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If you consider some U-K system (sorry), perhaps where U is given by mgh, then the work done by the conservative force which provides U is always equal to the negative of the change in kinetic energy, provided there are no other forces.

In the first example, the total energy changes and W=deltaK fails. In the second, the total energy is constant and W=deltaK holds. How do I know in general when to apply the work-energy theorem??