Gravitational Potential Energy (SQA National 5 Physics): Revision Note

Gravitational potential energy

• Gravitational potential energy is defined as:

The potential energy an object has due to its height in a gravitational field

• To lift an object through a gravitational field, work must be done against gravity, or the weight of the object

• Whenever work is done, energy is transferred, which means:

  • If an object is lifted, energy is transferred to it as gravitational potential energy 

  • If an object is lowered, its gravitational potential energy is transformed into a different type of energy

Gravitational potential energy of an object lifted through a gravitational field

Calculating gravitational potential energy

• The gravitational potential energy gained or lost by an object can be calculated using the relationship:

$E_p=mgh$

• Where:

  • $E_p$ = gravitational potential energy, measured in joules (J)

  • $m$ = mass, measured in kilograms (kg)

  • $g$ = gravitational field strength, measured in newtons per kilogram (N kg^-1)

  • $h$ = change in height, measured in metres (m)

• This relationship is found from:

Change in potential energy = work done

$E_p=E_w$

$E_p=Fd$

• Where:

  • the applied force $F$ is the weight, $mg$

  • the distance $d$ moved is the height, $h$

$E_p=mg\times d=mgh$