### In classical mechanics, the kinetic energy of a *point object* (an object so small that its mass can be assumed to exist at one point), or a non-rotating rigid body, is given by the equation

When an object is acted upon by conservative forces it can have a potential

energy, U, associated with those forces. Therefore, work also can be defined in terms of the change in potential energy as:

ΔU = −W

In the case of the force due to gravity, the change in potential energy is:

ΔU = −W = mgΔy = mgh

where h is the change in vertical height. The zero point of potential energy is arbitrary, so for convenience it can be set at y = 0. The gravitational potential energy thus becomes:

U = mgy = mgh

The work done by non-conservative forces is equal to the total change in kinetic

and potential energy as given by:

W = ΔK + ΔU

In the special case where no non-conservative forces are acting upon an object, W = 0 and the above equation becomes:

ΔK + ΔU = Δ(K + U) = 0

In other words, the total of the kinetic and potential energy does not change. Thus, the total mechanical energy, E, remains constant and is given by:

E = K + U = constant

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