AS Daily A Level Physics question
A 12 N load is hung from identical light springs in three configurations: (i) a single spring; (ii) two identical springs in series; (iii) two identical springs in parallel. All extensions remain in the linear region. Without calculating absolute extensions, which statement must be true about the elastic energy stored by the springs for the same 12 N load? Use proportional reasoning (how the effective stiffness changes) and, if helpful, check a limiting case.
Answer
The correct answer is B.
Correct: B — For a fixed load, two identical springs in series store twice the energy of one spring, while two in parallel store half as much. For a given force, the effective stiffness halves in series and doubles in parallel, so energy (proportional to 1/effective stiffness for fixed load) doubles in series and halves in parallel. A is wrong because two identical springs in series extend twice as much as a single spring, so the energy does not stay the same. B is correct for the reason above: k_eff(series)=k/2 gives twice the energy; k_eff(parallel)=2k gives half. C is wrong because in parallel the extension halves (not doubles), so the energy is reduced, not increased. D is wrong because the gravitational energy loss depends on the equilibrium extension, which differs between arrangements; energy stored is not the same across all three.