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**Unformatted text preview: **1 Momentum is a ________; there is a direction and magnitude. Momentum = mass x velocity p = _______ In general, we must worry about the x, y, and z components of momentum If the particle is moving with in an arbitrary direction then p must have three components which are equivalent to the component equations: p x = mv x p y = mv y p z = mv z Newton called m v the quality of motion . Impulse and Collisions – Ch 9 v v v A block and a ball of the same mass and downward speed v hit the floor. The block falls and “sticks” to the floor. x y The ball rebounds with the same velocity it hit the floor with. Change in Momentum v x y Change in Momentum We only have to consider the momentum in the _____ direction. Block Δ p y = p y,f –p y,i = 0 –m(-v) = ________ The change in momentum is mvupward. Ball Δ p y = p y,f –p y,I = mv–______ = ______ The change in momentum is upward. Be careful about the vector nature of momentum!!! Linear Momentum Newton's Second Law, which we have written as F = m a can also be written in terms of momentum, F = m a = m ______ = ________ F = d p /dt The force acting on an object equals the time rate of change of the momentum of that object. 2 Conservation of Momentum Consider two objects that "interact" or collide or have some effect on each other (billiard balls). From Newton's Third Law of motion, we know F 12 = - F 21 Where F 12 is the force exerted by particle 1 on particle 2 and F 21 is the force exerted by particle 2 on particle 1. In terms of momentum, this means d p 1 /dt = ________ d p 1 /dt + d p 2 /dt = 0 d ( ______ ) /dt= 0 d p Tot /dt= 0; p Tot = p 1 + p 2 Conservation of Momentum Lets look at that again! d p Tot /dt= 0 where p Tot = Σ p = p 1 + p 2 = _________ This statement may also be written as p 1i + p 2i = p 1f + p 2f Since the time derivative of the momentum is zero, the total momentum of the system remains __________ . This is Conservation of Momentum Conservation of Momentum is essentially a restatement of Newton's ________ Law of Motion. Conservation of Momentum We have said that ifthe particle is moving with in an arbitrary...

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