 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-2/14a/e/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

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.

 New to topics? Read the docs here!