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Mass (m1) moving with speed (v), has a head on elastic collision with a second mass (m2), that...

Question:

Mass (m1), moving with speed (v), has a head on elastic collision with a second mass (m2), that is 3 times the mass of the first object and is moving with the samespeed. Find the speed of each mass after the collision in terms of the initial speed (v).

Answers

Data:Mass of the first object = m1Mass of the second object, m2 = 3 m1Initial velocity of each = v1i = v2i = vSolution:Nature of collision: Head on elastic collision.Velocity of first object after collision:v1f = [(m1-m2)/(m1+m2)]*v1i +[( 2 m2/( m1+m2 )]*v2i= [( m1-3 m1)/(m1+3m1)]*v + [ 2 * 2m1 / (m1 + 3m1)]*v= (-v/2) + v= v/2Velocity of the second object after collision:v2f = [2 m1/(m1+m2)]*v1i + [(m2-m1)/(m1+m2)]*v2i = [2m1/(m1+3m1)]*v + [ (3m1-m1)/(m1+3m1)]*v = v/2 + v/2 = vAns:Speed of the first mass after collision = v/2Speed of the second mass after collision = v.

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