 Solution

ID: past-exam-of-the-physics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-1/section-b/6/e/solution

Let

x = 0.400 m

be the compression and

m_{t} = 0.550 kg

the combined mass. Starting from rest at the top, it falls through

H + x

before maximum compression. Hence

\frac{1}{2} k x^{2} = m_{t} g (H + x), k = 94.5 N m^{- 1} .

The gravitational drop during compression must be included. Equating

k x

to the weight would instead describe a static equilibrium, not the turning point after a fall.

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