An object with mass m slides on a frictionless surface with a velocity and colli

Question

An object with mass m slides on a frictionless surface with a velocity and collides with another object with the same mass that is initially at rest. A)What is the velocity of the center of mass of the two objects before the collision? B)If after the collision, the two masses stick and slide together, 1) What is the velocity of the center of mass of the two objects together in terms of m, and ? 2) What is in terms of m, and ? 3) What is the kinetic energy of the two objects before and after the collision in terms of m and ? C)If after the collision, the first mass stops and the second mass starts sliding with velocity , 1) What is the velocity of the center of mass of the two objects after the collision in terms of m and ? 2) What is the velocity in terms of m and ? 3) What is the kinetic energy of the two objects before and after the collision in terms of m and ?

Explanation / Answer

1) Vcm=m1u1+m2u2/m1+m2

Vcm=mu/2m=u/2   (u2=0 rest)

2) from conservation of momentum

m1u1+m2u2=(m1+m2)v

v=mu/2m=u/2

3)K before=1/2 mu^2

Kafter=1/2(m1+m2)v62=1/2(M1+M2)*U^2/4

K after=1/8*2m*u^2=1/4 mu^2

4)Vcm after=m1v1+m2v2/m1+m2=mv/2m=v/2

5)K before=1/2 mu^2

K after=1/2 (m1+m2)*v^2/4=1/4 mv^2

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