State the principle of conservation of mechanical energy for a conservative force.

(N/A) The principle of conservation of mechanical energy states that if only conservative forces act on a system, the total mechanical energy of the system remains constant.
Mathematically, the total mechanical energy $E$ is the sum of kinetic energy $K$ and potential energy $U$.
$E = K + U = \text{constant}$.
This implies that any change in kinetic energy is equal to the negative change in potential energy:
$\Delta K + \Delta U = 0$ or $\Delta K = -\Delta U$.