Ch15 Solutions to p486 + Evens

8/3/2019 Ch15 Solutions to p486 + Evens

1/23

15CHAPTER OUTLINE151 r,lol on or an ObjectAltached lo15.2 Anaysis Modelr Particein

S mp e Harmon'c Motion15.3 Enersyorthe simpe Hamonic154 Compdng Simpe Harmonic

(4oton w th Unifom Cncu ar

Oscillatory MotionANSWERS TO OBJECTIVE QUESTIONS

'NOQ15.l An*vc, (cl. wltcn ro olriecr ufd.ri,)c\ \i,i,flc l,rrnronic motiolr,llrc lrositjoI rs Lr lirn.Lirm ol tirrc rnxt bc\ritten rs r =,1cosrr/ = Acos1lt/;).al(nrtr irlgtlris !o th..gilcr Lclnlioll. e see lhrl lh. jlaqr.nc) oj'vibmtbr is/= I IL, xrrd rhc perjod is 7 = l1'l= l/il.*OQl5.2 Answer kl) is the only lrlsc \t.rtcrr!'nt. r\l lhe equlibriun Dosrtior, -r = 0. lhc ol!\Lic tolcnlinl energy(Pt, = L'rl2) is r min n,unr rncl ll,c li,rctic ene,:!i\ N nrr\ l,f, L.'+OQ15.3 Arslcr (rl. L) lhrs spritg mrts! slsrc.r. Lhc r(nrl

energ) cqurls thc cl:rslic pinenlill .r.r!l'xt thcnxrmenl lho ma\\ i! lenrporrrjly 11 r.sr !l i= 4 =6 cnl (i.e., rL Lho crlrcnrc cnds lrf dre simd. hr nronicmotioDl lhus. f = tlr/2 x|d \e \ee llrrl N longrs lhe spri.g constlrl li rud llrc lplilude 1 re n:rinunchanled,lhe lolrl cncrgl is uuth.ug.rd

I to^ rt t.= (-2.8 nr/\ I l-\10 l0'Nil

157

*OQl5.,l Arsscr (b). The lrequeDc] ol \ibratnD is

Thus.incrc.rsingthcmrssblal:lclorof9(illde.rcd\clhclicquencylol,'lolitsoriginrl\rlLr.'.Ans\\'er (d). When the objcct is it itr maxinnrm dilplaccrnc L. rhc rlr.iglriILr(I. ol thc lor.ccxened on it by the lprins is /, =t r,,,.- =, (8.0 Ninr)(0.10r!l = 0.80\ lhj\Li)r(.$rllgilc the rss an acceler,rtion of a = l'. /rn = 0 tio \/0.:10 kg = 2.0 m/\r.,\rsser (:r). The cilr will continue Lo con)pttss tlre sln jtg unril xll ol thc cu's oii:inrlkmclic cirergy has been conveled inlo clNjc pole.ti.rl cncrgl withi llre spri rg, i c.. until*)lt = n'ai lt. or

'ioQl5.s

*oQrs.6

.t=;=

rF rla I F It{i=t!t=rlt\l l=-"OQl5.7 Ans\!cr(d).TllcpeLiodofasinrplefcnduluruis/=2tJl,ir,ddit\licqtcrrc)i\| = tlt =(.lPn)".lslt..Thus.ifrhclcngthisdoubledsol' l/.thc,,c$ licqucr.) \

' An il!rerisli indic.tLcs

467


2/23

468 Oh.rpior 15rr,Ql5.ll

o()i5.9

A.s$cr Lc). Tl,c t(n.rl .no,g) ol the ohjc.r'*prirrg slncrl i\ +A r l'.''+Il"' r\'ro" tr'"ll)eliconer8yisl$iccrhefotcnrill.ne:), l*"=tl:^"l=-" idllrelotal'n'r!)i\

li) Ans$or'(c).Alll0crri!.lrxlethcrrrldtoirlhot\ti:cnthclLrrtilgfoinls nriLisdr'cquiLibillm Po!ilion d rhc l)oinL 01 nrrxi u n il^-c{lriil r\|sir.r (r). l. snnllc halnonr'molion thc xcc'l'!rlion i\ rtrxirrurrr $'hc| Ihc dnplr'o

lr,' , Ir.r'n'

Drcnl lionr equiliLrriunr is nrrlirlunr'Arsi!.r (r). b) the \rrnc iogic as in pxrl ( il)Ar\wer (c) At ;10 cfi \\c htrlc lhe .riJloinl hcN!c'rr thc lumilrg toinl! n) il is tho cquiLibir LI to\ilioD and lhc poLnl ol nrl\jr t 'r sl]('cd t d lheroli)l,: nrxrin]un' 'nonrcllunlAnsr.r rc ). Th. f(Nilion ol nrr\irnu.r slrced is rln) thc l)ositi(tr ol ' \rn irr Liicliceicryl

(iii) Ans$cr icl l hc tl)trl efcrgy ol drc slstcrn is corr\e^'cJ soil i\ the \x')r' r'1 '\cr\tosiLioll.+OQl5.l1 Th. rx|kifg i\ (c) > ic)> (.rl' (hl > ((l) The rrnllilu{l' tloes nor triLtct rlre pc od it siLllPlcLlmorric nxnioLr: ncilher do coisL rI li)racs thrl olli'L thc equilibrirLnr 1)osili(nr' Th I' rrr rn(lill lr.c equrl periocls rtro l)crio(1is riporllonrl to th' !uirLc rorrr ol nrirss tlj\idflL bl t|)1ing

corlsLIrt. So {c]. \'ith htg.r rlrtrss l s Lrryc' Period lhr! (xl AnJ 1d) wilh gr'!tcr stillrrcsshu" snrxllll pcriod lr \ilLrrLnlr (e) Lhc nrotio i! nol quitc srmfl' htrmorrir' but h'r! (Liqhll\srt]ail.r xlrlulu lrcquclrcl rnd so \liglrll) longei N xl

OQl5.l2 (r) \.\'Ifsirlllehr rnic miniorr' ofe hxll oi rtrclim' rh'r \cLocilJ isiirrh'sxrn'djtuctlortrs drc disllxcenr.rrl l$rr_ lrom oquilihriuri

(h) \ts \tlo.iLv rnd lcrelcrxnon rtu iLr lho \r|reclirecrit! hrr l thc liir''(cl No ihcsfringlinac.lnd.thcreLi)rc'lhcrccel'rrlionucalfx)\opfo'il'rlorhc|osili(trleclor. rnd n.!er in llre srnrc dir"lion

'}oQ15.l:}Als\'cl(d]'w'cltsnllrlethrtlhecoilsoi.lhcsplingdonolhitoncl|(jlhcl:Whcnlh.\p1l]!wilhtwohlocls]\\cL11ll()oscjllllil!l]nsl|Lce.Lll.coilin{heccnlcll)l.lllesIlillgdo.s'lotruo\c.NecxtinrrginecLurl)i1rgtlrccetrtc! coil inIh'cNilhotLullcclingthcrrl()li'r \!"rncila.ti\cl) (lul)lictri. the nnnioLr ol c'rch indn idudl blocli i *prcc b! hrrrgi rS l singlc l'lock oIr hlll striin.lr lrre on Elrlh The hrll spri'g \r!1h ils rentcr coil 'h]rrf'f or ir\ 01h'r lrrll 'nLoll hxs ti!ic.llre sl]rirrg c(nNIrrtl rs 1]re origi'rl uncnl !Ui1rg hcctrtr\c r llfli'd lirrcc ofihcs.ll|e\irc\oulcl|( ucc rnrl\ onc halllhc crletsion !listrnce lItsihc(NciLllti(nrli'clucrryt/,,, ....'l-]l;] =\r/ thc rhscncc ol 'rttr'ttequircdtolrlr)orrLhc\ibrrtirrgsl\tr!.,lr'.1 l I' r''l I"l r"n i l'

OQl5.l4 \is$ci(c) The.quilihriurrrfo\irlofis15rnrbclowthcsrrrtiIglniintlhcrnoll(Ni'synr!rclric xboul thc equilil)riLLnr l)osiliorr' nr lhe 1$r) lLLnrifg toi'ls 'trc i0 c'i' x]1rrt

"0QI5.10 1i)(ii)


3/23


4/23

470 Ctt.tpi.:t 15ao r5.5

c()15.12

cQls.7cQrs.8

cQ rs.9

"cQls.r{r

cQl5.6

COti.rI

(r)(b)

iL tl

N,) ii'rcc is.x.rl.d ol lbr prrr .1. lhctrrticLc.(r$\illjc,iLr\1lnllclrtril!Iho tr:(iclo lc.ls rLc.rl\1rn1 lur. l.$,Nr(l rh. lclt. lL irr^.\ !. illi cou\1 I il(.|(1rrnnbsr !l\c 1c{\.ll il\ in(i,\l \ru.li i! (\\x(1llN rithl. ir\ili:1(N do\!n. lL\rl\ .u('L\rtl. nndsF:i\ \\\'Nii\\\ \s\N\ i\\.\i'\\.1.\ \\: \.nti\r\ tr\\:\r \! ..$\\\i N \t\. \\ \N t\\\ \tcr{ \\}A.or\lNnL liJrr 1o$rrl thc ri!ht lcls on rhc prr rlc to |nxlLL.e.orrsrx|r rcrcldrtio]ll'h. t)r ticl. rno\r, i!r \lnrt)l! hlf olic rn(n o r lL)or 1 rh. tr$r( prilr ol Lh. t()tcr)lirl

Nlon c\c^drr !iIrrti rj rrc dN n|!:r1. lljc.r o\crlinti\ drc.to$,L th.lr cn.r!\ ji ll.lirj\lcIcdtu thcir \uroun(lifgr. 11(Nc\cr: ls lor will i.rrr tltei. lhrr\ in ttrc .rolcculcs trr!e !it,rrli(r.rod.r lhal d. fotdlr\) (r1._lhc !rcchxni.r e rcr.g) ol x {hmtell os.illxr.r .hli!.! l)xctt r r allh l,.rwccn l(i n]{ic drlpolerrirl \hile lr: duxlh rr(l I)cr rx .IrlI dccienics lIJ rrlnslo,rns n, rnlcnrrt c crg).\ts..\nos.jlhl'$ir|([n]|irgcrItibrr1.rlr$,!rrncc$jLhl t,ljrkt.thrrr.cIlrirbcrnrsrrrliir tirir.. WilhorLl rL rtiD!. th. lnrl)litu.lc \ oItd rn. nlsr $ ithour Ii ri{ rr rcnnlncc.No ll Lhc res \{i!c li)tu. is lrrg..olrflrc(l to lh. rrstorilg li)rcc (l1 ttro \frin:r rin t)xrricrtrr. i,r>.lrlI thes)rr.rr\i I heo\c anrfcitir.d$ittnoiosci||l..ll. t.r'" u. r' r ,r. 1., / -/ .tr ,.\llc.clcrrli,in!l g \iLl,ii(lilleieItatrhc1L,f.t llredtrtr.trir,1xrtfril\ti\(tjitorLrluktlhc lcnluilrf docs rr)r kc.f fedirci riiLic. l\\.IrLng\cx..ltcctthcr.cct.rrliofot!rui1!.thc 11)t ol rhc |rou Lxin ii tr(hcr tror. Lh. c.nld ot rlic trr h l rd ttrc n.r hir tifrc ]nrss ot ttr.rrxtrntlir uf(l$ 1h. t).!du ! n.r\r inf.r.elrl)1,- \lighr blcez(: il(^\ ins .\ef thc cclgc ol i t.lL c r fr(riuec flL,ucring in nrc\rnt wrt! lhrt l br.c/c.|f .rr\. x llxg ro Hrp of drc txcoIa Nrro\rs llri(tgc (r b.gin o{ilIxting Asllcrl tlli\ls jn rir!'sirtrl. Lh. libcr jnirs\L.nrtnirtcxr.\tr)rin!tofqtc. lt theli.qucrc\.1 lhc br.c/. nIrlcIcs Lh.I.rtrr]1ri lrcqrcrc\ ol \ibrrti(rr ot on. fl11iculxr icrt ,r\ tlhtrjiofil! Nnlulur.. rhrr l|li crlbc(1ll\e.iItNrl:Lr!.I ptixdrro!)rlrfrLr\jhr Li(!r \ot!,thxr i1 i!iol lhc rri. ol thc r\ i!in! tur.c thll s.(\ rh. l.rt iIro ra!!rx.r.. bLLl ll)c rrzlr,,.r o1thc dr \ i.i: liEc. ll th. lie(LUcir.\ rhinr:'c., .Irolhcr l.,rt $ itt t,c \.r inLo r\o Il oscjIrlio]r.$. rssrnn lhc ililnttc. crl th. bob is i,il \.r\ jrnr I co frr.ct r() rh. lcflrh ol lhc ctl'(l { r)1)oiri.! il ,\\ 1h. $rtei lcrks ou1. Lhe .rerilcr ol nrrss tn lh. t)i)h n\ cs (Lo$ll. ilcr.rsin! 1tr.

rl ..,r 't.!rr,., t\i.....,,., r...,.r \rt ...r'.1 ..rr!ihhleo 1.lh.r.r(:fl)1 i|lssr)l rheL)(il!^csbx.tLrfiot|cccrt.roi thcsrrtrcrc.lx1thcf.r.lulurr ii.qtu.rc! qUirkl) ircrusesto itsorifin,rl !utrc.Ih. lnglc (n lh. .il rk t)int\ A= ot.It\ , r,)o,d|rrt. i\\ =; c(tr 1l=; co\ .r/whcrc,\ i\ Lh. dinlLrer lionr ih.ceulcr ol ihc \r'h.el 1o lh. .rrr ( fin.This is oi rhr lil nr I =:i coJfdr + dl.$ lhc )okc l.(Lprston lro\. $ lhsirrtt. hrmo ric rrotiori.

cQls.r3

ANS FlG. CA15.l3


5/23

as llelarv llalian 471

Secton 15,:t 15.1 (a)

When the obJec!.omcs to cquihbrionr (al distxncc,-r b"l.,r the Lxrslrelched posiLi(D oi lhc endollhe springl.:1, = r( r,) ,'.,i '" 0 atd th. nnd'.onsr'nr is

lllotion of an Object Atiached to a SpringTaling Io the righl ;r\ tosiLi!c. lhe sptlng lbrce actiDg or thc block aI dre insrant ol

m) = l7 N o' [-] N to tl,e lei!

or d = 28 m/sr to the Lell

ll l"- ']= " ro\ r.snk\ lrllh2^l() rnl

tt\ = kti = (r30 N/ml(+0.13(b) At llris in\trnl, the rccelcl.llion is

/ l7N,r 0 60 llr',P15.2

P15.4

Seclion 15 2 Analysis lllodel: Particle in Simplo Harmonic Motion*P15.3 The spdn! corsta.L is fourd 11onr, t:. tt (o.olo ks)(e.80 ,n/sr) ') N/mJ.t u .,

Whcn lire object utlxched Lo l|c spring has $.rss /a = 25 g,lhc lcriod ofoscillation isEI'''=f= lroo'=#= Itnnr =?L=4=

i

'J, 1 ,i.00J-r co I \r / n. , L. uLrrr l.i t-J;l\6(h)

(t)

.,,'r'r''"[".{J

,rr r = o. r, = [-ikr u.ti'l

r.r e..lr-oo *l

*u')*'i,'.;] AL,=o a=


6/23

472 Chapter 15P1s.s .v = (.1.00 m)cos(3.007lr+r ) comparc rhis wirhr =Acos(a)/+(r) ro fi nd

at =2nI =z.oor,,l lso ulr=l=lo-or,r,l,t=!r-oo-lo=[t"alr.r=o.lsn.t ,ruun.i^.,t :r. !.-!,1 ;lr=Acosrrr ,4=0.05m != Aarsinar/ a=;kotcosror

Ii I =3600 rcv/min=60 Hz, ilen &) = 2n.l = 1201:" s(a) r,,,,,, =.,rr = 0.05 (120"; -7"=Fs: .1,:l(b) d,,,., =.,:,4 = 0 05(tr0z)' mA.= ftl I kn:,ElThe 0.500 s mult elapse bcrween one tumiDg point and fte other Thus rhe period is 1.00 s

^ =4=e .zzl"and !,,.,, =.r/ =(6 28A)(0.100 nr)= F.62Tt;ltur r=lf.o.=rhr t =l= l= o r|7 H7' I .4O r r

P15.9

(c)

r =!1,r z ln rl00 klr\orrrng r,r r. -' = 10 9 N/rn' I L:hn')l

+P15.l0 J, fne .trirE.o r.rJr' ^r rh..pfirgi.7 .. 1u.r50 kpl(o ro n, , ) 1l6 N/m.0.350 ln

a =21t f =2n (0117=Fit tatq

\Ve take thc a dxis poininrg downward. so d = 0, \r'..d = { r8.o,,.,co.[,f---", r., ., \rd.u cn ].,r(4 o.o .a,i1 f:-.-lL\i o rsn (f(b) Now 446.6 rad = 7lr 2,' +0.:197 lnd.In cach cycte rhc object moves 4(18) = 72 cm. soir has movedTl(72 cm)+(18 ls.S) clrl=f5LT;].

(a)

(b)G)(d)(e)

Pl5.6

15.7

P15.8


7/23

a) ll tat' lt/i | .t 473l\ru,.r!\tt /i (o'no t!)(e so,"'i ) i.I \/"

= rlll 0 = (18 0 c.rlcos (.1.13..r fttl) =

i,rr .1.1.1 I fld = 10.i6'r(:,{ll)i\r rfe frtrcd = l(l .6e(0.7: Ln)= I 50.s ,r

r. L, l .r',r 'l l.,tr''l ,r"l tl l l.,,r rl "' \e r' r''lt)rc!cnL. xr irrrt.s.lbilir).Pl5.l l 1rl |(r consLiril x..rlc rLi(!r l)osition is gitcn tr\ r l rclior ol tirrrc bv

" "*iJ*'"t'1..,.t;,

in th.rse but b.coming(\d, r Lnos'lcLlgc 01 the

I

..or; n,, tir.r+ n'i,)i,i i ,1, 11 o.r: ,rtsr)(r.5 s)l

(bI

1:,: /:1+.uo -1i i !'r.vr ,...1ro+ '1=itTt il

Pt5.t2

,' ,, rr 0l.l ,f,/\ (.):ll ,ritr)(a.5s)= lr0,,,ir]For 'ifrtLc lirnnoii. rtrnio r $,c hr\c ilrsrer(1 r =,1co\ (rJ 1+0 )urdr= lnr).i!1.,r/ rirll\llr.tud .r)rr.sorhrt 0l: nr/sr= rl) (il27m).r) = t.(),) r(L/s..\t/ -.0 {).ll nr =.{.oso xnd0.ll nr/s= A(109/slsiLrl l)niding' .ll , L, | . , \, t,r I.0.-lj n=.\ros( 15.5'l .A 0.:9t) m No\rrLr='r.ls., =(0 r{)(.),,,rc(\li {rL),rdb)(.r 5 s) 15.5 1 =(0.lee nr).o\('1.e0 a 25 j'J- {r) r,)t) i )co\ lr5'= E(lilla) I rn

r- (0lr)9nr)l (rt)islsiLrla5'= +0.-ll5 nr/\

Sif(c lhr.olli\lu is Icrli'rll\ .lxstic. the brll $illthcir l!f,r!l rIr rlnlir!r o\cr lf(l 1i\cr agtriLr' t hur,'ln lrtcrni.c lltri |erlo,L, \\c tr5" t = !/

ANS FlG. P15.11(a, b)

ANS FrG. P15.11(c, d)reLroun(lr) lhc hei3ht o1 .1.00 m rnd

rhe!Nnion i( f.ri,trli!'

lhe linrc li,r lh. bxil Lo hLl lhc grou d ls/ ='lhis o!lrl! o.c hrlllhe tcriotl (o 7 =l(0

..0.90+ s


8/23

474 Chaplet l::)ih. l]rolion is ol sinrplc hrtnoni.3i\or b) / = ,rg {e\ccfl tlhen ilthc lorrr ol llooke s llN.

. The nct lbrre rcting olr thc bxll is a consl.rnt, L(, ,,',,r. ',, "r.^ r.". .,.r.t .. r., I ir',P15.13

{b)

((i)

ir,, =rr . .1., = 2.0rj(].00n) .6.007r cm/s= tLsr *Fl(c) Thc fdicle hls tl)k sfe.d at I ' 0 xncllre\t alLcr half r |tliod:

l'hi\ posiljlc ulue ol rn jnnnn nccelenti(tr firsi o.cttrx whet rhc particle is rcvellitg its.hc rri { lr lre'J r" I '. I ,r J " / "inu

(Ll Si.c. xncll .l.00cnr.thcf licle$illl1alel 8.00 cm in onc cyclettcrrcc.ir 100 s= ]/ = t'lcyclcs. the prrrliclc willlru\'cl sottcm+'lttocn=F:n crrl

F15.1,1 ,r=1.00k3. /.=-l5ri \/nr. and 4 = 3 00 cnr Atr=0 r= 300crll

tb) i',., :v,=3.00rto ru1:oo na1')=-o:o -/ild,. =.A.rr =-l oilrl0 |r(500 taLl/s)r =

(c) Bccrusr r= -l 00 cnr l]-[d i,=0 rl / =0, the requircd solulion is r-'1cost'/", l,' jll!,r!l!tE '=1;t=L,5l:r ''rtl -.l"#=L11-9!!1E\hcrcri\incor'iri!irrcrdsrrnddriincm/slfa 1\ Ll \ ,,r,r = l = =+ 0s\,, \l 0 5uLr li

As\rniDg ihe psilioll oi1hc oblect is xl lhe origin aI / = 0 fosrtion is giler byr. 10.0\ir(a.00/),ihere-ris!tcm lrronthis,Bcliodlhrrl,='100cosl'l0t)l),wherci'i!in. n I l.'1 .\1e,..,: n.,' .

Tlre fcrioclol rhc oscillllion i\ 7.. l,'l = l/ 1 50 llz = l(:1./2 s r) '' 2/l Ilrl ,\1 / =0. .r = 0 rDd. is polili\c (to thc igh0 Ihcrclbre. this sitLration corresponds to! = J silld/rrtl . = " co\aJl. Sincc I = l SO llz. @ " 2n / = 3 |)On llnd /r = 2 00 cm:n,o,a',n. .". -1"" "f l' "

'itiI5. i 5

r 1 n ni lr r...*ihle rrbsit. ln uholc oi in


9/23

+P15.16

As.illalorj l\,,|alon 475(a) r,,.,, =rDA = (,r.00 r"d/s)(r0.0 cm)= F0r0 crn^.l(b) ,,.,., .:rrrA = (1.00 ..ar')' 1ro.o .n) = [cocnrlf

Froln onl rssumed crprcssion for j. wc n)lve tbr thc rime I :I I ... I o.oo' lour,l '" l,uo.J *n"" ' o00c'n / 1,.*,1'' "{ ;,,] " "'.\\. rndrhnrhr.,rt I r-l I rnc

a =40.0cix[4.00(0.r61)] = [:ro ;f, I -aa = -r60siD [:r oo(0. r6r)] = Fe0cnr^-f

r"r u';,s, - (lJ"i", (;) *" o"o,n,,.henr= 0. / = 0, rnd whenr=E 00 cm., =0.232 s. Thcrefore, * =l O::z il.EWe rssume lhat the mass ofthe sf.ing is ncgtigible and rhat $,e are on Earh. LcL nrepresent tlrc nrass of rhe objecl. Its hanging at resr is describcd byLF= o ,.r i:.r,,,e = o + r =4. whcre r = 18..J cm.To lind the pedod, we musr find the anguiar lnrctuency ? = 2/r. We ao not tnorv Lte,* r,L {. J, no,n.cJ """ , ,f =tr, =,t

rc)(d)

(a)(b)

From our \,arue for r, rve find r =2r/ ) =2n

Sect on T 5.3 Energy of the Simple Harmonic OscillatorI'15. I 7 Choose rhc car wirh its shock absorbing bumfer as the sy srcn I bv conselaarion of crcrgy,

Pls.f8 /,r=200g. r=0250s,r =2.0o Jt o =4= 2L=2s.1 ,fildls(a) i=7r.rr=0.200 kslzs.r 'oa7'1'=Fts N/.1tt n=4=t=,F=ffi=f"-''-l

3:010c'dgxgeL.xri-igALlRilhsReservcdr'l!ynolbcs.rrned,.op,dorduplicrred.orpokdlonprbticllacc.*,htewcbnc.in$holcrijrFan


10/23

476 Chaplet ltjPl5.l9 (rl 2=16 =11::o Nimt{i.00il0 l

, -,,,!t'-'=i1 J,1'-i.1 =[:s.0,',t

{l'l

(l)

' =tr,,,.*.nL,i[-

!r' = e !,,n" ! ,r"12= . = l!! N =! 0.1{)0 m

k * r=f =[1, c.](cl rr ,-.rA=\60rlto.:001. [r.tl ",1' ](dl \lrxinrum spccd occr rs $hef lh. obicct pxslc! thl.(ru:h irs oquilibiurrr po''t",,, ,' [-'=!ro) ,/ ,, =r,)rA =50.0(0.2(x)) = 10.0 nr/sl(ll l\,1.r\imLrfr r.ccLcrxtur occrLrs rher. rhc objc.( LcleNe\ ditu.riot. shich i\ shere (s

dishr)ce llonr ..luilibrir i\ u ,Il\i nrrnr. rt r =:f,1 = t 0.l0qtrr .rsr r-jr.r'=jrto0rto.:oo) =rr,t . =r,J.f i =,80rJlfr.:oot =!.:-'v;l1;1 a =ro'r -:,1,,i!!!ll=

],'" . i*' lr. =r1-r:.01 1.t.rn'to:APl5.l0 (rl

']l'15.21 (r) EIcrg) i(.onscr\,crl b) rn i\olrle(l\inrllc hurrrorrir osclllrrl(n:rlllL IA I T2222)2']-'=l't,r' "r

(hl

t,_;;,229

.',=j/,[; (1rJ']=:il,' ;l

r00 l

!ol9


11/23

-l','l=lilt o i'l, li,,l1

1^,.= 1,.i11Ir, = l 1,,.

ll24

r"r llt'=

Oscillatary Maltan 477{hl

I

r,r1 @ rl" -ur;mullr l!ncnLill erer-qy i\ cqult rc the rnll cnc[] ol rlrc sy\L.m: kjnericplu\ f(ncntill e|crg). llceruse the lotrl cn.rgv nNsL rc. iI conslart.lhc kinelic energy.r'r i'.!cr he grc.rl.r rhxn lhe nrl\ilrrun tolertille .rgl.Eq!4,'4r9ry!t,,.- r"{tr..

Ir,=\+a/ dl:rrD-o+o+1( rs m/s )/,

tlSfr

'rl'15.22 (r)(1,

(cllili

Ti,c slnefr .ir rhc bunlee iL,nrr)c,. rrr. sfrins ico ). .ud Lrk Frtrrh is I is;;J]lhc !ysieLll is is)hrcd so encry) js conse led $irlrin rhc sysrenr. 'Iirlte rhe j.jlirl tojnr\hcrc she nct)s oll thc b|drc xncl thc lifili poi t !r rhc bolrcrn ol trcr njotioll.

i(+..r- , rr,J =(r+r 'r,. j0+,/(r F0 = 0+0r ]/ir(65 kg)(e8 ./" )(n'-).-+{{15,n)',r=[nTN[l

'lh. spri,)g crrcn\tof 11c(1,it;t',;un, ',=I=I11=tl:lgl'yl Ii J s.r8,f .n)rhis5 kg{9.s nrl sr)t)oinl is I 8.68 Ir 1.).7 m lrcl(tr\ thc bridge 7-l .l N llrrrd Lhc !nrIijIr dc ol h.r osrillalior is-16 lt).7 = 16.3 ill

/L r.: rt l-,r ,,,=1i;=1 ,,'. ={gl Scrr.0r{thccr|rilihriu rf(^irionofrhcbLngocju.rperou{hcsfrirs.Retxli!ctothecqL'iUbriurn 1)l)siliorr. lhc lowcst p ltol th.cln)jrcorrcspondslo_r=+t6.j|r $.c hrletrke| do$n rs lnsitl!c rndthepoiLrriILlrodn)|r$hertlhcsi'ringL]eBj|slo\rrclchjsrrr= ll.6iinr'flketL.fhrse !z.ro.rlrrarinundo\\lrw ctcxre|sion(r=+t6tm).\\t hDd Nlur the phrk.,,. \ils 15 nr highor. Nhere I = t.68 nr (rbolc lhc oquitib

r ,l cosn)/:!lr |re / = 0. \ = l6 -l nco\0 = l6:r nr, rnd shcn r = it68=16.:rcos(.D/).ot = !1)1' =+). 3 rrd. \\ hl.h sitn do $c ticl( tor rrl1, Fnlrr ir tllr,= to,t;lirot.ar


12/23

478 Cheplet !t)

'rPl5.?3 1rl

"PI5.2,1 {a)

\= 8.68nr.risdor.$'r11.\lii.hllrcrr\htou! .r)iccr)l t)(\iln e dirt.rit, r' f isl)\iri!c. Picl\ rJl= L ll rrtl:,r = 1])rl \iu i 2 l.l tuLl ={rri (0 3.181, {hlrh i( lfuritilcTlrc eii)rc..,)r=l{)(r/= ] l:ltuLl ,t= lLr!'J ll)l i,incarirg/= l.l) sshcrrhcI 1)(rsfring hcgi|s lc nrer.h rrrl7 = {) $hcu Lhe lu ntci rcrcht\ rhc iiollo ol lh. lunur l;r.rr!=:.0 ' I I' Lt'., rl *" * "r \ hi.h th. st)r iri \ncr.h.s1lt.) r(nrLli r i 50 s+l0ls= r.i0\

F=ri r = (8r.s N/.r)(5.r.r 0rn) . r!!!\l, I / l. l,.,t, ,,.t. ., i. I

(.) Whilc lhc IJL_ock $.$,_,"f,f u",n",u^ rl-\ 5..16.n, 1/, /i+/ =1).orrhcsflin:li)rcc $.rs cqurl ir lrrxgnil|de rnd opposlrcl) d:.(1'lc(L lo thc rU|l cd r'r!.. \\hcn rh.xt)plicd lbrcc is \uddcLrlt r'erlo\'c(l. thcft: Ls ir fLrr n rc. I .l5N N dir..tcd lorrrl lhccquilibriurlr posili(nr rclrng oLr thc blork lhisgi\e\rhehlocl(rnrc.rtrxliorhr\ing

(l)

ilr

At thc cqujlibriur. pr^ition. r'L = 0. \o drc hl()clt hrs li.ctic crcrg) ( = t = (l 1:5 .l rl

1c) S )rllcr: Friclror\\oL,ldrr'ur!lolnn)ncl(ircli.cn.i:!i.loirl.inrlcn.rg\ll r', l .,,.,,, -, 1.11.. r.l .'.

T|cbl(rk$rll.oni.Lo.rsloprilcr\lid:Lr!rh,oLrgh(li\Irrrc./ r (1.05.16 n.t,

tL0 tio t.ll,r .0.r. l' :ittrl lrjrr \ q

hnr.r\)\lcrr i\ in thc id ll ol li cri.i\

lrlsi' ) irs n\l o 'r1' s0)l Thc pe od,:ii rn obtl'cl-"prlf! s\\refr l! rst)rirg is 2ir i,r,i /, . nr rh. lin.c .onslNnr ol lh.

lzt

I ^., l. ri, t1,.,tqt(81.n N/m)(0 {).16 irlo+io

lzLrt,\l llic o!uilibriunr r)osilioir. lhc r,nxlcIcrgy ol llrcc,rcrgy rr.l rrrj.,,/l = f. $ rlrc,rrr\i,run, itr.cd

, h)n .1r: (o 116 kg)1., (o l5o rl


13/23

asctllataryl,lolon 479Al lhe or nir!. fr)inLs. i =:ll. ihe rcirl cn.rg) ol tL!' s)slefr ij in lhc i(nm ol chslrcpotefrirl enci!). or | = iir{r/2. Sivifg rhc aintlitrdc $

15.4 Comparing Simple Harmonic lllotion with Uniform Circular Motion

l.l

(b)

Sect cnP15.25

Pt5.26

'lh.nnni(Dissa plehrurn)ni.hccausclhclireisloltrling\ithcoDstx lmrgolurlclocitl xrd yo! see rhe t.oicct(!r ol thc rnorion ol the humf in ! fhr)c perperdicnl:rrSi!rc. the crr is nrt)\ ing \ilir \tc.rd. 1.0() m/s. and irs rldius is 0.300 nr. wc hx\c

It).0 rad/s0. r00 rnlhcrcli)r1'.lhc period oi rhc Nnjor is

t=' ,) (10 0 h.l,s)

l5 5 The PendulumThe peiiod in loltr'o is 7, =lrrnd thc pcri.,Lr ,!r crn,h,irr:" l. r, =:"J!'

= 2.{)0 sL' I-

,,, != / !11!l=[ rr,ri!,/lr+rr-L ]''P15.2'7 Th. pcr(id ol r t)c dulLrnr ls lhc li.ro li)r orrc co|rplele os.ilhLion dn| is gi\cn b,"_i - Irji /1,\!hc i\ Ilre len:Lh r)l 1lr.l)cnduhut


14/23

480 Chaplet 15

l'l),){lllrrii)f\I I if,:##.t'*(br Thc lcnglh ol lhe pefduhrn is',"',1'"1..,-)llclcrril]g lo rhe skeirh ilc hN\ct,= t a:n)C rnrl tmd =i'' R

I or sirxll displ.rcc reur\. trLrd .., s rtl

l=m

Pt5.2'i

..xud r M'= i.,Sirce rh. rcsrori.g lirac is trrolortj.in.rl 1l) rhc dispLtrccnrcnL,,F rl,'ir Il, r r'urtr. r(lrrntoirg to /:= ,ri, \ sho\:

P15.29 I={l+:0 r/ 0..150 m . rr(l ,r = 2.10 ltg

It tn'!i tl =! ri.r,i ,ryrt

lor r Plry\icxl

tiit,l | \ ,i,,l'r=lt ; I tri(,I r)(rr li0)l? l0liO\ I ANS FtG. P15.29, =!,

it Jt) rl=ln I I =\,r'./ 'tt I,t,t=t ti\!= t t_+r li +r'

"P15.31 {-l*i|! rhe simplc hrrnxinic nrni(m rnodrl:"" li,s't"*ll= o.:r':

i11z.

I

2n

'lr

t)

ll .tr| ,


15/23

(rl(L'

. = 1,, = 0.162 n I I r/s r lr n2{) n/. Ilitr !imple h{nnouic nxnio . the m:[imrxn.rccclcrrijonr . =,1rDr=0.261nr(l l3/s) =li7 nr/s'. cqrrrl ro rhenruirnuln |rngcntial rccelcl1rtiot, o.curs at the c\lone

,, t5tm\:i lmIhc rraxinarm rcsloring li)rce canrcs Lbc marimunr

/ =,iri =0 2s kg (2 i7 nr/s )= 0..+l f'( ) Appllingencrgy conseNrlior to thc i$lated l)cndulunr_9rrlh

as.illatarvl"4alan 48'l

\I- -.,".:1,,,t'',lB

Pl5-32

(d)

(h)

/(,+U'. K. +.,r. .,rtO= :,,,,'.. r,,, = 0q/, = JzsL(1 co!0)=(b) Torque n](xlcl: ta = rntLsine

rlld ,=L(l cosd)

,, = lIt-!9 = l.,', e = ItJ ",,rr. l ,,,t1 I t-- )I Jr,'..r.:'r. 'l .l_'r., \..r1 ,' "'. rf'. r-**r'Drr


16/23

482 Chaplet 15

P15.33 (a) Thc \tring tensior nmsr sLrppod rhc wcighr ofrhe bob. rccclorrLc ir ufwrin. rd rtsotR)\ide rhc reltoridg iorce. iusl ns il thc cLevator werc ar rcn in r gra!il\, tield o1'(9.80+5.00) m/sr. Thus rlrc fc dis

(r)

. Jl4Pn,,,' ..',r,., ) r.,,.b. t:n['r'u" o.rr,l!(''orr' 'nn" ) L

l he p.rrallel- iis rhcorcnl.t| = l,,t + M.1 *- ML - Md'

1.,, rr!) +2 tl1 =t)

= lM (r.oo m)'+,'r'l (r.00 n,.)'n,6i

= tr!', il2{l9s l0l\

l.0l s

Pls.34

t*(b) For thc \irnflc pcn(lulLrnl

T =2n =20ls dillcrcncc =r=0.rs0 s. / =,,.r =i20.0x t0' kg)(5.00x r0' m)l(rl / =i5 00x r0 r rg ,',1,'r r!3 ^e. F =''=t',tr: !/ f

5.00 mI r.1 "r;

M ( r.r rn')I2l'lt (l.00 m)

0.:0i) mt.'\\ 1ro irl \\\\.

1.00 nr

trjo,taPts.3s

^-=/.,:=(5oo!ro )l#) =


17/23

as.illalatv Malton 483

Il'15.36 trl

(b) t =2n ri; lnL8= iThc cnlculatcd values for.,,,rre:

Pcdod.I (s) 2.00 1.73 L42c {'"4' g8l 9.89 9.79

l.trus. 8.,. = t).8s n/s: This agrees lvilb the accepted !.ll're of s = 9 80 rn/sll l, ,,1 ' l, .. * ,"'*" / \.r' r'/ ! ,!rlLl l

t*,,., = la =l q-* -/; 1. rhis i! wirhin l.s',i of the rcccpted.

50the mersurcd pedods arc:

ANS FIG. P15.3G

Pl5.3ll The toral encrgy is li

Secton 15 6 Damped Oscillationspts.-17 d, = t5.0. o(/=t000)=5.s0'

T:rklrs rhe rirne dcriraLire. !l' (lttJ\c Eqrrlion I'l5.l l, !4 I =

r,,,.,{?"! 5.50 .,1 m,,,,A r5.0l,l Lornl(l0= l-

2t1115.50Lrrrri=1t

hr

2

IE

r-cngLh. l- (ln) I0{)t) 0 750 0.500Peio{1. i (s) 2 (X) l.7l 1..11

= r,( r(. ,'r)+r.r!


18/23

P15.39

484

P15.40

Chapter 15

*"' [-;;]We hare pro\ed thar the mech.tnical energy ofa damped oscill.rloris always decreasing.

=,14.04.(a) Wiih danrping [! = [/ tr-,rl--]lzml l/\ \l \2106kJ,

=r[e:rx' olz =r+.0 1,r 440-

t=:=:=t 7ooH7 I' rr 2t\ '(b) In r = A!. "'1'"' cos((DI +O ) over one cyc1e. a tirne 7 = ?1, tle amplitude changes frorrA! to A zihlr"{) fo.,r foctlorat aecrease of d=l e "1r'a'l- r -? "''u'= r oerqqs=oo:00=E.00tl

(c) The energ] is proportional io the squarc oilhe amplitude, so itl fracrional rale ofdecrease is lwice as fast:

u =)a' = l^:"ii2)) - E\Je rh

0.05{, = 6oe !e60.05 = e r'io6

jL= rn zo =:.oor0.6

(1)

(2)

(-r)

, = l0.6lTo show rhar r =Aer"4"'cos(.r/ +4)rs r sulutron ol k\ b-=D1-dt dt'

We take r = ,4e r"/:"' cos (rr, + O ) and computc

# = * "- l- *)*" ro)t + o ) Ae' 11"a sin 0) t + Q ) (,1)


19/23

1,, ,, ,. ],11' lrrL \ l,tt Iascillalaly Matian 485

[," " ( f),.'"i-*,t)''r" ""'"0"..n'(0"' o)]$'e !ubslriurc (3). (.1) inlo thc lcti siJc of ( l) rnd (5) inr(i thc righL side ol (ll:

*r" "',, o*1,, *41*1' .rr',',, eori.y+o) ri,ar.tr "r' sir{r,rr+-rr)= 1l^""' i 1)*.t-,ot .ar,"''"',osin(.,+o)+1,r" "' a;si'rkor+qt) tD'At"" c$(LDt +Ii)

Comf rc the cocfli.icnts oi,1r " !' cos (.D/ +(' ) lnd'1' " r' \ilr ((,r +0 l:,, l,t ll,, I,'.l -' r "',"",*",, r., *ft,,l*f {,)=,",sincethccoethcicntsrrrccclurrl.r'=ier'!'cos("r+E)is'1\oluLiolroiL|eequrtiorr'

Section l5 7 Forced Oscillations+P15.]l'lhcl)l:odulUnlislcsol]lllilrgsiththcbeeN.Thchc.]|elNLslvihrxlc,tltholiequcnc)of{

simPlc pendultLm ol lieq cDcv 1 50 I17:l"- . grllm\- :n, .l 't r'rn '\/ l. , "'ll.' E:l

For ltson icc, her icqtrenc) r|ust nratch''rLr. rn. \ r' rlll' lr l,r!,r l,rl ll5l!

\rr' " l r''r'''Ilro r', \. ., ' . \"' r',a ' r ..lccelcrrLion i\Aor. \\'hen this becorics equrl lo lhc xc'eleralion duc lo grr!itl thenomrxl lirrcc c\elte(l on her h\ the mltlie!s \ill d()p lo zen) .tL onc point it thc cyclc:

j)

*P15.42 (.r)

.r=- =att I )t] a(b)


20/23

4a6

P15.46

Chaplet 15

!

(l)(21

(-1)

(1)

*Plq.41 /: = I00 sllr 1:tr).1= l0 0 N/rrr. xNd,r= 100 kgl'u lr.oo I (* illloo

I,L(rlr r' = 1.0(l \ii {:Jr/), rhc .riguLtu lrtqt cnc) ol Lltr' turcc is .D = l/' = lql\ L!(nr) cqtrltion l -i.:l6. Ihe rnrplilLr{1..1 (l1 1t !lritlar r)scilLrl{n, s i1h/) = 0 Si\os

A 1 . t,, '001i, l){i' ll. Ln IP15.,1,1 I iom lh..qu:rllon lor l!r. rLrrpliruclr irl 'r clri\dl oscill.rl,r $ilh fo danrPirg.=-ria a,i)

i,=rn l=(ro.or \ ) ,,, =1= :{ =+,,1).1,,r ltlr.0 q 8ol

th)

\ F, 111 l, nt _llr- ,,r '

r =f i' i'.,t. l )1r'tro +'rr 1= rr.rlI't5.,15 ;.--l: J1r,' ,,, ) +1r'o'.1'

. rrr I .:n + F..,inl'.,") 1(')' .',;) o a't ,, k ! \'r l \l. ,. ,. ,r, In,.-.in, U ,r

lhis)l.lclr .D=8.13 rrd/s oL .r=l0l rlrd/s11,,,n. I ..11g,r,cs cirl," /=[rnIt] ," /= 0.6a1 lL I

tl tl', \:i(ot L\= t -

1 - .v,,i,kdl ilr)'f l= r,rr. rsi,ur +ot,t,subsrirure (2)uul (.11 inri, (l): 1r si..r)/ l.a"\t'/+rt)='{ /li"r)'(r(r"/+01Sol!e li! Llre rnrdilL{lc: (r"r n'tr,r']t's(rLrr+o)=/ \itr,r/= /r co\(rl, (r0')


21/23

ADDITIONAL PROBLEMSD,,.,,,1 .t.l.tnoL(rr irnd one n.nln)n l(! br..,it! sc i('fel lo the .r)lccul. li)rrncd h) lwo deulerinnr rllomsr\, rnd lo lhc dirronric rnr)lcculc o1 h\drlser rri //

Os.tllaloty li,,lofiarr 487bc c( url. tr i(lerLonlythrl(rnruslbc+90 rnd /,.,1

r/ rr/, ' =.1I= 1L- il,, J/ r/, ! r/ \l

Pl5.,l7

"l'ts.l8

lhl

t?lxsler lh r !l dcr I lh.stringirNlrnlrneonn) hrs rr\inrunr(ot]rp'clsLon \'lr.n boLh :lid.r \c rr0!ir! trilh lh. \r.t spcc.lr, .NtudrentrLnr .orsor rrtior:,r ,rr ] ,.ir. = n ar , ] r.ii-,{0.11 ks){0.7,1. n,/sj+ (0. r0 lgl(().ll .r,/s)= (0 la kgit', + (1).16 kg)i,,t)"lll k' n -i.- 0la8 \lrri 0 11Encr:j conscArlion:(( +(.+r ) =in (.-u.),tlr/! + ,,.. o 1,,, +,rr I + Ll

,,,u| l" ,'ILloor r,gtio.u.s,,,/.j' +l(15 N1.).,'

ll.llr,t i I Lr1r.t[ ]- 1 15 \ l) I\ =r)(ttjt|r1,' ,,,,,., =11o.oo rrg110.r68 rr/s) =0.0.+06.r=

N/nr)(o.or5r(l) ll '=lt+s nr) .o.ot77.r-,


22/23

qr 11r(,. i.l) rnJ E(irLrtio| I I I i lo lilL trri'rr i I )^ll 'ttt.: ri; ./, ,11 *1 ,f- lt,l'l ,lr

tr r lJji I /'tl ''' I rr ''

i]rrrril!/llrr/ti.,iiorr 503Si l).(llutirg I

'17 =

,L 'J1r1' t I I ' tr ''f.- t L "r.iiT =il + - I.i r\ rt,l 1 lNhcn th.liqt,i(li\ gof. the( i\l 'rt ihc b'b is strd(lcli) lgri rrLhccenlcrol thc cuhc\\c hatl rgn,[.Ll rht:| * r) thc .r bc rl lflil rrN sin( 11 \xs enlll 'i!nl).llt(| lo thefrrss ol rh. liqLriJ. ThLr\' (!x'e thc jiquid !s:'nc. / = L

=i .tr!1Lbl

P 15.'1Pt,i.6PI5.ltPl5.l0

i.i() lN/Llr(ri.l.3-l triri rlrr j 00 crrr/'il (o l7 l.rt' : (dl I l'1' r.i ' (l(icrnrxl ll8 rr/\r rb) I il Lnr/!(r) L l(l s: tlri l) -i ll H1: l! I I 6l rrrd/s1r) l5lcrn:lh)j .lrI:i.l l59crf:{d)503uilf lhclllt'nr\ol r)scillrtiorr Llit'Lgc jroircrrclr ortrer. s nirrg ouL in pha\i hul bcronrirrg (!nrli!'loll on! '1 lhr\c To 'rl'r llLc tIc lrrturc'\., {inrll ne.J .!r r h),tr\l.dlc o t|c Pi cn'rrll rn inrf o\lilri irv(rJixninri\t)erl\lic:1bl l3 r'(cl lh(r|'titnL(nolsinplchrrnr!rl' flciLLlir'crclir! (!r lhc hrLl ls l co rslrrrl !i\ctr l)! l =,r3 {$"11 $btn it i\ l' co|l:Lcr $ilb lir' irnN lrl irh r. rrL irrthc lir,fi oL ll(i)ic i h!r,,ii16\:11)r0.1:larA.0.151)n/s:1.) f' t(J{)cos(5()0/+/lJ l50\in{''001 "rl rtnd15 {J..j (5 0(, + r)lu)Ir\iLbr\r*'cllrrlliL inil Lh.l)eriod 'l'e\ rrlf i'pcn(ioDI'rro\irrgth'nLtr\\: 7=08-iL)s1xl l16 N/rn: I b) 0. L /l I'l(rt l00N/!n:(l)lLllllTrl.l l:ll nt\:(dit=0:(tll00n/sr:(1)10101)rn:(3):00 1:lhl

I't:.i2Pl5. rllll5.la'P15. !8yr5.20Pt5.l2P1ii.2:1Pl5.:6I'15.:lt

l.l-l nts: (il r.l-1 m./sl1rl PIll. . r i(l.r c,i.s10rt rrc..lcrlli(!r: ibirhr bri!l:.:1i I I 06 rtr(L^: rg) 1:0l sr {lli lrxr,\ 9l r\ {h) 106 \/Ln: L.)l)l:ll rlL.00irrTi

l.5O rt (d rliiatct| (dl l-l _l \/Ln:1.r l!l.7rrlrellN5{) !

B itr lr" u rrL


23/23

504 ChapLet 15Pt5.l0Pl5.-12Pl5.-rlPls.-l('

ht +ttt tr.'r '" ll th) / , =,n/\ ,'\./(rl I 09 i: (h) .l0S%

ild I.nglh,/-(nrl: I000.0750 0 500 rrrd Pc.iod. / (sl: l'i:)0 17l i 'lll (b) lirr P'rio(ll-(s):2.;0. ll:1. 1..11!n.t((rn/s:l:9E7.r)N9.91) Tlris !!r(1:s \!irh rhe rccc|lcd \llLre ol'I =rl ill rn/s \ithin05tl:(.)9.r'1nr/sllL = t"" 'ttScc P !5.:10 lbr.o rPlclc \olurion(r Llr) H/:ib) 17.5 c'rr:lt8 NSee l'15..16 li)r comflcle \oluLion(r) 0 -l(rtj n/s: (b) I 5 I crri (O :10 6 lnjr {d) 27 7 rnI(xr.l :t I crrr: (hl When the tr)cli is on thc Ninl ol lilthg oll, the sur$uoding $ rlcr is alsoI'rrcl1- h lrtc lill. No prc"surc grr(li.nt e\isL! ilr thc srler' s) 1ro buol rf1 li)t'e rct\ on th'rock. lhc e1'lictol1h. surnNlilrg \\rlcr(lisdpperr\ xt thrr i nlnr',.,r \ ..,u.r,. t,/ ".. 'r,,t 'ln.',. -""'l ,'wlu. , is in cenlirnclers lrrti r is ir iecontic

P15.38P 15.,10I'13.42t15.,llP i 5.,16T'15.;18P15.50

l,l;.52

P15.5'1

P15.56t5.58

P15.62

P I5.6;l

i.l,., j.,,.1 ". '' lur""'r"t'r'l\ l/",= ! ,;(r) 1.00 s: (b) l'1.3.lr (.1 ll 25 5''ll hc encounleis \vashhorri bunNs trl lhc strmc lfeqrrcnc\ rrs Lho ltee !ihirliot t'so'rncc irilLmnke tho rnol(ncr_cle hource x l(n ll nrx) bou'cc so Druclt rs to rrrle irc\ilhlleri(lcr'(cot1r)l ol th. rmchi!rc: l0 rtr(r!SccA\SFIl.iPl5.6r(d):(b)1.7'1N/nr6r'1:(clSeclxbleinPl5o'l(c):(dlS'ellhlcirlPi5 6.1(d): (c) See ANS tlai Pl5.a)'1(el: lll I 8l N/rr 1-l'1: (g) rhcr- r!lrc': (h) lt grxrn! r 1l9i'(xl5 l0 sr (Lr) 2 60 si (c) ,\2E15.66P15.68

I'r5.70

t'7s.72Pl5.7,l

(r)Scel)15 6tilr)ibrlill.xpltnrLiorr:ll,)SecPl5.68(h)ld lill c)illrn!tion: {c) See A\Sf,lil Pl5 68(c)r (1) See I'15.68(d) lirl full crtlxndLion: (c) See l'15 68(c) lor inll ciflrnrtiollll lhe clxrnting connlnt i! doubled b/l,r = 120 s ' h thli c$c ho$cv'rr' b/l'i > 'J' mld rh'srste n is o\,eirttrled 1buI dcsign ol,icctilc i! lrot rrrcr becrun' thc !r-sleLn clocs 'oL oscrllrrc'

- h'l Al - '\/ J rF _'' r/.. , o "ttl ,.ifhrs is cvrctr; Lhc samc Linrc ;ntcrlrl ds lor ,"'o!r conrNlinn \) yorr ha\e no rd\'nnllgcl inllLcr. rou ltlr\e Llrc clisr,i'rlrlrgc ol thc ; ili l cr])itrrl ouLlxy n) bore Ihrough lhc colirc li rlhl

Ch15 Solutions to p486 + Evens

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Transcript of Ch15 Solutions to p486 + Evens