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?

Question

1333 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-26T23:02:12

The kinetic energy changes from 3 J to 2 J, with a loss of 1 J.

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).