Gravitational potential energy
When objects are above the ground, they have the potential to fall down to the ground.
When they do fall, they transfer that gravitational potential energy into kinetic energy as they speed up.
Calculating the change in gravitational potential energy
Section titled “Calculating the change in gravitational potential energy”If we know the:
- mass of the object, in kilograms,
- height the object is lifted up by, in metres,
- gravitational field strength, in newtons per kilogram,
…then we can calculate the change in gravitational potential energy when the object is lifted up or falls down!
The formula we use is:
Putting it into symbols, we get:
Where:
is the change in gravitational potential energy, in joules, is the mass of the object, in kilograms, is the gravitational field strength, in newtons per kilogram, is the change in the object’s distance from the ground, in metres,
Height
Section titled “Height”Make sure the height is the shortest distance from the object to the ground.
The height should be perpendicular to the gravitational field lines (or parallel to the force of gravity).
’Change in’?
Section titled “’Change in’?”We can’t directly calculate the gravitational potential energy of an object, but we can calculate its change in gravitational potential energy when it falls or is lifted up.
That’s why we put the
If we were calculating the actual gravitational potential energy, that would suggest that an object on the surface of the Earth has zero gravitational potential energy, which isn’t true - the surface of the Earth isn’t the absolute point where gravitational potential energy is zero, it’s just the point where we usually choose to measure it from.
Examples
Section titled “Examples”A 2 kg object is lifted up by 5 m. The gravitational field strength is 10 N/kg. What is the change in gravitational potential energy of the object?
Section titled “A 2 kg object is lifted up by 5 m. The gravitational field strength is 10 N/kg. What is the change in gravitational potential energy of the object?”The gravitational field strength on the Moon is 1.6 N/kg. A 3 kg object is lifted up by 4 m on the Moon. What is the change in gravitational potential energy of the object?
Section titled “The gravitational field strength on the Moon is 1.6 N/kg. A 3 kg object is lifted up by 4 m on the Moon. What is the change in gravitational potential energy of the object?”An object gains 49 J of gravitational potential energy when it is lifted up by 10 m. The gravitational field strength is 9.8 N/kg. What is the mass of the object?
Section titled “An object gains 49 J of gravitational potential energy when it is lifted up by 10 m. The gravitational field strength is 9.8 N/kg. What is the mass of the object?”An object loses 20 J of gravitational potential energy when it falls down by 2 m. The gravitational field strength is 10 N/kg. What is the mass of the object?
Section titled “An object loses 20 J of gravitational potential energy when it falls down by 2 m. The gravitational field strength is 10 N/kg. What is the mass of the object?”(the object loses energy, so the change in energy is negative) (the object falls down, so the change in height is negative)
How far does a 2 kg object fall if it loses 80 J of gravitational potential energy? Assume the gravitational field strength is 10 N/kg.
Section titled “How far does a 2 kg object fall if it loses 80 J of gravitational potential energy? Assume the gravitational field strength is 10 N/kg.”(the object loses energy, so the change in energy is negative) - So the object falls down by 4 m.