AS Daily A Level Physics question
A technician suspends the same 3.0 kg motor using two identical light springs, each of spring constant k. Configuration S: the two springs are connected in series between the ceiling hook and the motor. Configuration P: the same two springs are attached in parallel between the hook and the motor. Assume the springs remain within their elastic limit and their masses are negligible. Which statement must be true about the total extension from the hook to the motor?
Answer
The correct answer is B.
Correct: B — The total extension in S is four times that in P. For the same load, the effective stiffness is k/2 in series and 2k in parallel, so extension is inversely proportional to effective stiffness: x_S/x_P = (1/(k/2)) / (1/(2k)) = 4. A The extensions cannot be equal because the effective stiffnesses differ by a factor of 4. B This matches the inverse-stiffness ratio between series (k/2) and parallel (2k). C A factor of 2 would result only if you considered series halving k but forgot that parallel doubles it. D This inverts the correct ratio; parallel is stiffer, so its extension is smaller, not larger.