Prove P.E = mgh OR Ug = mgh

by • 04/07/2012 • GeneralComments (0)1277

Potential Energy

When a body is moved against a field of force, the energy stored in it is called its potential energy.

If a body of mass ‘m’ is lifted to a height ‘h’ by applying a force equal to its weight then its potential energy is given by

P.E = m g h

Potential energy is possessed by

1. A spring when it is compressed

2. A charge when it is moved against electrostatic force.
Prove P.E = m g h OR Ug = m g h
Proof

Consider a ball of mass ‘m’ taken very slowly to the height ‘h’. Therefore, work done by external force is

Wex = Fex . S = Fex S cos θ ……………………………. (1)

Since ball is lifted very slowly, therefore, external force in this case must be equal to the weight of the body i.e., mg.

Therefore,

Fex = m g

S = h

θ = 0º ……………………. {since Fex and h have same direction}

Therefore,

(1) => Wex = m g h cos 0º

Wex = m g h …………………………………………………………. (2)

Work done by the gravitational force is

Wg = Fg . S = Fg S cosθ …………………………………………. (3)

Since,

Fg = m g

S = h

θ = 180º …………………. {since Fg and h have opposite direction}

Therefore,

(3) => Wg = m g h cos 180º

Wg = m g h (-1)

Wg = – m g h …………………………………………………………. (4)

Comparing (2) and (4), we get

Wg = -Wex

Or

Wex = – Wg

The work done on a body by an external force against the gravitational force is stored in it as its gravitational potential energy (Ug).

Therefore,

Ug = Wex

Ug = – Wg ………………………… {since Wex = -Wg}

Ug = -(-m g h) ………………… {since Wg = – m g h}

Ug = m g h ……………………………………….. Proved

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