Alex was always interested in the marvels of science, and he was keen to show me his latest discovery. There it sat on the table. A double circular cone, resting on two inclined tracks, very much as I have sketched it here.

‘Look,’ said Alex, ‘I place the cone at the bottom of the tracks and let it go.’

I could hardly believe my eyes, but that cone actually ran uphill to the top of the tracks. There appeared to be no strings, magnets, or other trickery. I tried the experiment myself, and sure enough, again the cone ran uphill.

Now I have always believed that gravity causes things to run downhill, and I find it hard to believe that Alex’s room lies in some mysterious warp of the earth’s gravitational field!

But I really am at a loss to explain the behaviour of the cone. Are you?

Hint 1

What do you know about ‘centre of gravity’?

Hint 2

Think about the centre of gravity of the cone.
How does it move?

Solution

Assuming that there is no trickery associated with Alex’s cone, we expect the cone to roll in the direction for which the centre of gravity drops lower. We expect this to be ‘downhill’, as it would be, for example, if we placed a round pencil on the slope.

In fact, if the two inclined slopes are angled widely enough, the centre of gravity of the cone will actually drop as it rolls ‘upwards’. The upward slope of the inclines is more than countered by the downward movement of the centre of gravity due to the tapering of the cone. This is illustrated in the figure.

It is not hard to make a cardboard model which illustrates this behaviour.

Extensions

What would happen if a ball was placed on an inclined base like this?

Hint 1

Hint 2

Solution

Extensions