Beer dinamica 9e_manual_de_soluciones_c11a
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About This Presentation
dinamica beer 9 edicion solucionario
Slide Content
|
7 7 u ]
PROBLEM 11.1
‘The motion ofa partie defined by the relation 1.5 = 306 + 4410, where and are expressed in
etes and sols, respectively. Determine the poston, the veliy, and the acceleration of te patel
when 248
SOLUTION
Give or es
Evaluate expressions at 24 5
KEN? ES +10 -66 05 1-60 4
AY 6000-25 =149 més NU]
Ia) 60-228 mu Eon 4
PROPRIETARY MATERIA, © 209 Te Mein A Cay, rl er of Ml map be rt
‘apr rtd yf Ban ine ro wrap sar, mat von ee
Senn tnd thy Sth Hg ht Bane pte a ed
7 7 u ]
PROBLEM 11.1
‘The motion ofa partie defined by the relation 1.5 = 306 + 4410, where and are expressed in
etes and sols, respectively. Determine the poston, the veliy, and the acceleration of te patel
when 248
SOLUTION
Give or es
Evaluate expressions at 24 5
KEN? ES +10 -66 05 1-60 4
AY 6000-25 =149 més NU]
Ia) 60-228 mu Eon 4
PROPRIETARY MATERIA, © 209 Te Mein A Cay, rl er of Ml map be rt
‘apr rtd yf Ban ine ro wrap sar, mat von ee
Senn tnd thy Sth Hg ht Bane pte a ed
PROBLEM 11.2
“The motion of apatite is define by the relation = 127° 180421 5, where and fare expressed in
‘meters nd condo, espestively. Determine the postion and he velocity when he acceleration of the perte
‘sequal o zer.
SOLUTION
Given: O
Find the timo fora=0.
Substitute nto above expressions.
AOS) 180592 +2103) +5=3 x=300m 4
2603) 36408) 2
rm
mas |
OPE MATERIAL 030 Ts hi Cm, Apr os Mal wy be pen
PT daran 0 Arm y nr te he ir wie pum ne py e rd hdd nt
mi afer mtm oc man Mok
“The motion of apatite is define by the relation = 127° 180421 5, where and fare expressed in
‘meters nd condo, espestively. Determine the postion and he velocity when he acceleration of the perte
‘sequal o zer.
SOLUTION
Given: O
Find the timo fora=0.
Substitute nto above expressions.
AOS) 180592 +2103) +5=3 x=300m 4
2603) 36408) 2
rm
mas |
OPE MATERIAL 030 Ts hi Cm, Apr os Mal wy be pen
PT daran 0 Arm y nr te he ir wie pum ne py e rd hdd nt
mi afer mtm oc man Mok
PROBLEM 11.3
“The mation ofa particle is defined by the relation 308, where and aro espresed in
5 2
‘et und seconds, respectively Determine tb time he post, and the acceleration when v=
SOLUTION
AA
We have:
2
Then ve Kase 51-30
a
and
When v=o:
= IS pe a
Aum3e jor Lor es
atom or
PROPRIETARY MATERIA. © 200 as Mei Coogudos Is A fe Me o Mat dopo
‘cl dnd e e fa ty u ma, ml ps pri se e
‘Bother omer pod ten Mfr bi pe ko lé
ovo ng wn pon
“The mation ofa particle is defined by the relation 308, where and aro espresed in
5 2
‘et und seconds, respectively Determine tb time he post, and the acceleration when v=
SOLUTION
AA
We have:
2
Then ve Kase 51-30
a
and
When v=o:
= IS pe a
Aum3e jor Lor es
atom or
PROPRIETARY MATERIA. © 200 as Mei Coogudos Is A fe Me o Mat dopo
‘cl dnd e e fa ty u ma, ml ps pri se e
‘Bother omer pod ten Mfr bi pe ko lé
ovo ng wn pon
PROBLEM 11.4
he motion of a patch is defined by the relation x = 6/8 + 4004, where x and are expressed in
inches and seconds, respectively. Determine the position, the velocity and the acceleration when /=65.
E u a
SOLUTION
We have x26? 8480081
Then Hata ane sin ae
and ae À 12-40 cost
a
Auta6s 5-0 8 rind
va = 126) 402 sin 6 a nina 4
a 12-40 en Ri
“PROPRIETARY MATERIAL © 200 Ts Ss Kl Curie, nA rss pur of hr Mo he pane
ae Aha Are yy cae, a Dr pis fe pla, o od Rod de id
‘Snare poh en ne
he motion of a patch is defined by the relation x = 6/8 + 4004, where x and are expressed in
inches and seconds, respectively. Determine the position, the velocity and the acceleration when /=65.
E u a
SOLUTION
We have x26? 8480081
Then Hata ane sin ae
and ae À 12-40 cost
a
Auta6s 5-0 8 rind
va = 126) 402 sin 6 a nina 4
a 12-40 en Ri
“PROPRIETARY MATERIAL © 200 Ts Ss Kl Curie, nA rss pur of hr Mo he pane
ae Aha Are yy cae, a Dr pis fe pla, o od Rod de id
‘Snare poh en ne
PROBLEM 11.5
‘The motion ofa particle is dined by the elation x=0Y 2 12 +3143, where x and rate expressed in
ters and second, respectively. Determine the tine, the position, andthe velocity when «0.
SOLUTION
an
" ven
a
28) 8] (Qu coin 4
2Ÿ _{2Ÿ 2
Ge ross 4
PROPRES ara. € ED eu Cove ae rl eo Md et
en acer und ers porated Me fr me pp Je ln e Mase.
ins o porno
‘The motion ofa particle is dined by the elation x=0Y 2 12 +3143, where x and rate expressed in
ters and second, respectively. Determine the tine, the position, andthe velocity when «0.
SOLUTION
an
" ven
a
28) 8] (Qu coin 4
2Ÿ _{2Ÿ 2
Ge ross 4
PROPRES ara. € ED eu Cove ae rl eo Md et
en acer und ers porated Me fr me pp Je ln e Mase.
ins o porno
PROBLEM 11.6
“The motion of a particle is defied by the relation = 26 187° + 2är+d, where is expressed in meters
and in seconds. Determine (a) when the veoct is zor, (8) he psiton and the foal distance aveled when
Uo acceleration is ero.
‘SOLUTION
Pots aries
gg
des Or
Boop an
a 1-0
a
o 62 3002
arm
© a=0 sen 120-0
00% <
0x or
Ss
209"
SOS) 42425114
find otal distance tod, veto hat
EA ASF ar
For 120.
Diane traveled
From #=0t0¢=1s:
From ¢=tstor
ss nes seine
‘otal distance ave 13.5 2245 m «
PROPRIETARY MATERIAL © 200 the Mes Caps, eI ae pr of Mama o dene
Iu ha ny ey ao ina, on rein Par Flo af yd
TARDE cmon! uso nena one i ceca open Ppt mbr Se,
pm
“The motion of a particle is defied by the relation = 26 187° + 2är+d, where is expressed in meters
and in seconds. Determine (a) when the veoct is zor, (8) he psiton and the foal distance aveled when
Uo acceleration is ero.
‘SOLUTION
Pots aries
gg
des Or
Boop an
a 1-0
a
o 62 3002
arm
© a=0 sen 120-0
00% <
0x or
Ss
209"
SOS) 42425114
find otal distance tod, veto hat
EA ASF ar
For 120.
Diane traveled
From #=0t0¢=1s:
From ¢=tstor
ss nes seine
‘otal distance ave 13.5 2245 m «
PROPRIETARY MATERIAL © 200 the Mes Caps, eI ae pr of Mama o dene
Iu ha ny ey ao ina, on rein Par Flo af yd
TARDE cmon! uso nena one i ceca open Ppt mbr Se,
pm
PROBLEM 11.7
‘The motion of a particle i dena by the relation x=»
| and seconds, respectively. Determine a) hen the vel
Total distncetaveled when x =0,
61-40, where x amd rare expressed in feet
iy is zero, (6) the velocity, the acceleration, and the
SOLUTION
Weave
Then
aná
@ When you,
ar ET
a 25 (Rejet and 12600 4
6) When x Pat 360-400
Freeing Etam 20 or
Nowobsenethat Dean vO
sscrsios v>0
dat 20 27-00
(268: (6) (GP ~36(6) 40.
2560
DT do =1200)=36
wo
EN ES
Then In 6-4 216 8
Fy Fo 0250) 2256
Total dis tele (216 +256) 8472 «
[PROPRIETARY ATEM. © 2009 Te Min Cm A ie ok a ht Mow mayb ge
‘ep ov lista fb ny ose ern prin of yao, ed el i ha
Sein des ty oti en Ferma ag ee
‘The motion of a particle i dena by the relation x=»
| and seconds, respectively. Determine a) hen the vel
Total distncetaveled when x =0,
61-40, where x amd rare expressed in feet
iy is zero, (6) the velocity, the acceleration, and the
SOLUTION
Weave
Then
aná
@ When you,
ar ET
a 25 (Rejet and 12600 4
6) When x Pat 360-400
Freeing Etam 20 or
Nowobsenethat Dean vO
sscrsios v>0
dat 20 27-00
(268: (6) (GP ~36(6) 40.
2560
DT do =1200)=36
wo
EN ES
Then In 6-4 216 8
Fy Fo 0250) 2256
Total dis tele (216 +256) 8472 «
[PROPRIETARY ATEM. © 2009 Te Min Cm A ie ok a ht Mow mayb ge
‘ep ov lista fb ny ose ern prin of yao, ed el i ha
Sein des ty oti en Ferma ag ee
PROBLEM 11.8
“The motion fa article is defined by the elation x=0" 978 +248, where x and fare expressed in inches
and seconds, respectively Determine (a) when the velocity is zero, (9) the poston and the tia distance
eave when the acceleration ero.
SOLUTION
We have
then
and
(When PART
er 209-0
or 122405 and
0) When a=0: Gino où as
Arras y ETT
Fin ohne that 0-128 wo
Peer
Now
amo wo
aunts MO) 124) -8= 12,
#1
Pt,
STE] oar te
o as GS
Then
“Total distance traveled =(20+ 2)
PROPRIETARY MATERLAL. © 209 The Maye i Compre, A gs a of es Maa he rd
er A am fre ey ny an ah tr mvs ere ft ble ered on ie nd
Te Ri MA RAS pr msc Ma
“The motion fa article is defined by the elation x=0" 978 +248, where x and fare expressed in inches
and seconds, respectively Determine (a) when the velocity is zero, (9) the poston and the tia distance
eave when the acceleration ero.
SOLUTION
We have
then
and
(When PART
er 209-0
or 122405 and
0) When a=0: Gino où as
Arras y ETT
Fin ohne that 0-128 wo
Peer
Now
amo wo
aunts MO) 124) -8= 12,
#1
Pt,
STE] oar te
o as GS
Then
“Total distance traveled =(20+ 2)
PROPRIETARY MATERLAL. © 209 The Maye i Compre, A gs a of es Maa he rd
er A am fre ey ny an ah tr mvs ere ft ble ered on ie nd
Te Ri MA RAS pr msc Ma
PROBLEM 11.9
hat 224 o when y
distance uaveled when smile.
“The acera ofa parle is defined by the relation a = ~8 ms”. Knowing hat x
16 mvs, determine (a) he timo when the velocity is ein, (1) he veloc wa Ub ot
20 m when 1=4 and
[soLurion
We hase
‘hen
Aso
Arr 4x2 20m
When v 216 4 à = 4 m:
Combining
Simplifying
and
(a) When »=0.
(6) Velocity and distance se LL,
on mi
ja frase c
A+ C (ms)
La ferro
2-20 par 4.0%,
42 + Cure 84000)
or
16-84 C2
40 400-8486
OA ONE 4180
41+4=0
Ce ms
vase 32(ms)
CET
“8220
MD
non
«20m
Su SAU +320n-44=-176m
A]
sion 4
nn et ps ae ng a
EEE A Ri]
hat 224 o when y
distance uaveled when smile.
“The acera ofa parle is defined by the relation a = ~8 ms”. Knowing hat x
16 mvs, determine (a) he timo when the velocity is ein, (1) he veloc wa Ub ot
20 m when 1=4 and
[soLurion
We hase
‘hen
Aso
Arr 4x2 20m
When v 216 4 à = 4 m:
Combining
Simplifying
and
(a) When »=0.
(6) Velocity and distance se LL,
on mi
ja frase c
A+ C (ms)
La ferro
2-20 par 4.0%,
42 + Cure 84000)
or
16-84 C2
40 400-8486
OA ONE 4180
41+4=0
Ce ms
vase 32(ms)
CET
“8220
MD
non
«20m
Su SAU +320n-44=-176m
A]
sion 4
nn et ps ae ng a
EEE A Ri]
PROBLEM 11.9 (Continued)
Now observe tit
Then
otal distance taveled=(64-+196) m = 260 me «
PROPRIETARY MATERIAL. © 209 The M M Con, A ghee pr of mal e eo
D hare ry fre ay m is swe pers pan a ed Nene Bed
‘inten te a map an Ma
Now observe tit
Then
otal distance taveled=(64-+196) m = 260 me «
PROPRIETARY MATERIAL. © 209 The M M Con, A ghee pr of mal e eo
D hare ry fre ay m is swe pers pan a ed Nene Bed
‘inten te a map an Ma
PROBLEM 11.10
‘The acelraton ofa parucl i directly proportional 1 he square of the time. When £0, the pale is
st 5=24m. Knowing that at 36m and y= 18s, express x and io er of
SOLUTION
| Werne an aia
Now ke?
a mi: [o [ira
m QE)
zu an
Lo
or + = 216K)
Kunst
a Ceres
EE
Le
AmO mam - (Ji-tuo-
0 ae [fis jae-noja
“ perenne ee
ano tata)
Now
ıfı
126 296m no tal Mot
nenas molto]
0 ok me
5
yıyı
Then fie
EM alla 210)
“ et eimen «
| me
fi
mi vars (Eee
16) 2
1
e «
PROPRIETARY MATERIAL © 200 Te ene Conga, A ts cd a a his Mon yb tt
Grete ac naher tn RC ea deren Dann aoe
‘The acelraton ofa parucl i directly proportional 1 he square of the time. When £0, the pale is
st 5=24m. Knowing that at 36m and y= 18s, express x and io er of
SOLUTION
| Werne an aia
Now ke?
a mi: [o [ira
m QE)
zu an
Lo
or + = 216K)
Kunst
a Ceres
EE
Le
AmO mam - (Ji-tuo-
0 ae [fis jae-noja
“ perenne ee
ano tata)
Now
ıfı
126 296m no tal Mot
nenas molto]
0 ok me
5
yıyı
Then fie
EM alla 210)
“ et eimen «
| me
fi
mi vars (Eee
16) 2
1
e «
PROPRIETARY MATERIAL © 200 Te ene Conga, A ts cd a a his Mon yb tt
Grete ac naher tn RC ea deren Dann aoe
PROBLEM 11.11
“The acceleration of a parce is dice proportional to the tine £ At ¿=0, the velocity of the particle
is #216 ind, Knowing thet 915 in/s and that x= 20 in, when 171 1, determine the velocity, the postion,
std tet distanceteled when #27 5.
SOLUTION
Woh
Now
Are t.e=toins
or wei Lens)
7
avs 15 ind Sims 216 indo Zi”
o Din and vió
ao
saone
o [is
3
1 13
het an
Then
weisen? or y= B30 ins 4
US e 2-20 4
When v=0: or tess
PROPRIRTARY MATERNAL © 2059 Te Meri Compu I. A gh sen. o par of Me Ma dol
to ds yf ya nn me ts pra of te oe gon ee
sd pr Oi o e pr m sve nk
“The acceleration of a parce is dice proportional to the tine £ At ¿=0, the velocity of the particle
is #216 ind, Knowing thet 915 in/s and that x= 20 in, when 171 1, determine the velocity, the postion,
std tet distanceteled when #27 5.
SOLUTION
Woh
Now
Are t.e=toins
or wei Lens)
7
avs 15 ind Sims 216 indo Zi”
o Din and vió
ao
saone
o [is
3
1 13
het an
Then
weisen? or y= B30 ins 4
US e 2-20 4
When v=0: or tess
PROPRIRTARY MATERNAL © 2059 Te Meri Compu I. A gh sen. o par of Me Ma dol
to ds yf ya nn me ts pra of te oe gon ee
sd pr Oi o e pr m sve nk
PROBLEM 11.11 (Continued)
Now observe that
Aal _
+ 5
Ne is
»
Io -21=12-471=45in.
Prone un. © Ye kn Crono, eM i pl Me rn
ended er ele ero Franc ant righ Mama
Now observe that
Aal _
+ 5
Ne is
»
Io -21=12-471=45in.
Prone un. © Ye kn Crono, eM i pl Me rn
ended er ele ero Franc ant righ Mama
PROBLEM 11.12
The wecclration ofa parle ie dined by the elation aK, (a) Knowing that v=-32 Me when 4 = 0
and hat v=+32 (Vs when 14, determine the constant & (9) Waite the equations of motion, owing alse |
hat x=0 when r= 4s. |
wel
SOLUTION
©
©
3.000 4
© sin
an 4
em oe fee
De 3
ven wna
«e
san
PROPRIETARY MATERIAL © 20) Te Me Cop, be A ge WN uf i ana eu e pn
(nr dead ny roy ty rr an ft tk pres fdr or ra pend ed
nn rodean pr Meo Miler iba one pp aren unge Moo
Sooner wou prin
The wecclration ofa parle ie dined by the elation aK, (a) Knowing that v=-32 Me when 4 = 0
and hat v=+32 (Vs when 14, determine the constant & (9) Waite the equations of motion, owing alse |
hat x=0 when r= 4s. |
wel
SOLUTION
©
©
3.000 4
© sin
an 4
em oe fee
De 3
ven wna
«e
san
PROPRIETARY MATERIAL © 20) Te Me Cop, be A ge WN uf i ana eu e pn
(nr dead ny roy ty rr an ft tk pres fdr or ra pend ed
nn rodean pr Meo Miler iba one pp aren unge Moo
Sooner wou prin
PROBLEM 11.13
| The accleaton of a parce is defined bythe reiiona = AGF, where À à constant. AU 1-0 the
parle stars a a= wi v0. Knowing thal at TA v= 1010, doin () ls me at wi the
[somos 7
| We have
ve o
A Gove fu cera
or v= Ar 20 (més)
Ati=15,v=30 mis: 30 01-207"
Also. e
= «
O Gin
RTE
125 ess — es 995
PROPRIETARY MATERIAL © 200 The Wu Compare, te A pe mM ds Mn! ld
[phen ar dt je rl e mo, te rr vts prin pala. red Noe ed
{rao eased eater Go fh india erat rem ata
| The accleaton of a parce is defined bythe reiiona = AGF, where À à constant. AU 1-0 the
parle stars a a= wi v0. Knowing thal at TA v= 1010, doin () ls me at wi the
[somos 7
| We have
ve o
A Gove fu cera
or v= Ar 20 (més)
Ati=15,v=30 mis: 30 01-207"
Also. e
= «
O Gin
RTE
125 ess — es 995
PROPRIETARY MATERIAL © 200 The Wu Compare, te A pe mM ds Mn! ld
[phen ar dt je rl e mo, te rr vts prin pala. red Noe ed
{rao eased eater Go fh india erat rem ata
PROBLEM 11.13 (Continued)
Now observe that
Ten
spurt oe yer Soe teres tes er]
a pa pa fae eg
Now observe that
Ten
spurt oe yer Soe teres tes er]
a pa pa fae eg
PROBLEM 11.14
Tes know that ‘of patch is inversely proportional to the cube
ofthe me £ When 125, v=-15 m8, and when #=10 3, 90.36 mis. Knowing at the particle sie
35 far from the origin when #25 as i when 1=10s, determino (a) the postion of the pack
‘when 22 sand when (105, (9) the ttl distance we hy the particle Tun 4
SOLUTION
We have
Now
Ares va 15 a
AL /=10 5, v0.36 mé
a
@ Vene Pan:
In fa fear cso
or Luci
won easy veut)
“ cm
m Kerner
PROPRIETARY ur. © 200 Te Se Compas, A a sl. a af he ale Be pi,
‘rnb ha a frm by ny mon ine rrr lu, md a ad
‘Brenda poly tin Wf ip ne
Tes know that ‘of patch is inversely proportional to the cube
ofthe me £ When 125, v=-15 m8, and when #=10 3, 90.36 mis. Knowing at the particle sie
35 far from the origin when #25 as i when 1=10s, determino (a) the postion of the pack
‘when 22 sand when (105, (9) the ttl distance we hy the particle Tun 4
SOLUTION
We have
Now
Ares va 15 a
AL /=10 5, v0.36 mé
a
@ Vene Pan:
In fa fear cso
or Luci
won easy veut)
“ cm
m Kerner
PROPRIETARY ur. © 200 Te Se Compas, A a sl. a af he ale Be pi,
‘rnb ha a frm by ny mon ine rrr lu, md a ad
‘Brenda poly tin Wf ip ne
PROBLEM 11.14 (Continuod)
avers EC « nome
“ Ñ
seine mure “nern 4
9 When ved.
arate:
Now observe hat 28<7< 88: yO
Secrets: vo
IR
ad num 25)
ES (25)
‘Then By fr 17.2~352)- 18m
os =I76-172=04m
Total distance towel = (18408) m 18.40 m «
Nove: The val distance waved isthe same for bo cases
‘PROPRIBARY MATEHLAL © 200 e om Cong I. A gi Re Jus Smal ay ep,
‘ern or hated fm ty ar i rr itn pm llo ol ne
ro pared cv Morse nao icra Sea,
Dee
avers EC « nome
“ Ñ
seine mure “nern 4
9 When ved.
arate:
Now observe hat 28<7< 88: yO
Secrets: vo
IR
ad num 25)
ES (25)
‘Then By fr 17.2~352)- 18m
os =I76-172=04m
Total distance towel = (18408) m 18.40 m «
Nove: The val distance waved isthe same for bo cases
‘PROPRIBARY MATEHLAL © 200 e om Cong I. A gi Re Jus Smal ay ep,
‘ern or hated fm ty ar i rr itn pm llo ol ne
ro pared cv Morse nao icra Sea,
Dee
PROBLEM 11.15
‘he acceleration oF a patil i defined hy the raion hi, Khas been experimentally determined that
wets when +206 1 and that y=9 U6 when x=12 Determine (a) the velocity of te particle
‘when 2215, (9) the position ofthe parce at which ts velociy izo.
SOLUTION
ant,
ae
Separate and integrate using x = 0.6 N, y=15 Rés.
[pra
del = kins]
eo (ez o
doi fe
A Co]
; a
ec
aimee
© Sie BSR ant 13000.
Betas! mE
ess 4
o tere
ots)
"(as
PRÔNE MATERLA. © 209 The Metis Compu I. Ang sl. pr fr ma mo he uo!
oval er ib sx former ty ma a fe is rn fe ple tg Id
‘Kit actress psd co fr Bb capa iron eg a
Sova aufero
‘he acceleration oF a patil i defined hy the raion hi, Khas been experimentally determined that
wets when +206 1 and that y=9 U6 when x=12 Determine (a) the velocity of te particle
‘when 2215, (9) the position ofthe parce at which ts velociy izo.
SOLUTION
ant,
ae
Separate and integrate using x = 0.6 N, y=15 Rés.
[pra
del = kins]
eo (ez o
doi fe
A Co]
; a
ec
aimee
© Sie BSR ant 13000.
Betas! mE
ess 4
o tere
ots)
"(as
PRÔNE MATERLA. © 209 The Metis Compu I. Ang sl. pr fr ma mo he uo!
oval er ib sx former ty ma a fe is rn fe ple tg Id
‘Kit actress psd co fr Bb capa iron eg a
Sova aufero
PROBLEM 11.16
A parce sting fiom es at <1 fis accented so that it velocity doubles in manie between
À und À 80. Knight accion ofthe pale dein bythe relation aeäfe- ADI.
Akemi the vals of the ort 4 and ihe parte has a elo 029s when 167
SOLUTION
Weine
When af, v=0: fro [aras
o |
Lo amx-t)
pen aang)
1 E |
zar amz-4]=4(3 ue)
Le |
PAT er oe ee |
ws 1618-48) |
o |
|
“ Antes 4
1 Lao 285 |
Yon]
‘Noting that In(16)=41 |
mass |
Webave sua [236 ama
ee]
15284 |
PROPRIETARE MATERIA. 20 The Nh Crane ttc. prof ha Maa na e dep,
‘ree ote ny or ay ta oth tr ete pr faster al eon fee
Wine tae oul actor par DA ea
A parce sting fiom es at <1 fis accented so that it velocity doubles in manie between
À und À 80. Knight accion ofthe pale dein bythe relation aeäfe- ADI.
Akemi the vals of the ort 4 and ihe parte has a elo 029s when 167
SOLUTION
Weine
When af, v=0: fro [aras
o |
Lo amx-t)
pen aang)
1 E |
zar amz-4]=4(3 ue)
Le |
PAT er oe ee |
ws 1618-48) |
o |
|
“ Antes 4
1 Lao 285 |
Yon]
‘Noting that In(16)=41 |
mass |
Webave sua [236 ama
ee]
15284 |
PROPRIETARE MATERIA. 20 The Nh Crane ttc. prof ha Maa na e dep,
‘ree ote ny or ay ta oth tr ete pr faster al eon fee
Wine tae oul actor par DA ea
PROBLEM 11.17
A parie osiltes betwcen the puis x=40 mm and x =160 mun with an acceleration a 4100 - x),
‘whore und x ar expresso in mau" and mm, respectively, and kis constat. The velocity of the particle
is IS mov when x= 100 mm end is zero at bath
(0) the velocity when = 120 mm.
SOLUTION
(0) Wetave
When x=40 mm, v=0: [rare Lruo- ar
=)
Na
Lau vo]
o)
PROPRIETARY MATERIAL. 0250 e Mil Compra rl ut ot en ais
red ral muy ym mi apr ef e bl, ral od a
ret eras poy choi eal canta meando
A parie osiltes betwcen the puis x=40 mm and x =160 mun with an acceleration a 4100 - x),
‘whore und x ar expresso in mau" and mm, respectively, and kis constat. The velocity of the particle
is IS mov when x= 100 mm end is zero at bath
(0) the velocity when = 120 mm.
SOLUTION
(0) Wetave
When x=40 mm, v=0: [rare Lruo- ar
=)
Na
Lau vo]
o)
PROPRIETARY MATERIAL. 0250 e Mil Compra rl ut ot en ais
red ral muy ym mi apr ef e bl, ral od a
ret eras poy choi eal canta meando
PROBLEM 11.18
A particle starts from est at the origin and is given an acceleration A+ 4), where and ne expressed
in Ms and m, respectively, and & i a cortan. Krowing thatthe velocity ofthe parce l 4 més when
2x8 m, determine (2) the value of , (9) the position of de partici when +=4,5 m, (e) the maximum
velocity ofthe pace
SOLUTION
(0 Wehe
When x=0,
When x8 m, yd més
o kosa 4
(0) When v245 mis
(©) Notedhat when v= yg = 0.
Now 0 nn shat
190 mus À
PROPRISTARS MATERIA. € 290 ue Mean Comps, Ir. A it eae prt of th Bal wy e denne
sn ted ny fa 6 y ni. ve ptr ven pron fh fll llo e od
Ton armani ru Mh le proie Pomares mt Be Ma,
A particle starts from est at the origin and is given an acceleration A+ 4), where and ne expressed
in Ms and m, respectively, and & i a cortan. Krowing thatthe velocity ofthe parce l 4 més when
2x8 m, determine (2) the value of , (9) the position of de partici when +=4,5 m, (e) the maximum
velocity ofthe pace
SOLUTION
(0 Wehe
When x=0,
When x8 m, yd més
o kosa 4
(0) When v245 mis
(©) Notedhat when v= yg = 0.
Now 0 nn shat
190 mus À
PROPRISTARS MATERIA. € 290 ue Mean Comps, Ir. A it eae prt of th Bal wy e denne
sn ted ny fa 6 y ni. ve ptr ven pron fh fll llo e od
Ton armani ru Mh le proie Pomares mt Be Ma,
PROBLEM 11.19
A piece of electonic cqui
Fuster is dropred so Im
mus. After impact the equips experiences an acceleration
of a=—kx, where Ki a constant and i he compression of
‘he packing material. U the packing malcil experisnect a
maimum compresion of 20 mm, determino the maximum
acceleration of the equipment,
SOLUTION
Separate and iterate
Use 1) = mvs = 002 mand v, =0, Solve ford
= Laon? besos?
‘Maximum aceleracion.
ne = Ain (40, 0004002) = 800 més
a= 800 m7 4
PROPRIETARY MATERIA 3 2 he Nas Con Ni al Me of i Mam ma edie,
rar hurt ay aro yma hate se pron of phd pe eed
‘Sion tessa pty iT rsa nee pre ung am
A piece of electonic cqui
Fuster is dropred so Im
mus. After impact the equips experiences an acceleration
of a=—kx, where Ki a constant and i he compression of
‘he packing material. U the packing malcil experisnect a
maimum compresion of 20 mm, determino the maximum
acceleration of the equipment,
SOLUTION
Separate and iterate
Use 1) = mvs = 002 mand v, =0, Solve ford
= Laon? besos?
‘Maximum aceleracion.
ne = Ain (40, 0004002) = 800 més
a= 800 m7 4
PROPRIETARY MATERIA 3 2 he Nas Con Ni al Me of i Mam ma edie,
rar hurt ay aro yma hate se pron of phd pe eed
‘Sion tessa pty iT rsa nee pre ung am
PROBLEM 11.20
Based on experimental obewvatons tbe aceleration of: patil defined by the relation a =~(0.1+ sin 8),
‘where a and x are expres in mA and meters, sepoctivey. Knowing that = 0.8 m apd that y més
‘when 4 =U, determino (2) the velocity oF the parce when = 1m, () the position where the ven is
rim, () the maximum veloc
‘SOLUTION
Wehe
Wien x=0,v@1nis
E
© ICM 08e054-03
90328 ms 4
sun) =
m tos i )=0
“ oem 70mm 4
Wien x= 01080154
1 corona
7 0800 OT yy
Yan «0100001394 cu LU 0
nosed ma?
“ Yeu = 0 mis À
PROPRIETARY MATERLAL. © 209 the Minit Compr tA gh soo pf Mao be a
naa dd my font a ear vn he a person el pew Sie ae
Sento hdl Sth Se oa eons Paes Paden a
Based on experimental obewvatons tbe aceleration of: patil defined by the relation a =~(0.1+ sin 8),
‘where a and x are expres in mA and meters, sepoctivey. Knowing that = 0.8 m apd that y més
‘when 4 =U, determino (2) the velocity oF the parce when = 1m, () the position where the ven is
rim, () the maximum veloc
‘SOLUTION
Wehe
Wien x=0,v@1nis
E
© ICM 08e054-03
90328 ms 4
sun) =
m tos i )=0
“ oem 70mm 4
Wien x= 01080154
1 corona
7 0800 OT yy
Yan «0100001394 cu LU 0
nosed ma?
“ Yeu = 0 mis À
PROPRIETARY MATERLAL. © 209 the Minit Compr tA gh soo pf Mao be a
naa dd my font a ear vn he a person el pew Sie ae
Sento hdl Sth Se oa eons Paes Paden a
PROBLEM 11.21
String from x 20 wih ao initial velocity, pace is given an acceleration a = 0.5/0? 249, where a and
‘ae expressed in més and mé, respectively, Determine (a) the position of the particle when v=24 ms,
(0) the speed of te particle when x= 40m.
‘SOLUTION
Weine CT
When 120,90 Et fee
or IES
« Foios
(a) When y= 24 mis: 4 449-7
or send
o
er va ta ms €
morte Maru. 6300 e Mi Conan, nM el pt Hé a os
Eo e talco presio i ig nl concep ena le cg ee,
String from x 20 wih ao initial velocity, pace is given an acceleration a = 0.5/0? 249, where a and
‘ae expressed in més and mé, respectively, Determine (a) the position of the particle when v=24 ms,
(0) the speed of te particle when x= 40m.
‘SOLUTION
Weine CT
When 120,90 Et fee
or IES
« Foios
(a) When y= 24 mis: 4 449-7
or send
o
er va ta ms €
morte Maru. 6300 e Mi Conan, nM el pt Hé a os
Eo e talco presio i ig nl concep ena le cg ee,
PROBLEM 11.22
‘The section of a parle i defined by the ation a= À V5, whee sa constant, Knowing that 0
and y= 81 més at 4 = and that v= 36 més when x= 18 m. determine (a) the velocity ofthe pace when
220 m (0) the time required forthe particle t come to rest
| SOLUTION
Le) Webwe
sota
| Wien x=0 valia:
When sitcom Zoe us)
a Er
Finally
When «=20 m: 20° 2-190
A vr
0) Wetave Hanf
fa
as [00
|
Loa Ann |
Loa 20-919
Wien ve: a9
‘The section of a parle i defined by the ation a= À V5, whee sa constant, Knowing that 0
and y= 81 més at 4 = and that v= 36 més when x= 18 m. determine (a) the velocity ofthe pace when
220 m (0) the time required forthe particle t come to rest
| SOLUTION
Le) Webwe
sota
| Wien x=0 valia:
When sitcom Zoe us)
a Er
Finally
When «=20 m: 20° 2-190
A vr
0) Wetave Hanf
fa
as [00
|
Loa Ann |
Loa 20-919
Wien ve: a9
PROBLEM 11.23
The acceleration of panic is defined by the relation a = -O., there a is expressed inn and y in in
Knowing hat at = the velocity i 40 i, determine (a) the distance the partici wll vel before coming
to est, (6) time reputed forthe pate o come 1 es, (che time required or the pale 10 bs reduced
by SO percent fi intial value
‘SOLUTION
@
Separa and integra with
Distance ore,
Tor v=0,
¿Lucio <
10)
mon rauf)
turrones
O tros
a <
‘PROPRIETARY MATERIAL 290 To Mr Cal. a iis ced a por is Sal mp de pet
end el noon br np es erry pon oh aay, wa end ee
‘Ren cence panty Shon hel arp Prana Sh
The acceleration of panic is defined by the relation a = -O., there a is expressed inn and y in in
Knowing hat at = the velocity i 40 i, determine (a) the distance the partici wll vel before coming
to est, (6) time reputed forthe pate o come 1 es, (che time required or the pale 10 bs reduced
by SO percent fi intial value
‘SOLUTION
@
Separa and integra with
Distance ore,
Tor v=0,
¿Lucio <
10)
mon rauf)
turrones
O tros
a <
‘PROPRIETARY MATERIAL 290 To Mr Cal. a iis ced a por is Sal mp de pet
end el noon br np es erry pon oh aay, wa end ee
‘Ren cence panty Shon hel arp Prana Sh
PROBLEM 11.24
A Dowling ball s dropped om a boat so tht it tikes the
surface of à lake with a speed of 25 fs. Assuming the ball
‘experiences downward veelerion of 2100.92 thes
in the water, determine the velocity ofthe bl when it tis
‘the boom of the lake.
SOLUTION
WA 28 MS, rn
210-090 = -
. 10 y
ero 090 and nas
Wh 3-0 3
eo 33083 Me
Since vp > 6, write
4 =e)
he
Integrating,
Pod nn
eee
MIT
11238910" 1
335 €
[PROPRIETARY MATERIA. © 297 Ve BH Cnn, I sigh el Ne ps al e ld,
‘mer nbd fm by as mr. ii rir sis prin Pat, el god ep
Beano pr conn er dra pep par saa th
Jul ndo pom
A Dowling ball s dropped om a boat so tht it tikes the
surface of à lake with a speed of 25 fs. Assuming the ball
‘experiences downward veelerion of 2100.92 thes
in the water, determine the velocity ofthe bl when it tis
‘the boom of the lake.
SOLUTION
WA 28 MS, rn
210-090 = -
. 10 y
ero 090 and nas
Wh 3-0 3
eo 33083 Me
Since vp > 6, write
4 =e)
he
Integrating,
Pod nn
eee
MIT
11238910" 1
335 €
[PROPRIETARY MATERIA. © 297 Ve BH Cnn, I sigh el Ne ps al e ld,
‘mer nbd fm by as mr. ii rir sis prin Pat, el god ep
Beano pr conn er dra pep par saa th
Jul ndo pom
u -
PROBLEM 11.25
), where i a constant, Kong tha
= 4m, determine (a) the constant,
ofthe price,
‘The aceceratio of» particle is defined by the reluion a= 0.4 —
1 1=0 the particle starts om ees at x à m and thal when 4
(5) the position of ths article when v= 6 ms, (0) the masinum vlad
| sorurion
Werne
a
Aus (> [osa
1
m Lina sopas
ue
o toto o
Aminen ag 0409
a
Seva sm
10157 4
© Weine
Ten
a k
Wim: A)
aña arena
| osas
“ 12520 4
PROPRIETARY MATRELL. € 202 the Meur Compare, AY igh ey fr Aa be ied
‘vec a duet nar by a mn, at th tr wen prs lee od et
Soetoro onsen polly to ifr hse Com ron o sl hm
PROBLEM 11.25
), where i a constant, Kong tha
= 4m, determine (a) the constant,
ofthe price,
‘The aceceratio of» particle is defined by the reluion a= 0.4 —
1 1=0 the particle starts om ees at x à m and thal when 4
(5) the position of ths article when v= 6 ms, (0) the masinum vlad
| sorurion
Werne
a
Aus (> [osa
1
m Lina sopas
ue
o toto o
Aminen ag 0409
a
Seva sm
10157 4
© Weine
Ten
a k
Wim: A)
aña arena
| osas
“ 12520 4
PROPRIETARY MATRELL. € 202 the Meur Compare, AY igh ey fr Aa be ied
‘vec a duet nar by a mn, at th tr wen prs lee od et
Soetoro onsen polly to ifr hse Com ron o sl hm
PROBLEM 11.25 (Continued)
€ The maximum velocity occurs when a 0.
VAR
sam 4
Analtertive sohn so begin with a D).
Int Dar
040
ma jose
Thus y,
1
vet
2 store
[PROPRIETARY MATERIAL. © 203 he Mate Ccp, AY iis one Nee Mal be rind,
ed yo ar ay ma st or wien pas he al. ed aa ed
esas uds ro Ibid one Dorso mt,
€ The maximum velocity occurs when a 0.
VAR
sam 4
Analtertive sohn so begin with a D).
Int Dar
040
ma jose
Thus y,
1
vet
2 store
[PROPRIETARY MATERIAL. © 203 he Mate Ccp, AY iis one Nee Mal be rind,
ed yo ar ay ma st or wien pas he al. ed aa ed
esas uds ro Ibid one Dorso mt,
PROBLEM 11.26
A ati is projected to the righ rom the position x = with an inti! velocity of ms wecleaton
Of the particle is defined by the relation a=-0.60" where a and y ate express in mv and mis,
respectively, determine (a the distance the particle wil have travel when ls velocity 8 m, (8) the tins
when ¥= 104 () the time raja forthe parte o tuve 6
SOLUTION
Wehe E 06
Wien amt [vn [Losas
or avg 06%
= a w
0-4)
= am
© Werne ow”
When 0.29mi: [rss [ose
m Ae = 06
. foe
Wher v= mis q
=: 172225 4
Weine Klon
Now
PROPRIRFARY MATERIAL. © 2603 Te ei Cai oo of hs Ml ah
‘pbs or ted 0 Fran a ic rien pao po, ld Te
‘itn rnd aly Me Mf el app Boao ic,
A ati is projected to the righ rom the position x = with an inti! velocity of ms wecleaton
Of the particle is defined by the relation a=-0.60" where a and y ate express in mv and mis,
respectively, determine (a the distance the particle wil have travel when ls velocity 8 m, (8) the tins
when ¥= 104 () the time raja forthe parte o tuve 6
SOLUTION
Wehe E 06
Wien amt [vn [Losas
or avg 06%
= a w
0-4)
= am
© Werne ow”
When 0.29mi: [rss [ose
m Ae = 06
. foe
Wher v= mis q
=: 172225 4
Weine Klon
Now
PROPRIRFARY MATERIAL. © 2603 Te ei Cai oo of hs Ml ah
‘pbs or ted 0 Fran a ic rien pao po, ld Te
‘itn rnd aly Me Mf el app Boao ic,
PROBLEM 11.26 (Continued)
9
= ot
When x6 m
rd
An alternative solution i begin with Pa, CD.
“Ten
Now
Pr
io «fa
ne Tears
Mi =
“ CES EE
“Which last the same equation as above.
[PROPRIETARY MATERIAL © 298 Tac Men Cs, MeN ht ee prof i ad may Le der
pecker hoy moa lh trie pum of ys od de ed
ty on Haft dna cre pepe Gmc a
9
= ot
When x6 m
rd
An alternative solution i begin with Pa, CD.
“Ten
Now
Pr
io «fa
ne Tears
Mi =
“ CES EE
“Which last the same equation as above.
[PROPRIETARY MATERIAL © 298 Tac Men Cs, MeN ht ee prof i ad may Le der
pecker hoy moa lh trie pum of ys od de ed
ty on Haft dna cre pepe Gmc a
PROBLEM 11.27
‘Based on observations, the spect of a jogger can be approximated by the
relation v= 75(1~ 0.4)", where wand are expressed in mi and ils.
respectively. Knowing ae à 20 at 2=0, detemino (0) the distance the
Jonger has run whew 21h, (0) he jogger’ acceleration in RU at 2
{6) the time required forthe jogger o un 6 mi
aur-in
0) Wohne
ÉTECEEC
© Font)
When à = 6 mi
100049 =021 w
1 pa
PL Le
1 >
RAT
«= 715 mi 4
PRE)
PIM OREA "1
OS.
om ED
am)
E]
ERAN
A]
pr
va
= 0832205
1303 min À
PROPRIETARY MATERIA. © 200 Tus Mate Capi eg rent No ora the Move wa Be diet
ese tet hy om yey oa ae jot cr pene y Flot re
ttn tees ond svar ratty ate Mfrs be cpp Up ambas eee
‘Based on observations, the spect of a jogger can be approximated by the
relation v= 75(1~ 0.4)", where wand are expressed in mi and ils.
respectively. Knowing ae à 20 at 2=0, detemino (0) the distance the
Jonger has run whew 21h, (0) he jogger’ acceleration in RU at 2
{6) the time required forthe jogger o un 6 mi
aur-in
0) Wohne
ÉTECEEC
© Font)
When à = 6 mi
100049 =021 w
1 pa
PL Le
1 >
RAT
«= 715 mi 4
PRE)
PIM OREA "1
OS.
om ED
am)
E]
ERAN
A]
pr
va
= 0832205
1303 min À
PROPRIETARY MATERIA. © 200 Tus Mate Capi eg rent No ora the Move wa Be diet
ese tet hy om yey oa ae jot cr pene y Flot re
ttn tees ond svar ratty ate Mfrs be cpp Up ambas eee
PROBLEM 11.28
‘Experimental data indicate that in a region downsteearn of a
given louvered supply vet, the velocity of the emit ar is
defined by »=0 IAA, whore y and x are expresced in mis and.
meters, respectively, and x, isthe inal diverge veloc of
the aie For vy =3.6 mis, determine (a) the acceletion ofthe air
atx=2m, (0) sui ore air to flow from x= 10
rim.
SOLUTION
@ Werwe
|
When x 22 mi
© Weine
From xT mw 2
ae
"x
us sus)
v al x
a2-0052 mi 4
Lap a ea
BT mo
20
OO
6079
PROPRIFTARY MATERIAL © 209 ne Men Congres A ih oe ot af Mana nay be pie
rie yn i re of ee en ed
tn aceon Dir ang ahnt
‘Experimental data indicate that in a region downsteearn of a
given louvered supply vet, the velocity of the emit ar is
defined by »=0 IAA, whore y and x are expresced in mis and.
meters, respectively, and x, isthe inal diverge veloc of
the aie For vy =3.6 mis, determine (a) the acceletion ofthe air
atx=2m, (0) sui ore air to flow from x= 10
rim.
SOLUTION
@ Werwe
|
When x 22 mi
© Weine
From xT mw 2
ae
"x
us sus)
v al x
a2-0052 mi 4
Lap a ea
BT mo
20
OO
6079
PROPRIFTARY MATERIAL © 209 ne Men Congres A ih oe ot af Mana nay be pie
rie yn i re of ee en ed
tn aceon Dir ang ahnt
PROBLEM 11.29
‘The accctran due to gravity at an altitude y above the surf of
expressed as
“Toray
where a and y are expressed in "and fect, respectively. Using this expression,
‘compute the height reached by a prject red vertical upward from the trace
‘ofthe earth fit intl velocity i (a) 1500 As, (8) 3000 fe, (0) 36,700 fs,
SOLUTION
Wehave
When
(o »y=1800 N:
5 =3000 ni:
sou?
CR
Y “SOLO À
3000)" |
ae
Yang MOTION À
PROPRIETARY MATERIAL. © 30 The NC Mi Capen, eg No por ft Mi may be dg
‘er otal x mas ion ar ey pon thease, ma en a
‘ito aes ondo pued re Ie esac pro co emi ana
E
”
‘The accctran due to gravity at an altitude y above the surf of
expressed as
“Toray
where a and y are expressed in "and fect, respectively. Using this expression,
‘compute the height reached by a prject red vertical upward from the trace
‘ofthe earth fit intl velocity i (a) 1500 As, (8) 3000 fe, (0) 36,700 fs,
SOLUTION
Wehave
When
(o »y=1800 N:
5 =3000 ni:
sou?
CR
Y “SOLO À
3000)" |
ae
Yang MOTION À
PROPRIETARY MATERIAL. © 30 The NC Mi Capen, eg No por ft Mi may be dg
‘er otal x mas ion ar ey pon thease, ma en a
‘ito aes ondo pued re Ie esac pro co emi ana
E
”
PROBLEM 11.29 (Continued)
© 1 =36,700 Ms
or on 23090 €
he velocity 36.00 Ms is approximaly the escape velocity vg fom the earth. Bor 9
Youre 4
PROPRIETARY MATERLAL © 209 The Wem Compre Ine. A hs eee fart of ma ne be dy
‘oral ded ny oa a ns ia DJ mare fe pacers ad Bj te Hed
ria nar sd adas pc Me ford dr nc parao omar acne nant,
lv pr
© 1 =36,700 Ms
or on 23090 €
he velocity 36.00 Ms is approximaly the escape velocity vg fom the earth. Bor 9
Youre 4
PROPRIETARY MATERLAL © 209 The Wem Compre Ine. A hs eee fart of ma ne be dy
‘oral ded ny oa a ns ia DJ mare fe pacers ad Bj te Hed
ria nar sd adas pc Me ford dr nc parao omar acne nant,
lv pr
ry PROBLEM 11.30 Î
| ‘he sen dst iy of «pre tiling ad al
! ines gti ar nd fm coer af eth
|| hep iste ran ee a andr oe ace de
i I
Proce el un ee ete fi ca oo
A Bean (at 30 here)
SOLUTION
Vete
ven
ne
(emana merino mi
* mena vs 4
PROPRIETARY MATERIA. € 209 The Mi Copado, be, A ii remo. por is ol ea,
‘yee st yf sl y mae oa ro rt pra of ea roe ee eo
dende Arme Ptr coh a,
| ‘he sen dst iy of «pre tiling ad al
! ines gti ar nd fm coer af eth
|| hep iste ran ee a andr oe ace de
i I
Proce el un ee ete fi ca oo
A Bean (at 30 here)
SOLUTION
Vete
ven
ne
(emana merino mi
* mena vs 4
PROPRIETARY MATERIA. € 209 The Mi Copado, be, A ii remo. por is ol ea,
‘yee st yf sl y mae oa ro rt pra of ea roe ee eo
dende Arme Ptr coh a,
PROBLEM 11.31
‘Tho velocity of « particle is v=y[l-sinGa7J]. Knowing thatthe partite starts fo the origin with an
initial velocity», determine (0) ts position and is acceleration a = 37, () it average velocity dering the
interval 15010 4>7.
SOLUTION
@ Weine
ALTO =
©
mar,
sip 2236040 4
Also
Using Be. (0)
PROPRISTANY MATERIAL 6209 Th eC Cour, be, AL gt sor, Me pa fs Sa a e nd
dame ay om by ay na ps ven pon fh li, ml bd ad
‘Ree ref tly co ht cl app pont
‘Tho velocity of « particle is v=y[l-sinGa7J]. Knowing thatthe partite starts fo the origin with an
initial velocity», determine (0) ts position and is acceleration a = 37, () it average velocity dering the
interval 15010 4>7.
SOLUTION
@ Weine
ALTO =
©
mar,
sip 2236040 4
Also
Using Be. (0)
PROPRISTANY MATERIAL 6209 Th eC Cour, be, AL gt sor, Me pa fs Sa a e nd
dame ay om by ay na ps ven pon fh li, ml bd ad
‘Ree ref tly co ht cl app pont
PROBLEM 11.31 (Continued)
Auer: |
er)
fot
(5)
cor
tbe sgt o 0367-0
aro
PROPRIPEARY MATERIA. 200 Te Mine Conan Is AB hs ec at fi Moe arb pa
‘pm or ne lo fe na rar write poof nr et a ed
hance nen eh, ine fr ala o eatin rot are ae ae a,
Auer: |
er)
fot
(5)
cor
tbe sgt o 0367-0
aro
PROPRIPEARY MATERIA. 200 Te Mine Conan Is AB hs ec at fi Moe arb pa
‘pm or ne lo fe na rar write poof nr et a ed
hance nen eh, ine fr ala o eatin rot are ae ae a,
PROBLEM 11.32
‘The velocity o sider is defino bythe elation v= sin (a). Denoting the velocity and he postion
ofthe adc at 1-0 by amd. espectvch, and knowing thal the man displacement ofthe aides
is 26, show that (a) Y (1 +:300)/200,. (6) the maximum valve of the veloc occurs when
DR.
| SOLUTION
Le Asa += van
hen cp äh Se
exces
Now Lo avncag+9)
At 120.2%) [lam [sincere so
di = r
or sue]
+ ones 14
mt Dar)
Now ober th gg oes ten co 4/46) =. Then
San = 2419 ee CD)
Pa
Sinai or a . =.)
or sv =
Squaring bat ide of his équation
el ~ Dagan, + V9 =v? —
PURA
o OED.
An cs. on of Al Be pc,
PROPRIETARY MATERIAL. 209 ie Mei Coop.
PR did ym ry yes Ra de fe mane oros of ple a gon ed
Mote oxic ray ioe na repr pes
‘The velocity o sider is defino bythe elation v= sin (a). Denoting the velocity and he postion
ofthe adc at 1-0 by amd. espectvch, and knowing thal the man displacement ofthe aides
is 26, show that (a) Y (1 +:300)/200,. (6) the maximum valve of the veloc occurs when
DR.
| SOLUTION
Le Asa += van
hen cp äh Se
exces
Now Lo avncag+9)
At 120.2%) [lam [sincere so
di = r
or sue]
+ ones 14
mt Dar)
Now ober th gg oes ten co 4/46) =. Then
San = 2419 ee CD)
Pa
Sinai or a . =.)
or sv =
Squaring bat ide of his équation
el ~ Dagan, + V9 =v? —
PURA
o OED.
An cs. on of Al Be pc,
PROPRIETARY MATERIAL. 209 ie Mei Coop.
PR did ym ry yes Ra de fe mane oros of ple a gon ed
Mote oxic ray ioe na repr pes
PROBLEM 11.32 (Continued)
(9) Fes observe that nu, occur when au +=. “The comesponding value of is
fer]
Substtting fist for cos and hen for y
ol
aa iaa]
salia Y
met
PROPRIETARY MATERIA. © 30 The aCe Compases. A eh rose rt of Ml a oa
‘me reo oat ia e oo npr e e ad, ee ed
‘Sib snes ented af a dbl cana pre yoo aan sigs Mon
(9) Fes observe that nu, occur when au +=. “The comesponding value of is
fer]
Substtting fist for cos and hen for y
ol
aa iaa]
salia Y
met
PROPRIETARY MATERIA. © 30 The aCe Compases. A eh rose rt of Ml a oa
‘me reo oat ia e oo npr e e ad, ee ed
‘Sib snes ented af a dbl cana pre yoo aan sigs Mon
PROBLEM 11.33
A mori enters a fieeway at 45 Kavi and accelerates
itumly 10 99 kn. rom the ameter in the car, he
‘motors knoe hat she traveled 02 km ile aelerain.
Detenine (a) the acceleration of the ca, (9) the time
ruta rc 9 kh,
SOLUTION
0 jon of the
Data:
exo same
rm]
at to)
NS-125
1500
-10003 a
PROPRIETARY MATERIA. © 300 Ye Gen Cop, Inc A e se, pa of ral ey ipo
[du nr Say am athe rr wien pao ala, on ed
ero tant nda rca Screed te prea Tsk Ma
A mori enters a fieeway at 45 Kavi and accelerates
itumly 10 99 kn. rom the ameter in the car, he
‘motors knoe hat she traveled 02 km ile aelerain.
Detenine (a) the acceleration of the ca, (9) the time
ruta rc 9 kh,
SOLUTION
0 jon of the
Data:
exo same
rm]
at to)
NS-125
1500
-10003 a
PROPRIETARY MATERIA. © 300 Ye Gen Cop, Inc A e se, pa of ral ey ipo
[du nr Say am athe rr wien pao ala, on ed
ero tant nda rca Screed te prea Tsk Ma
= PROBLEM 11.34
A truck travels 220 m ig 10 while being decelerated at a
constan rae 006 mA, Dotermine (a) inal velo,
(0) its final velocity, (c) the distance waveled during the
fist 15
‘SOLUTION
CR
201
AO 1.259 ms 4
©) BinaLselciy votar
v=250+ (09400) 00 ms
€ Distance travel daring first LS.
La
ear
esco sain 4
[PROPRIETARY MATERIAL € 09 Th Main Cm a A ee ok an of hs Mona may Be ye
er dd yom oy np swf riven prin pe te pet
‘Sereno i ifs cc res a ch Ma
A truck travels 220 m ig 10 while being decelerated at a
constan rae 006 mA, Dotermine (a) inal velo,
(0) its final velocity, (c) the distance waveled during the
fist 15
‘SOLUTION
CR
201
AO 1.259 ms 4
©) BinaLselciy votar
v=250+ (09400) 00 ms
€ Distance travel daring first LS.
La
ear
esco sain 4
[PROPRIETARY MATERIAL € 09 Th Main Cm a A ee ok an of hs Mona may Be ye
er dd yom oy np swf riven prin pe te pet
‘Sereno i ifs cc res a ch Ma
Em PROBLEM 11.35
Assuming a uniform accleaton of 11 MAT and knowing
A. Aero tte mec fcr a pss 4 $30 mi, dermis
PHARE (a) the time required forthe cart reach 8, () the sped of
km | the car as it passes 8.
| souunion
© Tina onc
mi AA Rs, ya Melt, oat st
soho?
DT
suisse
44+ as)? ICI
u
sans
Rejecting the negative mo.
© Sposa
ug 504 mi À
RATA MATERIAL. 1320 x Me Ceogn eA a cc, p of Ma mr Be ie
‘emake don? nym By a a a DJ e por of the llo. alpen a
‘tron ans ens ported Selo a Ia ae Pian Drs me
Sonor on pr
Assuming a uniform accleaton of 11 MAT and knowing
A. Aero tte mec fcr a pss 4 $30 mi, dermis
PHARE (a) the time required forthe cart reach 8, () the sped of
km | the car as it passes 8.
| souunion
© Tina onc
mi AA Rs, ya Melt, oat st
soho?
DT
suisse
44+ as)? ICI
u
sans
Rejecting the negative mo.
© Sposa
ug 504 mi À
RATA MATERIAL. 1320 x Me Ceogn eA a cc, p of Ma mr Be ie
‘emake don? nym By a a a DJ e por of the llo. alpen a
‘tron ans ens ported Selo a Ia ae Pian Drs me
Sonor on pr
N | PROBLEM 11.36
LE a group af students anne n model rocket inthe vertical direcion. Rad on tacking
T ua, they determine that the altitude of the rocket was 89.6 fat the end of the powered
" ‘parachute failed to deploy sa that the racket fell fieely to the ground after reaching its
DT
: we
an |
ec - ama
aed At
Then 102 (282 MSN +2(-32.2 Ms” gas — 89.6) M
{PROPRIETARY MATERIAL € 3099 Ts Mind Camp eA ge emo pur Haul may Be pie
(nn dd as form hy ny ms, tte rape of pao, al en ead
‘Beanery onlay nt Meh
LE a group af students anne n model rocket inthe vertical direcion. Rad on tacking
T ua, they determine that the altitude of the rocket was 89.6 fat the end of the powered
" ‘parachute failed to deploy sa that the racket fell fieely to the ground after reaching its
DT
: we
an |
ec - ama
aed At
Then 102 (282 MSN +2(-32.2 Ms” gas — 89.6) M
{PROPRIETARY MATERIAL € 3099 Ts Mind Camp eA ge emo pur Haul may Be pie
(nn dd as form hy ny ms, tte rape of pao, al en ead
‘Beanery onlay nt Meh
PROBLEM 11.37
A sprimer in 100-m ace acelerates uniformly forthe Fest 35 m and the runs
‘with constant velocity. he sprinters time for the fst 35 m in 54 , determino
(a) his acceleration, (b) his final velocity (es time for the race,
‘SOLUTION
Given: O=x=35m, u 2 constan
35m<x 100m, »
ALO, 0=0 ven
Find
@a
© ywhen 2 =100.m
9 hen x=100m
@ Weine corola? fr as
1
36m Las 4 9
gas ss
“ a= 24005 ve
20m 4
CET for 38 msi 100,
Now 2042-0) foe 05138
When 235 m ac = 224005 mi )OS m)
or Yay 129628 ms Pis 21296 is 4
© Wehe Kan enl-n) ir 38m< 100m
When x=100.m: 10m 2 35m 4 (129628 mA 5.48
or nal: 4
PROPRIETARY MATERIAL. © 200 the Mc Cong, I. A or jr fa Mov! D pt
Per ced. fare ya nto je rl mas of rl, a on ld
eo rado pony Mc Mitr ttn ore repr Pan ot i a
ore hap
A sprimer in 100-m ace acelerates uniformly forthe Fest 35 m and the runs
‘with constant velocity. he sprinters time for the fst 35 m in 54 , determino
(a) his acceleration, (b) his final velocity (es time for the race,
‘SOLUTION
Given: O=x=35m, u 2 constan
35m<x 100m, »
ALO, 0=0 ven
Find
@a
© ywhen 2 =100.m
9 hen x=100m
@ Weine corola? fr as
1
36m Las 4 9
gas ss
“ a= 24005 ve
20m 4
CET for 38 msi 100,
Now 2042-0) foe 05138
When 235 m ac = 224005 mi )OS m)
or Yay 129628 ms Pis 21296 is 4
© Wehe Kan enl-n) ir 38m< 100m
When x=100.m: 10m 2 35m 4 (129628 mA 5.48
or nal: 4
PROPRIETARY MATERIAL. © 200 the Mc Cong, I. A or jr fa Mov! D pt
Per ced. fare ya nto je rl mas of rl, a on ld
eo rado pony Mc Mitr ttn ore repr Pan ot i a
ore hap
@ Ter
and
weine
Thea,
“u
sad D
CR
and
and
428
cap
458
CD,
ase
PROBLEM 11.38
A small package is released from rest al and
‘moves along the skate wheel eoaveyor ABCD.
‘The peckago has uniform pecceration of
D 45 més as moves down Setions AB and CD.
es fa eo am even a CF
2 the veloci of the package a D ix 72 má
ts determine (a) the distanced between C and Da
(0) the time required forthe package o each D.
Pal)
We =0+ 2(4.8 ms )3-0) m
Ame Ce = 52666 ms)
era damen
02m EEE
40m 4
vota
53666 me =0+ 8 m8 Yay
DATE
72 ole 5.3666 mis Ami Ve
Lo = 0381965
PROPRIRTARY MATERIA. 209 Te een! Cuisine At eel ds Man ma Be ed
Pen er nt la o Bayne thn jr wren pm of te yaar, nl oe
‘Kein sas lap Set ad re ppt wo sing an
and
weine
Thea,
“u
sad D
CR
and
and
428
cap
458
CD,
ase
PROBLEM 11.38
A small package is released from rest al and
‘moves along the skate wheel eoaveyor ABCD.
‘The peckago has uniform pecceration of
D 45 més as moves down Setions AB and CD.
es fa eo am even a CF
2 the veloci of the package a D ix 72 má
ts determine (a) the distanced between C and Da
(0) the time required forthe package o each D.
Pal)
We =0+ 2(4.8 ms )3-0) m
Ame Ce = 52666 ms)
era damen
02m EEE
40m 4
vota
53666 me =0+ 8 m8 Yay
DATE
72 ole 5.3666 mis Ami Ve
Lo = 0381965
PROPRIRTARY MATERIA. 209 Te een! Cuisine At eel ds Man ma Be ed
Pen er nt la o Bayne thn jr wren pm of te yaar, nl oe
‘Kein sas lap Set ad re ppt wo sing an
PROBLEM 11.38 (Continued)
Kom,
fr Bae,
weave eet ctas
o 3m 2 (82666 male
e hac 055901 à
Final ty Lan az len (LBD 0 58901 +038196) 5
o 120654
PROPRIETARY MATERIA. 200 ie No MA Con, A ii ote Se of e Al ma e gt
‘eh ore ny fon by ct, eh ra ori porcion oh Far ar on de nt
ert calc Sab iu hel ac por en sn i Mm,
Kom,
fr Bae,
weave eet ctas
o 3m 2 (82666 male
e hac 055901 à
Final ty Lan az len (LBD 0 58901 +038196) 5
o 120654
PROPRIETARY MATERIA. 200 ie No MA Con, A ii ote Se of e Al ma e gt
‘eh ore ny fon by ct, eh ra ori porcion oh Far ar on de nt
ert calc Sab iu hel ac por en sn i Mm,
PROBLEM 11.39
A police olor ina pat! car parked ia a 70 kn speed zone chere a passing automobile waveling a a
‘ow, consta poet Relieeing that the driver ofthe automobile might be stented, the officer sare hit
far, seceleratesunifornly to 90 km in $ 5, and, maintaining a constat velocity of 90 km, overakes he
motorist 42 safer he automobile passed him. Knowing that 18s elapsed before de lficer began pursuing
the motor, detennine (a Me dite Le air Ice befre overtaking the motors, (4) Uh
speed.
SOLUTION
er à
CR NS GE
Ger Tas as
Bra Gr =90 kav 90 kav = 25 mi
(Parolen
Deren)
a Pe
Abo, AUDE EL
arte Go ess com
pu scies staat 29
ares (oan wets nto
von
rn-asın 4
© temerity Dot
Arten men
“ me
« a. 191mn 4
ovata tans peo
A police olor ina pat! car parked ia a 70 kn speed zone chere a passing automobile waveling a a
‘ow, consta poet Relieeing that the driver ofthe automobile might be stented, the officer sare hit
far, seceleratesunifornly to 90 km in $ 5, and, maintaining a constat velocity of 90 km, overakes he
motorist 42 safer he automobile passed him. Knowing that 18s elapsed before de lficer began pursuing
the motor, detennine (a Me dite Le air Ice befre overtaking the motors, (4) Uh
speed.
SOLUTION
er à
CR NS GE
Ger Tas as
Bra Gr =90 kav 90 kav = 25 mi
(Parolen
Deren)
a Pe
Abo, AUDE EL
arte Go ess com
pu scies staat 29
ares (oan wets nto
von
rn-asın 4
© temerity Dot
Arten men
“ me
« a. 191mn 4
ovata tans peo
PROBLEM 11.40
As relay cannes 4 enters the 20-u lo exchange vr with w
Speed oF 129 mó, he begins o slow down. tle hands te baton (0
runner 41.82 ltr as they leave the exchange zone withthe
@ turas aorta
ars be
“e 210008 4
| ao (debt
Mans: Ga IRAN
5078 ms
Former: wa
When wer OTE Ws? +20)
Door ig "20603 mt
ae =20 4
(0) Forrummer ET
where 44 th tie at which be begin onu.
Aus: AS
or 107-2398
Runner 8 should stat to run 259 s before À reaches ino exchange one. «
PROPRIETARY MATERIA D 20 Te Mean Congo e. A es tof ie Mal may in
‘ota sad nye by ng as fear poof fab ow en ea
‘Rei ian sein stereos Pw aang ho
As relay cannes 4 enters the 20-u lo exchange vr with w
Speed oF 129 mó, he begins o slow down. tle hands te baton (0
runner 41.82 ltr as they leave the exchange zone withthe
@ turas aorta
ars be
“e 210008 4
| ao (debt
Mans: Ga IRAN
5078 ms
Former: wa
When wer OTE Ws? +20)
Door ig "20603 mt
ae =20 4
(0) Forrummer ET
where 44 th tie at which be begin onu.
Aus: AS
or 107-2398
Runner 8 should stat to run 259 s before À reaches ino exchange one. «
PROPRIETARY MATERIA D 20 Te Mean Congo e. A es tof ie Mal may in
‘ota sad nye by ng as fear poof fab ow en ea
‘Rei ian sein stereos Pw aang ho
PROBLEM 11.41
les À and B ae travcling in adjacent Nighy L
0 ave the posiios und spect shown. Kn
at automobile 4 has a constant acceleration of 18 Ws? and
that B has a constant deceleration of 1.2 4°, determine
(@) when and whore À will ovetake B, (5) the spe u ch
sutomobile a hat tine,
sa
een
TOS
—
nenne o
Le soessare us
ede taal COUT
0
(o
Kama: 35214096 = 754528 044
126, -75~0
150546
1222 and 4
Dre:
320150903415 05)"
PROPRIETARY MATERIAL. 290 Se Nie Canin, tN iis oe Me ft of he Ma mae Be pane
‘eed nn yf a a rage of per wae
s
les À and B ae travcling in adjacent Nighy L
0 ave the posiios und spect shown. Kn
at automobile 4 has a constant acceleration of 18 Ws? and
that B has a constant deceleration of 1.2 4°, determine
(@) when and whore À will ovetake B, (5) the spe u ch
sutomobile a hat tine,
sa
een
TOS
—
nenne o
Le soessare us
ede taal COUT
0
(o
Kama: 35214096 = 754528 044
126, -75~0
150546
1222 and 4
Dre:
320150903415 05)"
PROPRIETARY MATERIAL. 290 Se Nie Canin, tN iis oe Me ft of he Ma mae Be pane
‘eed nn yf a a rage of per wae
s
PROBLEM 11.41 (Continued)
| ® Yeats sn 15054
Es: 123524180505)
1,2629 0 1,7425 mith €
EG M =82.8-1.215.05)
vp 3474 Ms
PROPRIETARY MATERIAL. © 290 The Nu Capes, Aires. por e Ma may e ad,
‘ere o aa oar oa of er a od
a elder pde Gr rad are cn oar ag M
s
| ® Yeats sn 15054
Es: 123524180505)
1,2629 0 1,7425 mith €
EG M =82.8-1.215.05)
vp 3474 Ms
PROPRIETARY MATERIAL. © 290 The Nu Capes, Aires. por e Ma may e ad,
‘ere o aa oar oa of er a od
a elder pde Gr rad are cn oar ag M
s
PROBLEM 11.42
In a boat race, boat is Fading boat 120
and both boats are traveling ta constant speed
of 1OS mish. At 1=0, the boats accent a
constant rates, Knowing thal when 1 passes 4.
5 and yy =138 mi, determine (a) the
acceleration 04, (8) the accleraion o.
‘SOLUTION
@ Wehave
CRT
and
Aus:
rado ta
(2p =105 ai ECTS
Pet mith =198 Us
198 tvs =154 e+ a (8)
Pe
anne dad? Garon
rent rise
rons ass no eos ms
en
80 eas
ansia
at oo Ms a yb dhe,
‘ral sed ma hy eo i jr te prin oh yar ied joie ae
‘tite each nd tly Mere Trt dl ree pat ng Maw
In a boat race, boat is Fading boat 120
and both boats are traveling ta constant speed
of 1OS mish. At 1=0, the boats accent a
constant rates, Knowing thal when 1 passes 4.
5 and yy =138 mi, determine (a) the
acceleration 04, (8) the accleraion o.
‘SOLUTION
@ Wehave
CRT
and
Aus:
rado ta
(2p =105 ai ECTS
Pet mith =198 Us
198 tvs =154 e+ a (8)
Pe
anne dad? Garon
rent rise
rons ass no eos ms
en
80 eas
ansia
at oo Ms a yb dhe,
‘ral sed ma hy eo i jr te prin oh yar ied joie ae
‘tite each nd tly Mere Trt dl ree pat ng Maw
PROBLEM 11.43
Bones are placed on a chute at uniform intervals af time 1, and
slide down the chute with uniform acceleration. Knowing that as
ox Bis released, the precoding ox À has lead sid 6 m
nd tha ter they’ are 10 m apart, determino () the vale
OF ter (8) the acceleration ofthe boxes
SOLUTION
E Es,
Let 12 = 1 se the time when the boxes are 30 A apar,
ster te
ta na (as A
CE bon
AS
For lao Aa zu)
a ten ein 8 ba o
at Paty tye aga = 30
1 2.2
30= La v PE
D alg ak Hs ©
1
Lera
5 3
a ae o
Diving Fain (y EG
iat nes 4
a
(0 Soin £5.29 er
area |
ROPMIETANY MATERIAL. © 290 Te No Cena. me nh nte, o us ltd ar le did
‘phd vic ap foro ban oat pi M eon of Pt mad Ed o
‘teenie rt rap Poner no shoe
Bones are placed on a chute at uniform intervals af time 1, and
slide down the chute with uniform acceleration. Knowing that as
ox Bis released, the precoding ox À has lead sid 6 m
nd tha ter they’ are 10 m apart, determino () the vale
OF ter (8) the acceleration ofthe boxes
SOLUTION
E Es,
Let 12 = 1 se the time when the boxes are 30 A apar,
ster te
ta na (as A
CE bon
AS
For lao Aa zu)
a ten ein 8 ba o
at Paty tye aga = 30
1 2.2
30= La v PE
D alg ak Hs ©
1
Lera
5 3
a ae o
Diving Fain (y EG
iat nes 4
a
(0 Soin £5.29 er
area |
ROPMIETANY MATERIAL. © 290 Te No Cena. me nh nte, o us ltd ar le did
‘phd vic ap foro ban oat pi M eon of Pt mad Ed o
‘teenie rt rap Poner no shoe
PROBLEM 11.44
‘Two automobiles 4 and B ace approaching
eich ote in adjacent highway les. At
10, A and Bar I kon apar, hir speeds
fe ¥, =108 kin and vg = 63 ky and
they ine al Points P and Q, respectively.
Knowing that passes Point (240 safer
was there and that B passes Pint 2-42 s
fcr À wae there, determine (0) the
nor accelerations off and (0) wen
the vehicles pass each oer, (e) the speed.
‘of bat ie
SOLUTION
Wem steed? etant
mo, soe Sr
sea osa
“ aos ON:
(6) When ocu pas each other
‘Then O0 hy 0250 a 117.5 md
020005 mig 1000
o 0.05045tjg +98 ~2000
Solving
0822 5 and = 1908s
120-219-2085 4
PROPRIETARY MATERIA. 203 ir Men Cyan, A a ono pon o St may be dt.
‘wc rel nr rae io rr en pena of alada. me oa e ed
Re ps are tn
‘Two automobiles 4 and B ace approaching
eich ote in adjacent highway les. At
10, A and Bar I kon apar, hir speeds
fe ¥, =108 kin and vg = 63 ky and
they ine al Points P and Q, respectively.
Knowing that passes Point (240 safer
was there and that B passes Pint 2-42 s
fcr À wae there, determine (0) the
nor accelerations off and (0) wen
the vehicles pass each oer, (e) the speed.
‘of bat ie
SOLUTION
Wem steed? etant
mo, soe Sr
sea osa
“ aos ON:
(6) When ocu pas each other
‘Then O0 hy 0250 a 117.5 md
020005 mig 1000
o 0.05045tjg +98 ~2000
Solving
0822 5 and = 1908s
120-219-2085 4
PROPRIETARY MATERIA. 203 ir Men Cyan, A a ono pon o St may be dt.
‘wc rel nr rae io rr en pena of alada. me oa e ed
Re ps are tn
PROBLEM 11.44 (Continued)
Weine ep Cp yb aat
At va = 17.3 ms +(0.30045 OR.)
2375610
$ 997855 km 4
PROPRIETARY MATERIAL. 309 es ci Can be. AU re ene pa y ir Maal y e nna
id dba fm iy my me ts wre E os, a ed Roe ea
‘Ronen ony acct ml arpa ania he od
Weine ep Cp yb aat
At va = 17.3 ms +(0.30045 OR.)
2375610
$ 997855 km 4
PROPRIETARY MATERIAL. 309 es ci Can be. AU re ene pa y ir Maal y e nna
id dba fm iy my me ts wre E os, a ed Roe ea
‘Ronen ony acct ml arpa ania he od
PROBLEM 11.45
Car A is parked along the northbound
Jane of gay, and car is tve.
in the soulhbound lane at a constan!
speed of 60 mh. At £=0, A starts nd
ects ata constant rate ay. whl
at r= Ss, B begins to slow down ih a
constant deceleration of magnitude 4/6.
Knowing that when the cas pass each
her x=294 and 9, = vg, determine
(a) the accelention ay, (3 when the
vehicles pas euch oer, () te distance
ete the vehicles st 170.
SOLUTION
kur 20: moral
lie
ort
uses sOy 760 mi = Wis
Au=ss sa = ER MANSO = 440
For ass orto ale,
PO OR =~}
Gas +=) Pre)
A
Assume £5 «when the cars pass eae othe,
ime (uch
mi DAC ET
1
x, 72941: zu
‘PROPRIETARY SUATERLAL.& 200 Th Mn Comic, A gs i Mp of ie Moa a din
‘pd dung ay form eb sm, ht prion of aor, ced Net ad
‘Sei cond ater Wr tap tae a oh
Car A is parked along the northbound
Jane of gay, and car is tve.
in the soulhbound lane at a constan!
speed of 60 mh. At £=0, A starts nd
ects ata constant rate ay. whl
at r= Ss, B begins to slow down ih a
constant deceleration of magnitude 4/6.
Knowing that when the cas pass each
her x=294 and 9, = vg, determine
(a) the accelention ay, (3 when the
vehicles pas euch oer, () te distance
ete the vehicles st 170.
SOLUTION
kur 20: moral
lie
ort
uses sOy 760 mi = Wis
Au=ss sa = ER MANSO = 440
For ass orto ale,
PO OR =~}
Gas +=) Pre)
A
Assume £5 «when the cars pass eae othe,
ime (uch
mi DAC ET
1
x, 72941: zu
‘PROPRIETARY SUATERLAL.& 200 Th Mn Comic, A gs i Mp of ie Moa a din
‘pd dung ay form eb sm, ht prion of aor, ced Net ad
‘Sei cond ater Wr tap tae a oh
PROBLEM 11.45 (Continued)
ES
Then wae
e AA ML +520
Solving La 20.955 and 14-105
CRUE 296 R= 0 Y
er Pen
6 Fromabove La = 7.005 4
ote: An acceptable solution cannot be found fi assumed a 1 = 9
fo) Wehave dare,
= 204 [440 HRS
a
200 0
oe Anand
PROPRIETANI DUATERIA. © 200 «Men Compan. A rest Me pr of te ol y Be poe
em rn ny foe rca ke ten pom of palo rl end eed
“ect nod ol nif dal cs prin ps sina be a
ES
Then wae
e AA ML +520
Solving La 20.955 and 14-105
CRUE 296 R= 0 Y
er Pen
6 Fromabove La = 7.005 4
ote: An acceptable solution cannot be found fi assumed a 1 = 9
fo) Wehave dare,
= 204 [440 HRS
a
200 0
oe Anand
PROPRIETANI DUATERIA. © 200 «Men Compan. A rest Me pr of te ol y Be poe
em rn ny foe rca ke ten pom of palo rl end eed
“ect nod ol nif dal cs prin ps sina be a
PROBLEM 11.46
“Two blocks 4 and B are placed on an inline as shen. At
120, 4 is projected the incline with a initial velocity
OF 23 1 and Bis leased rom ret The blocks pass each
other 1 5 Inter, and A reaches the baton of the inline
‘rom
the bottom of the incline reached by block 41621 fe and
That the acceleration of 4 and (due to gravity and
Seton) ae consant and are directed down the incline,
‘determine a) he acccerations ofA nd (1) the distance
(E) espec A when he block pa each her.
=
SOLUTION
@ Wehe 00 ala 01 wh
a
When DER) La
Then 0-27 by 420,21
“ e, 113
« amet 4
Now norte
sa pdas
2
AL 121, the blocks pas each other
Hood
axé
1s ON
E fer mone rnasm anes]
[Joos fase
or ay 370
PROPRIETARY mar. © 200 Te cn Compas, Ic. Al gn eo uz Mol my Be.
pc ar dred nay frm ya) moos, te rr no be, ad ed de hd
‘Teint cher andar pr BO lf hr mbr sar pe Pp M,
cagon
“Two blocks 4 and B are placed on an inline as shen. At
120, 4 is projected the incline with a initial velocity
OF 23 1 and Bis leased rom ret The blocks pass each
other 1 5 Inter, and A reaches the baton of the inline
‘rom
the bottom of the incline reached by block 41621 fe and
That the acceleration of 4 and (due to gravity and
Seton) ae consant and are directed down the incline,
‘determine a) he acccerations ofA nd (1) the distance
(E) espec A when he block pa each her.
=
SOLUTION
@ Wehe 00 ala 01 wh
a
When DER) La
Then 0-27 by 420,21
“ e, 113
« amet 4
Now norte
sa pdas
2
AL 121, the blocks pas each other
Hood
axé
1s ON
E fer mone rnasm anes]
[Joos fase
or ay 370
PROPRIETARY mar. © 200 Te cn Compas, Ic. Al gn eo uz Mol my Be.
pc ar dred nay frm ya) moos, te rr no be, ad ed de hd
‘Teint cher andar pr BO lf hr mbr sar pe Pp M,
cagon
PROBLEM 11.46 (Continued)
© mitra os Lorna
© Were ra
Amis 9 227 sa
PROPRIETARY MATERIAL. 2919 Meo oem, Me A go rc. a at ay e
ind dd x fama yo sna M BS i pon of ef a mal Ed
Beeches
© mitra os Lorna
© Were ra
Amis 9 227 sa
PROPRIETARY MATERIAL. 2919 Meo oem, Me A go rc. a at ay e
ind dd x fama yo sna M BS i pon of ef a mal Ed
Beeches
PROBLEM 11.47
Slider block A moves tw the Jef with a constant velocity of 6 mé.
Deren (a) the velocity of block (9) the velocity of poston D of
‘he able, () the relative velocity of potion Co the cable with respect
to pontion D.
rom he diagram, we have
24437 =comata
tren eth 0
und arto, 20 @
(o) Substting ino Eq.(1) ms + 3, 20
er vins 4 |
6) Fromihedigrm 35135 =enmunt
then en
vo=2miel 4
(9 Frum hedingron xy ye “constant
Then PRET
6m) (2 ms) E me
von=smst 4
PROPRIETARY MATERIAL. € 2009 te Mn Capa M, A a eme D an a hs owe my el
hd er ind e 9 o oy ny macs. ws sr prof ae, ee Re a a
Sis nner ly Wr ha mim ins Bran
Slider block A moves tw the Jef with a constant velocity of 6 mé.
Deren (a) the velocity of block (9) the velocity of poston D of
‘he able, () the relative velocity of potion Co the cable with respect
to pontion D.
rom he diagram, we have
24437 =comata
tren eth 0
und arto, 20 @
(o) Substting ino Eq.(1) ms + 3, 20
er vins 4 |
6) Fromihedigrm 35135 =enmunt
then en
vo=2miel 4
(9 Frum hedingron xy ye “constant
Then PRET
6m) (2 ms) E me
von=smst 4
PROPRIETARY MATERIAL. € 2009 te Mn Capa M, A a eme D an a hs owe my el
hd er ind e 9 o oy ny macs. ws sr prof ae, ee Re a a
Sis nner ly Wr ha mim ins Bran
PROBLEM 11.48
lock & stats rom reat und moves demand with a constant
secceration. Knowing that fer slider block 4 has moved 400 wm is
velocity e 4 ma, termi (a) he acelerations of and B, (9) the
velocity and the Change in poston PA lr 2s.
‘SOLUTION
From the digran, we have
sg By Senna
Then ro 0)
and ayr3ay=0 @
(a) Fa.@X ag 1309 =0 and ay is constant and
positive =>, is constant and negative
Also, Ea, (1) and (re) =0= (0
Le iO 2e Ga)
When jAr,|=04.m: Em)" «24,004 m)
e. ms 9 4
‘Ten, substtuting imo Eg.)
-20 wis? +30, =0
6676 1 4
PROPRIETARY MATEREAL. © 300 The Mii Compro Ic sis eft of Ae Ma o be a,
Tusa ar ind yey ys at fos ee md pew etn ead
Sic alll terran Pane
lock & stats rom reat und moves demand with a constant
secceration. Knowing that fer slider block 4 has moved 400 wm is
velocity e 4 ma, termi (a) he acelerations of and B, (9) the
velocity and the Change in poston PA lr 2s.
‘SOLUTION
From the digran, we have
sg By Senna
Then ro 0)
and ayr3ay=0 @
(a) Fa.@X ag 1309 =0 and ay is constant and
positive =>, is constant and negative
Also, Ea, (1) and (re) =0= (0
Le iO 2e Ga)
When jAr,|=04.m: Em)" «24,004 m)
e. ms 9 4
‘Ten, substtuting imo Eg.)
-20 wis? +30, =0
6676 1 4
PROPRIETARY MATEREAL. © 300 The Mii Compro Ic sis eft of Ae Ma o be a,
Tusa ar ind yey ys at fos ee md pew etn ead
Sic alll terran Pane
PROBLEM 11.48 (Continued)
9 Webwe Deren
(Balen
or md
1
Alo ve One +04 ba
Au=2s
em |
[PROPRIETARY MATERIA, © 20 The Nro Compa, Ana rc. Apr Bun ma e pa
rep aed ay oy a a, aa mre pf he Yar od Sea e ld
nr ne D sr IA Cra ana at
9 Webwe Deren
(Balen
or md
1
Alo ve One +04 ba
Au=2s
em |
[PROPRIETARY MATERIA, © 20 The Nro Compa, Ana rc. Apr Bun ma e pa
rep aed ay oy a a, aa mre pf he Yar od Sea e ld
nr ne D sr IA Cra ana at
PROBLEM 11.49
The elevator shown in the figure moves downward with constan
velocity af 15 Ra. Determine (a) the velocity ofthe cable €, (6) the
velocity of the counterwsight (ete relative velocity ofthe cable C
vith respect 10 the cevator, (4) the relative velocity of the
‘ountensight I respeto e cesto
J
SOLUTION -
Choose the postive direction doused.
Veloce ofeabte €.
Ye +27 =eonstant Tu
+ =0
Bu, PET <
or PET ve 30047 4
© Velocity of commierseieh W.
Yar constat
he rr vy rs wem 4
(6) Relative veloc of C with respect 0 E.
on =e Me =(-30 Ws) (415 Me AS Re
(a) Relative velocity of IP with respect to E.
hog = = Ve CIS 8) 01 8) ==30 Ms
vine 7300 51 4
[PROPRIETARY MATERIAL. © 290 no Nien MI Cm, A Hi pr Mal y pine,
rc eo yo yc a ren permi that wa bd
‘oon eon churn SS ft eel re pron po avast th Sa
The elevator shown in the figure moves downward with constan
velocity af 15 Ra. Determine (a) the velocity ofthe cable €, (6) the
velocity of the counterwsight (ete relative velocity ofthe cable C
vith respect 10 the cevator, (4) the relative velocity of the
‘ountensight I respeto e cesto
J
SOLUTION -
Choose the postive direction doused.
Veloce ofeabte €.
Ye +27 =eonstant Tu
+ =0
Bu, PET <
or PET ve 30047 4
© Velocity of commierseieh W.
Yar constat
he rr vy rs wem 4
(6) Relative veloc of C with respect 0 E.
on =e Me =(-30 Ws) (415 Me AS Re
(a) Relative velocity of IP with respect to E.
hog = = Ve CIS 8) 01 8) ==30 Ms
vine 7300 51 4
[PROPRIETARY MATERIAL. © 290 no Nien MI Cm, A Hi pr Mal y pine,
rc eo yo yc a ren permi that wa bd
‘oon eon churn SS ft eel re pron po avast th Sa
PROBLEM 11.50
BB an perreo
acceleration. IF the eouncerseight W moves through 30 in $
(a) the secclerations ofthe elevator and he cable €, (5) the velocity of he
ly | q dar
SOLUTION
‘We choose Positive diction donnant for motion a counterweight.
demon
Auı=ss, PET
mn Lao?
pza 0 al
(o) Acedera of and C.
Since WA Ye SCOT Ye yy =O, and ay +
Thus Ae ty = CARS). ag =240 eT 4
Also, Yow Zn = consi, 442,0, and te 42g 20
Tous: eBay ZA) AS, aan 4
(0) Feloity of elevator afer 5.
ms
ve =p gl =0 24 MANS)
PROPRIETARY MATERIA. © 709 Te Mco A Campus ns: ad Ho pat of il Mab dpe
BL y faro ob yma ne ls ps of Paar rn a ed
ra erin pol RC ra ld
BB an perreo
acceleration. IF the eouncerseight W moves through 30 in $
(a) the secclerations ofthe elevator and he cable €, (5) the velocity of he
ly | q dar
SOLUTION
‘We choose Positive diction donnant for motion a counterweight.
demon
Auı=ss, PET
mn Lao?
pza 0 al
(o) Acedera of and C.
Since WA Ye SCOT Ye yy =O, and ay +
Thus Ae ty = CARS). ag =240 eT 4
Also, Yow Zn = consi, 442,0, and te 42g 20
Tous: eBay ZA) AS, aan 4
(0) Feloity of elevator afer 5.
ms
ve =p gl =0 24 MANS)
PROPRIETARY MATERIA. © 709 Te Mco A Campus ns: ad Ho pat of il Mab dpe
BL y faro ob yma ne ls ps of Paar rn a ed
ra erin pol RC ra ld
ar PROBLEM 11.51
Ë that ae 8
of alters.
termine (0) the accelraons of À
Collar À stas from rest and moves pur With constant aeccleaio. Knowing
relative veloety of colar # with respect to colar 4 is 24 ins,
118, (0) the velocity and the change in positon
SOLUTION
Then
and
(a
rom the digan
24+ a+ Ue =) const
1442950 Oo)
4g V2 =0 a
Fa (Hand On
Also, Eg. (2)and a, is consent and negative =, is constant
an positive
then DEP er
Now DRE er
From Eg.)
Sottar
[PROPRIETARY MATERIA. © 209 Re Mei Capo, Ve A gt ene pur of br M u be dor
‘rca ied as fora by mcs se rns mie pte ea ud ha
che ander posed ce rk chen ropas races Me
“
Ë that ae 8
of alters.
termine (0) the accelraons of À
Collar À stas from rest and moves pur With constant aeccleaio. Knowing
relative veloety of colar # with respect to colar 4 is 24 ins,
118, (0) the velocity and the change in positon
SOLUTION
Then
and
(a
rom the digan
24+ a+ Ue =) const
1442950 Oo)
4g V2 =0 a
Fa (Hand On
Also, Eg. (2)and a, is consent and negative =, is constant
an positive
then DEP er
Now DRE er
From Eg.)
Sottar
[PROPRIETARY MATERIA. © 209 Re Mei Capo, Ve A gt ene pur of br M u be dor
‘rca ied as fora by mcs se rns mie pte ea ud ha
che ander posed ce rk chen ropas races Me
“
PROBLEM 11.51 (Continued)
2in= Sa
o ayediniet 4
an then
o ay stint?
© armés
or Von
how
mimos
or Yeo
ROPRISTN MATERA. © 209 Te Mean Conn, te A ihe one My of Mt e pe
‘ved or taal sf yy oth tr en prs of A io ol
a cede poy a Pr
2in= Sa
o ayediniet 4
an then
o ay stint?
© armés
or Von
how
mimos
or Yeo
ROPRISTN MATERA. © 209 Te Mean Conn, te A ihe one My of Mt e pe
‘ved or taal sf yy oth tr en prs of A io ol
a cede poy a Pr
PROBLEM 11.52
Inthe post
(a) he velit
velocity of portion Cof te cable with respect a nr A.
sown, collar 5 moves downward with a velocity of
iy of collar, () the velocity of potion C ofthe cat
12 in. Determine
ble, (e) the relative
SOLUTION
rm hedge
2g tye == constant
Then u o
and ay+ay o
lo) Substring into #4.) vy #20228)
From the diagram By, ye constan
Then Berre
E nds) Hyp 0
er ven dtinal 4
CR
= (48 nds) (2 ind
“ Yon =36 A4 4
PROPRIETARY MATERIA. © 2109 YY Mini Campin I Aa oe pc Mal a, he rt,
‘il eat mn oy y ae aa tre
‘Ronse mt ade cos ps He
a porn
Inthe post
(a) he velit
velocity of portion Cof te cable with respect a nr A.
sown, collar 5 moves downward with a velocity of
iy of collar, () the velocity of potion C ofthe cat
12 in. Determine
ble, (e) the relative
SOLUTION
rm hedge
2g tye == constant
Then u o
and ay+ay o
lo) Substring into #4.) vy #20228)
From the diagram By, ye constan
Then Berre
E nds) Hyp 0
er ven dtinal 4
CR
= (48 nds) (2 ind
“ Yon =36 A4 4
PROPRIETARY MATERIA. © 2109 YY Mini Campin I Aa oe pc Mal a, he rt,
‘il eat mn oy y ae aa tre
‘Ronse mt ade cos ps He
a porn
PROBLEM 11.53
Slider block 8 moves to the right with constr
i ® Pe velocity of 300 mms Determine (a) the velocity
er ser block A. (0) he ey of tion Ca
en } i Sie he oly of no Date
aii cabe (4) the tive velocity of portion Co the
‘aie with resp sider block À
SOLUTION
from the diagram
| Ten o
ES o
Also, weiave
Then o
[a a Br
loa + 200 mn 4
À conte diagam p(y He) cotnt
ma aunt
TS 20 mm
ve = nnd
{PROPRIETARY MATERIAL. 92909 Yo Ms Cope, it eel N pa ol me e ed
vm oat a o ap mos, jr ten mon pe te eo ndo
‘iio ones andes m fr ibe eps ere rng Me
Slider block 8 moves to the right with constr
i ® Pe velocity of 300 mms Determine (a) the velocity
er ser block A. (0) he ey of tion Ca
en } i Sie he oly of no Date
aii cabe (4) the tive velocity of portion Co the
‘aie with resp sider block À
SOLUTION
from the diagram
| Ten o
ES o
Also, weiave
Then o
[a a Br
loa + 200 mn 4
À conte diagam p(y He) cotnt
ma aunt
TS 20 mm
ve = nnd
{PROPRIETARY MATERIAL. 92909 Yo Ms Cope, it eel N pa ol me e ed
vm oat a o ap mos, jr ten mon pe te eo ndo
‘iio ones andes m fr ibe eps ere rng Me
PROBLEM 11.53 (Continued)
(0 From the diam Bean constant
“thea De ee
Substituting 600 mms 24200 mans) =
(0 Webave
or ou = 400 mms 4
PROPRISTARY MATERIAL. © 260 Me Maton Coping Al ight sere. a ar fi am mn be dt
‘pro red aaa tr wien pms of he pr el pn ed
‘ith mon under parm cow hr die cepa oes mt
(0 From the diam Bean constant
“thea De ee
Substituting 600 mms 24200 mans) =
(0 Webave
or ou = 400 mms 4
PROPRISTARY MATERIAL. © 260 Me Maton Coping Al ight sere. a ar fi am mn be dt
‘pro red aaa tr wien pms of he pr el pn ed
‘ith mon under parm cow hr die cepa oes mt
PROBLEM 11.54
AL the instant show, sider Block 3 is moving
‘with a consant acceleration, and is speed 5
150 mms, Knowing that air der Dick À
has moved 240 mm to the right its velocity is
0 mm, determine a) the acceleration of À
srl) the aeceention of po he
able, () e velocity and change i position of
Slider block # ar 4 a
SOLUTION
Prom the ig Beta) 2a constant
Then 29,00 o
and 2ay Ba, a
(@) Firstobserve ati block 4 move the right, y, and Fg. (1) = ve >. Then, in
Bq, (Datr=0
2050 mms) ~ 3)
e 00
Also ba. 2) andy = constant “>a = constan
‘Then Vs = SET dd)
When x4 = (y =240 mn:
(ms) = (100 ms? 4 24,240 so)
or a0 nv
E
or a, 53m € 4
PROPRIETARY MATEKIAL © 200 The Welt Compt eA es euro fr wf be Mena edo
‘phe dh ey fom oly ym, tre pa e alla, el ad ed
‘Zener oso poset ee Mfr Ra aa care prepare. Dona snk Oe Mt
AL the instant show, sider Block 3 is moving
‘with a consant acceleration, and is speed 5
150 mms, Knowing that air der Dick À
has moved 240 mm to the right its velocity is
0 mm, determine a) the acceleration of À
srl) the aeceention of po he
able, () e velocity and change i position of
Slider block # ar 4 a
SOLUTION
Prom the ig Beta) 2a constant
Then 29,00 o
and 2ay Ba, a
(@) Firstobserve ati block 4 move the right, y, and Fg. (1) = ve >. Then, in
Bq, (Datr=0
2050 mms) ~ 3)
e 00
Also ba. 2) andy = constant “>a = constan
‘Then Vs = SET dd)
When x4 = (y =240 mn:
(ms) = (100 ms? 4 24,240 so)
or a0 nv
E
or a, 53m € 4
PROPRIETARY MATEKIAL © 200 The Welt Compt eA es euro fr wf be Mena edo
‘phe dh ey fom oly ym, tre pa e alla, el ad ed
‘Zener oso poset ee Mfr Ra aa care prepare. Dona snk Oe Mt
PROBLEM 11.54 (Continued)
‘hen, subsctatng into Ha. 2)
2e, 4
or Dee
(8) Prom the solution 10 Problem 1153
wine
Then antojo
AP
( y
© Wehme Mb rai
Auızes va =150 ss 1-200 Jn NS)
a ven 0 mi 4
A PRE
aus DC = 050 mms
1 :
| Lean mnie yay
LC 200 may
or A!
rad or oy om el a9 noo, eB le pn
comi Compara. A sgh so. Al e dopo
(End rer Menor HO o re pea a,
poorer upon
‘hen, subsctatng into Ha. 2)
2e, 4
or Dee
(8) Prom the solution 10 Problem 1153
wine
Then antojo
AP
( y
© Wehme Mb rai
Auızes va =150 ss 1-200 Jn NS)
a ven 0 mi 4
A PRE
aus DC = 050 mms
1 :
| Lean mnie yay
LC 200 may
or A!
rad or oy om el a9 noo, eB le pn
comi Compara. A sgh so. Al e dopo
(End rer Menor HO o re pea a,
poorer upon
PROBLEM 11.55
lock B moves wma with a constant velocity of 20 mays.
nd its Velocity is 30 mm King that at 3 slider Block C
Tas move 87 mm Lo the righ, determine (a) the velocity of sider
block Cat #0, (9) the accelertons of and €, (ey the lame in
positon of block falter 5s.
SOLUTION
rom the digram
Br yg + fe =consant
Then Brg tig bye = o
and Bay tay tac =0 e
Give vo =20 mus bs
(00730 mm?
(a) Sitio ino Fa (Dat 0
rm) +420 =
e =10 ms rl 4
0) Wehave seco Woh ttc?
some (opaca
ac = 6 mis? e muni? à 4
Now
PROPRIETARY MATERIAL. © 20 Me Ment Compu. A gh ir pr of Ma er
awh ont y arf mg rs nt srs pero of i bie a hn
‘Sen ec eto in fre a ps Po
lock B moves wma with a constant velocity of 20 mays.
nd its Velocity is 30 mm King that at 3 slider Block C
Tas move 87 mm Lo the righ, determine (a) the velocity of sider
block Cat #0, (9) the accelertons of and €, (ey the lame in
positon of block falter 5s.
SOLUTION
rom the digram
Br yg + fe =consant
Then Brg tig bye = o
and Bay tay tac =0 e
Give vo =20 mus bs
(00730 mm?
(a) Sitio ino Fa (Dat 0
rm) +420 =
e =10 ms rl 4
0) Wehave seco Woh ttc?
some (opaca
ac = 6 mis? e muni? à 4
Now
PROPRIETARY MATERIAL. © 20 Me Ment Compu. A gh ir pr of Ma er
awh ont y arf mg rs nt srs pero of i bie a hn
‘Sen ec eto in fre a ps Po
PROBLEM 11.55 (Continued)
“Then, substuting ito Fg. (2)
32, +440) +6 ms?) =00
Deere or td
| © Wehne DAT
Asse ah =H en,
78m
yasni 4
‘PROPRIETARY MATERIAL, © 203 Te Mia Camps 1 ih rar part of i Male ar,
Merah sordo fo ty yma a I rar wien pean er ra jo ied
Rained tly Me i ca rr or od Mm
“Then, substuting ito Fg. (2)
32, +440) +6 ms?) =00
Deere or td
| © Wehne DAT
Asse ah =H en,
78m
yasni 4
‘PROPRIETARY MATERIAL, © 203 Te Mia Camps 1 ih rar part of i Male ar,
Merah sordo fo ty yma a I rar wien pean er ra jo ied
Rained tly Me i ca rr or od Mm
PROBLEM 11.56
Bock 1 stars from rest, Block 4 moves with a consta
acceleration, and sides block C moves to the sight with a
‘cantantacelestion ol 75 mm, King that at ¢=28 the
ects of and Care 480 munis dowward and 280 mn io
the right respectively, determine (a) the accelerations of A and,
(6) the int velocities oF À und €, () the change in position of
Sidor Calera.
From the digram
Ba 14) te constant
Then Sr tag Hye 20 ©
ad 30, +4, 20090 o
iver Ge
(00-75
NRK. vq 480 wb
ve = 280 mm +
(2) Le (2)and a, constan and a = constant = ay = consta
Then vy =O at
Atr=2s 480 mms 0,625)
A0 mms? or 2.240 ms? L 4
Substituting ato ba.)
30444240 mas?) +01 mnie?) = 0
45 ms et
PROPRIETE MATERIA. 203 Tie Mein Corp A ae pr of he Malay Be ee
(er duel y om $ y ar. mh U Jrs rn prin per, cm a ed
ac pat er ie tia tao re alta has an,
ae i pero
Bock 1 stars from rest, Block 4 moves with a consta
acceleration, and sides block C moves to the sight with a
‘cantantacelestion ol 75 mm, King that at ¢=28 the
ects of and Care 480 munis dowward and 280 mn io
the right respectively, determine (a) the accelerations of A and,
(6) the int velocities oF À und €, () the change in position of
Sidor Calera.
From the digram
Ba 14) te constant
Then Sr tag Hye 20 ©
ad 30, +4, 20090 o
iver Ge
(00-75
NRK. vq 480 wb
ve = 280 mm +
(2) Le (2)and a, constan and a = constant = ay = consta
Then vy =O at
Atr=2s 480 mms 0,625)
A0 mms? or 2.240 ms? L 4
Substituting ato ba.)
30444240 mas?) +01 mnie?) = 0
45 ms et
PROPRIETE MATERIA. 203 Tie Mein Corp A ae pr of he Malay Be ee
(er duel y om $ y ar. mh U Jrs rn prin per, cm a ed
ac pat er ie tia tao re alta has an,
ae i pero
PROBLEM 11.56 (Continued)
@ Wetase Cora
Arz 280 mms (re), + 75 mm s)
Ve 130 mm for A 4
Then, substituting into Eg, (1) at =
36,040) + ((30 mm) 0
wem aint
lc) Weave Al
ai oo osa
Stem ma
MROPRULTARY MATERIA. 036 Te een! Cog, A ve pe Mal pr
Ieper eno e, o Js wien pri Ja. jon a
‘Sr o nad anden periods noo o ar Ibal career iia aa Mal
@ Wetase Cora
Arz 280 mms (re), + 75 mm s)
Ve 130 mm for A 4
Then, substituting into Eg, (1) at =
36,040) + ((30 mm) 0
wem aint
lc) Weave Al
ai oo osa
Stem ma
MROPRULTARY MATERIA. 036 Te een! Cog, A ve pe Mal pr
Ieper eno e, o Js wien pri Ja. jon a
‘Sr o nad anden periods noo o ar Ibal career iia aa Mal
PROBLEM 11.57
Collar A sars fom xt at 1=D and moves downward with a constant
cocon of 7 inde Collar B moves upward with corstentseceleation,
And its ina veloc I 8 ins. Knowing that collar moves through 20 in,
between 1=0 end £=2 5, determine () the sccclertions of collar 8 and
loe €, (ih time at wih the velocity of block Cs ee, () the tance
through which block C wil have moved at tht time,
SOLUTION
tee +0
- thes e ica D
HT
tl ai nu ag o
me Given;
i
J meds
Wehe
wi nes
en te
ents, 6
20 ind) in) ag =0
sin or ame
PROPRURTARY MATERIAL. ©9290 oe Netix Cn. A gi ro, e of ae Ma up be epee
‘een et yoo hy a i me evo Be para ao eed
itn chy os el pri a ag he
Collar A sars fom xt at 1=D and moves downward with a constant
cocon of 7 inde Collar B moves upward with corstentseceleation,
And its ina veloc I 8 ins. Knowing that collar moves through 20 in,
between 1=0 end £=2 5, determine () the sccclertions of collar 8 and
loe €, (ih time at wih the velocity of block Cs ee, () the tance
through which block C wil have moved at tht time,
SOLUTION
tee +0
- thes e ica D
HT
tl ai nu ag o
me Given;
i
J meds
Wehe
wi nes
en te
ents, 6
20 ind) in) ag =0
sin or ame
PROPRURTARY MATERIAL. ©9290 oe Netix Cn. A gi ro, e of ae Ma up be epee
‘een et yoo hy a i me evo Be para ao eed
itn chy os el pri a ag he
PROBLEM 11.57 (Continued)
(8) Substituting ito Eq (1) at 1 =0
20-829 Hr), 0 (dein
Now senna
Wen yo <0 zus
| or 2 8
| 2 ors 4
Lae
© Werne set ours tag
iol? auf
Au seman 2s) hein (2
0667 in. o Ye oh =0667in TA
PROPRIGTARY MATE © 2009 Di Mao Copa a, A ie a. Be par fi Mina mL pn!
Iwo red fo ae mar ta ae ie pensa pe a Sand at
‘an hrs ply hen af amd ra In cbt os a
(8) Substituting ito Eq (1) at 1 =0
20-829 Hr), 0 (dein
Now senna
Wen yo <0 zus
| or 2 8
| 2 ors 4
Lae
© Werne set ours tag
iol? auf
Au seman 2s) hein (2
0667 in. o Ye oh =0667in TA
PROPRIGTARY MATE © 2009 Di Mao Copa a, A ie a. Be par fi Mina mL pn!
Iwo red fo ae mar ta ae ie pensa pe a Sand at
‘an hrs ply hen af amd ra In cbt os a
PROBLEM 41.58
cece
Collar 4 and sat fom res, and collar A moves wand with an
of Min 2. King a colla A man doer witha
‘mst acceleration and that tz velocity is 8 i
eternine (a) the necleation of block C () the distance rough which
block Call have moved aes 3s
vs efter moving 32 in.
SOLUTION
Frame diagram
1 ea) #2pe A) coma
Then entre o
and aura +40 =0 o
Given: Oe
CE
DITS
a, = contnt L
Wien AL,
CET
(2 Weine Vale Cu]
When yy Co) 2 ins (into =20,(12 0)
or PS
Then, subsitating io La (2)
AP im A) (in) bag 20
oe rind
o
210) ~
Now
‘Substituting nto Lg. (at 20
Wan =0 OF OCI =0
eg acai
te ea lamer
DE + a 0-6)
PROPRIREARY MATERIAL 8 799 he Mtn Coupes N At yet of dé Ml ela
‘emda ny fr oy ni a ef lm i ed
arn pn Mt lf tbe amor prin Hn ang rt
cece
Collar 4 and sat fom res, and collar A moves wand with an
of Min 2. King a colla A man doer witha
‘mst acceleration and that tz velocity is 8 i
eternine (a) the necleation of block C () the distance rough which
block Call have moved aes 3s
vs efter moving 32 in.
SOLUTION
Frame diagram
1 ea) #2pe A) coma
Then entre o
and aura +40 =0 o
Given: Oe
CE
DITS
a, = contnt L
Wien AL,
CET
(2 Weine Vale Cu]
When yy Co) 2 ins (into =20,(12 0)
or PS
Then, subsitating io La (2)
AP im A) (in) bag 20
oe rind
o
210) ~
Now
‘Substituting nto Lg. (at 20
Wan =0 OF OCI =0
eg acai
te ea lamer
DE + a 0-6)
PROPRIREARY MATERIAL 8 799 he Mtn Coupes N At yet of dé Ml ela
‘emda ny fr oy ni a ef lm i ed
arn pn Mt lf tbe amor prin Hn ang rt
PROBLEM 114
(Continued)
Pie [jo-aña
Loa
ÿ Luca!
Loam
hs, reso
m
à
> me eds
‘Theo, ck City moves downy (>) nd hn mores up (<0)
re
Now PTE
Mure [de Lea
we Der
rm,
ES
Sa
tes eV = =D in.
A ON
“Total distance treed
PROPRIETARY MATERIA, © 20106 Mas Caps In: A tra por Mamma e ope
‘ponte end y Dr o to sei pc yb cd
‘Ber enema oly Krone ia ps Du b hand
(Continued)
Pie [jo-aña
Loa
ÿ Luca!
Loam
hs, reso
m
à
> me eds
‘Theo, ck City moves downy (>) nd hn mores up (<0)
re
Now PTE
Mure [de Lea
we Der
rm,
ES
Sa
tes eV = =D in.
A ON
“Total distance treed
PROPRIETARY MATERIA, © 20106 Mas Caps In: A tra por Mamma e ope
‘ponte end y Dr o to sei pc yb cd
‘Ber enema oly Krone ia ps Du b hand
PROBLEM 11.59
“The system shown sets from wet, ad each component moves with san
acceleration. I the roatve accelerion of block C with respect to collar B
‘paar andthe relative acceleration of tock D with respect o Bock À
un? downward, determine (2) the volociy of Black Cafe 3, (0) he
‘eign positon oF block D ater,
SOLUTION
al ee
SEE
rom the gram
atte Data ye zona
E Then 22,120 11090 o
an Lay Vay ice o
GX Go 79 10m ~ ro) constant
hes 14012930 o
and gy 2up =0 o
Givers At 120, v= alarcon constan
don = 60 mm, de
(O Werne dap Heap
md mu
Sabino E) 0 (8)
IE DEE Deren
æ Wera 0
BR hay M0) (ar +02 0
“e rn 6
Ne os pe a Ms y be rt
ri po of epi, a eed he
a rept oe ang a
“The system shown sets from wet, ad each component moves with san
acceleration. I the roatve accelerion of block C with respect to collar B
‘paar andthe relative acceleration of tock D with respect o Bock À
un? downward, determine (2) the volociy of Black Cafe 3, (0) he
‘eign positon oF block D ater,
SOLUTION
al ee
SEE
rom the gram
atte Data ye zona
E Then 22,120 11090 o
an Lay Vay ice o
GX Go 79 10m ~ ro) constant
hes 14012930 o
and gy 2up =0 o
Givers At 120, v= alarcon constan
don = 60 mm, de
(O Werne dap Heap
md mu
Sabino E) 0 (8)
IE DEE Deren
æ Wera 0
BR hay M0) (ar +02 0
“e rn 6
Ne os pe a Ms y be rt
ri po of epi, a eed he
a rept oe ang a
PROBLEM 11.59 (Continued)
Solving os. (3) and (6) foray and ap
10 munis?
AUIS 3s: (40 m/s? (3 8)
w ome 4
Lo Weine row
een poco
yor RS nt 4
Solving os. (3) and (6) foray and ap
10 munis?
AUIS 3s: (40 m/s? (3 8)
w ome 4
Lo Weine row
een poco
yor RS nt 4
PROBLEM 11.60
The system shown tarts from rest, andthe length ofthe upper cord is used so
that, 8, and € ae italy atthe sane level, Fach component moves with a
‘consist seecleration, and fier 2 the reaiv change in positon of Dick € with
respecto block 41s 280 mm upward. Anowing that when the relative velocity 07
lla 8 with espec o block is RO mun denn, ih dsplaoements ef A
ud B are 160 mn downwand and 320 mm downward, respectively, determine
(a) he sccleratins o À and 44 ay > 10 mms", (1) the change in position of
block D en te velocity block C's 600 mund pur,
Prom the gra
= y j wen 2y,12v 1 yo = constant
EN mm mern w
Ot om at a
| Cable 2: (yp =34)+0% =>) constant
à nu o
7 Ing +2 ~0 (0)
re
Oh = 0-60
All accelerations constant a 2
on 2280 man À
Vas mis
| Bien
nO 320 me
8 10m
PROPRIETARY MATERIAL. 5 208 D ero Cori, Le, A rom e or of eM o do
re rn yo ab ay ma. ont the tr wien pre fable or mt oa aed
‘iin a nina na het ht vpn eran Mas
The system shown tarts from rest, andthe length ofthe upper cord is used so
that, 8, and € ae italy atthe sane level, Fach component moves with a
‘consist seecleration, and fier 2 the reaiv change in positon of Dick € with
respecto block 41s 280 mm upward. Anowing that when the relative velocity 07
lla 8 with espec o block is RO mun denn, ih dsplaoements ef A
ud B are 160 mn downwand and 320 mm downward, respectively, determine
(a) he sccleratins o À and 44 ay > 10 mms", (1) the change in position of
block D en te velocity block C's 600 mund pur,
Prom the gra
= y j wen 2y,12v 1 yo = constant
EN mm mern w
Ot om at a
| Cable 2: (yp =34)+0% =>) constant
à nu o
7 Ing +2 ~0 (0)
re
Oh = 0-60
All accelerations constant a 2
on 2280 man À
Vas mis
| Bien
nO 320 me
8 10m
PROPRIETARY MATERIAL. 5 208 D ero Cori, Le, A rom e or of eM o do
re rn yo ab ay ma. ont the tr wien pre fable or mt oa aed
‘iin a nina na het ht vpn eran Mas
PROBLEM 11.60" (Continued)
© Wetwe roza
and Per Gen HOH
! 2
Then Dar ever Hee a
AE 28, Ju 280 mus
a
ñ
280 mm 2
a
o ge 704-140 o
Sabin ito Eg.)
2a, +20, +(0, -140)=0
or 6
Now
DEA
CE]
fs
Ako aby MO Lag
When a 80 mm Le 80 (ox ~0,38 o
Then 160
Using En. OY ne más
then e. a= 20 mis À
and o ay 40m 4
Not that Ea, (6) 5 not used; ths, the problem i over determined.
PROPRULEARY MATERIAL, 0500 He em Compa nc. A gb ch par of Ma y pi
apr 0 tty fo a nt re ee prin do, ed go ed
com nd pty Sn for es a cae pr orcas e a
© Wetwe roza
and Per Gen HOH
! 2
Then Dar ever Hee a
AE 28, Ju 280 mus
a
ñ
280 mm 2
a
o ge 704-140 o
Sabin ito Eg.)
2a, +20, +(0, -140)=0
or 6
Now
DEA
CE]
fs
Ako aby MO Lag
When a 80 mm Le 80 (ox ~0,38 o
Then 160
Using En. OY ne más
then e. a= 20 mis À
and o ay 40m 4
Not that Ea, (6) 5 not used; ths, the problem i over determined.
PROPRULEARY MATERIAL, 0500 He em Compa nc. A gb ch par of Ma y pi
apr 0 tty fo a nt re ee prin do, ed go ed
com nd pty Sn for es a cae pr orcas e a
PROBLEM 17.60" (Continued)
Altematve ston
Weine CETTE
W504 2s Che]
Tien Maa Ha v4 Bars Cdt at, Cool
Wien Veg =80 mens La
50 mons = V2{ yep 320 m) — fa ¿A mr) |
& 20-20, Vo.)
Solving Eqs. (6) and (8) yields a, and ay
€) Subaiuting into Hg (5)
= 20-140 -120 eit
and into Ea.)
20 mms!) 40 nnd?) 20,
or ap 30 mv
Now Deren
Wien ve 000 ns 120 sm
Also
Ares
Le PACA
®
375 mn L 4
etic tm i are Mo ofr na ay ean
Intro rte e Jara e y es ot i re i ern fbi ml he eit
Terao hanes perl re mh carpe nase a,
Altematve ston
Weine CETTE
W504 2s Che]
Tien Maa Ha v4 Bars Cdt at, Cool
Wien Veg =80 mens La
50 mons = V2{ yep 320 m) — fa ¿A mr) |
& 20-20, Vo.)
Solving Eqs. (6) and (8) yields a, and ay
€) Subaiuting into Hg (5)
= 20-140 -120 eit
and into Ea.)
20 mms!) 40 nnd?) 20,
or ap 30 mv
Now Deren
Wien ve 000 ns 120 sm
Also
Ares
Le PACA
®
375 mn L 4
etic tm i are Mo ofr na ay ean
Intro rte e Jara e y es ot i re i ern fbi ml he eit
Terao hanes perl re mh carpe nase a,
PROBLEM 11.61
A panicle moves in righ ine
the igure, Knowing that stars rom the origin with y =
(a) plot the v 2 and x 2 curves for 0. 1. 206, (0) detemine ts
velocity, is posi, and he al distance rele sehr 2 125,
‘SOLUTION
(a
Initial conditions: 120, 162185, gi
Change in v equal sre under amt un
TA
OSI: ETC MAEM 66.8
ancien nen MENO RIE Mg = 130
Deren Ba S WERDE na 120 «
rare vy Hy ETES ION ra 20
PET
PROPRIETARY MATERIAL) 309 MC Covi I A he werd o of Mama u be pt
‘rhe or dred yor by ry mar mühe te rr inp of pao, or et pond rad
‘Katine oad Ser eo tn Cc pra Y paar cc mt
A panicle moves in righ ine
the igure, Knowing that stars rom the origin with y =
(a) plot the v 2 and x 2 curves for 0. 1. 206, (0) detemine ts
velocity, is posi, and he al distance rele sehr 2 125,
‘SOLUTION
(a
Initial conditions: 120, 162185, gi
Change in v equal sre under amt un
TA
OSI: ETC MAEM 66.8
ancien nen MENO RIE Mg = 130
Deren Ba S WERDE na 120 «
rare vy Hy ETES ION ra 20
PET
PROPRIETARY MATERIAL) 309 MC Covi I A he werd o of Mama u be pt
‘rhe or dred yor by ry mar mühe te rr inp of pao, or et pond rad
‘Katine oad Ser eo tn Cc pra Y paar cc mt
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