A ball with a mass of # 6 kg# is rolling at #2 m/s# and elastically collides with a resting ball with a mass of # 8 kg#. What are the post-collision velocities of the balls?

1 Answer
Mar 30, 2018

Answer:

The post collision velocities of the balls are #=-2/7ms^-1# and #=12/7ms^-1#

Explanation:

As the collision is elastic, there is conservation of momentum and conservation of kinetic energy

#m_1u_1+m_2u_2=m_1v_1+m_2v_2#

#1/2m_1u_1^2+1/2m_2u_2^2=1/2m_1v_1^2+1/2m_2v_2^2#

The mass the first ball is #m_1=6kg#

The velocity of the first ball before the collision is #u_1=2ms^-1#

The mass of the second ball is #m_2=8kg#

The velocity of the second ball before the collision is #u_2=0ms^-1#

The velocity of the first ball after the collision is #=v_1#

The velocity of the second ball after the collision is #=v_2#

#6*2+8*0=6v_1+8v_2#

#3v_1+4v_2=6#

#v_1=(6-4v_2)/3#.....................#(1)#

#1/2*6*2^2+1/2*8*0=1/2*6*v_1^2+1/2*8*v_2^2#

#6v_1^2+8v_2^2=24#

#3v_1^2+4v_2^2=12#...........................#(2)#

From equations #(1)# and #(2)#, calculate #v1# and #v_2#

#3*((6-4v_2)/3)^2+4v_2^2=12#

#36-48v_2+16v_2^2+12v_2^2=36#

#28v_2^2-48v_2=0#

#4v_2(7v_2-12)=0#

#v_2=0# or #v_2=12/7#

#v_1=2# or #v_1=-2/7#