Sphere A of mass travels at along the -axis on a frictionless horizontal surface and…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
Sphere A of mass 0.30kg travels at 4.0ms−1 along the +x-axis on a frictionless horizontal surface and collides with identical sphere B, which is initially at rest at the origin. After the glancing collision, sphere A moves with speed 2.5ms−1 at 30∘ above the +x-axis. External forces are negligible during the brief interaction.
(a) Determine the magnitude and direction of sphere B’s velocity immediately after the collision.
(b) Calculate the total kinetic energy of the two-sphere system before and after the collision, then find the percentage of kinetic energy retained.
(c) For an otherwise identical but perfectly inelastic head-on collision between the same spheres, what percentage of the initial kinetic energy would be retained? Show your reasoning briefly.
(d) Using the results from parts (b) and (c), explain why a glancing collision can retain more kinetic energy than a head-on perfectly inelastic collision, even though both obey the same conservation laws.