1. If work is done on the body, then its energy changes. During the free fall of the body, the force of gravity performs work on the body; whereas the kinetic energy of the body at the moment it hits the surface of the Earth, is equal to its potential energy at the moment of the beginning of the fall, which means that the mechanical energy of the body did not change. Do we have any contradictions here?
No. The mechanical energy of the body conserves because the work is done by the conservative force.
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