A ball with a mass of $5 kg$ is rolling at $9 m/s$ and elastically collides with a resting ball with a mass of $2 kg$ . What are the post-collision velocities of the balls?

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Answer 1 · 2017-04-08T09:16:19

The velocity of the first ball is $=3.86ms^-1$
The velocity of the second ball is $=12.86ms^-1$

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

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

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

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

$m_1=5kg$

$m_2=2kg$

$u_1=9ms^-1$

$u_2=0ms^-1$

Therefore,

$v_1=3/7*9+4/7*(0)=27/7=3.86ms^-1$

$v_2=10/7*9-3/7*(0)=90/7=12.86ms^-1$

Verificaition

$m_1u_1+m_2u_2=5*9+2*0=45$

$m_1v_1+m_2v_2=5*3.86+2*12.86=45$

A ball with a mass of 5 kg 5 kg is rolling at 9 m/s9 m/s and elastically collides with a resting ball with a mass of 2 kg2 kg. What are the post-collision velocities of the balls?