Momentum Question 2

Trolley A (mass 1.5 kg) moves to the right at 4.0 ms^-1 on a smooth, level track. It collides head-on with trolley B (mass 1.0 kg), which is moving to the left at 2.0 ms^-1. After the collision A continues to the right at 0.40 ms^-1.(i) Calculate the velocity of B after the collision.(ii) Show whether the collision is elastic.Choose a positive direction. Momentum is a vector, so take to the right as positive. B's initial velocity is then -2.0 ms^-1.(i) Total momentum before the collision:(1.5 × 4.0) + (1.0 × -2.0) = 6.0 - 2.0 = 4.0 kg ms^-1No external force acts, so the total momentum after the collision is also 4.0 kg ms^-1:(1.5 × 0.40) + 1.0v_B = 4.0   so   v_B = 3.4 ms^-1The answer is positive, so B moves to the right at 3.4 ms^-1: it has been knocked back the way A was travelling.(ii) Kinetic energy is a scalar, so no signs are needed.Before: ½(1.5)(4.0)² + ½(1.0)(2.0)² = 12 + 2.0 = 14 JAfter: ½(1.5)(0.40)² + ½(1.0)(3.4)² = 0.12 + 5.78 = 5.9 JKinetic energy is not conserved: about 8.1 J is transferred, mainly to thermal energy and sound. The collision is therefore inelastic. Momentum is still conserved, as it is in every collision where no external force acts.