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6-2Conservation of momentumMOMENTUM IS CONSERVEDSo far in this chapter, we have considered the momentum of only one object ata time. Now we will consider the momentum of two or more objects interactingwith each other. Figure 6-6 shows a stationary soccer ball set into motionby a collision with a moving soccer ball. Assume that both balls are on asmooth gym floor and that neither ball rotates before or after the collision.Before the collision, the momentum of ball B is equal to zero because the ballis stationary. During the collision, ball B gains momentum while ball A losesmomentum. As it turns out, the momentum that ball A loses is exactly equalto the momentum that ball B gains.6-2 SECTION OBJECTIVES• Describe the interactionbetween two objects interms of the change inmomentum of each object.• Compare the total momentumof two objects beforeand after they interact.• State the law of conservationof momentum.• Predict the final velocities ofobjects after collisions, giventhe initial velocities.(a)(b)A B A BTable 6-1 shows the velocity and momentum of each soccer ball bothbefore and after the collision. The momentum of each ball changes due to thecollision, but the total momentum of the two balls together remains constant.Figure 6-6(a) Before the collision, ball A hasmomentum p A and ball B has nomomentum. (b) After the collision,ball B gains momentum p B .Table 6-1Momentum in a collisionBall ABall BMass Velocity Momentum Mass Velocity Momentumbeforecollisionaftercollision0.47 kg 0.84 m/s 0.40 kg•m/s 0.47 kg 0 m/s 0 kg•m/s0.47 kg 0.04 m/s 0.02 kg•m/s 0.47 kg 0.80 m/s 0.38 kg•m/sCopyright © by Holt, Rinehart and Winston. All rights reserved.Momentum and Collisions215
NSTATOPIC: RocketryGO TO: www.scilinks.orgsciLINKS CODE: HF2062In other words, the momentum of ball A plus the momentum of ball B beforethe collision is equal to the momentum of ball A plus the momentum of ball Bafter the collision.p A,i + p B,i = p A,f + p B,fThis relationship is true for all interactions between isolated objects and isknown as the law of conservation of momentum.CONSERVATION OF MOMENTUMm 1 v 1,i + m 2 v 2,i = m 1 v 1,f + m 2 v 2,ftotal initial momentum = total final momentumIn its most general form, the law of conservation of momentum can bestated as follows:1. Ice skatingIf a reckless ice skater collideswith another skaterwho is standing on the ice, isit possible for both skaters tobe at rest after the collision?2. Space travelA spacecraft undergoes achange of velocity when itsrockets are fired. Howdoes the spacecraftchange velocity in emptyspace, where there isnothing for the gasesemitted by the rocketsto push against?The total momentum of all objects interacting with one another remains constantregardless of the nature of the forces between the objects.Momentum is conserved in collisionsIn the soccer-ball example, we found that the momentum of ball A does notremain constant and the momentum of ball B does not remain constant, butthe total momentum of ball A and ball B does remain constant. In general, thetotal momentum remains constant for a system of objects that interact withone another. In this case, in which the floor is assumed to be frictionless, thesoccer balls are the only two objects interacting. If a third object exerted aforce on either ball A or ball B during the collision, the total momentum ofball A, ball B, and the third object would remain constant.In this book, most conservation-of-momentum problems deal with onlytwo isolated objects. However, when you use conservation of momentum tosolve a problem or investigate a situation, it is important to include all objectsthat are involved in the interaction. Frictional forces—such as the frictionalforce between the soccer balls and the floor—will be disregarded in mostconservation-of-momentum problems in this book.Momentum is conserved for objects pushing away from each otherAnother example of conservation of momentum is when two or more interactingobjects that initially have no momentum begin moving away from eachother. Imagine that you initially stand at rest and then jump up, leaving theground with a velocity v. Obviously, your momentum is not conserved; beforethe jump, it was zero, and it became mv as you began to rise. However, thetotal momentum remains constant if you include Earth in your analysis. Thetotal momentum for you and Earth remains constant.If your momentum after you jump is 60 kg •m/s upward, then Earth musthave a corresponding momentum of 60 kg •m/s downward, because totalCopyright © by Holt, Rinehart and Winston. All rights reserved.
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Page 3 and 4: 6-1Momentum and impulse6-1 SECTION
Page 5 and 6: Figure 6-2When the ball is moving v
Page 7 and 8: Stopping distances48 km/h (30 mi/h)
Page 9: (a)(b)Now consider a falling egg. W
Page 13 and 14: SAMPLE PROBLEM 6DConservation of mo
Page 15 and 16: F 1 is the force that m 2 exerts on
Page 17 and 18: 6-3Elastic and inelastic collisions
Page 19 and 20: PRACTICE 6EPerfectly inelastic coll
Page 21 and 22: PRACTICE 6FKinetic energy in perfec
Page 23: SAMPLE PROBLEM 6GElastic collisions
Page 26 and 27: CHAPTER 6SummaryKEY IDEASSection 6-
Page 28 and 29: CONSERVATION OF MOMENTUMReview ques
Page 30 and 31: 43. A 0.10 kg ball of dough is thro
Page 32 and 33: 56. A 55 kg pole-vaulter falls from
Page 34 and 35: PROCEDURECBL AND SENSORSConservatio
Page 36: 12. Find the average of these three

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