1. 1
   A technician hangs a spring vertically from a clamp stand and adds masses to the free end one at a time, measuring the total extension after each addition. Below the elastic limit, the extension increases in equal steps for each equal increase in load.

   (a)

   Which equation correctly relates the force applied to the spring, its spring constant and its extension?

   [1 mark]

   • A$F = k \times e$
   • B$F = \dfrac{k}{e}$
   • C$F = k + e$
   • D$e = F \times k$

   (b)

   The technician continues adding masses beyond the point where the extension stops increasing in equal steps for equal increases in load. What is the name given to this point on the spring's force–extension behaviour?

   [1 mark]

   • AThe centre of mass
   • BThe limit of proportionality
   • CThe terminal point
   • DThe equilibrium point

   (c)

   The spring has a spring constant of 25 N/m. When a mass is hung from it, the spring extends by 0.12 m and this extension is within the limit of proportionality. Calculate the force applied to the spring by the mass. Give your answer in newtons.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student stretches a rubber band by pulling its ends apart, then releases it and observes that it returns exactly to its original length and shape. She repeats the test with a strip of modelling clay, stretching it by the same amount, and finds that the clay stays stretched after she lets go.

   (a)

   Which term describes this type of distortion?

   [1 mark]

   • APlastic distortion
   • BInelastic distortion
   • CElastic distortion
   • DPermanent distortion

   (b)

   Based on the behaviour described, which term correctly describes what happens to the modelling clay when it is stretched and does not return to its original shape?

   [1 mark]

   • AReversible distortion
   • BElastic distortion
   • CProportional distortion
   • DInelastic distortion

   (c)

   Explain, in terms of the forces applied and the shape of the materials afterwards, why the rubber band shows elastic distortion but the modelling clay shows inelastic distortion.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A different spring is tested by hanging a 4 N weight from it, which produces an extension of 0.08 m, remaining within the limit of proportionality throughout. The student then adds further weights so that the total extension increases to 0.15 m, but this new extension is now beyond the limit of proportionality for the spring.

   (a)

   Calculate the spring constant of this spring, showing your working and stating the correct unit.

   [3 marks]

   (b)

   Explain why the spring constant calculated in part (a) can no longer be used to reliably predict the force needed to produce the extension of 0.15 m, and describe how the force–extension graph for the spring would look different once this larger extension is reached, compared to below the limit of proportionality.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A group of students carries out the core practical investigating the extension and work done when applying forces to a spring. They clamp a spring vertically, measure its unstretched length, then add a series of slotted masses one at a time, recording the total length of the spring after each addition and calculating the extension each time. They repeat the whole procedure three times and average their extension values for each force.

   (a)

   Describe a suitable method the students could use to carry out this investigation safely and accurately, including how they should control variables and reduce experimental error.

   [6 marks]

   (b)

   Using their averaged results, the students find that within the limit of proportionality, a spring with spring constant 40 N/m stores elastic potential energy when stretched. One student claims that if the spring is stretched beyond the limit of proportionality, the work done stretching it will always be exactly equal to the elastic potential energy stored, calculated using $E_e = \frac{1}{2} \times k \times e^2$. Evaluate this claim, explaining whether the student is correct and justifying your reasoning using ideas about energy and the force–extension relationship beyond the limit of proportionality.

   [6 marks]

   Total for question 4: 12 marks

End of questions