A cone is in unstable equilibrium, has its potential energy

Analyze the question

The question asks what happens to the potential energy of a cone in unstable equilibrium when it is slightly disturbed. The cone is balanced on its tip (apex), and the question is about the effect of a small displacement.

Concept

There are three types of equilibrium:

• Stable: When displaced, the centre of gravity rises, so potential energy increases. The body returns to its original position.
• Unstable: When displaced, the centre of gravity falls, so potential energy decreases. The body moves further away from its original position (e.g. a cone balanced on its apex topples over).
• Neutral: When displaced, the centre of gravity stays at the same height, so potential energy is unchanged (e.g. a cone lying on its side).

Solution

1. A cone standing on its apex has its centre of gravity at the highest possible position. This is the maximum potential energy position.
2. A slight push makes it topple, and its centre of gravity moves lower.
3. Since PE = mgh and h decreases, the potential energy decreases.
4. The cone does not return, because lowering its PE is energetically favourable. This is why the equilibrium is unstable.

Answer

The potential energy is decreased when the cone is displaced from unstable equilibrium.

Tip

Remember: Unstable = Under (goes down). In unstable equilibrium, a displacement lowers the centre of gravity, so PE decreases. In stable equilibrium, a displacement raises it, so PE increases. In neutral equilibrium, PE stays the same.