Tuesday, June 8, 2010

Gravitational potential energy

Let us study what is meant by potential energy,

Potential energy is the energy stored in a body or a system by virtue of its position in a field of force or by its configuration. A force acting on a body or a system can also change its potential energy.

Here we shall discuss two cases:

(i) Potential energy of a body due to gravity, called gravitational potential energy.

(ii) Potential energy of a spring when it is elongated or compressed by an external force called elastic potential energy.

Gravitational Potential Energy : On anybody (of mass m) a constant force, given by F = mg, acts. It is directed towards the earth. Here g is acceleration due to gravity.

Consider a body of mass m moving vertically downward from height y2 to y1, as shown in the Figure given below, the work done by this constant force of gravity is given by

W = -mg(y2-y1) = - (mgy2 - mgy1)

Here W depends on the difference the height or position. So we can define gravitational Potential Energy associated with the body as

U = mgy

Hence W = -(V2 - V1) = -ΔV

The negative sign implies that when gravity does positive work, the potential energy decreases. When gravity does negative work (the body moves upward), the potential energy increases.

We can observe that when a body falls from a height, it accelerates and increases its speed and hence gains K.E. This is at the expense of gravitational P.E. Hence we can relate potential energy and kinetic energy.
Hope the above explanation helped you, now let us learn expressions for potential energy

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