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AS Daily A Level Physics question

2026-03-27 OCR A Materials (Module 3.4) OCR A Physics AS Module 3.4 Materials — Springs in series and parallel OCR A Physics AS Module 3.4 Materials — Elastic strain energy in a spring

Two identical light springs, each with constant 30 N m^-1, are used to suspend a 3.0 N weight. Arrangement P has the springs side by side sharing the load (parallel). Arrangement S has the springs one below the other (series). Which statement must be true for the total extension and the energy stored by the springs?

  1. A Parallel gives 0.20 m while series gives 0.050 m; the series stores less energy.
  2. B Series gives 0.10 m while parallel gives 0.10 m; the energies are different.
  3. C Series gives 0.10 m while parallel gives 0.050 m; the series stores twice the energy.
  4. D Series gives 0.20 m while parallel gives 0.050 m; for the same load, energy is proportional to extension so the series stores four times as much (0.30 J vs 0.075 J). (correct)

Answer

The correct answer is D.

Correct: D — Series gives 0.20 m while parallel gives 0.050 m; for the same load, energy is proportional to extension so the series stores four times as much (0.30 J vs 0.075 J). With identical springs (k = 30 N m^-1) and a 3.0 N load: k_eq(series) = 15 N m^-1 so x_S = 3.0/15 = 0.20 m; k_eq(parallel) = 60 N m^-1 so x_P = 3.0/60 = 0.050 m; energy for a given load is 0.5 F x, hence a factor of 4 in energy. A Confuses the roles: parallel is stiffer so cannot extend 0.20 m; it also wrongly claims less energy for the larger extension. B Claims equal extensions in series and parallel, which is false because the equivalent stiffness differs. C Underestimates both the series extension (should be 0.20 m) and the energy ratio (it is fourfold, not twofold). D Matches the correct extensions and uses the correct proportionality of energy to extension for a fixed load.

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