conservation of energy and mechanical power.pdf

conservation of energy and mechanical power.pdf

7. Example 1

A ball of mass 0.4 kg swings on the end of a thin rod with negligible mass with length 60
mm. The ball is held horizontal and released. Calculate the following à

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i. The yelocity of the head as it passes through the lowest position. ©
ii. The loss of potential energy
À ha lor to mm
iii, The gain in kinetic energy 9 1 115

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8. Exercise 1

1. An object of mass 20 kg is dropped onto a surface from a height of
energy and velocity just before it hits the surface

50 m. Calculate the
(9810 J and 31.3 m/s)
= ン st
KE i
A swinging hammer must have 50 Joules of e and a vel t the bottom

of the swing. Calculate the mass and height of the hammer before it is r

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kg and 0.204m)

v

3. A swinging hammer has a mass of 2 kg and is raised 0.2 m. Calculate the energy and
velocity at the bottom of the swing. ーー

(1.98 m/s).

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11. Example 2 PE

A pulley is used to raise a mass of 85 85 kg a distance of 2m m. The efficiency is 60%.
Calculate the work done.
——

P と = Maz = EE x Aglx 12 = IO “yj
W yk Lima = lo uj lo

——. 一 = lé cru
60 ol 7,

12. Exercise 2

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p ety Ae ER w,

5 000 J of energy is used up in 20 seconds. What is the power? (250 W) uv

A vehicle is propelled 25 000 m by a force of 2 000 N in 12 seconds. Calculate the work
done and the power used. (4.17 MW) 442 ÊX = zw kz テング の = 56000 es
Pr wre > 2 る の の ッ プ 12 = ん / の と 667 War)
A block of mass 500 kg is raised at a constant rate by a hoist at a rate of 0.15 m/s. 447 uw
Calculate the force in the rope and hence the power used. (4905 N and 735.8 W) >

A load is raised by a pulley. The force in the rope is 40 N and it moves 3 m in 11
seconds. The process is 70% efficient. Calculate the mechanical power. (15.6 W)

A rocket flies at 120 m/s under a propulsion force of 3 000 N. Calculate the power used.
(360 kW)

A lifting jack must raise a force of 4 kN a distance of 0.3 m. Due to friction the efficiency
is only 35%. Calculate the energy used to raise the load. (3429 Joules)

An electric hoist raises a mass of 60 kg at a rate of 0.2 m/s. The process is 30% efficient.
Calculate the power input to the hoist. (392 W)

17. Example 3
A vehicle has a force of 400 N applied to it for 20 seconds. Calculate the impulse?

Example 4
A vehicle of mass 5 000 kg changes velocity from 2 m/s to 6 m/s. Calculate the change
in momentum.

19. Example 5

A mass of 8 kg accelerates at 6 m/s? for 5 seconds. Calculate the following:

1. the force producing acceleration
ii. the change in velocity

iii. the change in momentum

iv. the impulse.

20. Exercise 3

A vehicle of mass 1100 kg moves at 3 m/s. The brakes are applied and the vehicle
reduces speed to 0.5 m/s in 45 s. Calculate the force needed.

A rocket of mass 200 kg in outer space moves at 360 m/s. It accelerates in a straight line
by firing its motors with a force of 50 N. Calculate how long it takes to reach a velocity
of 700 m/s.

21. The Effect Of Friction Friction is an external force that always acts to oppose motion.

When a body is accelerated, the force causing acceleration is the NET FORCE.
Net Force = Applied Force - Friction Force.

Exercise 4

1. The applied force on a vehicle is 6000 N but the wind and road resistance is 2000 N.
Calculate the acceleration of the vehicle. The mass is 2000 kg

2. Calculate the force needed to accelerate a piston of mass 0.8 kg in a cylinder at 3 m/s2 if
the resisting force is 3 N.

23. Exercise 5

1. Calculate the force required from a rocket engine if it must accelerate the rocket upwards
at 3 m/s2. The mass is 5 000 kg.

2. A lift of mass 500 kg is accelerated upwards at 2 m/s2. Calculate the force in the rope.

3. The same lift is accelerated downwards at 2 m/s2. What is the force in the rope then?

25. Example 6

Using d’Alembert’s principle, solve the reactions Ra and Ry for the free body diagram shown.

28. Example 7 F+F+F+W=0

A spring is fixed at the left end and has a sliding mass of 10 kg at the other as shown. A
force of 100 N is applied to move the mass. At the given instant shown, the spring force
is 130 N. A friction force of 20 N also exists. Draw the free body diagram and calculate
the acceleration of the mass at that instant.

Applied Force

Friction Force
20N Mass
10 kg

Acceleration
Spring Force
130N

29. Exercise 6
Calculate the acceleration of the mass at the instant shown for the system in the diagram.

Applied Force
60N
Friction Force
15N Mass
18 kg
Acceleration
Spring Force
190 N

(Ans. 1.75 m/s? down)