1.4 Gravitational Potential Energy Stores

A free GCSE Physics lesson for AQA (8463) from OBA School: changes in the gravitational potential energy store: ΔEp = m g Δh. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

• Describe what happens to the gravitational potential energy (GPE) store of an object when it moves up or down
• Explain why lifting an object at a steady speed needs a force equal to its weight
• Calculate changes in GPE using ΔEp = m g Δh, including rearranging and converting units
• Explain why it is easier to lift an object on the Moon than on the Earth

Key words

• Gravitational potential energy (Ep): Energy in the GPE store of an object because of its height in a gravitational field.
• Weight: The force of gravity on an object, in newtons. W = m g.
• Gravitational field strength (g): The force of gravity on each kilogram, in N/kg. On Earth g = 9.8 N/kg.
• Mass: The amount of matter in an object, in kilograms. It is the same everywhere.
• Δ (delta): Means “change in”. Δh is the change in height.

Lifting and lowering

When you lift an object you do work on it. Energy is transferred from the chemical store of your muscles to the GPE store of the object.

• To lift something at a steady speed, the upward force must be equal and opposite to its weight. A box of weight 60 N needs a lifting force of 60 N.
• Moving up: the GPE store increases by the work done by the lifting force against gravity (weight × height).
• Moving down: the GPE store decreases by the work done by the gravitational force on the object.

Worked example: using weight × height

A boy of weight 650 N climbs a flight of stairs 3.2 m high.
increase in GPE store = weight × change in height = 650 N × 3.2 m

Answer: 2080 J (about 2.1 kJ)

The GPE equation

Because weight = mass × gravitational field strength, the change in an object’s GPE store is:

• ΔEp = m g Δh m = ΔEp ÷ (g Δh) Δh = ΔEp ÷ (m g); Symbols and units ΔEp = change in GPE store, in joules (J) m = mass, in kilograms (kg) g = gravitational field strength, in newtons per kilogram (N/kg) Δh = change in height, in metres (m)

Worked example: a tin of paint lifted onto a shelf

A 2.5 kg tin of paint is lifted 1.6 m onto a shelf. g = 9.8 N/kg.
ΔEp = m g Δh = 2.5 kg × 9.8 N/kg × 1.6 m = 39.2 J

Answer: 39 J (2 significant figures)

Worked example: rearranging to find a height

A 450 g drone gains 26.5 J of GPE. How high does it rise?
Convert: 450 g = 0.450 kg
Δh = ΔEp ÷ (m g) = 26.5 ÷ (0.450 × 9.8) = 6.0 m

Answer: Δh = 6.0 m

Exam tip: Always convert grams to kilograms (÷ 1000) and centimetres to metres (÷ 100) before you substitute.

Lifting on the Moon

The gravitational field strength at the Moon’s surface is only about 1.6 N/kg – roughly one sixth of the Earth’s. An object has the same mass on the Moon, but a much smaller weight. So a smaller force is needed to lift it, and less energy is transferred to its GPE store for each metre it rises.

Going up a slope

Worked example: a cyclist on a hill

A cyclist and bike, total mass 80 kg, ride 400 m along a road that climbs 24 m vertically.
ΔEp = m g Δh = 80 × 9.8 × 24 = 18 816 J (the 400 m is not needed)

Answer: about 19 kJ

Measuring your own GPE gain

Measure your mass on bathroom scales (kg). Measure the height of a sturdy step or low box with a metre rule (m). Step up onto it: your GPE store increases by m g Δh. Step up 20 times and the total work done against gravity is 20 × m g Δh. Make sure the box is stable and cannot slip.

Key fact: Your body transfers much more energy than m g Δh, because your muscles also heat up. The calculation gives only the energy transferred to your GPE store.

Common mistakes

• Using mass in grams, or height in cm, without converting.
• Using the distance along a slope instead of the vertical height.
• Mixing up mass (kg) and weight (N). If you are given a weight, ΔEp = weight × Δh – do not multiply by g again.
• Saying an object has “less mass on the Moon”. Its mass is the same; its weight is smaller.

Revision questions

Try these, then check your answers below each one.

Question 1. A 3.0 kg bag is lifted through 2.0 m. Calculate the increase in its GPE store. (g = 9.8 N/kg)

Answer: 58.8 J

Working: ΔEp = 3.0 × 9.8 × 2.0 = 58.8 J.

Question 2. A 600 g book is lifted 1.5 m onto a shelf. Calculate the increase in its GPE store, to 2 significant figures. (g = 9.8 N/kg)

Answer: 8.8 J

Working: m = 0.600 kg. ΔEp = 0.600 × 9.8 × 1.5 = 8.82 J ≈ 8.8 J.

Question 3. An object gains 196 J of GPE when it is raised 4.0 m. Calculate its mass. (g = 9.8 N/kg)

Answer: 5 kg

Working: m = ΔEp ÷ (g Δh) = 196 ÷ (9.8 × 4.0) = 5.0 kg.

Related lessons

• Previous lesson: 1.3 Energy and Work
• Next lesson: 1.5 Kinetic Energy and Elastic Energy Stores
• In this chapter: 1.1 Changes in Energy Stores
• In this chapter: 1.2 Conservation of Energy
• In this chapter: 1.6–1.7 Energy Dissipation and Efficiency

Continue in the full course

This lesson is section 1.4 (AGCPH0104) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.