Mechanical energy is the energy associated with an object's motion and its position. In other words, an object's mechanical energy is the sum of its kinetic energy and its potential energy.

Principle of the Conservation of Mechanical Energy

As long as the only forces acting are conservative forces, the total mechanical energy is constant.

ΔU + ΔK = 0

U_i + K_i = U_f + K_f

This is just our master equation with the work term set to zero.

Mechanical energy can be lost when non-conservative forces act (like friction), but the energy merely gets transformed into other kinds of energy.

The Law of the Conservation of Energy

Energy can neither be created nor destroyed, just transformed from one kind to another.

Mechanical energy that is lost or gained generally comes from work done by non-conservative forces. Call this W_nc:

ΔU + ΔK = W_nc

U_i + K_i + W_nc = U_f + K_f

A law is far more fundamental than a principle. Laws apply all the time. Principles have fine print.

If you slide a book across a table, it comes to rest. What happened to the kinetic energy?

Friction is very good at turning kinetic energy into thermal energy.