Collisions in 1-d

Change the masses mA, mB of the trolleys and the initial velocity uA press play to watch the collision.

In the animation above, the conservation of momentum is illustrated by the collision between two trolleys A and B. Initially, trolley B is stationary and trolley has a velocity v_A also the masses m_A and m_B are the same.

Applying the conservation of momentum gives, m_A u_A+ 0 = m_Av_A + m_Bv_B. In the event that the two masses are the same, then mass m_B will move off at the same speed and mass m_A will stop.

To calculate what happens when the masses are different we need to use a second equation. u_A = v_A+v_B. This states that the incoming velocity is equal to the sum of the final velocities. Using this equation we obtain a general solutions for v_A and v_B.

v_A=(m_A-m_B/m_A+m_B)u_A

When both masses are allowed to move, their final velocities are given by:

v_A=(m_A-m_B/m_A+m_B)u_A+(2m_B/m_A+m_B)u_B

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