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NIU PHYS 210 - Momentum Conservation

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Momentum ConservationLaw of Action RedefinedBounceTwo BallsTwo BodiesMomentum ChangeInternal ForcesIsolated SystemLaw of Reaction RedefinedDouble BounceMomentum Momentum ConservationConservationLaw of Action RedefinedLaw of Action RedefinedNewton originally framed the second law Newton originally framed the second law (acceleration) in terms of momentum, not velocity.(acceleration) in terms of momentum, not velocity.•The rate of change in momentum is proportional to the net The rate of change in momentum is proportional to the net force and the change is in the same direction as the forceforce and the change is in the same direction as the forcetpFRocket: has momentumForce: changes momentumInitial momentumFinal momentum: changed by the forceBounceBounceA falling ball has a A falling ball has a momentum.momentum.After hitting the floor there After hitting the floor there has been a change in has been a change in momentum.momentum.The change is due to a force The change is due to a force from the floor.from the floor.pipfFNTwo BallsTwo BallsTwo balls fall at the same Two balls fall at the same rate due to gravity, but with rate due to gravity, but with different momenta.different momenta.Ball 1 bounces from the Ball 1 bounces from the ground.ground.Ball 2 bounces from ball 1.Ball 2 bounces from ball 1.pf1pf2pi1pi2Two BodiesTwo BodiesWhen two bodies strike each other they exert a force When two bodies strike each other they exert a force on each other.on each other.The forces are equal and opposite.The forces are equal and opposite.F12F21Momentum ChangeMomentum ChangeIf two forces are equal in magnitude, then the If two forces are equal in magnitude, then the changes in momentum are equal in magnitude.changes in momentum are equal in magnitude.F12pi1F21pf1pf2pi2tppFif1121tppFif2212Internal ForcesInternal ForcesTwo objects can be Two objects can be considered together.considered together.This is called a system.This is called a system.The internal forces cancel The internal forces cancel out from the law of reaction.out from the law of reaction.The external forces remain.The external forces remain.Fg1Fg2F12F21Isolated SystemIsolated SystemA system with no external forces is A system with no external forces is isolatedisolated..•Only internal forces that cancel outOnly internal forces that cancel outThe net change in momentum for all internal forces The net change in momentum for all internal forces must be zero.must be zero.Total momentum in an isolated system is constant.Total momentum in an isolated system is constant.•Zero change means constant valueZero change means constant valueLaw of Reaction RedefinedLaw of Reaction RedefinedThe law of reaction can be defined in terms of The law of reaction can be defined in terms of momentum.momentum.•In an isolated system the total momentum is conserved.In an isolated system the total momentum is conserved.rocketreaction force acts on the rocketrocket momentum increaseshot gas is forced outtotal momentum of the rocket and gas stays the sameCONSTANTpF0intDouble BounceDouble BounceInitially both balls Initially both balls go down together go down together with the same with the same velocity.velocity.nextpi1pi2The lower ball The lower ball gets a force from gets a force from the floor and the floor and changes changes momentum.momentum.pm1pi2The lower ball The lower ball hits the upper hits the upper ball and ball and momentum is momentum is conserved conserved between the between the


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NIU PHYS 210 - Momentum Conservation

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