2001 November 15 Exam III Physics 191

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1 1 November 15 Eam III Physics 191 Physical Consans: Earh s free-fall acceleraion = g = 9.8 m/s 2 Circle he leer of he single bes answer. quesion is worh 1 poin Each 3. Four differen objecs wih masses: m = 1 kg, m B = 2 kg, m C = 3 kg, m = 4 kg, were a res unil forces aced on hem. The graphs of force (in kn) versus ime (in µs) for each objec are displayed below. (F is he force acing on objec, ec.) Which objec ends up moving he fases? 1. In erms of basic unis (kg, m, s recall radian is really uniless) a orque over a momen of ineria (i.e., τ/i) has he same unis as: F F B B. kineic energy over momen of ineria (i.e., K.E./I) B. angular velociy squared (i.e., ω 2 ) C. angular acceleraion (i.e., α). all of he above F C C F 2. uniform bar resing on fricionless ice is kicked near is end providing a horizonal impulse J as shown below. The cener of mass (labeled below as CM) will hen: CM. remain a res wih he bar roaing around i. B. move in a sraigh line a consan velociy. C. wobble due o he unbalanced impulse.. none of he above J =, an iniially saionary bo on a fricionless floor eplodes ino wo pieces: piece (doed line) wih mass 1 kg and piece wih mass 2 kg (dashed line). Which of he below graphs properly displays he posiions of he pieces versus ime B C

2 ω. (rad/s) 5. Objec (projecile) srikes he saionary arge objec head-on in an elasic collision. The arge mass, m 2, and iniial projecile speed, v 1i, are pre-deermined, bu you may selec he mass of of he projecile, m 1. To achieve he larges possible arge-objec kineic energy you should:. choose m 1 m 2 so he recoiling momenum is as large as possible. B. choose m 1 = m 2 so 1% of he kineic energy ends up in. C. choose m 1 m 2 so he reducion in he kineic energy of is as large as possible.. minimize he reduced mass o minimize he relaive kineic energy. 6. Two cars ( wih mass 2 kg and B wih mass 3 kg) moving fricionlessly along a sraigh line have a head-on collision sofened by spring bumpers. uring he collision he springs compress, he cars reach minimum separaion, and hen he springs re-epand unil he cars are again separaed. uring he insan when he cars reach minimum separaion: B. boh cars have he same momenum B. he poenial energy of he sysem is a maimum C. he kineic energy of he sysem is a minimum. boh B and C 7. The below graph displays he angular velociy, ω, of an objec as a funcion of ime. Circle he labeled ime when he objec has he maimum angular acceleraion. (Noe: negaive numbers are smaller han any posiive number.) 8. Saring from res, a record player is urned on so he plaer spins up o is usual speed. shor ime laer he record player is urned off, so he plaer slows and comes o res. Which of he below graphs of angle vs. ime bes displays his moion? C 9. bel drives (wihou slipping) a large radius pulley () from a small radius pulley () as shown below. Please compare he angular velociy of each pulley (ω 1, ω 2 ) and he speed a he edge of each pulley (v 1, v 2 ). Which combinaion of saemens is correc?. ω 1 < ω 2, v 1 > v 2 B. ω 1 = ω 2, v 1 > v 2 C. ω 1 < ω 2, v 1 = v 2. ω 1 = ω 2, v 1 = v 2 B B C (s)

3 1. wheel sars from res and spins wih consan angular acceleraion. s ime goes on he acceleraion vecor for a poin on he rim:. says consan in magniude, bu becomes more angenial as he wheel spins faser. B. increases in magniude, and becomes more nearly (inwardly) radial. C. increases in magniude, and becomes more nearly angenial.. none of he above. 11. The meer sick shown below roaes abou a pivo poin a he cm mark (shown below marked ). Five forces ac on he sick. The magniudes of hese forces are he same bu he direcions and poins of applicaion vary as shown below. Rank (from leas o greaes) he orque produced by hese forces abou he pivo poin. We define a posiive orque as one in he couner-clockwise direcion. (The orque produced by F 1 is denoed τ 1, ec.) 13. forward force acing on he ale acceleraes a rolling wheel on a horizonal surface. If he wheel does no slide he fricional force on he wheel is:. zero B. poins righ C. poins lef. poins up F 1 F 2 F 3 F 4 F τ 1 < τ 2 < τ 4 < τ 3 < τ 5 B. τ 1 < τ 2 = τ 4 < τ 3 < τ 5 C. τ 1 < τ 2 = τ 5 < τ 4 < τ 3. τ 2 = τ 5 < τ 4 < τ 1 = τ We may apply conservaion of energy o a cylinder rolling down an incline wihou sliding and eclude fricion because:. he fricional force is zero. B. he angular velociy of he cener of mass abou he poin of conac is zero. C. he velociy of he poin of conac relaive o he surface is zero.. he kineic fricional force cancels he saic fricional force.

4 The following quesions are worh 5 ps each 14. Consider hree paricles which have he following posiions (in unis of meers): paricle mass (kg) posiion (m) 1 m 1 = 1 r 1 = 2 î + 4 ĵ 2 m 2 = 3 r 2 = 2 î y m 1 = 1 kg 3 m 3 = 4 r 3 = 3 î ĵ m 2 = 3 kg m 3 = 4 kg. Find he locaion of he cener of mass R cm (i.e., boh and y componens). B. Calculae he momen of ineria of his sysem for roaions abou he y-ais. 15. Bulles leaving a rifle are spinning a a surprisingly fas rae (he gyroscopic effec prevens umbling, bu we ll need anoher lecure o ge o ha). For eample, he 4 gram, 5.6 mm diameer bulle from a M16 rifle is spinning a 3, rpm. This high spin rae is achieved in jus 2 revoluions of he bulle as he bulle spirals down he barrel. (Yes, he bulle goes from zero o 3, rpm in jus wo revoluions: a huge consan angular acceleraion you ll wan o calculae.) pproimaing he bulle as a cylinder (I = 1 2 MR2 ), wha orque is required o achieve his bulle spin?

5 16. Paricles 1 and 2 collide in space where here are no eernal forces presen. Paricle 1, wih mass m 1 = 1 kg, moves sraigh down parallel o he y ais and collides wih paricle 2 (which has mass m 2 = 4 kg). The below liss a pre-collision (unprimed) and a pos-collision (primed) posiion (in m) and velociy (in m/s). paricle pre-collision pos-collision 1 r 1 = î + 4 ĵ v 1 = 4 ĵ r 1 = 7 î ĵ v 1 = 16 5 î 4 5 ĵ 2 r 2 = 2 î v 2 = r 2 = 4 î 2 ĵ v 2 = 4 5 î 4 5 ĵ. Show ha he iniial momenum in he direcion equals he final momenum in he direcion. B. Show ha he iniial momenum in he y direcion equals he final momenum in he y direcion. C. Calculae he oal kineic energy in he pre-collision sae and in he pos-collision sae. Is his an elasic collision?. Calculae he relaive velociy vecor: v = v 1 v 2 in he pre-collision and pos-collision saes. Should he relaive speeds be equal? 1 y 2 2' 1' kg block of wood was a res on a horizonal fricionless surface and conneced o an unsreched spring (k=3 N/m) whose oher end remains fied o a wall. 7 g bulle moving a 9 m/s slams ino he wood and remains lodged in he wood. s a resul of he collision he block/bulle combinaion moves o he lef and compresses he spring. (The objecs remain in a line.) Find he maimum compression of he spring. k v M m

6 18. n wood s machine is a device firs described in George wood s book Treaise on he Recilinear Moion and Roaion of Bodies (1784) as a ool o accuraely deermine g. The machine consiss of masses m 1 and m 2 conneced by a sring which sreches over a pulley (radius R, momen of ineria I). erive a formula reporing he acceleraion a of he masses in erms of he oher quaniies. Of course your answer will include a free body diagram (showing and clearly naming all he forces) for each mass. You should show ha: m 2 m 1 a = g m 1 + m 2 + I/R 2 g T 1 T 2 m 1 m 2 I, R

2002 November 14 Exam III Physics 191

2002 November 14 Exam III Physics 191 November 4 Exam III Physics 9 Physical onsans: Earh s free-fall acceleraion = g = 9.8 m/s ircle he leer of he single bes answer. quesion is worh poin Each 3. Four differen objecs wih masses: m = kg, m