10 GCSE Physics questions about trampolines and bungee jumps, from Foundation to Higher, each with a full worked solution.
Every bounce on a trampoline is a chain of energy transfers. As you fall, your gravitational potential energy becomes kinetic energy. When you land, the springs stretch and store elastic potential energy – which then throws you back up into the air. A bungee cord does the same job, just with a much longer stretch.
Course: Combined Science + Separate Physics | Tier: Foundation + Higher | Topics: Forces · Energy
📌 KEY DEFINITIONS – learn them word for word
Weight: the force acting on an object due to gravity.
Elastic potential energy: the energy stored in a stretched or compressed spring.
Limit of proportionality: the point beyond which the extension of a spring is no longer directly proportional to the force applied.
Conservation of energy: energy can be transferred usefully, stored or dissipated, but it cannot be created or destroyed.
Equations you’ll use
| Quantity | Symbol | Unit |
|---|---|---|
| weight | W | newtons (N) |
| mass | m | kilograms (kg) |
| gravitational field strength | g | newtons per kilogram (N/kg) |
| force | F | newtons (N) |
| spring constant | k | newtons per metre (N/m) |
| extension | e | metres (m) |
| elastic potential energy | Eₑ | joules (J) |
| gravitational potential energy | Eₚ | joules (J) |
| height | h | metres (m) |
| kinetic energy | Eₖ | joules (J) |
| speed | v | metres per second (m/s) |
Use FIFA for every calculation
- F – Formula: write the equation as it appears on the sheet.
- I – Insert: put in the numbers (convert to standard units first).
- F – Fix: rearrange to make the unknown the subject.
- A – Answer: calculate and always give the unit.
Foundation: aim for Q1–8. Higher: aim for Q4–10.
Questions
Q1 (F) A gymnast has a mass of 50 kg. Calculate her weight. (g = 9.8 N/kg)
Show solution
F: W = m g
I: W = 50 × 9.8
F: W is already the subject
A: 490 N
Q2 (F) Each trampoline spring has a spring constant of 5000 N/m. Calculate the force needed to stretch one spring by 4.0 cm.
Show solution
Convert first: 4.0 cm = 0.040 m
F: F = k e
I: F = 5000 × 0.040
F: F is already the subject
A: 200 N
Q3 (F) The 50 kg gymnast rises 1.5 m above the trampoline bed. Calculate the gravitational potential energy she gains. (g = 9.8 N/kg)
Show solution
F: Eₚ = m g h
I: Eₚ = 50 × 9.8 × 1.5
F: Eₚ is already the subject
A: 735 J
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Q4 (F) Describe the energy transfers during one bounce, from the top of the jump to the lowest point and back up again. [4 marks]
Show answer
• At the top, energy is in her gravitational potential energy store.
• As she falls, it is transferred to her kinetic energy store.
• As the springs stretch, energy is transferred to the elastic potential energy store of the springs; she slows down.
• The springs then return to their original length, transferring energy back to kinetic and then gravitational potential energy as she rises.
Q5 (F/H) The gymnast falls 1.5 m back onto the trampoline. Using your answer to Q3, calculate her speed just before she lands. Ignore air resistance.
Show solution
Energy lost as GPE = energy gained as KE = 735 J
F: Eₖ = ½ m v²
I: 735 = 0.5 × 50 × v², so 735 = 25 × v²
F: v² = 29.4, so v = √29.4
A: 5.4 m/s
Q6 (F/H) Calculate the elastic potential energy stored in one spring (k = 5000 N/m) when it is stretched by 4.0 cm.
Show solution
Convert first: 4.0 cm = 0.040 m
F: Eₑ = ½ k e²
I: Eₑ = 0.5 × 5000 × 0.040²
F: Eₑ is already the subject
A: 4.0 J
Q7 (H) The trampoline has 72 identical springs (k = 5000 N/m). At the lowest point of a bounce, the 735 J from Q3 is shared equally between all 72 springs. Calculate the extension of each spring in centimetres.
Show solution
Step 1 – energy per spring: 735 ÷ 72 = 10.2 J
F: Eₑ = ½ k e²
I: 10.2 = 0.5 × 5000 × e²
F: e² = 10.2 ÷ 2500 = 0.00408, so e = √0.00408 = 0.064 m
A: 6.4 cm
Q8 (F/H) A bungee cord has a spring constant of 120 N/m. At the lowest point of a jump, it is stretched by 20 m. Calculate the elastic potential energy stored in the cord.
Show solution
F: Eₑ = ½ k e²
I: Eₑ = 0.5 × 120 × 20²
F: Eₑ is already the subject
A: 24 000 J
Q9 (H) The bungee jumper has a mass of 70 kg. From the platform to the lowest point, she falls a total of 35 m. Show that the gravitational potential energy she loses is about the same as the elastic potential energy stored in the cord in Q8. (g = 9.8 N/kg)
Show solution
F: Eₚ = m g h
I: Eₚ = 70 × 9.8 × 35
F: Eₚ is already the subject
A: 24 010 J ≈ 24 000 J
This matches the 24 000 J stored in the cord, because at the lowest point she is momentarily still: all the GPE lost has been transferred to the cord’s elastic potential energy store (ignoring air resistance).
Q10 (H) A gymnast stops jumping and just bounces. Each bounce is a little lower than the one before. Explain why, using ideas about energy. [4 marks]
Show answer
• Energy is conserved, but not all of it stays in useful stores.
• On each bounce some energy is dissipated …
• … by air resistance, by heating the springs and the mat, and as sound.
• So less energy returns to her gravitational potential energy store, and she rises to a lower height each time.
⚠️ Where students lose marks
- Using the extension in centimetres in F = k e or Eₑ = ½ k e² – convert to metres first.
- Forgetting to square the extension (or the speed) before multiplying.
- Saying energy is “lost” or “used up” – say it is dissipated to the surroundings.
- Using the stretched length instead of the extension (stretched length − original length).
More devices: all 40 everyday devices · Forces · Energy
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