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?

1 Answer
Jan 29, 2016

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.