1. 1
   A bungee jumping company inspects its elastic bungee cords before each jump. After a jump, an inspector notices that one cord has stretched permanently and no longer returns to its original length, while a second cord returns fully to its original length once unloaded.

   (a)

   What type of deformation has occurred in this cord?

   [1 mark]

   • AInelastic deformation, because the cord does not return to its original shape
   • BElastic deformation, because the cord stretched under force
   • CInelastic deformation, because the cord is made of rubber
   • DElastic deformation, because a jumper was attached to it

   (b)

   A second bungee cord is tested and found to return completely to its original length once the jumper is removed and the load is taken off. What type of deformation has occurred in this second cord?

   [1 mark]

   • AInelastic deformation, because a force was applied to the cord
   • BInelastic deformation, because the cord stretched at all
   • CElastic deformation, because the cord is permanently longer
   • DElastic deformation, because the cord returns to its original shape

   (c)

   Explain why the company should immediately remove from service any bungee cord that shows inelastic deformation, rather than continuing to use it for jumps.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A furniture designer tests a spring used inside a sofa cushion by hanging weights from it and measuring how much it stretches, while the limit of proportionality is not exceeded.

   (a)

   When a force of 40 N is applied, the spring extends by 0.08 m. What is the spring constant of this spring?

   [1 mark]

   • A0.002 N/m
   • B3.2 N/m
   • C500 N/m
   • D48 N/m

   (b)

   The designer plots a graph of force applied against extension for the sofa spring while testing it. What shape would this graph have, provided the limit of proportionality is not exceeded?

   [1 mark]

   • AA curve that becomes steeper as force increases
   • BA straight line through the origin, showing force is directly proportional to extension
   • CA horizontal straight line, showing extension is constant regardless of force
   • DA curve that levels off completely at high force, showing no further extension

   (c)

   Calculate the elastic potential energy stored in the sofa spring when it is stretched by 0.08 m, given that its spring constant is 500 N/m.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   An archer draws back a bow, bending its two flexible limbs to store energy before releasing an arrow.

   (a)

   Explain why bending the bow's limbs requires more than one force to be applied, and describe the forces involved when the archer draws the bowstring back.

   [3 marks]

   (b)

   The archer's bow has an effective spring constant of 200 N/m when treated as a simple linear spring, and the string is drawn back by 0.5 m, remaining within the limit of proportionality. Calculate the force needed to hold the string at full draw, and the elastic potential energy stored in the bow at this point.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A materials engineering company is testing a new type of spring for use in vehicle suspension systems, applying increasing loads and measuring the resulting extension. During testing, one prototype spring is accidentally overloaded and shows a permanent increase in length once the load is removed.

   (a)

   Explain the relationship between force and extension for a spring within the limit of proportionality, and discuss how the engineers could determine, from their test data, whether the limit of proportionality has been exceeded.

   [6 marks]

   (b)

   During testing, one prototype spring is accidentally overloaded and shows a permanent increase in length once the load is removed. Discuss what this observation tells the engineers about the spring's behaviour, and explain why this matters for the safety and reliability of a vehicle suspension system using this type of spring.

   [6 marks]

   Total for question 4: 12 marks

End of questions