A ball with a mass of $3 kg$ is rolling at $3 m/s$ and elastically collides with a resting ball with a mass of $1 kg$ . What are the post-collision velocities of the balls?

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Answer 1 · 2016-01-02T11:43:31

Equations of conservation of energy and momentum.

$u_1'=1.5m/s$

$u_2'=4.5m/s$

As wikipedia suggests:

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

$=(3-1)/(3+1)*3+(2*1)/(3+1)*0=$

$=2/4*3=1.5m/s$

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

$=(1-3)/(3+1)*0+(2*3)/(3+1)*3=$

$=-2/4*0+6/4*3=4.5m/s$

[Equations' source]

Derivation

Conservation of momentum and energy state:

Momentum

$P_1+P_2=P_1'+P_2'$

Since momentum is equal to $P=m*u$

$m_1*u_1+m_2*u_2=m_1*u_1'+m_2*u_2'$ - - - $(1)$

Energy

$E_1+E_2=E_1'+E_2'$

Since kinetic energy is equal to $E=1/2*m*u^2$

$1/2*m_1*u_1^2+1/2*m_2*u_2^2=1/2*m_1*u_1^2'+1/2*m_2*u_2^2'$ - - - $(2)$

You can use $(1)$ and $(2)$ to prove the equations mentioned above. (I tried but kept getting two solutions, which is not right)

A ball with a mass of 3 kg3 kg is rolling at 3 m/s3 m/s and elastically collides with a resting ball with a mass of 1 kg1 kg. What are the post-collision velocities of the balls?