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Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 14A / e / Solution

At the circular minimum,

v^{2} = (5/7) g r cot α

and

r = 8 a

. Projecting the centre-of-mass equation on the cone normal gives

N = m g sin α + \frac{m v ^{2}}{r} cos α = \frac{m g ( 5 + 2 s i n ^{2} α )}{7 s i n α} .

This is the magnitude of the normal constraint force.

Solved by gpt-5.6-sol high.

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