solutions to fe exam 2 - calstatela.edu · solutions to fe exam “dynamics” review problems;...
TRANSCRIPT
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!
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,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<
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: o * (z)ts)(,'?=-too
?- /o7e" - -{oo:- -,Oo!, pg=-{ooW
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19
Trne ftr A *o4= SA
q
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a rrire a* C
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loo sin 3e "
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a
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too r
t
1.
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= ?.1-? r+1 \ru
, !db,r. iz' {s
:
!E-L tX_
KD
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= 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= Zcloy''l = (r)p.rt)(2 s;" 7", - (r)Fa:24)*(2";, ze) (zeo" "c)14?-/42-7 N-ttM = /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 -
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Intt;^ltn olnen/t'Yn
Co//ft icnTnTaa/ se-r
Fina/lr1Op, gn*a
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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-= O2
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{,)
t(o o
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t3,n TGh,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- Jl2 /"4' tr-r
An'' '<-
I 4,s m=tlg+
L
L
f=lgy--3
2j*{4,*2i-s/, w/,
\\,1. s Jl Itto-z{l3 z -r[H=
-of 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
wR4f,-_
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,?-KD
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.x
w,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: mqF- 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 ili'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