# How does a freely falling body work according to the law of conservation of mechanical energy?

The statement of the law of conservation of mechanical energy:

"The total mechanical energy of a system is constant, if the internal forces doing work on it are conservative and the external forces do no work."

And this statement is verified by the case of a freely falling body where the energy is always mgh.

How is that possible? Doesn't gravity do work and isn't it an external force?

When you consider the earth (with its gravitational field) and the freely falling body together as the system, then the force of gravity is an internal force and not external force to the system. Then if a body freely falls from a height of $$h$$ near the surface of the earth where it initially has potential energy of $$mgh$$, gravity does positive work taking away its gravitational potential energy and giving it kinetic energy equal to $$\frac{mv^2}{2}$$. Energy is conserved because
$$\frac{mv^2}{2} = mgh$$.