# Learn it: Potential Energy

##### Potential energy

Definition: Energy due to position or mechanical condition is called potential energy

Potential energy is the energy a body has because of its condition or position, e.g. a compressed spring or a rock at the top of a cliff. In the latter case, the rock has energy due to the gravitational force between it and the earth. This, then, is an example of gravitational potential energy.

(Gravitational) Potential Energy

If an object of mass m is lifted from ground level to a height h above the ground, then the potential energy it has gained is equal to the work done in lifting it to this height. This work is

W = Fh

The force F on the body is its weight, which is equal to mg. Therefore, the work done is

W = mgh

Since this is the work done, it is also the energy that the body had before it fell, therefore

EP  = mgh

where

· EP = Energy (in Joules)
· m = mass (in kilograms)
· g = gravitational acceleration of the earth (9.8 m/sec2)
· h = height above earth's surface (in metres)

[This is the equation for gravitational potential energy based on the assumption that the potential energy at ground level is zero.]

Hydroelectric power station: potential energy of the water is converted to electrical energy in the generators

The water stored behind a dam has potential energy due to its height above the downstream river. As the water is released at the base of the dam it is being converted from potential energy to kinetic energy. The water flows through a turbine which converts the kinetic energy into mechanical work used to drive an electric generator.

Worked example :
A ball of mass 1 kg is thrown up to a height of 12 metres.

Calculate the increase in its potential energy.

Solution:
EP  = mgh
EP  = (1)(9.8)(12)
EP  = 117.6 J

Worked example :
How far above the surface of the earth would the same ball (1 kg) have to be thrown for its potential energy to increase to 1 MJ?

Solution:
EP   =   mgh
1 × 106    = (1)(9.8) h
h  = 1 × 106 ¸ 9.8
h  = 102 040.82 m

Next: Learn It - Mass as a Form of Energy

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