Solutions To FE Exam 2 - Cal State LA

Transcription

Solutions to FE Exam “Dynamics” Review Problems;Problems are Online at McGraw-Hill WebsitePrepared byStephen F. FelszeghyCSULA Emeritus Professor of Mechanical EngineeringStart the web page for the book: Beer and Johnston, Vector Mechanics for Engineers, Statics and Dynamics,Ninth Edition, 2010, at: nformation center view0/ .Look for the “Online Learning Center” box on the left. Click on the “Student Edition” link. Select a chapter fromthe pull-down menu. My solutions, which you will find below, are for the online problems that are associated withthe following chapters and topics:Chpt. 11:Chpt. 12:Chpt. 13:Chpt. 14:Chpt. 15:Chpt. 16:Chpt. 17:Chpt. 19:Kinematics of ParticlesKinetics of Particles: Newton's Second LawKinetics of Particles: Energy and Momentum MethodsSystems of ParticlesKinematics of Rigid BodiesPlane Motion of Rigid Bodies: Forces and AccelerationsPlane Motion of Rigid Bodies: Energy and Momentum MethodsMechanical VibrationsClick on “FE Exam Review.”Solve the problem, and select the answer from the multiple choices at the bottom. Click on the right-arrow tocontinue to the next problem. This process ends when you click on the right-arrow for the third time. To try tosolve 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 andanswers are wrong. For this reason, I have prepared a separate document that lists the errors and corrections.You can access this document sers/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 itsWebsite.The online problems are not numbered, except for being associated with chapter numbers. For this reason, Idownloaded 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 problemsnumbered 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 includesketches in my solutions to allow you to identify the problems to which my solutions apply without necessarilyhaving 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, /l11.1aJot(,r-tT-s-'-/o4--c,y t-/{(@LY,,dt-tl4i t f rad. ra.(1-s- Uo* N.t -u. JA.f t, -.{36"-o '{fG4 st. /@ t 96"04s;?r o-o (ca- e)t, Zsob-' t"fse'.0411.3u tlt l0 n/s/0"frA4a-ckreac/tes lin e-,!-- An"aZfr sin 4{?.9//g,oz s--4 637 t znT A.'/2ad. rrr"tron in,7-/tredIt#t /6os-ft*rut(f 4u 7ot,7/ 0 af { q3g ,X lo nJ qnQ ta;ltof' r- af t 20 /.zst-B/o cw loe&o - 9/doq.s/uthen e- C : , 7/(1tg1P* 3.{3 th .tsAn,r.i*-,rt aa/ B rez,a in "lxed'a#a"ldmortng r-J &yesr e t 2.03t s ; V. trr/cQia /o)g taQ;1to) z,os11.4.z{s;n e - 3',.Lrtf C){du*{t&t Q ary' t Zs11.29/Otn ,,)-eo{ frnt,{o?,7 h

11.5Asu ye/ar ca a ,4/ct t ate r&r Y - r0\4a,?nra-o { Lt(s)(toJu m- {oo s'2i!: o * (z)ts)(,'? -too nWAr"./o7e" - -{oo:- -,Oo!, p O-- fA osg -{oo ?11.6-/r,(-/-/ [ne-Lft B fo a rrire a* CSls- (n/et to"4 z.a?4 slaatea--.1t-19Trneftr4 /QoYtoaoll- l\ 3eoo /A *o Arr[y'e a"/C tloo sin 3e "SAqftoo x toaal@/too r1.I*oC *rtt a /B ;s behtnoL A -h-nn qe-fn cby'drat uB ge// fod P.aq4-t.slloo*loY)\rur 1?.1-? 5'o, !db,r.'iz{s12.1:KDL!EtX4t % at 5-4.?A{ t,f A ,rrhot 5 l.O/Asv.16 fiz-l'1pqJ& -sin 9o ?,lv-, Q.I t s; n 3e" .-1 ?OrC4.2G5f@ 6! 1,o/Q r: i{ rrt o at /, / l.eosIl{iq)nL 2u,{{aZ G)(t.aa)Ans.,/

rN.sERr12.2Ik9Q5rFED1,4d.z. ra. ir a-tftcar'4{o 4a6L (!,3t)eo 4{"AFTER@

12.3NolectI'On2nlvin- p/an eatVfolee{cocyl ar Shcounhdn.KD- Ln&n L cp's ZooM - *g L sln Zoo -- - in (afL sinZd") L co Zcloy''l (r)p.rt)(2 s;" 7", - (r)Fa:24)*(2";, ze) (zeo" "c)N-tt14?-/42-7G ZU" M /42.7 A/- t?,*7fr*E:,"12.4KDf tma- (4)(ts) 6c A/12.5Nt.'6a"*Ant'a* 5FBDZF C T:12.6It,,Lbla* -,.// \,FBDtng gT- geetCc' C6c" lt-7LA/ #co"r60" (s-)(?.tt)c.pAnn,ye -,Cfu&nKD(a,ranqt fry")

7 F, - lv1drJ -T sin 4 -tud n erTF )J O 4Tc.o- -kact O @Elintaa:fe- T- be*uzea O V @,tam 0 : /b{ah4Jo"LL sin Ga?.8/ -ntsa,a adc6"v T 6*4er/\ 6'tA 56-0'FBP10 '712.7KOtrvm.l/7nC.n,147:zr henn,Xor.g 7rn fG4(q.tr)An'"rr la"/ /c 4r- (g13.IcA" . rs13.1 4Q AT AV,it" -: ;l ,f" !%;. ,LtJu,'AT Jl* {.t* *to10.t1- rc (t);J 2L l.ttZ--\-tAV dAT - 4V, : 5.s?- rn,3alf uta[ - ,,-j, ::,,oo (r,")' ) o 17"*i) ( tlS?"//20r 1,37/ % 0rl 4,3?f 4

C"rrt rra*r'au ,f fota t13.2/,44@ ox-2c0- /0q 20.6 A/{ -t5' t4' @zee * 30o /0%'* 2o4'3oaAr3cA' 13.3fa,q,/ u%'i:?'"(tdyto)t- (zo)(-){) )7orot zo.Tu' 3'-3r,*e ?'-3'*0.,{o- {slo - c- ts)o-en'/*** :o ,t1tust'3 tuAo)'*- - //--ru-ln ear* {o0- /6, t, */ ""Cabte. /eng h i.s caxsi" TAerefore-,2xat frs* consf. (ansf,2zxn - A*uc2*n- - xBI'oFBDFsoryna9'l,Mej* ei erg1iHeglo"o* 2trAro . IA axn*BjAxu- F AxB * r*;@9 /tl;fute Q ,rto @, a',nat @ ,"Vt @rano(add rer otl *in9 u?fut ron rfLIW,zrk@**siz * Hsl)zxu Ar*n' ws4i;)?" s i G ,t "to) (t u? -- (,t u 8o) to'Gi; Z{eL, rA t.os J"'13.4zsa n/s-- :HArva/roo "f ht"/ l;n ear kle n e tt*u vJ'Cnn rn ry{% ( o au)rr'(o-os G,so)4/, lnA !ACoarerha4 m6 4rt:/. tZt -A.J!-*' la'oi{fln";

)3,513.5SUVro b,/str*nn*-fJ*TntFF MnTAIntt; ltn olnen/t'Yne q;-uiCo//ft icnTnTaa/ se-r%-T{o zrr- /O,z a?'-{,o/oCaatewcLf i-ona FdtIFina/lr1Op,f t"/" I/to ea, k\gn*ac rLl e ntuto,*i4 tuA T * tuE %'(e ooo) (/ 4 6000 q7'* lcoo -;tnA'?rn/y inyt,i or10 %'*?-u'/ //O(@i t7 %r'Apr,wu{u'@;!'o" ,Z')r::ttrilt we%'B;lru - f. wet/ @co)(to.z) o"3AI)2 /13.6JL I'iK, -' O.OZ r-, t %%, #m/s. ,n* (re w)Q AT AVA rAV.trrslotc ?g.lx lo-s1-,-(rJ{,)*-q,,1;u-7; ? Fr,d (q.s r)(a-oz - ?t-/ x r6's) * j to t(o o z' rg.tt* to-'')l'AnrC a 2irn -mq( E.6lV @,-K,) LJ.?: mv -/. CZ S'-*ruq (tc)gf.tt)X'sPnne-44 o. t JIUTOwhen a- O2jr. - ruf"l:,?.EI"TfuE*tno, An''ls6-U/p

t3,n13.7TG tr,,rOh,lTr.lL- d- att?n(r,',,*.rqw(%),O AT AVo/ Zi* [(-;, J :'-tLI6a, W,*,.*9h' Oi-n [(';)-)* 7ot @a / (q"), , a /SoireC ano(gabrTr lite- in Q-*,,(-r),b7." belit t t"a)4.14.1t7sL'h(u;)(v;),0.8?1 -{-Ceater of nass : /.,z/- / 4AcU fl-xLln-'-tltYnu'efI 3w3tn lp',2, ru (za:) I x 2m (t -)6w.d c())(t) 3oMtt4.L14.2S're ;rttddle. fr.@'/Z/Afue*yConserr, of *olal lin drr'aihuur- %u, *rt'u* y-,(o. i) (e) o.t-u; * ( 0 {vo q, t'%Q * C.{x @ : An.rtaaa*t-- -Anten/uv' iie -ds '*-ii r':aE' qr' -4wJHA 3*'Hyn' 3x(t)(4) l2 /"4'r-r t6 l,{ t7' -"T-@ - An'''.

2j*{4,*y--3 L 2i-s/, w/,m tlgI 4,s14.3H -of lgf X pt4jto-z{l3 z -r[F-3Z{"5' / 3a 4, -&A- thL- t 4 ,yi O 4T- 4V,c {o - * , (-r)'] * *r, [2-- iJ-t.z *KG)- r 0,8t{n9' %twtB.S14 14.5wR4f,-YvCoi/r s r'o,vzo/z5y.smo%--Effi a{n/ms3Hru" *odn!n,r{Ltwflo q;on/rnb"trl"u,'oi;LuPftns,hrcrCo//fsi"n belween ,u/1r{, a\'ItS-. @ boltom 3'is Jl\\,1t [ ! (rc -/o) -j (- s6 .- t,t) 4 k, *, )) /4-114.4.5- L*yfup[*nfK U.n11,?D rny m*fi'/vhy.r T w. {Y T t.{fZAnt '

14.6ZF d /'o'L-s -o--.,-A/AtZF* ffi; Q.125.(o"t-N *ry/1t J- . tfLnPIl.J?ou /615.1u*AB OG o.es;n ,1)?(?.ffarl-f9" too *qo O: a -[a.) /'a,)1-e/B/nVe/e/s-BeB -fnm ftol'(o"a) ' 6C r./s'lsing ICE o7 BC : bu. .*E %e - (tqG.t-)o"3 c,3o,3 2oCto"/r), o *1 il' ed'{E* 6IVeJor diaTna' cl @: 268.39*ln,t 6(%tu)" ttu{ c/B/n3s'14\3'Jz6N15.2536.7 b53 s.'zF. VMS\n(& ,-)L c:/F/e, N-B -. Bc cor,a--l,a,- Jt-fr"'-1ft-- 4t*frR-TI l0cru -!Ir.!oo.An'r'

15.3r1Usin3fc? o/ Ecr tur" 9pa,t dv75e. bnfto2n of @4O *AB 9r 4f'uu' u o R-o.t' 79-rfu.o u*B ftEg"eo'tUV.?r rEOlft (a,2") 15.46ear A , Ca ZoenGear E i4s {-pilA Zo raoL/: 4 'od/s*At poiot "f eng g er-ent , dn G NB .BdANF *uE 4eB /G 4c15.52lz-x4fE -rel-- Lo(- %", 2-rz, 2tz a;,(i"-!))"(#,)V' '!)e----/&2-rz- rE iael JL-Anr,- --

15.6O 4EoQos 'Y#*4nu ,0 # -1.Using tA e ZcE&ut"ffsBC.@ttau)&rPv uotB Cl o't lElQo,l {r e,f e ilno'l O,{4rct- Q.pd.vg. CD- (- r eO.go.L 98 e4uJ(e.)*" (t.), (g)o o (es),* (tru)**@")n 40.; TD F.s)'(o.zo) l, Zr-V(t.7), A /s'(a")r &ns B (to)(o.t4t4) t.4l4 */t'(ou),-- afi AB cs)'(o,t tt)(o-/r) doriFe - (fl'(ol) 2. f -/sVeetar ilingr ,A "f O to(a.),(o"/u)r(a)"r-(o")t tP-rw- 3.ts{v!(ae), 4Cas)t(a"/u)"t?lxQ,- -C-Jl'414,/s-ttT- 4!- l,z{ jAns.*(oq)n'z {,7,4

Chff.16Fsol D7,e/ .f16.17-4,-\c1m-qIlJcLfuoQ-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), ou ir:' 6 radls- ?t ,) : - WA,--#,(o.t 5.:: 8"24N rrt ZC .AgFBDt r 7"t tos?)F*) zMe z.&(fi- F), rud.FBpF &)e- dttutAz0't tS.S t AlO )o*DNQ-;#i''f hzta-.CJ m,g - w?g - wato) zo zo *-zl 16.2aP 67FelarY/z b fi,Hanalbaak)t)d zr(etuTi.* i) zGE"/(ed "nl?(zc)\o'zr1rur: iCZ.e ran(/s',o,t o a* t # ry * o-tlo t!:"

16.3,/* O'3i\2"nJ-5 zNn */6t7&t2 FBofn KDo "','r3d @rc-j - 2d 0 / il O u n Q 4-, tuo- /aa*rn\-t2e:4t@@-@J"*Qr Znx CFo '/u'F G)@ (e:ar/r,t@ex)Il- L6&6:16.4 ,/*r31"4 lV\'ra 1ZFV (TI-its) (o,ss)'4 n(o. ss) (o .sA.!--FBD#:s)nr,KDC N 9 Cf k a @F ,4tM 6'FropO,@(6,d- *ftll Q-4(?"st) 3.q, lr.#A nu.

16.5.V')[sFBDt Prugc& r,/t ZM" tnar*fe*tn g l. S;n 9on cL mar LFar"*2q sin 3o"'Z(?,gt) s,n36)& 3.Zz m/s16.6A KOG*!na-L iS@-A 4, n/j-, u tAX- 7*g ?/O/4 Z.e N *-W LQ z-o fi 4 *mg -tAaQ2l -JknA * L-.,xZeyt4a?zMa ,oL\'/ L w& r-Lr L" 4Ltnq,l 2 nt'J xelnA,qE12o

chp*.t7FeoslI)7"17.1KDd{ \utfr'rnlAi'd- GZFl:mqF- ta9 ha.F ha * hq tffi(e { tqooo /1o/q ilZMo rn*T-Fr fon T Fr 4 o/. 1- - rdius of gTraho, (, otr)(o. s) * @,{)?o.)C,)/o.r 57O? A/. t Pl7,L17.2A bo,re g -- f,7o?WAnc'P /'?C'Lt// n Patun,--T-at T-f njP F rfig "u t og-'- (tCI,o",e)(#) ).67 -l-til 4Comserra*r?h of angca/a.r t'r1e, -ten*otp, a-beu,/ O:17"3witr/ ( a * mn) @ t)d17.3wAE -- 1f(o.o ss)(scc) (soa" ozr): dr*rtng merten/,-ninpacf' C'onseti of./Sa.,)(/) O"O4Z0 .//st figu{e .'""6:2;17.4('O,u)t &-) ' Z Aot't,ffiw', 4z (nrdqLi--Z? rwLlslr1o,o3{)tr (3zr.oii1@,r*):} nt -/6,32q /,(,:c;30") - Ans"

ZPaE;liox I17.5lz,;Fasi*ian 21',/1Pnglu *n&"Hand baole2 bh*/r"'G' ceater { nnttTt ?-fo (Trn Ts) f ,,Therehr", M( .{)iv1o zT ZY ( , dr0"- E *) )o.",- (F.9 3AlL')' ( )J''Zo. 3 u9r*(/, . rt'l'-'t/enn/7 lh;"t rest hhpt/ ?I,o - it 12 ilal,') o)Tc.;la,n ? s t-71(?IJ' 4i{lG' "&) o,ri717,/17.6A*acwr-:64*,{*il FAtO frrT'r4' u)*

!on"urr*lrom of angn/ur t eryenfo.p, a.boerf A.rnslr L H r./r'L I.u. * rur', trrL" ?' f ,rr;' wr-' * ?-rq'Ytns,?rL M".l/'L * r{\arQ- o-( 2*.'--?f(r)(to) @ @*! @(,)-'.rr.'?(to)(o.z)(to) -L' Z-r'to-qrc).1r't lg)-'3/3"0P ?Ant.

cl . lqj too,v/-19.1tn 6 &l,[Tdn IWt]s*-l/T/ /.st4J!-Ant.19.2KPFsp*,te(c-o7e"fer-is')*a -0rZAlha-" Jn*zMo -I7(2U," JL')z'oc ffi*( )-*rt fo* uLLnIoO * (] , 4-)L*e Qja oox z(.4.,* A-) L'(1,u X.)Lil n a)hil44--a'ZZtrT3O-zt7V/-//19.3laI,t2 14Lr' T42 7 ra/./-r2/.s -FBPfrns'KDAuQ-&rc&--urC ZM, Inc.r fee'Zr-/-*r r74ir*ln.ti(C"nt4nextf te)

3ri*-'4- Q- 7'f3iln rc'L-rq O.OZ Co (atn!)* o,oz cun C sin (a4 4) o.cL dn -- C. )s tlrl *19.419.519.6hbo,r. f,'g reFgaruohdn ZY-7t? O.9?5sAnt.Anr,*of of Feg" @f 0.O3o ce? (u, t)i - O.O3 6 )2 si'm C n t)An sl*l * Qp3 uh /.316 4s #A - o,o3 u; caz (atrt)Antl*l *: O-oTarno 4 n/s-

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_