Question

A ball with a mass of `4 kg` moving at `6 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

We can answer this question by recognizing that momentum is conserved, but kinetic energy is only conserved in a fully elastic collision.

Explanation:

The momentum before the collision is all in the 4 kg ball:

`p=mv`
`p=4kg*6m/s`
`p=24kgm/s` or `24Ns`

Since momentum is conserved, and the first ball comes to a stop, all the momentum goes to the 2nd ball:

`p=mv`
`24Ns=9kg*v`
`v=24/9`
`v=2.667m/s`

So the second ball moves away at `2.667m/s`

The full equation, should it be needed, is:

`m_1v_(i1) + m_2v_(i2) = m_1v_(f1) + m_2v_(f2)`

Now, the second part of the equation asks about energy, so we need to find the difference between the two kinetic energies:

`Delta E_k = E_(kf) - E_(ki)`
or the kinetic energy of the 9 kg ball after the collision, minus the kinetic energy of the 4 kg ball before the collision:

`Delta E_k =1/2 m_2v_(f2)^2-1/2m_1v_(i1)^2`
`Delta E_k =1/2 *9*2.667^2-1/2*4*6^2`
`Delta E_k =32-72`
`Delta E_k = -40J`

So 40 J of kinetic energy is lost to entropy in the collision.