Question

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?

Answer 1

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,

`mv+0=0+mv'`

so,`v'=v`

so,kinetic energy before the collision =`1/2 mv^2 +0=1/2mv^2`

and after the collision,kinetic energy became =`0 +1/2 mv'^2 =1/2 mv^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`