Question

A ball with a mass of `12` `kg` moving at `8` `ms^-1` hits a still ball with a mass of `20` `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

Initial momentum of `96` `kgms^-1` transfers to the `20` `kg` ball, giving it a velocity of `4.8` `ms^-1`. This corresponds to `E_k=230.4` `J`, a loss of `153.6` `J` from the initial `384` `J`.

Explanation:

Momentum is conserved, so the momentum of the `12` `kg` ball before the collision, which is `p=mv=12*8=96` `kgms^-1`, is all transferred to the `20` `kg` ball. (Stationary objects have `0` momentum.)

Rearranging to make velocity the subject:

`v = p/m = 96/20 = 4.8` `ms^-1`

Now we know the masses and velocities of both objects before an after the collision. Stationary objects have `0` kinetic energy.

The total kinetic energy before the collision is given by:

`E_k=1/2mv^2=1/2*12*8^2=384 J`

The total kinetic energy after the collision is:

`E_k=1/2mv^2=1/2*20*4.8^2=230.4 J`

Now, energy is conserved, but kinetic energy is not conserved in an inelastic or partially elastic collision. Some of the kinetic energy is converted into other forms, such as heat. The 'missing' energy in this case is `384-230.4=153.6` `J`, and this is the heat energy the question asked about.