# 6.2.2 Gravitational Potential Energy

### Gravitational PE v Elastic PE

• Gravitational potential energy (GPE) is the energy stored in an object that is held at a height above the Earth’s surface
• The amount of gravitational potential energy an object has depends on its height and mass
• The heavier the object, and the higher it is above the ground, the more gravitational potential energy it holds
• GPE is equal to: • Elastic potential energy (EPE) is the energy stored in objects when they are stretched or compressed
• The more an object can stretch, the more elastic potential energy it has
• EPE is equal to: • The key distinction between the two:
• Gravitational potential energy is associated with the interaction between bodies due to their masses
• Elastic potential energy is possessed by an object due to its state of deformation

### Force & Potential Energy

• In a uniform field, a body experiences the same force (F) at all points
• If this force moves the body along a distance Δx in its direction, then the work done (W) by this force is
• W = FΔx
• However, by conservation of energy, this work must be compensated by a decrease in potential energy equal to −ΔU, so:
• W = FΔx = −ΔU
• Therefore, the force acting on the point mass/charge placed at that particular point in the force field is equal to:
• At the surface (to the right), GPE = 0
• As the object moves to the left, GPE increases
• So, GPE increases from X to Y
• GPE = mgh
• Weight = mg = 0.200 N
• At point X, the mass already has 1.00 J of GPE
• Therefore, GPE at Y = 1.00 + (0.2 × 0.3) = 1.06 J

### Derivation of GPE = mgh

• Gravitational potential energy is energy stored in a mass due to its position in a gravitational field
• When a heavy object is lifted, work is done since the object is provided with an upward force against the downward force of gravity
• Therefore energy is transferred to the object
• This equation can therefore be derived from the work done

### Gravitational Potential Energy

• Gravitational potential energy (GPE) is energy stored in a mass due to its position in a gravitational field
• If a mass is lifted up, it will gain GPE (converted from other forms of energy)
• If a mass falls, it will lose GPE (and be converted to other forms of energy)
• The equation for gravitational potential energy for energy changes in a uniform gravitational field is: Equation for GPE

• The potential energy on the Earth’s surface at ground level is taken to be equal to 0
• This equation is only relevant for energy changes in a uniform gravitational field (such as near the Earth’s surface)

#### GPE v Height graphs

• The two graphs below show how GPE changes with height for a ball being thrown up in the air and when falling down Graphs showing the linear relationship between GPE and height

• Since the graphs are straight lines, GPE and height are said to have a linear relationship
• These graphs would be identical for GPE against time instead of height

#### Exam Tip

This equation only works for objects close to the Earth’s surface where we can consider the gravitational field to be uniform. In A2 level, you will consider examples where the gravitational field is not uniform such as in space, where this equation for GPE will not be relevant. ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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