
D
E
k
A
B C
4 ft
4 ft
2 ft
2 ft
uu
11 Solutions 44918 1/29/09 12:42 PM Page 1063

1064. 1064
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•11–33.A 5-kg uniform serving table is supported on each
side by pairs of two identical links,ABand CD, and springs
CE. If the bowl has a mass of 1 kg, determine the angle
where the table is in equilibrium. The springs each have a
stiffness of and are unstretched when .
Neglect the mass of the links.
u=90°k=200 N>m
u
A
C k
250 mm
250 mm150 mm
150 mm
B
D
E
u u
11 Solutions 44918 1/29/09 12:42 PM Page 1064

1065. 1065
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–34.If a 10-kg load Iis placed on the pan, determine the
position xof the 0.75-kg block Hfor equilibrium. The scale is
in balance when the weight and the load are not on the scale.
B C F
I
H
ED
A
100 mm100 mm
100 mm
50 mm
x
11 Solutions 44918 1/29/09 12:42 PM Page 1065

1066. 1066
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–35.Determine the angles for equilibrium of the
200-lb cylinder and investigate the stability of each position.
The spring has a stiffness of and an
unstretched length of 0.75 ft.
k =300 lb>ft
u
A
B
CE
k
D
3 ft
1.5 ft
u u
11 Solutions 44918 1/29/09 12:42 PM Page 1066

1067. 1067
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*11–36.Determine the angles for equilibrium of the
50-kg cylinder and investigate the stability of each position.
The spring is uncompressed when u=60°.
u
A
BC
1 m 1 m
u
k 900 N/m
11 Solutions 44918 1/29/09 12:42 PM Page 1067

1068. 1068
© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•11–37.If the mechanism is in equilibrium when
determine the mass of the bar BC. The spring has a stiffness
of and is uncompressed when . Neglect
the mass of the links.
u=0°k=2 kN>m
u=30°,
600 mm
450 mm
B
C
D
H F
A
k 2 kN/m
u
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–38.The uniform rod OAweighs 20 lb, and when the rod
is in the vertical position, the spring is unstretched.
Determine the position for equilibrium. Investigate the
stability at the equilibrium position.
u
3 ft
k 2 lb/in.
A
O
1 ft
u
11–39.The uniform link ABhas a mass of 3 kg and is pin
connected at both of its ends. The rod BD, having negligible
weight, passes through a swivel block at C. If the spring has a
stiffness of and is unstretched when ,
determine the angle for equilibrium and investigate the
stability at the equilibrium position. Neglect the size of the
swivel block.
u
u=0°k=100 N>m
k 100 N/m
400 mm
400 mm
D
C
B
A
u
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© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*11–40.The truck has a mass of 20 Mg and a mass center at
G. Determine the steepest grade along which it can park
without overturning and investigate the stability in this
position.
u
G
u
3.5 m
1.5 m
1.5 m
•11–41.The cylinder is made of two materials such that it
has a mass of mand a center of gravity at point G. Show
that when Glies above the centroid Cof the cylinder, the
equilibrium is unstable.
C
G
a
r
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–42.The cap has a hemispherical bottom and a mass m.
Determine the position hof the center of mass Gso that the
cup is in neutral equilibrium.
h
r
G
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–43.Determine the height hof the cone in terms of the
radius rof the hemisphere so that the assembly is in neutral
equilibrium. Both the cone and the hemisphere are made
from the same material.
h
r
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*11–44.A homogeneous block rests on top of the
cylindrical surface. Derive the relationship between the
radius of the cylinder,r, and the dimension of the block,b,
for stable equilibrium.Hint: Establish the potential energy
function for a small angle , i.e., approximate , and
.cos uL1-u
2
>2
sin uL0u
b
r
b
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•11–45.The homogeneous cone has a conical cavity cut
into it as shown. Determine the depth dof the cavity in
terms of hso that the cone balances on the pivot and
remains in neutral equilibrium.
r
d
h
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–46.The assembly shown consists of a semicylinder and
a rectangular block. If the block weighs 8 lb and the
semicylinder weighs 2 lb, investigate the stability when the
assembly is resting in the equilibrium position. Set h=4 in.
h
4 in.
10 in.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–47.The 2-lb semicylinder supports the block which has
a specific weight of . Determine the height h
of the block which will produce neutral equilibrium in the
position shown.
g=80 lb>ft
3
h
4 in.
10 in.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*11–48.The assembly shown consists of a semicircular
cylinder and a triangular prism. If the prism weighs 8 lb and
the cylinder weighs 2 lb, investigate the stability when the
assembly is resting in the equilibrium position.
4 in.
6 in.
8 in.
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
•11–49.A conical hole is drilled into the bottom of the
cylinder, and it is then supported on the fulcrum at A.
Determine the minimum distance din order for it to remain
in stable equilibrium.
d
A
r
h
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–50.The punch press consists of the ram R, connecting
rod AB, and a flywheel. If a torque of is
applied to the flywheel, determine the force Fapplied at the
ram to hold the rod in the position .u=60°
M=50 N
#
m
F
0.1 m
M
B
R
A
u
0.4 m
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© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–51.The uniform rod has a weight W. Determine the
angle for equilibrium. The spring is uncompressed when
. Neglect the weight of the rollers.u=90°
u
k A
B
L
u
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*11–52.The uniform links ABand BCeach weigh 2 lb
and the cylinder weighs 20 lb. Determine the horizontal
force Prequired to hold the mechanism at . The
spring has an unstretched length of 6 in.
u=45°
P
10 in.
B
A
u C
10 in.
k = 2 lb/in.
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•11–53.The spring attached to the mechanism has an
unstretched length when . Determine the position
for equilibrium and investigate the stability of the
mechanism at this position. Disk Ais pin connected to the
frame at Band has a weight of 20 lb.
uu=90°
1.25 ft
1.25 ft
A
B
C
uu
u u
k 16 lb/ft
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–54.Determine the force Pthat must be applied to the
cord wrapped around the drum at Cwhich is necessary to
lift the bucket having a mass m. Note that as the bucket is
lifted, the pulley rolls on a cord that winds up on shaft Band
unwinds from shaft A.
P
c
C
B
A
b
a
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11–55.The uniform bar ABweighs 100 lb. If both springs
DEand BCare unstretched when , determine the
angle for equilibrium using the principle of potential
energy. Investigate the stability at the equilibrium position.
Both springs always remain in the horizontal position due
to the roller guides at Cand E.
u
u=90°
A
u
k 2 lb/in.
k 4 lb/in.
2 ft
4 ft
D
B
C
E
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
*11–56.The uniform rod ABhas a weight of 10 lb. If the
spring DCis unstretched when , determine the angle
for equilibrium using the principle of virtual work. The
spring always remains in the horizontal position due to the
roller guide at D.
u
u=0°
A
k 50 lb/ft
1 ft
2 ft
C
u
B
D
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•11–57.Solve Prob. 11–56 using the principle of potential
energy. Investigate the stability of the rod when it is in the
equilibrium position.
A
k 50 lb/ft
1 ft
2 ft
C
u
B
D
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exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–58.Determine the height hof block Bso that the rod
is in neutral equilibrium. The springs are unstretched when
the rod is in the vertical position. The block has a weight W.
B
A
kk
l
h
11 Solutions 44918 1/29/09 12:42 PM Page 1088