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let , 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.

Potential energy for near-Earth gravity

For small height changes, gravitational potential energy can be computed using

where m is the mass in kilograms,

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