Physics

Physics

Problem

Derive an expression for the fraction of kinetic energy lost when a mass mm moving at speed vv collides head-on and sticks to a mass 2m2m that is initially at rest on a frictionless surface. Provide your final answer as the ratio ΔKKinitial\displaystyle \frac{\Delta K}{K_\text{initial}} in terms of the given variables.
Intuitive explanation

This is a perfectly inelastic collision problem where momentum is conserved but kinetic energy is not. The key insight is to use conservation of momentum to find the final velocity of the stuck-together mass, then compare the initial and final kinetic energies. Since the surface is frictionless, momentum is the only quantity that stays constant—energy is lost to deformation and heat when the masses stick together.

Intuitive explanation

This is a perfectly inelastic collision problem where momentum is conserved but kinetic energy is not. The key insight is to use conservation of momentum to find the final velocity of the stuck-together mass, then compare the initial and final kinetic energies. Since the surface is frictionless, momentum is the only quantity that stays constant—energy is lost to deformation and heat when the masses stick together.

Browse the problem library