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

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

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

A ball with a mass of 2 kg2 kg is rolling at 4 m/s4 m/s and elastically collides with a resting ball with a mass of 4 kg4 kg. What are the post-collision velocities of the balls?