IB Physics SLTopic A.3 โ Work, Energy & PowerPaper 1 & 2Gravitational PE~6 min read
Gravitational PE
Gravitational potential energy is the energy stored in an object simply because of where it is in a gravitational field. Lift something up, and you’re loading it with energy it didn’t have before.
๐ What you need to know
Gravitational PE depends on an object’s mass, the local gravitational field strength, and its height
Close to the Earth’s surface, it’s calculated using ฮEp = mgฮh
Lifting an object increases its gravitational PE; letting it fall decreases it
You can choose any reference height as “zero” โ only the change in height actually matters
This equation only holds in a uniform field, such as near the Earth’s surface โ a different equation applies far from a planet
What Is Gravitational PE?
Gravitational potential energy is the energy an object has stored due to its position within a gravitational field. Raise a mass up, and you do work against gravity to get it there โ that work doesn’t disappear, it’s stored as gravitational PE, ready to be released the moment the object is allowed to fall.
Gravitational potential energy equation
ฮEp = mgฮh
Where ฮEp is the change in gravitational PE in joules, m is mass in kilograms, g is gravitational field strength (9.8 N kgโปยน near Earth’s surface), and ฮh is the change in height in metres.
Gravitational potential energy: the energy stored in a mass by raising it through a height h
Choosing Your Reference Point
Ground level is often taken as the “zero” for gravitational PE, but this is just a convenient choice โ any height can be used as the reference point. Since the equation above only calculates a change in gravitational PE, it doesn’t actually matter where you set zero, as long as you’re consistent.
This equation is only valid in a uniform gravitational field, which is a good approximation close to a planet’s surface. Far from the surface โ where field strength itself changes with distance โ a different, non-linear equation for gravitational PE is needed instead.
Gravitational PE and Height: A Linear Relationship
Because ฮEp = mgฮh has height appearing to the power of one, gravitational PE increases in direct proportion to height. Plotting gravitational PE against height for an object being thrown upward and then falling back down gives two straight lines: rising as it climbs, falling as it descends.
Gravitational PE varies linearly with height โ these graphs would look identical plotted against time instead of height
Quick recap: ฮEp = mgฮh applies close to a planet’s surface, where g is roughly constant. Gravitational PE rises in direct proportion to height gained.
WE 1
A librarian carries a stack of books with a mass of 4.5 kg up a staircase made of 6 identical steps, each 0.22 m high. Calculate the change in gravitational PE of the books.
Step 1 โ Find the total height gainedฮh = 6 ร 0.22 = 1.32 mStep 2 โ Substitute into the equationฮE_p = mgฮh = 4.5 ร 9.8 ร 1.32โ 58 J (2 s.f.)
WE 2
A window cleaner’s bucket of mass 3.2 kg is lowered from a ledge 9.0 m above the ground down to 2.5 m above the ground. Calculate the change in the bucket’s gravitational PE, and state whether it is a gain or a loss.
Step 1 โ Find the change in heightฮh = 9.0 โ 2.5 = 6.5 m (a decrease)Step 2 โ Substitute into the equationฮE_p = mgฮh = 3.2 ร 9.8 ร 6.5โ 204 J lostThe bucket’s height has decreased, so this is a loss in gravitational PE, not a gain.
๐ก Top tips
You can set your reference height (zero point) anywhere โ the equation only cares about the change in height
Keep track of whether height is increasing or decreasing so you know whether it’s a gain or a loss
Use the symbol ฮEp, not just “GPE,” when writing out your working in exams
Double-check you’re using total height gained, not the length of a sloped or winding path
โ Common mistakes
Using the distance travelled along a slope instead of the vertical height gained
Forgetting that ฮEp = mgฮh only applies in a uniform field near a surface, not far out in space
Mixing up g (gravitational field strength) with G (the gravitational constant used elsewhere in the course)
Assuming ground level must always be the zero reference, when any convenient height will do
Up next: Elastic PE โ where we look at the energy stored in stretched or compressed springs.
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