# A billiard ball of mass .155 kg moves with a velocity of 12.5 m/s toward a stationary billiard ball of identical mass and strikes it in a head on collision. The first billiard ball comes to a complete stop. Was the collision elastic?

Mar 18, 2018

Suppose,a ball of mass $m$ moving with velocity $v$ collided with a mass of $m$ at rest and the first mass came to rest.

Let,after the collision velocity of the 2nd mass will be $v '$

So,applying law of conservation of momentum,

$m v + 0 = 0 + m v '$

so,$v ' = v$

so,kinetic energy before the collision =$\frac{1}{2} m {v}^{2} + 0 = \frac{1}{2} m {v}^{2}$

and after the collision,kinetic energy became =$0 + \frac{1}{2} m v {'}^{2} = \frac{1}{2} m {v}^{2}$

So,kinetic energy before and after the collision remains the same.

Hence it was an elastic collsion.

Remember,in an elastic collsion,two identical mass just exchange their velocity.

And,coefficient of restitution is $1$