A2 Daily A Level Physics question
A frictionless mass–spring system is released from rest at its right-hand extreme (+A). When the kinetic energy first equals the spring’s elastic energy, which combination of displacement and speed is correct?
Answer
The correct answer is A.
Correct: A — x = +A/√2; speed = v_max/√2. A: When the energies are equal, the spring energy fraction is x^2/A^2 = 1/2 so x = +A/√2 on the first pass from +A, and with KE half of its maximum, the speed is reduced by √2 because KE ∝ v^2. B: At x = 0 the spring energy is zero and KE is maximum, so energies are not equal and the speed would be v_max, not v_max/2. C: At x = A/2 the spring stores only 1/4 of E, so KE is 3/4 E and the speed is about 0.87 v_max, not v_max/2. D: The magnitude and speed factor match the equal-energy condition, but the sign is wrong for the first time after release; the mass is still on the + side before crossing equilibrium.