Problem 1
A body of mass m moving in a straight line at speed u sticks to a stationary body of mass M on a smooth horizontal surface. The two bodies move together after impact; the collision is brief so external horizontal impulse is negligible. (a) Use momentum conservation to find common velocity v. (b) Calculate kinetic energy before and after impact and the mechanical energy converted to other forms. (c) Express the loss relative to initial kinetic energy and discuss limits M≫m and M→0. Use SI units throughout and treat components as ideal exactly as specified. State sign conventions when writing equations and retain units in final results.
problems.proof.stepOf
problems.proof.analysis
Insert the intermediate result into the relevant definition or equation to obtain the final expression. Checking signs and limits catches a wrong branch or omitted constraint.