Q7 — Hooke's Law / extended evaluation (6 marks)

Question: A student investigates how a spring extends when loads are added. They plot a graph of force (y-axis) against extension (x-axis). (a) State Hooke's Law and the equation linking force, spring constant and extension. (2) (b) The graph is a straight line through the origin up to point P, then curves. Explain what point P represents and how the spring's behaviour differs beyond P. (2) (c) The spring constant from the linear region is 25 N/m. Calculate the elastic potential energy stored when the spring is extended by 0.080 m within the linear region. (2)

Mark scheme (6 marks):

(a) 2 marks:

• Extension is directly proportional to the force applied, provided the limit of proportionality is not exceeded (1)
• F = k e (with terms defined) (1)

(b) 2 marks:

• P is the limit of proportionality (1)
• Beyond P the extension is no longer proportional to force; the spring may deform inelastically / not return to its original length (1)

(c) 2 marks:

• E = ½ k e² = ½ × 25 × (0.080)² (1)
• E = 0.080 J (accept 8.0 × 10⁻² J) (1)