CIE AS Physics

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First teaching 2020

Last exams 2024

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5.2.1 Gravitational Potential Energy

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Derivation of GPE = mgh

What is Gravitational Potential Energy?

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

How can the equation for Gravitational Potential Energy be derived?

  • This equation can therefore be derived from the work done

Derivation of GPE = mgh, downloadable AS & A Level Physics revision notes

Derivation of GPE = mgh

 

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:

GPE equation, downloadable AS & A Level Physics revision notes

Equation for GPE

 

GPE diagram, downloadable AS & A Level Physics revision notes

GPE: The energy an object has when lifted up

 

  • 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

GPE graphs, downloadable AS & A Level Physics revision notes

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

 

Worked example

To get to his apartment a man has to climb five flights of stairs.

The height of each flight is 3.7 m and the man has a mass of 74 kg.

What is the approximate gain in the man's gravitational potential energy during the climb?

A.     13 000 J               B.     2700 J               C.     1500 J               D.     12 500 J

WE - GPE answer image, downloadable AS & A Level Physics revision notes

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.

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