1996 Paper 3 Q9

Year: 1996
Paper: 3
Question Number: 9

Course: UFM Mechanics
Section: Circular Motion 2

Difficulty: 1700.0 Banger: 1516.0

circular motion particle on hemisphere energy conservation projectile optimisation leaving surface normal reaction

Problem

A particle of mass $m$ is at rest on top of a smooth fixed sphere of radius $a$. Show that, if the particle is given a small displacement, it reaches the horizontal plane through the centre of the sphere at a distance % at least $$a(5\sqrt5+4\sqrt23)/27$$ from the centre of the sphere. [Air resistance should be neglected.]

No solution available for this problem.

Rating Information

Difficulty Rating: 1700.0

Difficulty Comparisons: 0

Banger Rating: 1516.0

Banger Comparisons: 1

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Problem source

A particle of mass $m$ is at rest on top of a smooth fixed sphere of radius
$a$. Show that, if the particle is given a small displacement, it reaches
the horizontal plane through the centre of the sphere at a distance
% at least
$$a(5\sqrt5+4\sqrt23)/27$$
from the centre of the sphere.
[Air resistance should be neglected.]

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