Solutions to FE Exam “Dynamics” Review Problems; Problems are Online at McGraw-Hill Website

Prepared by Stephen F. Felszeghy

CSULA Emeritus Professor of Mechanical Engineering

Start the web page for the book: Beer and Johnston, Vector Mechanics for Engineers, Statics and Dynamics, Ninth Edition, 2010, at: http://highered.mcgraw-hill.com/sites/0073529400/information_center_view0/ .

Look for the “Online Learning Center” box on the left. Click on the “Student Edition” link. Select a chapter from the pull-down menu. My solutions, which you will find below, are for the online problems that are associated with the following chapters and topics:

Chpt. 11: Kinematics of Particles Chpt. 12: Kinetics of Particles: Newton's Second Law Chpt. 13: Kinetics of Particles: Energy and Momentum Methods Chpt. 14: Systems of Particles Chpt. 15: Kinematics of Rigid BodiesChpt. 16: Plane Motion of Rigid Bodies: Forces and AccelerationsChpt. 17: Plane Motion of Rigid Bodies: Energy and Momentum Methods Chpt. 19: Mechanical Vibrations

Click on “FE Exam Review.”

Solve the problem, and select the answer from the multiple choices at the bottom. Click on the right-arrow to continue to the next problem. This process ends when you click on the right-arrow for the third time. To try to solve other problems from the same chapter, you will need to exit by clicking on, say, >Chapter XX> at the top, and restart “FE Exam Review.” Now you will be presented with all new, or a mixture of old and new, problems. After repeated trials, no new problems will appear.

As I mentioned in class, some of the online problem statements have errors in them, and some solutions and answers are wrong. For this reason, I have prepared a separate document that lists the errors and corrections. You can access this document at: http://www.calstatela.edu/sites/default/files/users/u28426/felszeghy/fe_exam_review_rev3.pdf . Although I shared the errors and corrections with McGraw-Hill, the company has not made any corrections on its Website.

The online problems are not numbered, except for being associated with chapter numbers. For this reason, I downloaded the online problems in no particular order, and numbered them consecutively in a decimal format, XX.X, where XX refers to the chapter number, and X stands for the sequence number. All the online problems numbered this way are included in the above “FE_Exam_Review_rev3.pdf” document under the heading: “Part 1, FE Exam Review, Online Problems and Solutions.”

My own solutions, which you will find below, follow the problem numbering scheme I established above. I include sketches in my solutions to allow you to identify the problems to which my solutions apply without necessarily having to refer to Part 1 of the above “FE_Exam_Review_rev3.pdf” document.

I wish you all the best on your computer-based FE exam!

tA*i, /laJo

,yt

= -/o4--c

= { ra.(t-/ 1-

s-

(,r-t = Uo* N.t = - /O *{tAn" .

&t=Q ary' t=Zs -,!--

(@LY,,dl4i= f rad. t-t T-'

t s-

u.=J

rtf =C)

.z{s;n e -

A.f t,=

.L

3',4

a

Zfr sin 4{-.{

9 -o '{f t.= 36" G4 s

/@ t=96"04s;

?.9/

- /g,oz s

?r = o-o (ca- e)t, = Zsob-'+t"fse'.04 -- 637 t zn

An,r.<

rt aa/ B rez,a inmortng r-J &yes

tlt T+ A.'

lxed i*-," 'a#a"ld

u/0"

A fr4a-ck reac/t es lin e

/2ad. rrr"tron in ,7 - /tred lo n

J= qnQ^ta;ltof <r- af t = 20

= /.zst g' -B /o cw loe

r e t = 2.03t s ; V. trr/cQia /o)g = taQ;1to) z,os 1

= 3.{3 th . P*

{du = l0 n/s

ts

I t /6os-t#(f = 4u 7ot,7/=0 af {=

&o= - 9q /do tn ,,) frnt,3 q.s/

ft*rut X = g^^, uthen e-= C : ,^7/(1t -eo{ = {o?,7 h

11.1

11.2

11.3

11.4

m

s'?n{_L

t

Asu ye/ara,

&r= Y/r,(-/

ca a ,4/ct t^ ate r\4

- r0- (s)(toJ

u= - {oo

ra-o<

_s O--= fA+ 2i!o

: o * (z)ts)(,'?=-too

?- /o7e" - -{oo:- -,Oo!, pg=-{ooW

-Ln

Ar".<_

laa

-/ [ne ft B fo

4= Sls-te -- -.1t

19

Trne ftr A *o4= SA

q

*rtt a^/'drat^^u

a rrire a* C

(n/et to" =

/QoYtoaoll-+l\ 3eoo /

Arr[y'e a"/ C

loo sin 3e "

ftoo x toaa I

l@/

a

z.a?4 s

too r

t

1.

5'o n qe-fn

B ge// fo*oCcby

B ;s behtnoL A -h-nd= P.aq4-t.slloo*loY)

= ?.1-? r+1 \ru

, !db,r. iz' {s

:

!E-L tX_

KD

4t= % +at = 5-4.?A{ t,f=A ,rrho- t= 5

= l.O/As4.2G5

v.16 fiz-l'1pq sin 9o= lv-, Q.J

&= - ?, I t s; n 3e"=.-1 ?OrC

f @ 6!=1,o/Q r : i{ = rrt o at= G)(t.aa)- l.eosIl{iq)n =2u,{{aZ /, / L Ans.,/

11.5

11.6

12.1

rN.sERr AFTE R @

I

k9

5

rQ1,4d.FED

-t_z. ra.= ir<a

ftcar'4{o= 4a6L = (!,3t)eo=4{"

12.2

c 2nlv in- p/an e

folee{ atVNole tOn I'

KD

cocyl < ar<Shcoun .

hdn

G ZU" = - Ln&n L cp's Zoo

M - *g L sln Zoo -- - in (afL sinZd") L co= Zclo

y''l = (r)p.rt)(2 s;" 7", - (r)Fa:24)*(2";, ze) (zeo" "c)14?-/42-7 N-tt

M = /42.7 A/- t?, 7 * fr*

f = tma-=

E:,"KD

(4)(ts) = 6c A/ * Ant'

Nt.'6a" a*^5

FBD

ZF^ =C + T- ^geetCc'=

C

T: ^g

co"r60"= (s-)(?.tt)c.p 6c" Ann ,

= lt-7LA/ #

ye

(a,ra

bl/ >-,./ \,a*tng

FBD

It<-,Cfu&n

KD

,,L

nqt fry")

7 F, = - lv1drJ -T sin 4 = -tud n

TF^ = O 4 Tc.o-€-kact = O)JElintaa:fe- T- be*uzea O V @,

tam 0 : /b{ah4Jo"LL sin G

er@

a

,a ad ?.8/ -ntsac6"v= _T= 6*4er\ 6' / t

A = 56-0'

10 '7

7rKO

m.l/

7nC.n

FBP

trv

,147

:-zr n

,Xor.g =

= hen

n€f4r-= (g = G4(q.tr)

4

rr= la"/ ^/c = An'"

13.I cA"+. rsQ = AT+ AV,

AT= it" -:=;l+^,f" !%;. ^,LtJu,'= Jl* {.t*+ *to 10.t1-+ rc (t);J a[

2L=l.tt Z--\-t= 5.s? ut

- rn,3 + - ^,,-j, ::,,oo=(r,")' ) o 17"*i) ( tlAV^ :

d

0r=1,37/ %=0rl = 4,3?f 4AT=- 4V, + alf = S?" // 2

C"rrt<rra*r'au ,f fota t fa,/ ln ear ,44 o ,t1 en'/*** : q,/

-+ / i:? '"

tust'3 = tuAo)'* ^u%'

-ru- - /-

(tdyto)t- (zo)(-){)= )7orot+ zo.Tu' -^_zee = /0q +20.6 A

e=?'-3'*0., = 3'-3r,* /{= -t5'+t4' @{o- {s lo - c- ts)

I'o

ryna9

fLI

'l,Mej

c@

I .<

A^axnFBD

Fso

zsa n/s--+:HA

fln"!-*

o- ^ox @+ -2c0 * 30o = /0%'* 2o4'

3oaAr3 * {o0

cA'= - /6, t, + */+""

Cabte. /eng+h i.s caxsi" TAerefore-,2xat frs* consf. = (ansf,

2zxn ^ - A*u

2*n- - xB

W,zrk * ei^erg1i

Heg lo"o* 2trAro =

*BjAxu- F AxB = *^r*; @

9^/tl;fute Q ,rto @, a',nat @ ,"Vt @rano(add rer otl *in9 u?fut ron r

G **siz * Hsl)zxu = + Ar*n'+ ws4i;)?" s i G ,t + "to) (t u? -- (,t u 8o) to'

i; = Z{eL, rA= t.os+ J"'

Coare rva/roo "f ht"/ l;n ear kle n e tt*u v ;J'C

r nn rn + ry{% = (^o+au)rr'4/,= lnA !A

= (o-os| G,so)

ha4+m6 ' la'oi{

4rt : /. tZt -A.J

13.2

13.3

13.4

)3,5

)2 /

SUV ro b,/sMnTAtr*n

+Fdtn*-f

J*Tnt -

wu{u'FFe= q;-ui

^%-T{ozrr- / I

O,z = a?'-{,o/o

Intt;^ltn olnen/t'Yn

Co//ft icnTnTaa/ se-r

Fina/lr1Op, gn*a

Caa tewcLf i-on a f t"/" I / to ea, k\ c rLl e ntuto, itnA'?rn + *i4+ = tuA T| * tuE %'

(e ooo) (/ 4 = 6000 q7'* lcoo -;or 10=%'*?-u' @

/+//O(@i t7=€%r'

Apr, /y inyt, lru - ^,Z')r::t ;!'o" B ;

trilt = we%'f.= wet/

= @co)(to.z) = ls6-U/AI o"3

An'' '

-

JL I'i - | ruf"l:,?.EI"TfuE* X'sPnne#

-44 = o. t JIUT n* (re w)

Q = AT+ AVA

K, -' O.OZ r-, t % =%,= tno, when

jr.= ^,q = (tc)gf.tt)

c

-

lot= ?g.l x lo-s 1-,

r AV.

trrs p

*ru

z'^ rg.tt* to-'')lAnr

O m/s.a-= O

2

C = *-q,,1; a^ 2 @,- K,) +LJ. (rJ-

u-7; ? Fr,d (q.s r)(a-oz - ?t-/ x r6's) * j to

{,)

t(o o

irn= E.6lV € ?:= -/.€CZ '--mq( mv S

t3,nTG

h,l

lL-tr,,rO

Tr. ?

d-_attn(r,',,*.rq

= W,*,.w(%), I

O= AT+ AVo +/

Soire C ano(gabrTr lite- in

"a

' -tLZi* [(-;, J :

i-n [(';)-)*Q-*,,(-r),b7." belit^t t(u;)-(v;),

6a,*9h' O= ^7ot @a^/ (q"), , a^/

An.r .

0.8?1 -{-

)4. t L'h ,z/- / 47s AcU+fl-xLln-'-tlt Yn

ufI'e

Ceater of nass : /. = 3w3tn

= lp',2, ru (za:) + I x 2m (t -)6w.d= c())(t)= 3oM

tAnt "--<=-

'/Z/A

fue *y

S're ;rttddle. fr.@ Conserr, of *olal lin€dr taaa*t en/uv' ir'a i ihuur- %u, = *rt'u* ^y-,

(o. i) (e) = o.t-u; * ( 0 {vo =

q, t'%

t4.L

i = €r':aE' +

€'*-i @e=-ds

Q * C.{x @ :> 6 = l,{<t7' - qr'

HA = 3*'Hyn'= 3x(t)(4) =

-4wT-J

l2 /"4' tr-rAn'' '<-

I 4,s m=tlg+

L

L

f=lgy--3

2j*{4,*2i-s/, w/,

\\,1. s Jl Itto-z{l

3 z -r[H=-o

f X pt4j - 5

= t [ ! (rc -/o) -j (- s6 .- t,t) + 4 k, *, ))= 3Z{"5' + / 3a 4, -&A- thL

/4-1 S-. @ boltom + -+t= 4+

3'

F- ftns,-t.z *KG)- r 0,8t{n%t

,yi O = 4T-+ 4V,c = {o - *^, (-r)'] * *r, [2-- iJ

9'=

14 .S wtB Yv

wR

4f,-_

vzo/z5y.

s

Coi/r s r'o, b"trl"u, Lu'oi; P ms3

^rny=

/

T=t.{f

H ru"=*odnhrcr

mo% -- !n,r{L fup[*

i Co//fsi"n belween ,u/ *y1r{, a\

nfU.n11,?-K

D

twflo+ q;o' n/rn ffi a{n

m*fi'/v

Ant '<_w.+{Y=Z

E hy.r=T=

ZF = d^ /'o' -o--.,At L-s -A/

ZF*=ffi; (o"t- G o.es;n=,1)

= Q.125 N *ry.

/1t J- tfLnP I . l.J

?ou = /6

u =O*AB

?(?.f

farl

-f

9"= too *qo O: a -[a. ) +/'a, )

-B Ve/e/s 1-e/B/n

eB = -fnm = ftol'(o"a) ' 6C r./s'lsing ICE o7 BC : bu.=.*E

= %e -_ (tqG.t-)

=2oCo"3 c,3 o,3

to"/r), = o *1 il' = ed'{E* 6I- = 268.3 9*-

VeJor diaTna'^ cl @:

(%tu)"=ln , 6tu{ tt c/B/n 3

536.7 bs''Jz

6

N F.=53 s.'z

VMS

14\3

\n

= $co

,a,(&^,-) = N- . BcL c:/F/e, B<-

r,a--l -^ fr"' '

-1Jt-

ft-- 4t*-T-

I l0cruI

r.! oo.

A n'r-!-

frR

14.6

15.1

15.2

5e. bnfto2n of @

.?r =

fu.o

4O=*AB 9r^4f r 1

=9p dv7 a,t

= g"eUV o't

Usin3fc? o/ Ecr tur"

'uu'

u^o R-o.t'$79-r

= u*B ftE =rEO lft (a,2")

6ear A , Ca = Zoen

Gear E i 4s = {-p

ilA = Zo raoL/:

dA = 4 'od/s*At poiot "f eng^g er-ent , dn G = NB .B

NF = *uE=

eB = /G 4c_

4 (#,) Anr,

V' ' -<--

-+Lo_

2lz-x4f =-

E -rel

=

2-rz, )" (- %", !)2tz=a;,(i"-!)

e----/&

2-rz-<r JLE iael -

15.3

15.4

15.5

O = 4Eo

Qos='Y#*4nu=,0 #

-1.

Using tA e

&ut =

4rc

t-=

d.v =

@")n = 40.; TD = F.s)'(o.zo) =

(a")r = &ns B = (to)(o.t4t4) =

(ou),-- afi AB= cs)'(o,t+tt)(o-/r)^= doriFe - (fl'(ol) =

Veetar ilingr^,A "f O t

o

(a)"

r-(ae),

ZcE "ffs@t

BC ..

&r- = uotB= Cl tau)Pv

lQo,l lE o't

= {r+e e,f

= ilno'l= O,{Q.p CD

O.g - (-o.L

l, Zr ^/s't.4l4 */t'

2. f -/s-

r^e -VJ

g. = 98 + e4u

(e.)*" (t.),= (g)o o (es),* (tru)** (t.7), A

(a.), (o")t=tP-rw *(oq)n

- 3.ts{ l'414 ' z {v! ttT

= 4 ,/s-

Q,-= - 4!- l,z{ j-C-J

Cas)t

t?lx,4,7

Ans.

(o"/u)r

(a"/u) "

15.6

FsoChff. 16 l<D

m-qIlJ

7,e,-\

c1

7-4cL

fuoQ-w,&,

G Z )'to= w,&tfr, + r,d + wLaLcZ'+rtx

&,= {C,*, &.= ft.xw,3 fu, o M-jE- = Io e

(zo) 6o s) + (2,)ci) = trW)''. +ff.r), a #i''f^=ou==ir:'=6 radls- ?

t ,) : - WA,- hzta-.

CJ^ m,g - w?g = - wat - tutAz

o)= zo +zo * #,(o.t^ 5.:: "

t< tos?)

=8"24N +

/€.f

l€ -z rrt = ZC .Ag 0't tS.S t AlO )

o*DNFBp

F

d

Q-; = &)e- dt ,

t r>7 F

*) zMe = z.&(fi- F), =+^rud.

P = FelarY/z b fi, Hanalbaak)

= zr(etuTi.* i) _ zGE"/(ed="nl? t)rur (zc)\o'zr1

: iCZ.e ran(/s'o,t = o a* t = #= ry *= o-tlo t !:"

FBD

,/*= O'3i

\2"

)I

@+(e:

@-@

@J"* KD

ex

ar/r,t =*/6t7 &t2= -j - 2d 0 / il = O u|<n Q = 4 :

-, tuo- /aa*rn\-t (

2e \'ra 1 TI

nJ FBo

-5 zNn = fn o<

Qr =Znx CFo = '/u'F G)

r3d= "',' @rc

:4t@6

l- = L6&

=,/*r

: 31"4 lV

-its) (o,ss)'4 n

(o. ss) (o .s s)A nr,.!--

FBD

#KD

ZFV = C+ N=^9 Cf= k^a @F=,4tM 6'

d-= *ftll = Q-4(?"st)

= 3.q, lr. A nu.#

FropO,@(6,

16.3

16.4

[s ').Vc

FBD

rug

t<P

&= r,/

t ZM"= tnar*fe*tn g l. S;n 9on = mar + LFar"*

cL=

& = 3.Zz m/s-

2q sin 3o "' Z (?,gt) s,n36 o

)

A nt'+

KO

GJ^xe

lnA, Q=L-o<z

* yt4a fi 4l -JknA * + L-.,xZe

w&+r-Lr^L" 4

!na-L+ ^=iS@-A ^ 4, n/j-,^u= tAX- 7*g = ?

= /O/4 = Z.e N *-W

qE12

?zMa=,oL =\'/ L

tnq L =,l 2

*mg=-tAaQ2

16.5

16.6

chp*.t7

\utfr'

sl

ZFl: mq

F- ta9 = ha.

F= ha * hq= tffi(e { tqooo

=G ZMo = rn*T-Fr=fon

T = Fr + 4 o/. 1- - rdius of gTraho, =

= (, otr)(o. s) * @,{)?o.)C,)/o.r= 57O? A/. t^

P = Patun, -- T-at = T- g -- f,7o? WP= /'?C'Lt// n Anc'

KD

dFeo

{

+rnl

)7" I

A

/1o/q il

i'd- = ^

l7,L A bo,re fig^"u P= F<r f= nj= t og-'- (tCI,o",e)(#) = ).67 -l-til 4

17"3Comserra*r?h of angca/a.r t'r1e,+-ten*otp, a-beu,/ O:

witr/= (^a * mn) @ t)d(o.o ss)(scc) = (soa" ozr) ('O, Sa.,)

(/) = O"O4Z0 ..//s < Aot'wAE>--+

1f

t figu{e .'""6:2; t,ffiw',| 4z' C'onseti of merten/,-n u)t=

'+: dr*rtng inpacf- &-) = Z -Z? rwLls./lr1o,o3{)tr= (3zr.oii1@,r*) :} nt - /6,32q ^/,

(nrdqL- i (,:c;30")

Ans"<-

PaE;liox I

Fasi*ian 2 G' ceater { nntt

Z

o=ilal,')

c.;l-71

,/1 Png " n&

H and baole 2' lu * =bh*/r"' Tt=?-

Therehr", fo = (Trn Ts) f ,,

=M(€.{)iv1 = hhpt/ ?I,o= - (F.9

zT+ ZY - it^ 0"- = ^3 Al

+ d E - * ) L')'=

^$+o)T (+)J''

+ (+ r +) a,n= ? s t {lG' " 4i (?IJ'^, o.", Zo.== 3=u9&) = o,ri7 r*(/, . rt'l'

1

12 = /enn/7't = lh;"t rest

lz,;

17,/ A*ac

*,{*il

wr-:+

FAt frrT'r4' =u)*

O+

!on"urr*lrom of angn/ur t^eryenfo.p, a.boerf A.

rnslr L = H r./r'L + I. u. * ^ rur',

tns,?rL = M".l/'L * trrL" ?' f ,rr;'+

= wr-' * ?-rq'Y=

2*.'- o-(-?f

(r)(to) = (,)-'. ?(to) rr.'

(o.z)(to) = -L'+ Z-r'

^r{\ar__

Q->

@+

@*!̂ @ to-qrc).1r'

t+ lg)-'3/

3"0P ?An t.

cl +. lq

Ant.!-st4

J/ /.

j=too,v/-tn= 6 &l

,[T t]s*dn= IW -- l/ T

KP

il44

-I zMo =

* U," JL')z'o

c<

IoO * (]

Fsp *,te

(c e"fer-o7

-is') -0rZA

l-ha-"+Jn*

7(2

= ffi*(+)-*rt n

= fo*

,+4-)L*e = Q

a= uLL

il nr'2a'Z

2/.

ZtrT

=

a)h --

(1,u X.)L

T4

(.4.,* A-) L',t2I 14L

3

ja oox z

la

7 ra/./-r

-//

V/ O-zt7 s - frns'

FBP

-&r

ZM, = Inc.r+ fee

-/-*r=r74ir*ln.ti'Zr

KD

AuQ

c

&--ur

C+

(C"nt 4 next f^te)

19.1

19.2

19.3

3ri* -'4- = Q

hbo,r. f,'g ^redn=

-7 t = O.9?5s

Fgaru oh *of of Feg" @f = 0.O3o ce? (u, t)

i = - O.O3 6<)2 si'm C^n t)

iln= - 7'f3 rc'L-r

q= O.OZ Co (atn!)

* = o,oz cun C sin (a4 4)

lrl^* = o.cL dn -- C. )s t ?Z-Y

Ant.+

Anr ,

An s-

l*l^^* = Qp3 uh = /.316 4s #A = - o,o3 u; caz (atrt)

l*l^*: O-oTarno = 4 n/s- Ant<_

19.4

19.5

19.6