Mechanical energy is the sum of kinetic and potential energy:

When only conservative forces act on a system, the total mechanical energy remains constant. This principle is conservation of mechanical energy:

or equivalently (in this case):

Energy transforms between kinetic and potential forms, but the total $E$ does not change.

Derivation from the work-energy theorem:

The work-energy theorem states $W_{\text{net}} = \Delta K$. When only a conservative force acts, $W_c = \Delta K$. Since conservative forces satisfy $W_c = -\Delta U$, we have:

This proves conservation of mechanical energy.

Free fall example:

Consider an object released from rest at height $h$. Initially, all energy is gravitational potential energy: $E_i = mgh$. As it falls, $U_g$ decreases while $K$ increases by the same amount. Just before impact, all energy has transformed to kinetic: $E_f = \frac{1}{2}mv^2 = mgh$.

Pendulum example:

A pendulum swinging from maximum height exhibits the same conservation.

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