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
The equation follows by applying the physical law to the chosen system; ideal constraints link the variables. Signs must remain consistent with the defined directions.
problems.proof.pitfall. Pitfall: do not change sign conventions between equations; a negative sign may encode direction rather than an invalid result.