A spring is hung from a clamp. When a load of 2.0 N is hung on the spring, it extends by 4.0 cm.
(a) State Hooke's law. [1]
(b) The load is increased to 5.0 N. The spring does not go past its limit of proportionality.
Calculate the new extension of the spring. [2]
(c) The load is then increased until the spring goes well past its limit of proportionality. When the load is removed, the spring does not return to its original length.
State whether the spring behaved elastically under this larger load. Give a reason for your answer. [1]
- (a) extension is (directly) proportional to the force / load (applied) allow force ∝ extension or $F = kx$ with symbols defined; reject 'length is proportional to force'; 'up to the limit of proportionality' not required(1)
- (b) extension per newton $= 4.0 / 2.0 = 2.0$ cm/N or $\dfrac{x}{5.0} = \dfrac{4.0}{2.0}$ allow spring constant $k = 2.0 / 4.0 = 0.50$ N/cm (50 N/m) used correctly; allow scaling 4.0 × 2.5(1)
- (b) 10 cm allow 0.10 m; correct answer with no working scores 2(1)
- (c) not elastic because it does not return to its original length / shape when the load (force) is removed both 'not elastic' and the reason needed; allow 'it has been (permanently / plastically) deformed' or 'inelastic' with the reason; reject 'elastic'(1)
- Answer: (a) extension ∝ applied force (b) 10 cm (c) no (not elastic) — it did not return to its original length when the load was removed
- Examiner tip: Hooke's law is about extension, not length — 'the length is proportional to the force' scores 0.