A ball with a mass of #1# #kg# moving at #9# #ms^-1# hits a still ball with a mass of #21# #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 · 2016-02-16T08:37:08

Momentum is conserved in this collision, kinetic energy is not.

Using the momentum, the speed of the #21# #kg# ball will have velocity #v=21/9# #ms^-1#. The lost kinetic energy is #38.6# #J#.

Momentum is conserved.

Momentum before the collision:

#p=m_1v_1+m_2v_2=1*9+21*0=9# #kgms^-1#

Momentum after the collision:

#p=9=0*9+21*v_2# #kgms^-1#

Rearranging:

#v_2=9/21# #ms^-1#

Kinetic energy before the collision:

#E_p=1/2m_1v_1^2+1/2m_2v_2^2 = 1/2*1*9^2+1/2*21*0^2 =40.5# #J#

Kinetic energy after the collision:

#E_p= 1/2*1*0^2+1/2*21*(9/21)^2 =1.9# #J#

The kinetic energy lost as heat (and probably sound) = #40.5-1.9=38.6# #J#