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?

Question

1117 views around the world

You can reuse this answer
Creative Commons License

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.