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Here's a picture: There is a planet where there is no air, and nothing else there at all except the force of gravity and a surface. On this planet, there is a single post, placed perfectly perpendicular to the ground. Now imagine a circular cloth, made out of a material that doesn't experience any forces other than gravity, electromagnetic force between atoms, and the strong nuclear force. Lets say you dropped this cloth from about a foot above the post. The cloth is perfectly flat and is not wrinkled in any way.

How would the cloth drape/fold over the post?

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closed as off-topic by ACuriousMind, Kyle Kanos, innisfree, tom, Neuneck May 5 '15 at 12:10

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  • $\begingroup$ Does the Planet rotate on its axis, if so what is the latitude? Does the cloth fall so that the center of the circular cloth falls on the post? Is here any solar wind? $\endgroup$ – user78939 May 3 '15 at 18:11
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    $\begingroup$ This is your second "assume unphysical symmetry and then then try to disambiguate the situation with physics" question. The answer to these is always going to be the same: you will not actually have that level of symmetry and the system is sensitive to the atomic scale asymmetries that are present. $\endgroup$ – dmckee May 3 '15 at 18:13
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    $\begingroup$ I'm voting to close this question as off-topic because you are asking an open-ended, hypothetical question: “What if ______ happened?” which is additionally about a situation that will not occur in reality. $\endgroup$ – ACuriousMind May 3 '15 at 18:26
  • $\begingroup$ What is the location of the post in relation to the cloth? $\endgroup$ – LDC3 May 3 '15 at 18:56
  • $\begingroup$ @LDC3 the post is directly below the center of the cloth. $\endgroup$ – Tdonut May 3 '15 at 18:58
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Original facetious answer involving a ghost cloth

Since the material

doesn't experience any force other than gravity

the cloth will fall through the post, through the planet, come out the other side and then fall again. It will oscillate about the planet's centre, exhibiting perfectly undamped simple harmonic motion, assuming the planet has constant density with radius.

You need the cloth's atoms to experience electromagnetic forces if you want it to be unable to pass through the post, and probably want the constituents of their nuclei to experience the strong nuclear force as well so they behave in a way that's at least somewhat reasonable...

Answer to corrected question

If the top of the post is larger than the cloth (so it's basically a table) and the cloth is dropped from a perfect horizontal alignment, it will maintain its horizontal alignment as it falls.

Ignoring quantum uncertainty in atomic positions & assuming the cloth has cooled to absolute zero given the lack of any other energy sources (including no cosmic microwave background at 3K) in this universe, so its atoms are not vibrating, every atom will make contact with the post at the same time and potentially bounce back directly upwards. Depending on the coefficient of elasticity between the post and the cloth's atoms, the cloth will rebound some height and then fall again. If the coefficient of elasticity is 1, the cloth will return to its original height before falling again and the bouncing will continue forever. If it's less than 1, the bouncing will gradually die away until the cloth's gravitational potential energy has been converted to heat in the post and cloth, which will then be radiated into the vacuum.

If we take into account quantum uncertainty and/or classical vibrations of atoms for the cloth not at absolute zero, roughly the same thing happens, except that there will be some differences between neighbouring atoms' touchdown times. However, all this chaos will only be apparent over extremely small scales (~1 atomic diameter) and so on the scale of the cloth itself would cancel out and give no significant difference in behaviour (ignoring the possibility of some fancy effects which can happen at or near absolute zero, like superfluid helium, since you haven't mentioned the chemical constitution of the cloth).

If the cloth lands on the edge of the post it will slide off and land on the ground, assuming this cloth doesn't experience friction. If it does experience friction then it may fold over the edge of the post and stay there or slide off, depending on whether product of the coefficient of static friction between the cloth and the post and the weight of the cloth on the post is greater than the weight of the cloth hanging over the edge.

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