Mechanics

When an object moves on or near the earth's surface it experiences a force due to the gravitational interaction with the earth. This gravitational force has the special property that the total work it does as the object moves between two positions is independent of the path taken between these positions. Forces of this type are said to be "conservative." The work done by the gravitational force as an object is moved through a height, h, along an arbitrary path is mgh, where g is the "acceleration" due to gravity, DV_g = mgh.

In general, it is only the change in gravitational potential that is of interest and setting V_g = 0 at the lowest point of interest gives the potential at a location, h,: V_g = mgh where V_g is said to be the "Potential Energy" of the object at this location.

From: Meriam, "Dynamics," Wiley (1975)

Combining this change in potential energy with the previously considered change in kinetic energy due to the action of a non-conservative force on the body gives an expression for the Work-Energy equation: U = D(Kinetic Energy) + D(Potential Energy).

If only conservative forces act on the body, U = 0, and the change in the kinetic energy is equal in magnitude and opposite in sign to the change in the potential energy. For this case, total energy is conserved as it converts from one form to the other. This is a useful concept since the change in potential energy is path independent and permits easy computation of the path dependent kinetic energy change.