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A cube of oak wood with very smooth faces normally floats in water. Suppose you submerge it completely and press one face flat against the bottom of a tank so that no water is under that face. Will the block float to the surface? Is there a buoyant force on it? Explain.

My thoughts:

  1. Buoyant force is a well known consequence of pressure difference across fluids, and if there's no fluid under the object then there should be no buoyant force?

  2. Practically speaking, the block should rise to the surface again.(I tried it) However, according to my understanding of fluid mechanics, as long as there is no net upward force on the block, it can't start moving upwards

Could someone please explain this, and also tell whether buoyant force really does vanish if the block is pushed to the bottom of the vessel?

Thanks!

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    $\begingroup$ Yes, if there is a perfect seal. This is exactly how suction cups work, except with air instead of water. $\endgroup$ – knzhou Dec 8 '17 at 23:27
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The question is posed as a thought experiment. So arguing with any complications due to limits of technology doesn't help in answering it.

The answer is yes. When you evacuate the space between the object and the bottom of the water vessel, there is no buoyancy on the object (which goes upward). There is however a net resultant down force on the object due to the water pressure difference between the top and the bottom of the object, pushing it down.

What complicates the matter (adding a little more reality to the thought experiment) is that the water to the left and right of the object exerts a pressure near the bottom which will make water flow underneath it. This then creates the pressure difference that causes the object to move up. But that's not really hydrostatics anymore.

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The practical problem is the requirement that the block and tank have to have "very smooth" faces. A normal block of wood does not meet this requirement, so it can't form a seal with the bottom of the tank. Water can still get under the block and push it upwards.

Try the experiment with a plunger. The wood and rubber float, but you will be able to get it to stick to the bottom of a tank of water. Once the bell is pressed to the bottom, the rubber keeps any more water from getting under it. The water pressure above the plunger presses the plunger into the bottom, making it stick.

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  • $\begingroup$ So in this case, as there is no water below the block; its weight and pressure due to water above it is balanced by the normal force from the vessel? $\endgroup$ – arya_stark Dec 8 '17 at 4:32
  • $\begingroup$ Yes, although the normal force also has to balance the force of gravity on the block (just to be complete). $\endgroup$ – Mark H Dec 8 '17 at 5:47

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