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?

Question

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?

Leo Abeyta · Accepted Answer

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

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.

Nora Arzate · Answer

undefined The post-collision velocity of the 6 kg ball is 12 m/s, and the post-collision velocity of the 9 kg ball is 24 m/s.