A ball with a mass of 2kg is rolling at 7ms and elastically collides with a resting ball with a mass of 1kg. What are the post-collision velocities of the balls?

1 Answer
Dec 19, 2016

In a perfectly elastic collision, v1=73ms and v2=283ms

Explanation:

In a perfectly elastic collision, momentum and mechanical energy are conserved.

As two objects collide, all of the kinetic energy they possess is transferred into elastic potential energy in their molecular bonds, and then all of that energy which is stored in the bonds is transformed back into the post-collision kinetic energy of the object. Although energy is transformed into potential energy during the collision, the mechanical energy before and after the collision is purely kinetic energy.

We are given that m1=2kg, v1=7ms, m2=1kg, and v2=0.

You can determine the final velocities in terms of the given quantities using these equations(1):

v1=(m1m2m1+m2)v1o+(2m2m1+m2)v2o

v2=(2m1m1+m2)v1o(m1m2m1+m2)v2o

Because the second ball is initially at rest (v2=0), these simplify to:

v1=(m1m2m1+m2)v1o

v2=(2m1m1+m2)v1o

Therefore, the post-collision velocity of the first ball is:

v1=(2kg1kg2kg+1kg)(7ms)

v1=73ms

and the post collision velocity of the second ball is:

v2=(2(2kg)2kg+1kg)7ms

v2=283ms