ENftf4 SOUAT'CN5 'tfr TLw+ffir,ftFair fr4 *o*=, KOnAf+D M. STEIN Phvsics 120 Exam #2 (Fall 2014) Show All Work. Use Energy Methods when appropriate!! TURN OFF YOUR CELL PHONES!!! 1. lt is well known that bullets and other missiles fired at Superman simply bounce off his chest as in the figure below. Suppose a gangster sprays Superman's chest with 3 gram bullets at the rate of 100 bullets/min, the speed of each bullet being 500 m/s. Suppose too that the bullets rebound straight back with no loss in speed. Calculate the average force exerted by the stream of bullets on Superman's chest. F= 5r.f Dors tT suRrRtsn Yct, T}+AT Tl+E ForcE t5' 5p sl4 HLLT' NoTF 5N e I' Lh r:R 18 OZ I I 6 K, sTnrnJ 2. William Tell shoots an apple from his son's head. The speed of the 125-g arrow just before it strikes the apple is 25.0 m/s, and at the time of impact it is traveling horizontally. lf the arrow sticks in the apple and the arrow/apple combination strikes the ground 8.50 m behind the son's feet, how massive was the apple? Assume the son is 1.85 m _b tall. Lnr ffi= fYl+ss ol= AnnoW = lr5g= la5 xto ru M = fnAss 0F BY CCl.tsERVfti?un/ cl- {+?fLE LINFAR Mcl"lEn{Turt, " = (rYl+ '| ra)n (Y\V"tO ( penpp.rLY rN*.osrl( \ cot-tls,sr', (ta5 xrC)Gs/ = f,ragxrD3) + Hltr oNcE ThE A-(not^., Flrts Tr+F l+?Pl_E iT ts %= A PRc;FcTt LE (1o',0)x-#* 2_ o FbK -/ -\ 3 e=O + k=X -9t /eY $= axaf = (8,a) (q, y) l<-x--l 3Q"ar) fA= 13,83 nls & M-W-0"'t{ oR. vg = ourotry fl= lel $wns f,= 8'5 t* ,0= - l.85rt ) K- srFlN 3. A uniform spherical shell (1.,' = ;MR') rotates about a vertical axis on frictionless bearings. A light cord passes around the equator of the shell, over a pulley of radius r and rotational inertia l, and is attached to a small object of mass m that is otheruvise free to fall under the influence of gravity. What is the speed of the object after it has fallen a distance h from rest? BY Con tsERvATlD,{ oF ENen6Y) M,R AK+ A1/ = C *(3Mfr)'f + *rwl } - t*rnvzt No\d (/)r = P/il Yvrgh 1 cda = *rntf- ilvz+ YY\gh: = G*l,h) (Yr) + gr (ut )' o%,]u' +%flv = H[+# B+g o 9tr {= . ag\ Z Pno 6PF K, 4. @) AK+ STEIN A 68 kg skier approaches the foot of a hill with a speed of 15 m/s. The surface of this hill slopes upward at 40o above the horizontal. The coefficients of static and kinetic friction are 0.75 and 0.25 respectively, with the skis. (a) Use energy conservation to find the maximum height above the foot of the hill that the skier will reach. (b) Will the skier remain at rest once she stops, or will she begin to slide down the hill? Prove your answer. N{:U \7, a 15 rn/e '---> (o - *rnvl) t (i'n6h -o)= - dA -*rnv; + ry'g [ = - /* b1*ru)( n/r,nr) t Fg + r.rng cD+{: h= -6?E i rnvi + v: a t0* )^nc*+E h= 8.8+ ?FKD Srn (rs)' a$,r/[*(o,u)(r,r{ D: VA + m (b) Wr$rl T$p sKtFR Comns rc REst or{ Tl+E SACIP F/ TIIF DotnNruerD RBcE TFNliNq T0 n/LL l+E( $f+c*, gownJ F--([lt ods,me) = (68)U1.8)srn +d = tl-av u ) *N Tl+F l4[XrMuM RrRcE oF ST-Arrl FRt cttorr,t opibsir.J6 T*rs 50 IS Tt+F SKIFR tl:tll gFd,N Tb sl-r DF &AcK l1+F $rLL. q Duu,,r.l K, sTE/N 5. The cable of an 1800 kg elevator snaps when the elevator is at rest on the first floor so that the bottom is a distance d = 4 m above a cushioning spring whose spring constant is k = 1 .46 x 105 Nlm. A safety device clamps the guide rails so that a constant friction force of 4.45 x 103 N opposes the motion of the elevator. (a) Find the speed of the elevator just before it hits the spring. (b) Find the distance s that the spring is compressed. (c) Find the distance that the elevator will "bounce" back up the shaft. (a) AKtAUz=q *(rroo) + *rqvl ytgA= -$ul- t f = E,,ooXt,v/ - (u*.tr (+) + l@ (b)-Mtr (.1+d + **x'= - f(/+x) (+tx) + *(t'q" ,'3 )f = - $+ro)(++x) (z,or, xiu) - (t;zr,r,J)x + (7,3DXp) xt= - (r ,n x#) - (++ro)x -( r tooX4,v/ {= 0, q+5 rn (c) **- (a"1+Ef + flZU= 51 -* ( I r'tbx r6/(c "q45)t + ( tsoo)(c 'ilV = (++ra) \ e (o,laxl# = K- lJt xlo+) -(++r ';lu + yl = e,qs M