Solutions to Problems The following pages contain my solutions to selected problems from Engineering Mechanics, Dynamics, 10th Edition, R. C. Hibbeler, Pearson Prentice Hall, 2004, pp. 655-670. Chpt. 12. Kinematics of a Particle Chpt. 13. Kinetics of a Particle: Force and Acceleration Chpt. 14. Kinetics of a Particle: Work and Energy Chpt. 15. Kinetics of a Particle: Impulse and Momentum Chpt. 16. Planar Kinematics of a Rigid Body Chpt. 17: Planar Kinetics of a Rigid Body: Force and Acceleration

cAf"r'. l2

D- 2.*4 <rz'- VAm/s

lrdt = a dl

-rt = 2a- Ax

?00

a- = 4.5 *,/t-

xt tPIOO m

A ns.+

D-3 . oP+S

'sg = (tz t" * 2t'+ 3t) r-s=36t'+4t+3;=7zt+4 Ant.

.'J,

A* /= 2s, i =(sa)(a)+6a)P)+3=,n#

s=(zz)(z)n4=l4t-*

t-1,9 ]?1

1 = tro (us 3o") tg = % (s in 3o") t - 7'-tt g'

zA+B: lo=?;(cos36")t O

t. 5 = {n (sin go") * - ?,?7-^,-@I

c)-*@ ) /.5 = |o ta-n 30'- ?.9 t /-

l-2\

'= /t3, O

= t2.37 ^/t

uA

/rr"A

/ ccz \ <l;tcozo 3ooA

Ans "<--

af=6,q/s , et= Zn/s- ^-?cL-

17 = ?- - 39 = l.Z y-/snL1-h-

7 =

T= t''-'vt/t>

6lrn + 6L o' =

2.33 -/ r'

&=

a=

4+/.2-Ans"

D- t2.

&=A--A/E

_A

!A = Ie+feiBf=fr-A/s -A -Bir.-A/B _A _B

x = "o(-*t.#t)-rt:',,&nft,= -7?. I i' + i4. t4 I ,1*/h

4r en z ^4.- \<-' io. tso -trhs '"!,+/n = go'4 + X tlo'''" !'

= zo- /_t " * L.i) r-A^/n-Lr,l tyz: l€!'9o = / zoo .i .2m / u*

(z*zt- tzao)i' + 7sz8! = /€zt ! o 2828i , *nf n'3zaz 11 k''" *A*'

h-

.7r'a. = 'uA (L i + -L t)-A /, \\E- E!,

a- Alrs

6L- A/B

r_A

D- tz -

i,=tr=

- 2 r-/s{,

4'xt ,, tz4 i, * /".[r= Kt

- .-L

4

=-4;,f' 4ns'mls

-

7r = gF

cAFf, t3D-tr.

'fFhB9

m^^=E

m KD'sl( *uo

14FBD,S

D- 15. Canl'dMAt

fuB t

O"@

+7F= ^Au+ T= w^a OlrZf =*Bo+ m"g-T=tuBo @

^"i = (ha+ ruo) a-

a-=fus = Se'St =6"54

gs = 6.54 Ys. l, (nt

@ a -- rnecl = (4Ce .r+) = ts.o8 NAns.

-<<-

D- )7.

P=6lb

zotb {s re.lalnie *o B?= O,4 , /*= O,3

tuoj

fs P'P- e bF*o*=@.4)(2a)=* tb

P- tr :7 14 does net s /;de r./aliVe to E ,hax

Does

F8D

4 s /i/.

"f A t

*oJ?1^*=/rNo= A NA

- + rau)a-

LlKD

.+7tr = ('^u+ n*) aP = (*o**B) d

G = t (zonso)^32.2

4 - Z,ZG f*/ "'a = 2.76 tl/ta--e- g-E " r

FBD4=-A

D-/ I

FF = F^^,

FBD KD

>\ = tuen

F= F^o*=./rt-g = hd.n= tneoo,.

D- 18. Can*'d-

D-za.

?,g l(o.=) *6 = wr cu'(z)

&.) = l.ztj rol/r(r= py = 2.43 */s Ars.

--

t-J = l5o lb

FBD

/4chPt.

N= r-(or-g)=

4tb

KD

N = rnj cb 30"

F=7*N= "/*,aJ eos 3o'

= (o.z)(zo)een 3co =316 tb

{21= M&,L

N+mg= hQn=*7--)to l-4- 3z-z) = t7,7c tb3z,z | 4oo /

AJ = n'7o tb l' * Ans"

P 7tr =O1' 6/D- 24

etr

t(

Ur*r. = AT*AVJ(f'* tr)

^x = +^ (-)- t:) + n1 4h

(<o - s.46) to = L A@)- zt) - (zo)(/o) sin 3oo

!-= 3?-o {*/t f" ' Ant'

-* 4r- t2o{+/s:.

ffi&,

,bg

7.2A

D-2AT+ AVJ -- O

lnd =-^t ah

-r'^ Q"rt)6t"s1621 = z?-13

{z = 5.42 ^/ t Ans '

eI

A} B: I'*f"o:o-JT

KDFFD

zn = tuen'T-ne= )n'a'Jr

f = z(2?'43 "

r.sr)=58.q N' /.s

An-s"1

D-zs.

l35- ib

eallar

AI

AT+AVr+$Vu=O)L:i4.t {, * -g ZO - +.4 (r.}- rr.) = O

;#)t; €)e r) * t7)k,-,'t)-- (z s-o r)]

n-- _ (zo)(e+ <) = Q

-z'4--:- bA ns,

{ = l6.Of {*/t -r(-

l-4.= 4 to/ft

( o., fr' ^n tt". /.A ed)

Iff

tff

cA P/. tsD-3a.

FED,SEo//,'n.1 -t' F-

resi rf r>-nce s

Cbrs: ZFAt = A(m.-)(r- F.) at = m./<t-

(+qaoo - zsaa)zt = e'?;r:, Go - z o)

At=4.14s .Ans'

m"9

F.=D_

= 30 *onsiI

(so)qro) iu I

Cri,r;ng foree

7 -z- Rcl);n9' c- resislZnce

*.9 = 25o *ens

Q = pso)(to) tbT= g)Ao),rl

Fngix a

D - zo. Conl'd

Ergrne: ZfZt= A(*g)(P- T- Fe)at= ru.au-

(P - 4o,oco - 3ao) 1. /4 = ,ry (so- zo)

p=44rsoo tb =An"'

: D-32 " m^9 ^o/na:ZFAt=A(Z-.-)_l_

,o,n jat l---=,

r rr*.||-_ _l_tN

[,'l '',i

maj

(- n * ^rs7) ztt = (^an *u) Aqr

('-F+ g){ = (to+s) 6,7

32. z

F='7.8? lbf = 4*N =,lA lO

.l* = Q'7gq -A*Mu; !trAt = Z(rnu"-)

(^u9-r)ze = tuB Z<t

D*34 . erO.{z n/s

J ?4/s

Cbns er',rc-'l r'otn of tt/rx/ / ;o "^.f-l --sr?lA I l;lztg

t*

t1/1 eh apr-f uw, !

Mn-o* *u.% = aouo'r ,un i A

n, ( - -z-'O.t= "B 'A

7+g

_>

: -"'* o^'@o)- -s

e,-G, .-

Q).sx@4 ft.s-)(s)=7-o'Tu'= t.t ? --*l 17 ns ,

Tu'= t# * )

3.t = -fA' * no' @

.tu' = z-{ ^/ t or

4r|=-/ n/s or

CnvL /6

D*38.fAQA=

(,t) n =,:>

A)=_B

TB, d,g

ua=

(/t) =-c

rBa

fe,

Tuo du

tt=) -- z-4

2.4 roJ v1s

Ans^<-

Ya= 4;'" 2= 3 ;n

='f- L)-cc

4 (n-o)= 5 in,

= Zin.35 An st.€4a

-f

@o= 3 rat/ s

D-3? "

0-_o,du=O,a* r=o.

t\J re.v1sAns.l-o

;1.//,//111/.../

OZ

a)

o= 61t = 2t @

=dtn lt @z

)al f<flV-

tIOO r<vs.

t=5stz !0s :

: o,)

B=

TCR0.6 m'lD-45. Esto^-bl;sh Icp j"" *e^ bu. BC.

U.o CD +%=Hs. 4r- 4

fr dron36"

u", =

A-E=turrTE=rrrJ#- 6a

eno -- Tu = T,

rlt> M ., O/sin Bo"

u - I (4r"- \'b'+ts E \X tvr+3o") Ez*3o"

T.'?/=o'

ene = y' r,//s ) = A'"'

300 D

4 rad./ *

Cr"rt" 17

D-4q. 3tOO- lb car{s

v

)

NA

>F'1-- I

/

Lttg sin

trBD

= w6,a -CZO = l.7z 4

KD

) zM-L2

2\Q+

& = e sin Zo" = (=r.z) sin Zoaa-=u/t.at f*/I- . ^"t

=Q€z -3No+4Nu=C O- Q =+ No * Nts = ,"tg@?Za" @

3x@ 7Mu= G)Ggoo)coszoo

NB = l4/o lb *A+ A/A = / 97? tb *ry

trDD

Ans,<.--

D* sz

strt_, I -"t<2

KDa=*ftZf*=Q 4 Or= O

Z M" = rna& * In* = tha & * ,i= toz L-3

FSF = via4[r * 7,';''n To

?.8 t = oLt + %,")(o.zt)l -) oL =

ZFb = n^a -- o, - hg = -/-aaob: Qa)(?.t t) - (2") 12"4s) :) 9a

2.15 z-S'

zo Jzg2m

(

= 147"2 Nl3

D-53.

lsv

2o-*g

,4=e

wA"./ i *"= o.8 m

ra.d ias ofgyratro n

- KD

Q= r<

(o.s) I xA ns.<_-

) ZUo - r./tar + In aygrsin Zo" = Turi=a.+ -4jyo-

(2. g 0 tt" zf,) sin zoo = fQ.zs)^nd_= t.?o4 4 E)

s*

D-S{,

lgv

2-lq Q€a-r , *u= O,3 i*'tJ, !

/O.+m

ZF* = H &G

f = t^eC

ZF,= O:=> N= ng

€ 7Mu = *&GR - a"no = fi (a^* * 4-6)E-*t1 ** (E* -q) = ooE

rdk.a)

H&nIJ

A

KD

a =A +A-6 --A';e/n

o"/o= aE&o +< Sela

&A

&e = aA- aeln

t tt/S

Gda. ra-<.K

O.4 -+ O.3.8 -r*d t4s-

=gA ns.

#-