Question

A ball with a mass of `6 kg` moving at `1 m/s` hits a still ball with a mass of `9 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 kinetic energy changes from 3 J to 2 J, with a loss of 1 J.

Explanation:

The momentum of ball 1 is `6(kgm)/s`. This is also the total momentum of the system, as ball 2 is at rest initially.

After collision, the first ball stops, so ball 2 must now have the `6(kgm)/s` momentum.

Its speed therefore, is found by

`v=p/m=6/9=2/3m/s`

The initial kinetic energy was that of ball 1

`KE_i=1/2mv^2 = 1/2(6)1^2 = 3J`

The final kinetic energy is that of ball 2:

`KE_f=1/2mv^2 = 1/2(9)(2/3)^2 = 2J`

Therefore 1 J of kinetic energy was lost (converted to heat).