t{O \irtr cal think of thc r\'ork-kinetic en(jrq\ the(r.cm aj asccolrd theorl ol lnotion. parallcl ro t'.cwtol's laNs indescribing ho\ outsiclc influenccs af'fect the Ilx)tion of anobiect. In this problcm, solvc parrs (a) and (b) sepaftreh.fi"onr parls (c) al)d (d) so that rou can c()nrparc tlle prcdictions of rhe trro thcolirs. In it rille barrel, a l-.r.0g btrllct is irccclelrled liom iesl to a speed ol 780 nl/,s.(a) Fincl the work thar is donc on rhc buller. (b) Assum,ing thc rifle balr'el is 72.0 cm lon{, finci rhc ma€nillL(lc tlll'thc a|crailc ne( fi)rce that acled oD it, as )l =ll'/(lrcos fl). (c) Fincl thc colsr.tlr accclcration of a bullct that starts fionr rcsl ancl gaitrs a spced ()l7lJ0 m/s o\.crlt dis(arlcc ol 72.0 cm. (cl) .\ssrrrnine notr the bullct hasnrass 15.0 g. firr(l thc net fo( e thilt acted an) it as I /. = rn(_/rt \\'lr.rt ,',rrrlrr.ro ,. r \i,u (lt.r\! tr,,rrr r,'rrrlarinq r,,rrrrcsulls:U,(= lf ?Vo --oi\r: )fcu^^) v.J It) ".A\Fb)AF: )zcr,^ &unt7 utlk/J5 A/,r.^fb\vt. )touhW=A\nrr)^L{12,rtbu7\\ '{4<-l*'*-V/2-0.12uN, ; *vl. = ) ,rrto-7+(+uF)'. q,t( v7- L bYcl/V, L Av = A\s, l^vt' r/"!:6 Et.0.72 u= 6.7f kN/)F1 A^t\r = 1g --o4z uc-Jd. l2Acf-Irarv,,--; irr4 -- tsrlo'th ' qz?,nb ?r[rt:: d.lrt tsNt5A.100\ chilcl is il a s$ing that is alachcd ro ropes2.00 rn lolg. Find thc gralitetional potential cncrql ol thcchil(l-Lrrtll slstcm rclativc l() the child s ltxrcst positionrrten (a) the Iopcs arc lrolizorrlal, (b) the ropcs makc :r30.0" anslt'rvith thc vcrtical, aDd (c) thc child is ar rhcbotto))l ol the circular arc.b,'LU'*ttLz 7.qhf uoo r.lFu^I U *k.,-..;a) ft--10.b)Y=3o',) 6r="/, -,"r U)^) u ("'t.') =r) U /u,1.'\t/\la -,olt )'(Iyut L. r,.^ t 1z\z; L-LraJD :t t^^t Ln-: [doJ- U'\ \ I- c*= lo? )u (n -r"r b)c\U/t'"")f0A 6 (XXlkg fieiglrt car rolls akrng rails tith nteligiblc friction. Thc car is btouglrt to rcsl br a corubinatiol of nr'<rcoilccl splings as illusnatcd in Figurc P7.21. Both sprinssarr rlcsrrilrrrl I'r H'"'lc.larr r'irh I I rit,r, \ In ilr(llj- .tlUU \ In. \lrcr rlre lir.r:prrrrrg (onrl,rr\\\ r,f,, i^{t-{. \rJrl,e f,l :lrr.U r'rrr. rlrr sernrrrl .prinq .r, r. r'rrlr rlrc lir.r t,, Iinclcase thc fbr'ce es additionel conprcssiou occrtts asslxrwrr in thc glaph. The car cornes (() r'cst 50.{) cm alicrlirst colltactiDg the lwr) sprine svstcrn. Find the car's initialspeed.x,:oXr,. 3o tl.=orSlu".\\' 0'l tnu^.-61L,>16raNf*,,Y.1 --)(aa N/u^ertl^r.A.rlNeAruJrDK./"ti, :/r . /^u|o,211nsI---I- 11\ k, d.' + k2o(1\, t \i\rAXJ - X, . 0,f vlXl-X>'0.2txV\lroo" = \AJ, +\Al. . Akfu, *iL,d,,Itfhe ball launcher in a pinball machine has a spring thathas a firrce constant of 1.20 N/cm (Fig. P7.57). The sur-face on which the ball moves is inclined 10.0" with respcctto thc horizontal. 'fhe spring is initiallv compresscd5.00 cm. Find the launching speed of a l00g ball whenthe plunger is released. F ictioD and the mass of theplunger are negligible.k -- r.to N/"^ = lI" Et=to-AX: S.q = O,0S taW\--(so, = 4tF'v 'd-Vr,'*it4l \/,q \t. V l1 a\*\itt: NtnWb - AKCoJ}k,'= okt= ;2,^.U 1w,r j qrW1 : u<1 Ay =,^? o^ (otVjf lx" **tAxror$ =rffiu= V(f AK + 2X-^s)nxIL.^V Lz (.687t,\ crate of mass 10.0 kg is ptrllcd up a rotrglr inclinc rsitlral irritial speecl ol 1.50 rnrs. The pulling forcc is 100 Nparallcl to the incline. ulrich nrakcs an arrgle ol 20.0' rriththe horizontal. Thc coefllcient of kinctic liiction is 0.'100.ald the cratc is pullecl ir.00 lt. (ir) Hot, mtrch tor-k isdone bv thc gralitatiollal lorce on the cretci (b) Deter-mine thc inclrasc irt internal encrel of the crate-inclileslstern or,ing to frictiol. (c) How rr)lrch rvorl is donc bvthc 10(l-r- lirrce on the cratc? (d) \\'hat is the chaDge inkinetic eDers of fhc cratc? (e) \\'hat is thc speed of thc, r.rr(.rlter lrcine lrrllt'd i l)11 rr:,r\ ? .^''rrta) W6 ?.l) aLn trN. ?.AK ?.e) vt ".t) bzt = McI8y,r: lo byv; = l,f \s(=(ooN*= 2o'r.. o.4!'-s^")r)-1 J) --1d[Nu.. ni.t = -t (c"t(tts) . - tb81 It\E^'4d)F(r"10' : R >zA rvJt4-)'t-),- Fk . e = 1. N 't -- lz u^trcolV .( cu(t|,.)t L-Ju "t-1co l&tr-tl; F.{ =.)[J=i*vt' - l^n,q=Ylsa) \k"r{rJ it+: ,.65-f. bov il a l,hcelchair (total mass .17.0 kg) rvins a raccrrjrlr.r q|lrreho:rlrlrl flrr hor ha\.pr.c.t l.ll rn , ar th(.lc(l ol ..r \l',llc 2.r10 m lritlr.rnrl 12. Irn l,,,rg. At rhe burtorr ()l the sl()pe his spced is ti.20 mts. Assumc air rcsis-tince aDd rolling rcsislance can bc mftlcled ils a consttnth-ictior lorce of 41.0 N. Firrd the rvork he did in prrshilgbnvard on his lhcels dur.ing the rlolnhill ridc.t4IA = 't) h;{,': ).( t'r1!''( = D.q ",-r[1= 6.zliAK . tlJ.W1 = W. +WlcN.= Wt = tuX{f.hh* ^[\'-v,'l - &ttr, :F* ( ,.y(r,') +WFV; >d,{o't1tFc= 4tr,.J\Jo,r0.1^1.=[rl* +tAJ"AL' Wx.: Wq +Wpak-+NUWr+ WpIz*[v('-v;'] - *11:+F*( =EI A A block of mass 0.500 kg is pushed against a horizon-tal spring of negligible mass until the spring is com-pressed a distance x (Fig. P8.59). The force constant ofthe spring is,150 N,/m. \{hen it is released, the block trar.els along a frictionless, horizontal surface to point B, thebottom of a vertical circular track of radius fi = 1.00 m,and continues to move along the rrack. The speed ol theblock at the bottom of the track is u, : 12.0 m/s, and theblock experiences an average friction force of 7.00 N whilesliding up the track. (a) What is x? (b) \4'hat speed do youpredict for the block at the top of the track? (c) Does theblock actually reach the top of the track, or does it fall offbefore reaching the top?A,-.0,5t<yQ : 49tNf,^_R: tr^"\Yg.lZw.(tFK ' )^ia)x r.b) v..r ?I) Ag = N/n,.Vr xo*xAE=o , Ux'Ks..V?-E- 'k'/i' =-F 'Ajo^" = jI"-- lfd u( \KItE, -8-, : -eA.nKunt\'.tJvuxY,.*Vs2 = -rfRFr2r(-\ V"' 't 'ro {r I") lt 1^tl, / a" < t^. --tk' t(.8 uf1, >7 ,H elAt tulh