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)





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

It is important to understand that gravitational potential energy (= force x distance) is a scalar.

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:






It is important to realise that Dh 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.

This means that the change in gravitational energy for a certain object moving within a gravitational field depends only on the vertical height through which it travels and NOT on the particular path it takes. So, if you have two staircases to the upper floor of your school your change in gravitational potential energy is the same if you go from the ground floor to the top floor – no matter which way you go. Scientists call the gravitational field a conservative field.