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Momentum Conservation

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Law of Action Redefined Newton originally framed the second law (acceleration) in terms of momentum, not velocity. The rate of change in momentum is proportional to the net force and the change is in the same direction as the forceThe rate of change in momentum is proportional to the net force and the change is in the same direction as the force Rocket: has momentum Force: changes momentum Initial momentum Final momentum: changed by the force

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Bounce A falling ball has a momentum. After hitting the floor there has been a change in momentum. The change is due to a force from the floor. pipi pfpf FNFN

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Two Balls Two balls fall at the same rate due to gravity, but with different momenta. Ball 1 bounces from the ground. Ball 2 bounces from ball 1. p f1 p f2 p i1 p i2

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Two Bodies When two bodies strike each other they exert a force on each other. The forces are equal and opposite. F 12 F 21

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Momentum Change If two forces are equal in magnitude, then the changes in momentum are equal in magnitude. F 12 p i1 F 21 p f1 p f2 p i2

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Internal Forces Two objects can be considered together. This is called a system. The internal forces cancel out from the law of reaction. The external forces remain. F g1 F g2 F 12 F 21

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Isolated System A system with no external forces is isolated. Only internal forces that cancel outOnly internal forces that cancel out The net change in momentum for all internal forces must be zero. Total momentum in an isolated system is constant. Zero change means constant valueZero change means constant value

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Law of Reaction Redefined The law of reaction can be defined in terms of momentum. In an isolated system the total momentum is conserved.In an isolated system the total momentum is conserved. rocket reaction force acts on the rocket rocket momentum increases hot gas is forced out total momentum of the rocket and gas stays the same

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Double Bounce Initially both balls go down together with the same velocity. next p i1 p i2 The lower ball gets a force from the floor and changes momentum. p m1 p i2 The lower ball hits the upper ball and momentum is conserved between the balls. p f1 p f2

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