Fully submerged block in a pool of water

[adjurovich]

Let’s say we let a block of iron sink into the water and it reaches the bottom.

Would the force pushing on body towards the bottom be: $F_{downwards}=mg+F_P$
where $F_P$ is the force caused by hydrostatic + atmospheric pressure.

The force acting upwards should be then: $F_{upwards}=F_B+N$
Where $F_B$ is buoyancy and $N$ is the normal force (reaction force exerted by the bottom of pool or anything else that’s filled with water).

So these two balance each other: $F_{upwards}=F_{downwards}$

We are assuming that we are dealing with non-viscous ideal fluid. And the block is in full contact with the bottom of pool.

 

[jbriggs444]

Let’s say we let a block of iron sink into the water and it reaches the bottom.

Would the force pushing on body towards the bottom be: $F_{downwards}=mg+F_P$
where $F_P$ is the force caused by hydrostatic + atmospheric pressure.

The force acting upwards should be then: $F_{upwards}=F_B+N$

No. This is not a good list of forces.

Buoyancy and hydrostatic pressure are the same thing. You can use one. Or you can use the other. You should not use them both at the same time.

For example, consider a submarine in the water. You can compute the upward force from water pressure on the bottom surface of the submarine. You can compute the downward force from water pressure on the top surface of the submarine. You can subtract the two. The net of those two forces will exactly match the weight of the water that the submarine displaces. [The appropriate integral of] hydrostatic pressure difference is buoyancy.

If you add the force of buoyancy to the force from hydrostatic pressure difference, you will be counting the same forces twice!

But there is another problem lurking here. What is the texture of the bottom of the iron block?

If free flowing water can make its way under the block so that hydrostatic pressure applies on all sides then buoyancy is applicable. One can summarize hydrostatic pressure as buoyancy. One might assume that some negligible surface area (bumps on the bottom) is subject to non-negligible total normal contact force.

However, if free flowing water cannot make its way under the block then buoyancy is not applicable. [Think of a suction cup]. One can consider hydrostatic pressure on the top of the block only and plain old vanilla total contact force on the bottom. You have clarified that this is the actual situation.

 

[adjurovich]

No. This is not a good list of forces.

Buoyancy and hydrostatic pressure are the same thing. You can use one. Or you can use the other. You should not use them both at the same time.

For example, consider a submarine in the water. You can compute the upward force from water pressure on the bottom surface of the submarine. You can compute the downward force from water pressure on the top surface of the submarine. You can subtract the two. The net of those two forces will exactly match the weight of the water that the submarine displaces. [The appropriate integral of] hydrostatic pressure difference is buoyancy.

If you add the force of buoyancy to the force from hydrostatic pressure difference, you will be counting the same forces twice!

But there is another problem lurking here. What is the texture of the bottom of the iron block?

If free flowing water can make its way under the block so that hydrostatic pressure applies on all sides then buoyancy is applicable. One can summarize hydrostatic pressure as buoyancy. One might assume that some negligible surface area (bumps on the bottom) is subject to non-negligible total normal contact force.

However, if free flowing water cannot make its way under the block then buoyancy is not applicable. [Think of a suction cup]. One can consider hydrostatic pressure on the top of the block only and plain old vanilla total contact force on the bottom. You have clarified that this is the actual situation.

Thanks for help, I get it now!

 

[sophiecentaur]

However, if free flowing water cannot make its way under the block then buoyancy is not applicable.

It's all a matter of the timescale involved and whether or not water can flow in underneath. This is a fun video which 'we' have all seen and it makes the point with air, rather than water.
PS Have you ever stepped out of a wellie boot when you were walking in deep mud? Same thing.