A large block of Aluminum has a perfect cylindrical hole of diameter 3 meters. On top of the hole sits a perfect, solid glass sphere of diameter 3.05 meters. Your job is to get the glass sphere to traverse the hole in the block. Oh yeah, when you are done, the block and sphere are indistinguishable (macroscopically and microscopically) from their condition before you started. Is this possible?

Heat the aluminum and cool the glass.

The linear thermal expansion coefficient (expansion per degree Celsius) for aluminum is between 23 * 10^-6 and 24 * 10^-6 (reference dependant) and the linear thermal expansion coefficient for glass is between 3 * 10^-6and to 9 * 10^-6.

The melting point of aluminum is 660 C. If one heats the aluminum from 20 C (room temperature) to 659 C, this gives an expansion of:

3.00 m * (659 C - 20 C) * 0.000023 = .044 m expansion

The contraction of the glass will have to be at least .006 m.

If one cools the glass to -270 C then one needs glass with the following linear thermal expansion coefficient:

.006 m / (3.05 * (20 C - (-270 C))) = 6.78 * 10^-6

So the glass could fit through the hole with extreme temperature changes for both objects.

Posted by Leming on 2006-12-28 09:32:55