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Momentum Conservation 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 force Initial momentum Rocket: has momentum Force: changes momentum Final momentum: changed by the force p F t 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. pf pi FN 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. pf2 pi2 pf1 pi1 Two Bodies When two bodies strike each other they exert a force on each other. The forces are equal and opposite. F12 F21 Momentum Change If two forces are equal in magnitude, then the changes in momentum are equal in magnitude. F12 pf1 pi1 F21 pi2 pf2 F21 p f 1 pi1 t F12 p f 2 pi 2 t 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. F12 Fg2 F21 Fg1 Isolated System A system with no external forces is isolated. • Only 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 value Law of Reaction Redefined The law of reaction can be defined in terms of momentum. • In an isolated system the total momentum is conserved. total momentum of the rocket and gas stays the same Fint 0 rocket hot gas is forced out reaction force acts on the rocket rocket momentum increases p CONSTANT Double Bounce Initially both balls go down together with the same velocity. The lower ball gets a force from the floor and changes momentum. pi2 pi1 The lower ball hits the upper ball and momentum is conserved between the balls. pf2 pi2 pf1 pm1 next