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Lunar Leaper

Gravity on the Moon is about 1/6th that on the Earth. A pole-vaulter 2 metres tall can clear a 5 metres pole on the Earth. How high a pole could he clear on the Moon?

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Bridge Builder

In this short problem we investigate the tensions and compressions in a framework made from springs and ropes.

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More Bridge Building

Which parts of these framework bridges are in tension and which parts are in compression?

Wobbler

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
This is all about taking moments. You could consider replacing the hemisphere and the cone with two point masses at the centres of mass of these two parts of the rigid body.

For different ranges of values of $h/a$ you have to consider all possible positions of equilibrium of the body and whether the positions are stable or unstable.