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Let's say a 10N cube (in air, on Earth) rests flat on a scale at the bottom of a tank of water, and the scale reads 8N, so there is 2N of buoyant force on the cube. How does the buoyant force manifest itself on the cube? I assume the force is normal to the surface of the scale, but if there isn't any water under the cube, how does the water push up on the cube?

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    $\begingroup$ You should have a sketch. $\endgroup$
    – enbin
    May 6, 2019 at 20:34

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If the system is constructed in such a way that no water can get under the cube, then there will not be a buoyant force on the cube. The net force on the cube will result from the pressure of the water pushing down on its upper surface, and this force will point downward on the cube.

One way to understand this on an intuitive level is to think of suction cups. Suction cups work precisely because there is a partial vacuum on one side of the cup and atmospheric pressure on the other side holding them down.

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    $\begingroup$ Nice analogy :-) $\endgroup$ Apr 3, 2013 at 6:07
  • $\begingroup$ Interesting -- so if I throw a cube of iron into a pool with a flat surface, I can generally assume that there will still be a layer of water under the cube when it rests on the bottom? Or, is there going to be some extra force necessary to "release" the cube from the bottom? (i.e., similar to a static friction-->kinetic friction break) $\endgroup$ Apr 3, 2013 at 6:12
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    $\begingroup$ @ChrisGregg I speculate it's safe to assume that there will usually be a layer of water under the cube. $\endgroup$ Apr 3, 2013 at 14:50
  • $\begingroup$ @ChrisGregg There must be enough water to generate buoyancy. Water must be able to flow in to generate buoyancy, and no buoyancy can be generated without flowing in. Too narrow will not flow in. $\endgroup$
    – enbin
    May 6, 2019 at 21:01
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    $\begingroup$ I found a related article in "European Journal of Physics" Using surface integrals for checking Archimedes' law of buoyancy F M S Lima Published 22 November 2011 • 2012 IOP Publishing Ltd European Journal of Physics, Volume 33, Number 1 , iopscience.iop.org/article/10.1088/0143-0807/33/1/009 $\endgroup$ Sep 24, 2020 at 8:33
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This interesting problem, the so-called "bottom case", was discussed and solved by me in the last section of the paper mentioned above by Adamenko (Eur.J.Phys.). That theoretical result has been confirmed experimentally in a more recent work, namely

https://www.scielo.br/j/rbef/a/w7VfCBmYgN46Wm77ttMmQ7d/?lang=en

See the references therein for other independent experiments revealing the same "downward" buoyant force!

Prof. Fabio M. S. Lima

Institute of Physics, University of Brasilia

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    $\begingroup$ Your answer could be improved with additional supporting information. Please edit to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center. $\endgroup$
    – Community Bot
    Jan 21 at 2:50
  • $\begingroup$ +1, thanks for the excellent work. I do agree with Community, you could have the leading answer if you add more detail. $\endgroup$ Jan 22 at 5:09

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