Bouyant force when there is no liquid beneath an object

[Titan97]

Homework Statement

A block floating on water contained in a vessel is pushed inside until it touches the bottom of the vessel and then released. Will the block come back?

Homework Equations

The Attempt at a Solution

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Bouyant force acts because the pressure on the bottom of the block is more than that at the top.

If the block was cubical and its top surface is at a distance $h$ from the surface of water, and had a side length $a$, then the pressure on top will be $P_0+\rho gh$

Pressure on bottom surface will be $P_0+\rho g(h+a)$

Pressure difference = $\rho g a$

Force acting is = $\rho g a\cdot a^2=a^3\rho g$

If the bottom surface of the cube were to touch the bottom of vessel, then there is no water beneth it to exert pressure upwards. So won't the block remain in the bottom even if its density is less than that of the liquid?

 

[SDewan]

The block was floating "on the water" initially. So the buoyant force exerted by the water at this position was equal to the weight of the block. Equilibrium was established.
So at no position other than the initial position will the block be in equilibrium.
Hence it will rise back up to its initial position after you take it to a certain depth.

 

[Buzz Bloom]

If the bottom surface of the cube were to touch the bottom of vessel, then there is no water beneth it to exert pressure upwards. So won't the block remain in the bottom even if its density is less than that of the liquid?

Hi Titan:

If the cube and the bottom are perfectly smooth, and someone forces the cube so that the bottom side of the cube was pressed against the bottom, then is there any substance between the bottom side of the cube and the bottom of the vessel? If not, is this the same as a vacuum? Compare this with a somewhat rough cube and/or a rough bottom.

Hope this helps.

Regards,
Buzz

 

[Titan97]

So its same as a suction pump.

 

[Buzz Bloom]

So its same as a suction pump.

Hi Titan:

I am not sure what the antecedent is of "its".

Regards,
Buzz

 

[Titan97]

The situation. The block attached to the bottom.

 

[Buzz Bloom]

So its same as a suction pump.

The situation. The block attached to the bottom.

Hi Titan:

I am still having a problem with the phrasing. Supposed I snugly put the cube into a vertically oriented square-shaped cylinder and lowered the cylinder to the bottom of the tank. Then I used a suction pump to remove all the water in the cylinder below the cube. The vacuum in the cylinder below the cube would cause the cube go to down the cylinder to the bottom of the tank.

Is this the meaning you have in mind for the quotes above?

Regards,
Buzz

 

[Titan97]

Have you seen suction cups? The cube being stuck to the bottom of the vessel is just like a suction cup stuck to a wall. There is no medium beneath cube.

 

[Buzz Bloom]

Have you seen suction cups? The cube being stuck to the bottom of the vessel is just like a suction cup stuck to a wall. There is no medium beneath cube.

Hi Titan:

That is mostly right, but not completely correct. A suction cup has tension in it that maintains the (partial) vacuum which helps make the suction stable. The cube pressed onto the bottom doesn't have this, and any small disturbance of the cube will allow water to get beneath it, and it will rise. Heisenberg's Uncertainty Principle implies that there is a positive probability that after a sufficient time quantum effects will allow water to get underneath the cube and let it rise.

Regards,
Buzz