Gravitational Potential Energy

Definition of Gravitational Potential Energy

Gravitational potential energy (GPE) is the energy stored in an object because of its position above the ground. The higher an object is, the more gravitational potential energy it has.

The amount of gravitational potential energy depends on three factors:

• Mass of the object (measured in kilograms, kg)
• Height of the object above a reference point (usually the ground), measured in metres (m)
• Gravitational field strength (g), which is the force of gravity acting on each kilogram of mass. On Earth, this is approximately 9.8 newtons per kilogram (N/kg)

This means that the energy stored is due to the work done against gravity to raise the object to that height. Note that gravitational potential energy is always measured relative to a chosen zero height, usually the ground.

Calculating Gravitational Potential Energy

The formula to calculate gravitational potential energy is:

$\text{GPE} = m \times g \times h$

• $m$ is the mass in kilograms (kg)
• $g$ is the gravitational field strength (9.8 N/kg on Earth)
• $h$ is the height in metres (m)

The unit of gravitational potential energy is the joule (J).

For instance, if a 2 kg book is placed on a shelf 3 metres high, its gravitational potential energy is:

$\text{GPE} = 2\ \text{kg} \times 9.8\ \text{N/kg} \times 3\ \text{m} = 58.8\ \text{J}$

Energy Changes and Gravitational Potential Energy

When an object is lifted higher, its gravitational potential energy increases because it is further from the ground.

If the object falls, its gravitational potential energy decreases as it loses height. This lost gravitational potential energy is transferred to other forms of energy, such as kinetic energy (energy of movement), but the total energy in the system remains constant. This is an example of energy conservation.

For example, when a ball is thrown up, its kinetic energy is converted into gravitational potential energy as it rises. When it falls back down, the gravitational potential energy converts back into kinetic energy.