A ball with a mass of 6 kg6kg is rolling at 18 m/s18ms and elastically collides with a resting ball with a mass of 9 kg9kg. What are the post-collision velocities of the balls?
1 Answer
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)v1=(m1−m2m1+m2)v1o+(2m2m1+m2)v2o
v_2=((2m_1)/(m_1+m_2))v_(1o)-((m_1-m_2)/(m_1+m_2))v_(2o)v2=(2m1m1+m2)v1o−(m1−m2m1+m2)v2o
We are given
We can use each equation to solve for
v_1=((6kg-9kg)/(6kg+9kg))(18m/s)+0v1=(6kg−9kg6kg+9kg)(18ms)+0
=-3.6m/s=−3.6ms 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)-0v2=(2(6kg)6kg+9kg)(18ms)−0
=14.4m/s=14.4ms 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.