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# Introductory Physics I PHY 231

MSU

GPA 3.67

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This 7 page Class Notes was uploaded by Quinn Larkin on Saturday September 19, 2015. The Class Notes belongs to PHY 231 at Michigan State University taught by Staff in Fall. Since its upload, it has received 51 views. For similar materials see /class/207627/phy-231-michigan-state-university in Physics 2 at Michigan State University.

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Date Created: 09/19/15

Chapter 6 Momentum and Collisions Momentum De nition Important because it is CONSERVED proof 6 a r m E At At 1 A Since F12F21 A131 A132 2 0 213 for isolated particles never changes Vector quantity Both 2px and Zpy are conserved Example 61 An astronaut of mass 80 kg pushes away from a space station by throwing a 075 kg wrench which moves with a velocity of 24 ms relative to the original frame of the astronaut What is the astronaut39s recoil speed 0225 ms Center of mass does not accelerate mle1 mzsz m3Ax3 m1 m2 m3 cm 2A to m1Ax1 Atm2Ax2 Atm3Ax3 At m1 m2 m3 At p1p2p3 m1m2m3 0 if total P is zero Do the backtoback demo Example 62 Ted and his iceboat combined mass 240 kg rest on the frictionless surface of a frozen lake A heavy rope mass of 80 kg and length of 100 m is laid out in a line along the top of the lake Initially Ted and the rope are at rest At time t0 Ted turns on a winch which winds 05 m of rope onto the boat every second a What is Ted39s velocity just after the winch turns on b What is the velocity of the rope at the same time quotvs c What is the Ted39s speed just as the rope finishes s d How far did the centerofmass of Tedboatrope mo6e e How far did Ted move 12 m f How far did the centerofmass of the rope move 375 m Example 63 A 1967 Corvette of mass 1 1450 kg moving with a velocity of 100 mph 447 ms slides on a slick street and collides with a Hummer of mass 3250 kg which is parked on the side of the street The two vehicles interlock and slide off together What is the speed of the two vehicles immediately after they join 138 ms 309 mph Impulse Useful for sudden changes when not interested in force but only effects of force Bunjee Jumper Demo Graphical Representation of Impulse Mi miquot 7 For complicated force Ap is area under F vs t curve Total Impulse At 1 A pitcher throws a 0145kg baseball so that it crosses home plate horizontally with a speed of 40 ms It is hit straight back at the pitcher with a final speed of 50 ms Example 64 a What is the impulse delivered to the ball b Find the average force exerted by the bat on the ball if the two are in contact for 20 x 10 3 s c What is the acceleration experienced by the ball a 1305 kgms b 6525 N c 45000 msz Elastic amp Inelastic Collisions ELASTIC Bofh energy amp momenfum are conserved INELASTIC Momenfum conserved not energy Perfecfly inelasfic gt objecfs s rick Losf energy goes fo heaf Examples of Inelastic Collisions o Cafching a baseball 0 Foofball fackle 0 Cars colliding and sficking 0 Sat eafing an insecf Examples of Perfectly Elastic Collisions 0 Superball bouncing o Elecfron scaHering Ball Bounce Demo Example 65a A superball bounces off file floor A The nef momenfum of file earfhsuperbal is conserved B The nef energy of file earfhsuperbal is conserved C Bofh file nef energy and file nef momenfum are conserve D Neifher are conserved Example 65b An asfronauf floafing in space cafches a baseball A Momen rum of file asfronaufbasebal is conserved B Mechanical energy of file asfronaufbaseball is conserved C Bofh mechanical energy and momentum are conserved D Neifher are conserve Example 65c A profon sca ers off ano ler profon No new particles are creafed A Nef momentum of fwo profons is conserved B Nef kinefic energy of fwo profons is conserved C Bofh kinefic energy and momentum are conserved D Neifher are conserved Example 66 A 5879 lb 2665 kg Cadillac Escalade going 35 mph smashes inTo a 2342 lb 1061 kg Honda Civic also moving aT 35 mph1564 ms in The opposiTe direcTionThe cars collide and sTick a WhaT is The final velociTy of The Two vehicles b WhaT are The equivalenT brick wallquot speeds for each vehicle a 673 ms 151 mph b 199 mph for Cadillac 501 mph for Civic Example 67 A proTon mP167x103927 kg elasTically collides wiTh a TargeT proTon which Then moves sTraighT forward If The iniTia velociTy of The projecTile proTon is 30x10 ms and The TargeT proTon bounces forward whaT are a The final velociTy of The projecTile proTon b The final velociTy of The TargeT proTon 00 30x10 ms Work in centerofmass frame elastic 1 Find com velociTy and subTracT if From boTh v1 and v2 V m1V1i m2V2i com m1 m2 VLi gt V1i Vcom V2i gt V2i Vcom NoTe m1V1i m2V2i 0 2 Problem is easy To solve in This Frame 39 E1ast10v1 i v1i v2 v2 i Working out answer in centerofmass 3 RelaTive velociTy swiTches sign V1f V2f V2 1 V1 For elasTic headon collisions EquivalenT To energy conservaTion Example 68 An proTon mP167x103927 kg elasTically collides wiTh a TargeT deuTeron mD2mP which Then moves sTraighT forward If The iniTial velociTy of The projecTile proTon is 30x10 ms and The TargeT deuTeron bounces forward whaT are a The final velociTy of The projecTile proTon b The final velociTy of The TargeT deuTeron vP 10x10 ms vd 20x10 ms Head on collisions wiTh heavier objecTs lead To reflecTions v0 k Example 69a The mass M1 enTers from The lefT wiTh velociTy v0 and sTrikes The mass M2M1 which is iniTially aT resT The collision is perfecle elasTic a JusT afTer The collision vz v0 Agt B lt C Example 69b The mass M1 enters from the left with velocity v0 and collision is perfectly elastic Just after the collision v1 0 strikes the mass M2M1 which is initially at rest The v0 k Example 69c The mass M1 enters from the left with velocity v0 and strikes the mass M2M1 which is initially at rest The collision is perfectly elastic Just after the collision P2 Mlvo Example 69d The mass M1 enters from the left with velocity v0 and strikes the mass M2M1 which is initially at rest The collision is perfectly elastic At maximum compression the energy stored in the spring is 12M1v02 833 A v vo k Example M The mass M1 enters from the left with velocity v0 and strikes the mass M2lt M1 which is initially at rest The collision is perfectly elastic Just after the collision v1 0 Example 69e The mass M1 enters from the left with velocity v0 and strikes the mass M2lt M1 which is initially at rest The collision is perfectly elastic Just after the collision v2 v0 Agt Blt c The mass M1 enters from the left with velocity v0 and strikes the mass M2lt M1 which is initially at rest The collision is perfectly elastic Just after the collision P2 Mlvo vo k Example M Agt Blt c v0 k Example M The mass M1 enters from the left with velocity v0 and strikes the mass M2ltM1 which is initially at rest The collision is perfectly elastic At maximum compression the energy stored in the spring is 12M1v02 A gt B lt C The mass M1 enters from the left with velocity v0 and strikes the mass M2gtM1 which is initially at rest The collision is perfectly elastic Example 69i Just after the collision v2 v0 Agt Blt v0 k I Example 69j The mass M1 enters from the left with velocity v0 and strikes the mass M2gtM1 which is initially at rest The collision is perfectly elastic Just after the collision v1 0 A gt Blt C v0 k Example M The mass M1 enters from the left with velocity v0 and strikes the mass M2gtM1 which is initially at rest The collision is perfectly elastic Just after the collision P2 Mlvo Agt Blt C The mass M1 enters from the left with velocity v0 and strikes the mass M2gtM1 which is initially at rest The collision is perfectly elastic Example 69i At maximum compression the energy stored in the spring is 12M1v02 Agt Blt C Example 610 7 g m1 m2 V12 7 l m1 gt m2 gt h 2003 Thomson BrooksCole i Ballistic Pendulum used to measure speed of bullet 05kg block of wood swings up by height h 65 cm after stopping 80g bullet 227 mS Example 611 A 5g bullet traveling at 500 ms embeds in a 1495 kg block of wood resting on the edge of a 09m high table How fa does the block land from the edge of the table 714 cm Example 612 Ta39zan M80 kg swings on a 12 m vine by letting go from an angle of 60 degrees from the vertical At the bottom of his swing he picks up Jane m50 kg To what angle do Tarzan and Jane swing 58 degrees indepedent of L or g Example 612a Ta39zan M80 kg swings on a 12 m vine by letting go from an angle of 60 degrees from the vertical At the bottom of his swing he picks up Jane m50 kg To what angle do Ta39zan and Jane swing To calwlate Ta39zan39s speed just before he picks up Jane you should apply A Consa39vation of Ena gy B Conservation of Momentum Example 612b Ta39zan M80 kg swings on a 12 m vine by letting go from an angle of 60 degrees from the vertical At the bottom of his swing he picks up Jane m50 kg To what angle do Tarzan and Jane swing To calculate TarzanGJane39s speed just after their collision given the previous 5 9 5 a 4 m i 3 lt B Conservation of Momentum Example 612c Ta39zan M80 kg swings on a 12 At the bottom of his swing he picks up Jane m50 kg To what angle do Ta39zan and Jane swing To calwlate Ta39zanGJane39s final height given the previous answa you should quly A Consa39vation of Ena gy B Conservation of Momentum Perfectly Inelastic Collisions in Two Dimensions SKIP LAST 4 SLIDES Two Equations Two unknowns vfx v mlvm msz ml Javale mlvlLy mzvzLy m1 m2vy

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