Question

A ball with a mass of `11` `kg` moving at `18` `ms^-1` hits a still ball with a mass of `22` `kg`. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

Answer 1

The post-collision velocity of the `22` `kg` ball is `9` `ms^-1`. The difference in kinetic energy before and after the collision is `1782-891=891` `J`, and this is the energy lost as heat (and probably sound).

Explanation:

Momentum is conserved. A stationary ball has no momentum.

Momentum before the collision:

`p=mv=11*18=198` `kgms^-1`

The momentum after the collision will be the same, so rearranging we find:

`v=p/m=198/22=9` `ms^-1`

Kinetic energy before the collision is:

`E_k=1/2mv^2=1/2*11*18^2=1782` `J`

Kinetic energy after the collision is:

`E_k=1/2mv^2=1/2*22*9^2=891` `J`