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?

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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).