Skip to content
Dabour HubLEARN · PRACTICE · EXPLORESign inStudent

1.5.3Motion, Forces and Energy

Gravitational Potential Energy — Cambridge IGCSE Co-ordinated Sciences 0654 - Physics Revision Notes & Topical Questions

5 min read 9 parts Lesson 26 of 36

📚 Cambridge IGCSE Co-ordinated Sciences 0654 - Physics Hub / Topical Revision
🩺
100% Curriculum Specification Match Lesson Doctor Verified
The only platform with 100% curriculum specification match and verified interactive question banks.
0%read

Section 1 of 9What GPE is

Gravitational potential energy (GPE) is the energy stored in an object because of its position in a gravitational field. Lifting an object against gravity requires work, and that work is stored as GPE. If the object is released, the stored energy is transferred to the kinetic store as it falls.

Only changes in GPE have physical meaning, which is why we usually measure height from a convenient reference such as the ground or the bench top. Whatever reference you choose, the change in GPE between two heights is the same.

Section 2 of 9The equation

change in gravitational potential energy = mass × gravitational field strength × change in height

ΔEp = m g Δh

What the symbols mean: Ep = gravitational potential energy gained (J) · m = mass (kg) · g = 9.81 N kg−1 · h = change in height (m)

where ΔEp is the change in GPE in joules (J), m is mass in kilograms (kg), g is the gravitational field strength in newtons per kilogram (N kg−1), and Δh is the change in vertical height in metres (m). On Earth, g is 9.8 N kg−1, though some papers use 10. On the Moon it is about 1.6 N kg−1, so the same lift stores about one-sixth of the energy.

The equation uses the vertical height. A ramp that is 5 m long but rises only 1 m gives a change in height of 1 m.

Section 3 of 9Why mgh works

To lift a mass m at steady speed the lifting force equals its weight, mg.

1
Using work done = force × distance, the work done in raising it through height h is mg × h.
2
That work is stored as GPE.
3
The same value is released if it falls back.
4
So GPE links to the idea of work done from the previous sub-topic, and through conservation of energy, to kinetic energy on the way down.

The mass cancels in free-fall speed calculations because both GPE and KE are proportional to m. That is why a bowling ball and a tennis ball dropped together (without air resistance) hit the ground at the same time and speed.

Section 4 of 9Using the equation

Common forms of question:

1
Direct calculation of GPE gain when lifting.
2
Finding height: h = ΔEp ÷ (m g).
3
Finding mass from the energy and height given.
4
Comparing planets: change g.
5
Connecting to power: a motor lifts a load at constant speed; useful power = ΔEp ÷ time.

A hydroelectric dam stores energy in water held high above the turbines. Pumped storage plants pump water uphill using spare electricity at night and release it at peak demand, converting between electrical and GPE stores with an efficiency of about 70 to 80%.

Section 5 of 9Graphs and units

A graph of GPE against height for a fixed mass is a straight line through the origin, with gradient mg (the weight in newtons).

Graphs and units
A graph of GPE against mass at fixed height is also a straight line, gradient gh.
Check units: kg × N kg−1 × m = N m = J.
If a height is given in centimetres or a mass in grams, convert to metres and kilograms before substituting.

Section 6 of 9Examples in the real world

GPE explains many everyday devices.

Examples in the real world
A grandfather clock runs on a falling weight that slowly releases stored GPE to the mechanism.
A diver on a 10 m platform has about 10 times more GPE per kilogram than one on a 1 m board, and converts it to kinetic energy as she falls,
  • then to thermal and sound energy and the motion of water as she enters the pool.
Hydroelectric dams, roller-coasters, ski lifts and even a hammer lifted before a blow all rely on the same relation.

Notice that when a rollercoaster car goes down, the loss of GPE equals the gain in KE only if resistance is small.

Examples in the real world
In practice about a tenth or more of the energy may be dissipated by friction and air resistance.
Engineers use the equation to estimate the height needed for the first hill so that the train has enough energy to complete the whole circuit, with some margin to spare.

Section 7 of 9Worked examples

  1. A 3.0 kg bag of flour is lifted from the floor onto a shelf 1.5 m high. Calculate the gain in GPE. (g = 9.8 N kg−1)

  2. A hiker of mass 70 kg climbs from a village at 340 m above sea level to a summit at 1240 m. Find the GPE gained.

  3. A 0.40 kg ball gains 12 J of GPE when thrown up. How high does it rise? (g = 9.8 N kg−1)

Section 8 of 9Key terms

TermMeaning
Gravitational potential energyEnergy stored by an object due to its height in a gravitational field.
Gravitational field strengthForce per unit mass, 9.8 N kg−1 on Earth.
Vertical heightHeight measured straight up, not along a slope.
Pumped storageStoring energy by pumping water uphill and releasing it later.
JouleUnit of energy.

Section 9 of 9Exam technique

1
Using the length of a slope instead of the vertical height.
2
Using grams instead of kilograms in the calculation.
3
Forgetting g, which gives the weight conversion from mass.
4
Thinking GPE depends on the path taken; only the vertical height change matters.
5
Confusing gravitational field strength g (N kg−1) with acceleration units; they are numerically equal but the unit here is N kg−1.

Last updated: