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| The Giant Marble (Posted on 2006-12-28) |
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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?
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Submitted by Kenny M
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Rating: 4.0000 (2 votes)
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Solution:
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Assuming you start at room temperature (20C), heat the aluminum to block slowly to 650C (the melting point is ~660C). Thermal expansion will increase the size of the hole to just larger than 3.045m. Meanwhile, slowly (very slowly – so as to cause no distortion or cracking) cool the sphere to -220C. This will shrink the diameter of the sphere to just under 3.045m. Any small force will allow the sphere to roll thorough the hole. Do it quickly, since the hot aluminum will reheat the sphere and it might get stuck!
Equations for Thermal expansion:
dL / L = A* dT where
L = original length, dL = length change, A = coefficient of Thermal expansion, dT = Temperature Change
From Wikipedia
Aluminum: A = 24e-6 per deg C Glass: A= 9-e6 per deg C
dL (Al) = L*A*dT = 3*24e-6*(650-20) = .04536 ; New Diameter of Hole = 3.04536
Similarly for the Glass Sphere:
dL(Glass) = 3.05*9e-6 (20-220) = -0.00459 ; New diameter = 3.04451
The glass sphere will now fit in the hole. After it is through, let both pieces return to room temperature.
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