Physics

Problem

A small pellet of mass 5.0 g is fired horizontally into a wooden pendulum bob of mass 0.50 kg that is suspended from a 0.75 m long light string. The pellet embeds in the bob, and the combined system swings to a maximum angular displacement of 12° from the vertical before momentarily coming to rest. Assume air resistance is negligible and the string remains taut throughout the motion. (a) Determine the vertical height

h

gained by the center of mass of the bob–pellet system between the instant just after the collision and the highest point of the swing. (b) Calculate the speed

v_{f}

of the bob–pellet system immediately after the collision. (c) Determine the initial speed

v_{0}

of the pellet just before impact. (d) Calculate the percentage of the pellet’s initial kinetic energy that is converted to non-mechanical forms during the collision.

Intuitive explanation

This problem chains together two fundamental conservation laws: momentum during the collision, then energy as the pendulum swings. The key insight is that the pellet-bob collision is perfectly inelastic (they stick together), so momentum is conserved there—but kinetic energy is lost. Once they move together, mechanical energy is conserved as the system converts that kinetic energy into gravitational potential energy at the highest swing. Work backwards from the final height to find the velocity just after impact, then use momentum to find the pellet's initial speed.

Intuitive explanation

Browse the problem library