A bungee cord is made from a polymer material. When a person jumps and the cord stretches, the cord stores elastic potential energy and then returns the person upwards. Explain why the bungee cord is described as having a low Young modulus, and describe how the force needed to stretch the cord changes as extension increases beyond the limit of proportionality.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A bungee cord stretches considerably under the weight of a jumper, storing energy and then recoiling to return the jumper upwards.
Model answer (5 marks)
A bungee cord is made from a polymer that has a low Young’s modulus, meaning that for a given applied stress it undergoes a large strain – it stretches a lot. Young’s modulus is defined as stress divided by strain; a small value therefore indicates that the strain is large relative to the stress.
When the cord is stretched within its elastic limit, Hooke’s law applies: the force required is proportional to the extension. Once the limit of proportionality is exceeded, the force–extension relationship is no longer linear. The cord becomes easier to stretch, so a smaller additional force produces a larger increase in extension.
Thus the cord’s low modulus allows it to stretch significantly under the jumper’s weight, and beyond the elastic limit the force needed per unit extension decreases.
When the cord is stretched within its elastic limit, Hooke’s law applies: the force required is proportional to the extension. Once the limit of proportionality is exceeded, the force–extension relationship is no longer linear. The cord becomes easier to stretch, so a smaller additional force produces a larger increase in extension.
Thus the cord’s low modulus allows it to stretch significantly under the jumper’s weight, and beyond the elastic limit the force needed per unit extension decreases.
Examiner tips
- Use the definition of Young’s modulus to link low value with large strain.
- Show the Hooke’s law relationship up to the limit of proportionality.
- Explain the change in the force–extension curve beyond that limit.
- Keep the answer concise and use the exact terminology from the mark scheme.
Common mistakes
- Confusing Young’s modulus with the spring constant.
- Saying the force increases beyond the limit of proportionality instead of decreases per unit extension.
- Using vague terms like ‘soft’ without linking to strain or stress.
Mark scheme (5 marks)
- A low Young modulus means the material stretches a large amount (large strain) for a given applied stress
- Young modulus = stress ÷ strain, so a low value means a large strain relative to the stress applied
- Up to the limit of proportionality, force and extension are proportional (Hooke's law is obeyed)
- Beyond the limit of proportionality the relationship is no longer proportional / Hooke's law is no longer obeyed
- Beyond the limit of proportionality, a smaller additional force produces a larger increase in extension (the cord becomes easier to stretch / less force needed per unit extension)
Key terms in this question
Young modulus · limit of proportionality · elastic potential energy
Related
- All AQA A-Level Physics (7408) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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