Balls are usually pumped of air and do not break! So when a force is applied to the ball ( dropping it, kicking it ) it hits the ground with energy. Remember that energy can neither be created nor destroyed, it can only be transformed or transferred from one form to another! So most of the energy from the ball hitting the ground remains as kinetic energy which gives the ball the ability to bounce back, some of the kinetic energy ( or bounce energy ) is lost as some energy is lost in sound and friction.
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