Question

The bumper cars A and B in Fig. Q5 below each have a mass of 150 kg and are coasting with the velocities shown before they freely collide head on. If no energy is lost during the collision, determine their velocities after collision. [10]

Answer 1

$m_a=m_b = 150 \; kg \\ (v_A)_1=3 \;m/s \\ (v_B)_1 = 2 \;m/s$

No energy lost

$E_l=0 \\ e=1 \\ e = \frac{-[(V_B)_2 -(V_A)_2]}{(V_B)_1 -(V_A)_1}$

A and B are in opposite direction

$(V_A)_1 = 3 \;m/s \\ (V_B)_1 = -2\;m/s \\ 1 = \frac{-[(V_B)_2 -(V_A)_2]}{-2-3} \\ (V_B)_2 -(V_A)_2 = 5$

Conservation of momentum

$m_a(V_A)_1 +m_b(V_B)_1 =m_a(V_A)_2 +m_b(V_B)_2 \\ m_a=m_b \\ (V_A)_1 -(V_B)_1 = (V_A)_2 +(V_B)_2 \\ 3-2 = (V_A)_2 +(V_B)_2 \\ 1 = (V_A)_2 +(V_B)_2 \\ 5 = (V_B)_2 -(V_A)_2 \\ (V_A)_2 = -2 \;m/s \\ (V_B)_2 = 3 \;m/s$