Gravitational Potential Energy in a Non-Uniform Field (HL)

Gravitational Potential Energy in a Non-Uniform Field

In a radial field, gravitational potential energy (GPE) describes the energy an object possesses due to its position in a gravitational field
The gravitational potential energy of a system is defined as:

The work done to assemble the system from infinite separation of the components of the system

Similarly, the gravitational potential energy of a point mass is defined as:

The work done in bringing a mass from infinity to a point

Near the Earth's Surface

The gravitational potential energy near the Earth's surface is equal to

$E_{p} = m g ∆ h$

The GPE on the surface of the Earth is taken to be zero
- This means work is done to lift the object

This equation can only be used for objects that are near the Earth's surface
- This is because, near Earth's surface, the gravitational field is approximated to be uniform
- Far away from the Earth's surface, the gravitational field is radial because the Earth is a sphere

Examiner Tip

You should be able to interpret areas under curves by thinking about what the product of the quantities on the axes would represent. Since, in this case, force × distance = work done, then it follows that the area under the curve represents the change in energy between two points. Specifically, this would be a change in gravitational potential energy.

The equation GPE = mgΔh is very rarely used in this topic. This is only relevant for objects on a planet's surface.

The only difference between GPE and g is GPE = mg where m is the mass of the object in the gravitational field of mass M.

This equation is not given on your data booklet, but you must understand its significance

Gravitational Potential Energy in a Non-Uniform Field (HL) (HL IB Physics)

Revision Note