A rubber bungee cord is stretched by a person jumping from a bridge. At first, the cord extends in proportion to the force applied to it. As the jump continues, the cord is stretched further until it no longer obeys Hooke's law. Explain the behaviour of the bungee cord during the jump, referring to the limit of proportionality and elastic deformation.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
A bungee cord has a spring constant of 50 N/m. During a jump, the cord is first stretched gently, then stretched to a much greater extension as the jumper falls.
Model answer (4 marks)
Initially the bungee cord obeys Hooke’s law: the extension x is directly proportional to the applied force F, with F=kx (k=50 N m⁻¹). This proportionality holds only up to the limit of proportionality. When the jumper’s weight increases the cord is stretched beyond this limit; the extension then grows more slowly than the force and Hooke’s law no longer applies. As long as the elastic limit is not exceeded the cord is in the elastic deformation region – it can return to its original length when the force is removed. If the elastic limit is exceeded the cord undergoes plastic (permanent) deformation and will not return to its original shape.
Examiner tips
- Show the Hooke’s law equation and the concept of limit of proportionality
- Explain the change in behaviour beyond the limit
- Mention elastic vs plastic deformation and recovery
Common mistakes
- Confusing limit of proportionality with elastic limit
- Saying the cord always returns to its original shape
- Using the wrong sign for the spring constant
Mark scheme (4 marks)
- Initially, the extension of the cord is directly proportional to the force applied (Hooke's law is obeyed).
- Beyond the limit of proportionality, the extension is no longer directly proportional to the force applied.
- As long as the elastic limit is not exceeded, the cord undergoes elastic deformation and returns to its original shape/length when the force is removed.
- If the elastic limit is exceeded, plastic (permanent) deformation occurs and the cord will not return to its original shape.
Key terms in this question
limit of proportionality · elastic deformation · Hooke's law
Related
- All Pearson Edexcel International GCSE Physics (4PH1) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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