 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/f/solution

Immediately after the parcel leaves, the spring still stores

\frac{1}{2} k x^{2}

, but only the

m_{s} = 0.300 kg

sledge is launched. Choose gravitational potential zero at the ramp base. Its initial position is

- x

, so conservation of energy to the apex gives

\frac{1}{2} k x^{2} - m_{s} gx = m_{s} g H_{s} .

Therefore

H_{s} = \frac{k x ^{2}}{2 m _{s} g} - x = 2.17 m

above the ramp base. Its upward travel from the compressed position is

H_{s} + x = 2.56882 m

, a different distance from the height above the base.

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