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.
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Collect results in the order asked. Dimensions and physical signs provide independent checks; they do not replace the derivation but can expose algebraic errors.