Question

A brick falls a distance Ah, with a potential energy change of Delta U g =|mg| Delta h . If no work is done on the earth-brick system, what is the change in the brick's kinetic energy , AK?

Answer 1

Since the earth-brick system is closed (no work by the external forces is done), the total energy is conserved

$$E=K+U=\rm const.$$

Hence

$$\Delta E=\Delta K+\Delta U=0,$$ $$\Delta K=-\Delta U=mg\Delta h.$$