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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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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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Nice analogy :-) –  John Rennie Apr 3 '13 at 6:07
    
@JohnRennie Thanks Rennie! –  joshphysics Apr 3 '13 at 6:09
    
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) –  Chris Gregg Apr 3 '13 at 6:12
    
@ChrisGregg I speculate it's safe to assume that there will usually be a layer of water under the cube. –  joshphysics Apr 3 '13 at 14:50
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