A ball with a mass of #8# #kg# moving at #5# #ms^-1# hits a still ball with a mass of #32# #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 · 2016-05-07T12:44:57

The final velocity of the #32# #kg# ball is #1.25# #ms^-1#, and the energy lost to heat is #75# #J#.

Momentum is conserved. The total momentum before the collision is:

#p=mv=8xx5=40# #kgms^-1# (the stationary ball carries no momentum)

The momentum after the collision will be the same, and rearranging the equation yields:

#v=p/m=40/32=1.25# #ms^-1#

In an inelastic collision, kinetic energy is not conserved. In this case, the kinetic energy before the collision is:

#E_k=1/2mv^2=1/2xx8xx5^2=100# #J#

The kinetic energy after is:

#E_k=1/2mv^2=1/2xx32xx1.25^2=25# #J#

The difference, the 'missing' #75# #J# was lost as heat (and possibly sound) in the collision.