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

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Answer 1 · 2017-05-09T08:25:43

The velocity of the first ball is #=-1.33ms^-1#
The velocity of the second ball is #=2.67ms^-1#

In an elastic collision, we have conservation of momentum and conservation of kinetic energy.

The velocities before the collision are #u_1# and #u_2#.

The velocities after the collision are #v_1# and #v_2#.

#m_1u_1+m_2u_2=m_1v_1+m_2v_2#

and

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

Solving the above 2 equations for #v_1# and #v_2#, we get

#v_1=(m_1-m_2)/(m_1+m_2)*u_1+(2m_2)/(m_1+m_2)*u_2#

and

#v_2=(2m_1)/(m_1+m_2)*u_1+(m_2-m_1)/(m_1+m_2)*u_2#

Taking the direction as positive #rarr^+#

#m_1=2kg#

#m_2=4kg#

#u_1=4ms^-1#

#u_2=0ms^-1#

Therefore,

#v_1=-2/6*4+8/6*(0)=-4/3=-1.33ms^-1#

#v_2=4/6*4-2/6*(0)=8/3=2.67ms^-1#

Verificaition

#m_1u_1+m_2u_2=2*4+4*0=8#

#m_1v_1+m_2v_2=-2*4/3+4*8/3=8#