Engine (such as pneumatic motors), springs (clockwork motors) and elastic bands. Historic military siege engines included large catapults, trebuchets, and (to some extent) battering rams were powered by potential energy. A pneumatic motor is a machine that converts potential energy in the form of compressed air into mechanical work. Pneumatic motors generally convert the compressed air to mechanical work though either linear or rotary motion. Linear motion can come from either a diaphragm or piston actuator, while rotary motion is supplied by either a vane type air motor or piston air motor. Pneumatic motors have found widespread success in the hand-held
Potential energy function associated with potential energy. This is done by introducing a parameterized curve γ(t)=r(t) from γ(a)=A to γ(b)=B, and computing, For the force field F, let v= dr/dt, then the gradient theorem yields, The power applied to a body by a force field is obtained from the gradient of the work, or potential, in the direction of the velocity v of the point of application, that is Examples of work that can be computed from potential functions are gravity and spring forces. For small height changes, gravitational potential energy can be computed using where m is the mass in kg,