Gravity or the gravitational force is the most crucial force in the universe. An object with mass in a gravitational field exerts a force known as weight and when it is lifted in a gravitational field, energy is transferred to a store because of the gravitational force. This store is termed as gravitational potential energy.
In simple terms, we can say that gravitational potential energy is the energy possessed or acquired by an object due to a change in its position when it is present in a gravitational field.
You can understand the basic definition of gravitational potential energy if you think about a book resting on top of a bookshelf. The book has the potential to fall to the floor because of its elevated position relative to the ground, but one that starts on the floor can’t fall, because it’s already on the surface. The book on the shelf has a GPE, but the one on the ground doesn’t have one.
The formula for gravitational potential energy (GPE) relates mass (m), the acceleration due to gravity on the Earth (g) and height above the Earth’s surface (h) to the stored energy due to gravity. It can be represented as:
Gravitational Potential Energy (GPE) = mass (m) × gravitational field strength (g) × height (h)
GPE = mgh
The equation for gravitational potential energy is:
GPE = m⋅g⋅h
gravitational potential energy is measured in joules (J)
m is the mass measured in kilograms (kg)
h is the height measured in meters (m)
gravitational field strength (g) measured in newtons per kilogram]
The acceleration due to Earth’s gravity has a (roughly) constant value anywhere on the surface and points directly to the centre of mass of the planet: g = 9.81 m/s2. Hence, the only things you need to calculate GPE are the mass of the object and the height of the object above the surface.
Example: Imagine a 10 kg mass suspended height of 5 meters above the ground by a pulley system. How much gravitational potential energy does it have?
Solution: Using the equation and substituting the known values gives:
GPE = mgh
=10kg × 9.81m/s2 ×5m