A ball with a mass of 6 kg is rolling at 18 m/s and elastically collides with a resting ball with a mass of 9 kg. What are the post-collision velocities of the balls?

1 Answer
Morgan
Aug 5, 2017

v_1=-3.6m/s and v_2=14.4m/s

Explanation:

Momentum is conserved in all collisions, but an elastic collision is one in which both momentum and mechanical energy are conserved. For elastic collisions, we use these equations to determine unknown values:

v_1=((m_1-m_2)/(m_1+m_2))v_(1o)+((2m_2)/(m_1+m_2))v_(2o)

v_2=((2m_1)/(m_1+m_2))v_(1o)-((m_1-m_2)/(m_1+m_2))v_(2o)

We are given m_1=6kg, v_(1o)=18m/s, m_2=9kg, and v_(2o)=0

We can use each equation to solve for v_1 and v_2.

v_1=((6kg-9kg)/(6kg+9kg))(18m/s)+0

=-3.6m/s

the negative value indicates that the ball is now moving in the opposite direction that it approached from

v_2=((2(6kg))/(6kg+9kg))(18m/s)-0

=14.4m/s

the positive value indicates that the second ball moves off in the direction opposite of the first

You can verify these answers using momentum and energy conservation.

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