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written7 - Homework 7 Due 1 The velocity of the center of...

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Homework 7 Due February 27 2007 - 1 - 1) The velocity of the center of mass for a system of particles is defined to be total cm total p v m = G G where p total is the total momentum of the system and m total is the total mass of the system. Consider a system of two particles that undergo an elastic collision in 1-dimension . Particle A has mass m A , initial velocity v A 1 and final velocity v A 2 . Particle B has mass m B , initial velocity v B 1 and final velocity v B 2 . a) Which conservation implies that the center of mass velocity of the system does not change during the collision? Show that: 1 1 2 2 A A B B A A B B cm A B A B m v m v m v m v v m m m m + + = = + + b) We will consider the motion of these particles in two frames of reference, the "lab" frame which is stationary and the “center of mass” frame which is moving at v cm . What is the relation between v A 1 /lab and v A 1 /cm ; v A 2 /lab and v A 2 /cm ; v B 1 /lab and v B 1 /cm ; v B 2 /lab and v B 2 /cm v cm/lab and v cm/cm . c) Using conservation of momentum and energy in the center of mass frame, show that in an elastic collision, the center of mass velocities satisfy: 2/cm 1/cm 2/cm 1/cm A A B B v v v v = − = −
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