A ball with a mass of #2 kg# is rolling at #3 m/s# and elastically collides with a resting ball with a mass of #4 kg#. What are the post-collision velocities of the balls?

Question

A ball with a mass of #2  kg# is rolling at #3  m/s# and elastically collides with a resting ball with a mass of #4  kg#. What are the post-collision velocities of the balls?

Lily Adams · Accepted Answer

Speed of moving ball after collision #"= 1 m/s"# (in the direction opposite to it’s initial direction of motion)
Speed of resting ball after collision #"= 2 m/s"# Apply conservation of linear momentum #"Initial total momentum = Final total momentum"# #m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2# #(2 × 3) + (4 × 0) = 2v_1 + 4v_2# #6 = 2v_1 + 4v_2# Didvide both sides by #2# #3 = v_1 + 2v_2 color(white)(xxxxxxxxxxxxxxxx)(1)# Now, use formula of coefficient of restitution (#e#) #e = (v_2 - v_1)/(u_1 - u_2)# For an elastic collision #e = 1# #1 = (v_2 - v_1) / (3 - 0)# #v_2 - v_1 = 3 color(white)(xxxxxxxxxxxxxxxxx)(2)# Add equations #"(1) & (2)"# #3 + 3 = v_1 + 2v_2 + v_2 - v_1# #6 = 3v_2# #color(blue)(v_2 = "2 m/s")# Substitute #v_2 = "2 m/s"# in equation #(1)# #3 = v_1 + (2 × "2 m/s")# #color(blue)(v_1 = -"1 m/s")#

Parker Abbott · Answer

undefined The post-collision velocities are: 2.33 m/s for the 2 kg ball and 3.33 m/s for the 4 kg ball.