# Changes in force required to push buoyant object under liquid/water

If we have buoyant object, for the sake of this question, let's say it is a cylinder, 1" in diameter and 4" long. This cylinder is completely sealed so not liquid can enter and we have it arranged vertically. Also, let's assume it has little weight to it (meaning it is hollow and empty and the only weight to it is the material it is made of, like a float).

With that visual setup, the question is, imagine I have a deep tub of water. As I start to submerge this float but pushing down on the top of it, I know it is going to take more force pushing down on top, to submerge it the deeper I go. So, if only the first 1" is submerged, that would take less force on the top than if I submerged to 2". That is correct, right?

Now, to follow up on that, once the item is completely submerged (in this case, all four inches of it are under water) does the force required max out and become consistent? In other words, If I am holding it 8 inches underwater versus 16 inches under water, would that take the same amount of force now that I am fully submerged?

Thanks!

• Archimedes' principle : Archimedes' principle indicates that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and it acts in the upward direction at the centre of mass of the displaced fluid. See also my answer here (user82794) : physics.stackexchange.com/questions/196840/… Dec 14 '16 at 20:44

## 1 Answer

The force required to push something underwater can be found from Archimedes principle:

$F_B = p_w V g$

Where $F_B$ is the buoyant force, $p_w$ is the density of water (1g/ml), $V$ is volume of the water displaced, and $g$ is gravity. The key here is $V$.

If the cylinder is pushed halfway under the water, then the volume of water displaced is equal to half of the volume of the cylinder. If it's pushed completely under the water, then the volume of water displaced is equal to the volume of the cylinder, and so on. (Let's assume this cylinder is rigid and won't crumple from the water pressure) As long as the cylinder is completely submerged, the volume of water displaced does not change, so the buoyant force doesn't change, no matter how deep it is.

So in conclusion, yes, as the cylinder gets deeper, the force required to push it down increases until it become completely submerged. At that point it does not require any extra force to push down the further it goes.

• Thank you. So, if I want to know the depth I have two options. I either can use another method like hydrostatic pressure or something similar OR I have to make the length of the cylinder float long enough that it will never be fully submerged so I can measure the force required to push it and as it goes deeper, the force required increases and I can get depth submerged from that. Dec 14 '16 at 21:07