10 GCSE Physics questions about the bungee jump and zip wire, from Foundation to Higher, each with a full worked solution.
A bungee cord is a giant elastic band. Once it goes tight, it stretches and stores elastic potential energy, pulling with a bigger and bigger force until the jumper stops. A zip wire does the opposite job: it lets gravity transfer gravitational potential energy into kinetic energy as you slide down a sloping cable, while friction and air resistance limit your top speed.
Course: Combined Science + Separate Physics | Tier: Foundation + Higher | Topics: Forces · Energy
📌 KEY DEFINITIONS – learn them word for word
Hooke’s law: the extension of an elastic object is directly proportional to the force applied, provided that the limit of proportionality is not exceeded.
Elastic potential energy: the energy stored in a stretched or compressed elastic object, such as a spring or bungee cord.
Terminal velocity (S only): the steady, maximum velocity reached by a falling object when the resistive forces are equal to its weight, so the resultant force is zero.
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) |
| acceleration | a | metres per second squared (m/s²) |
| efficiency | – | no unit (or %) |
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 bungee jumper has a mass of 70 kg. Calculate his weight. (g = 9.8 N/kg)
Show solution
F: W = m g
I: W = 70 × 9.8
F: W is already the subject
A: 686 N
Q2 (F) A bungee cord has a spring constant of 80 N/m. Calculate the force needed to stretch it by 15 m.
Show solution
F: F = k e
I: F = 80 × 15
F: F is already the subject
A: 1200 N
Q3 (F) A 60 kg rider on a zip wire starts 30 m higher than the end of the wire. Calculate the gravitational potential energy she loses. (g = 9.8 N/kg)
Show solution
F: Eₚ = m g h
I: Eₚ = 60 × 9.8 × 30
F: Eₚ is already the subject
A: 17 640 J (17.6 kJ)
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Q4 (F) Describe the energy transfers as the rider goes down the zip wire, and explain why she does not reach the speed predicted by energy calculations. [4 marks]
Show answer
• Energy is transferred from her gravitational potential energy store …
• … to her kinetic energy store as she speeds up.
• Some energy is dissipated: work is done against friction in the pulley (heating it) and against air resistance, and some is transferred as sound.
• So less energy ends up in her kinetic store, and her speed is lower than if all the GPE became kinetic energy.
Q5 (F/H) Calculate the rider’s speed at the bottom if all 17 640 J of GPE were transferred to her kinetic energy store. Give your answer to 2 significant figures.
Show solution
F: Eₖ = ½ m v²
I: 17 640 = 0.5 × 60 × v², so 17 640 = 30 × v²
F: v² = 588, so v = √588
A: 24.2 m/s = 24 m/s (2 s.f.)
Q6 (F/H) Her actual speed at the bottom is 18 m/s. Calculate her kinetic energy, and the percentage of the GPE lost that ends up as kinetic energy.
Show solution
F: Eₖ = ½ m v²
I: Eₖ = 0.5 × 60 × 18²
F: Eₖ is already the subject
A: 9720 J
Percentage: 9720 ÷ 17 640 × 100 = 55%
Q7 (F/H) The bungee cord (k = 80 N/m) is stretched by 25 m at the lowest point of a jump. Calculate the elastic potential energy stored, assuming it obeys Hooke’s law.
Show solution
F: Eₑ = ½ k e²
I: Eₑ = 0.5 × 80 × 25²
F: Eₑ is already the subject
A: 25 000 J (25 kJ)
Q8 (H) A bungee company wants the 70 kg jumper to stop 50 m below the platform. The cord is 20 m long when unstretched. Calculate the spring constant needed, to 2 significant figures. Ignore air resistance. (g = 9.8 N/kg)
Show solution
Step 1 – extension: e = 50 − 20 = 30 m
Step 2 – GPE lost over the full 50 m: Eₚ = 70 × 9.8 × 50 = 34 300 J
At the lowest point he is still, so all of this is stored as Eₑ
F: Eₑ = ½ k e²
I: 34 300 = 0.5 × k × 30², so 34 300 = 450 × k
F: k = 34 300 ÷ 450 = 76.2 N/m
A: 76 N/m (2 s.f.)
Q9 (H · S only) On a very long zip wire, a rider reaches a steady top speed before the end. Explain why, and explain why a heavier rider reaches a higher top speed. [4 marks]
Show answer
• At first, the force pulling the rider down the slope (a component of her weight) is greater than the resistive forces, so she accelerates.
• As her speed increases, air resistance increases.
• Eventually the resistive forces balance the driving force, the resultant force is zero, and she travels at a steady terminal velocity.
• A heavier rider has a bigger weight, so air resistance must be bigger to balance it – this happens only at a higher speed.
Q10 (H) At the lowest point of the jump in Q8, the cord (k = 76 N/m) is stretched by 30 m. Calculate the resultant force on the 70 kg jumper and his acceleration, to 2 significant figures. State its direction.
Show solution
Step 1 – cord force: F = k e = 76 × 30 = 2280 N upwards
Step 2 – resultant force: 2280 − 686 = 1594 N upwards
F: F = m a
I: 1594 = 70 × a
F: a = 1594 ÷ 70 = 22.8 m/s²
A: 1600 N and 23 m/s² upwards (2 s.f.) – more than twice g, which is why the bottom of a jump feels so strong.
⚠️ Where students lose marks
- Using the total length of the cord instead of its extension (stretched length − unstretched length).
- Forgetting to square the extension in Eₑ = ½ k e².
- Using only the stretch of the cord for the height in Eₚ = m g h – the jumper falls the cord length plus the extension.
- Saying the jumper has no forces on him at the lowest point – he is momentarily still, but the resultant force is large and upwards.
More devices: all 40 everyday devices · Forces · Energy
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