# Gravitational Potential energy

A body has energy if it is capable of doing work. In this case it is the position of the body in a gravitational field that gives it this possibility.

The energy associated with the position of a body of mass m in a gravitational field is the gravitational potential energy of the body compared with some chosen reference point where h = 0, usually the surface of the Earth. (Figure 1)

Gravitational potential energy (GPE) = mgh

where g is the intensity of the gravitational field (assumed uniform here) and h is the vertical distance moved in the field.

The energy is converted to other forms when the gravitational potential energy changes due to a movement within the field. (Figure 2) If the distance moved parallel to the gravitational field is Dh then the change in potential energy is:

Gravitational potential energy change = mgDh

It is important to realise that D h is measured parallel to the field. Any other direction of movement will cause a smaller change in the gravitational potential energy and a body that moves at right angles to the field will have no change at all in their gravitational potential energy.

Example problems
1. A crane lifts a load of 300 kg through a distance of 2.5 m onto a truck. Calculate the gain in gravitational potential energy. Gravitational field intensity = 9.8 Nkg-1.
Gravitational potential energy gained = mgDh = 300x9.8x2.5 = 7350 J

2. A mass of 25 kg is moved a distance of 35 m at an angle of 20o to a gravitational field of intensity 9.8 Nkg-1. Calculate the change in gravitational energy.
Change in gravitational potential energy = 25x9.8x35cos 20 = 8057 J

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