Gravitational Potential Energy
Get to grips with Gravitational Potential Energy for GCSE Physics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA, Edexcel and OCR. Raising an object stores gravitational potential energy equal to mgh, which is transferred to kinetic energy as it falls.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Topic overview
The gravitational potential energy store of an object depends on its mass, its height, and the gravitational field strength. The equation is gravitational potential energy = mass × gravitational field strength × height.
On Earth the gravitational field strength is about 9.8 N/kg, though 10 N/kg is often used for simplicity. Height must be the vertical height, measured from the reference level, not the distance travelled along a slope.
When an object falls, energy is transferred from its gravitational potential store to its kinetic store. If air resistance is ignored, the energy transferred is equal, which allows the impact speed to be calculated by setting the two equations equal to each other.
Revision notes
The equation
Gravitational potential energy = mass × gravitational field strength × height, or Eₚ = mgh.
Mass in kilograms, gravitational field strength in N/kg, height in metres, energy in joules. On Earth g is about 9.8 N/kg.
Using vertical height
The height in the equation is the vertical height gained or lost.
If an object moves along a slope, the distance along the slope is not the height. Only the vertical component counts, which is a common trap in exam diagrams.
Falling objects
When an object falls, energy is transferred from the gravitational potential store to the kinetic store.
Ignoring air resistance, the energy transferred is equal, so mgh = ½mv². The mass cancels, giving v = √(2gh) — the impact speed does not depend on mass.
Key points
- Gravitational potential energy = mass × g × height.
- On Earth g is about 9.8 N/kg.
- Height must be the vertical height.
- Energy is in joules.
- Falling transfers energy from gravitational to kinetic store.
- Ignoring air resistance, mgh = ½mv².
Worked examples
Example 1
Calculate the gravitational potential energy gained when a 60 kg person climbs 5 m. Take g = 9.8 N/kg. [3 marks]
Model answer
Gravitational potential energy = mass × g × height = 60 × 9.8 × 5 (1 mark). 60 × 9.8 = 588 (1 mark). 588 × 5 = 2940 J (1 mark).
Example 2
A 2 kg object is lifted 3 m. Calculate the energy transferred. Take g = 10 N/kg. [2 marks]
Model answer
Energy = mass × g × height = 2 × 10 × 3 (1 mark) = 60 J (1 mark).
Example 3
Explain why the mass of a falling object does not affect its speed on impact, ignoring air resistance. [3 marks]
Model answer
The energy transferred from the gravitational potential store equals the energy gained in the kinetic store, so mgh = ½mv² (1 mark). The mass appears on both sides of the equation and cancels (1 mark), leaving v = √(2gh), which does not contain the mass (1 mark).
Common mistakes
Using the distance along a slope as the height.
Only the vertical height counts in the equation.
Forgetting the gravitational field strength.
The equation has three quantities: mass, g and height.
Using g = 9.8 when the question specifies 10.
Use whichever value the question gives.
Saying heavier objects fall faster.
Ignoring air resistance, mass cancels and does not affect impact speed.
Exam tips
- Check whether the question gives g as 9.8 or 10.
- Use only the vertical height.
- Show each multiplication step for method marks.
- Set mgh equal to ½mv² for falling-object problems.
Key terms
- Gravitational potential energy
- Energy stored by an object raised above the ground.
- Gravitational field strength
- The force per kilogram, about 9.8 N/kg on Earth.
- Vertical height
- The height measured straight up, not along a slope.
- Reference level
- The height from which the potential energy is measured.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.