Buoyancy Force and Pressure: A Thought Experiment

[Darth Frodo]

I may be completely out of whack here but this kept me up last night...

Suppose a cork from a wine bottle is taken down to a depth of X metres. Since cork is less dense than water it will obviously float to the surface. I was thinking about manipulating the formulae.

Buoyancy force = Vρg

Pressure = Force/Area $\Rightarrow$ Force = ρghA

Is there a point in the liquid where ρghA = Vρg and the cork remains stationary.

hA = V


My physics teacher said I am completely off track (I'm beginning to agree with her because it's extremely non intuitive) but never gave me a real reason as to why...


Any help appreciated, thanks.

 

[sandy.bridge]

For an object to remain stationary, an external force antiparallel to the Bouyant force and equal in magnitude would be required. However, the Bouyant force increases with depth, and therefore, delving deeper below the surface only increases the external force required to remain stationary.

 

[Darth Frodo]

How does the buoyancy force increase with depth?

 

[sandy.bridge]

There are two factors I can think of: temperature as one descends deeper, and the density of the water.

 

[Darth Frodo]

What if we assume the liquid is uniform?

 

[sandy.bridge]

Then the Bouyant force will remain constant. However, you indicated that the object floats; thus, if it floats at point A due to the Bouyant force, it does so at point B as well since Bouyant force will remain constant.

 

[Darth Frodo]

But is there not a greater force pressing down on the cork as it's depth increases

 

[Darth Frodo]

Wait, the pressure increases with depth, therefore so does the force, and it acts in all directions... thanks you really made me think about the problem