# Force and pressure equation

ML

## Main Question or Discussion Point

I was wondering a couple of things about an object of mass 20kg and volume 1m3 being submerged under say 50 metres of water. Basically I'm looking for the two equations that would help me figure out the force and pressure surrounding the object to make it rise.

similar to that of a fishermans' bhoy being submerged.

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LURCH
The bouyancy should be the same at 50m as it is at the surface, since bouyancy is dependant on the mass of the fluid displaced. Although the pressure being exerted on the sides of the object would be much greater, this would be equally true from all directions, so the extra force pushing up from underneath is the same as the extra force pushing down from above.

But so long as the object remains 1m3 in volume, it will displace 1m3 of water, and the mass of that water will be the same at depth as it is on the surface because despite the great pressure, water doesn't compress (well, not much, anyhow). So the object displaces 1,000kg of water at any depth.

jcsd
Gold Member
Lurch, have you ever been scuba diving? What you find happens is that the air in the object gets compressed due to the pressure and your buoyancy decreases with depth. IIRC you find that the air in an object will occupy 10/(D + 10) times volume than it will at the surface (where D is the depth).

LURCH
Quite right, jc. You don't mind if I call you that, do you? Makes me feel like I'm in the movie business.

Anyways, that's why I made a point of it to mention that the object's bouyancy remains the same "So long as the object remains 1m3 in volume". But it's good to reinforce the pointthat if the object gets shrunk by the pressure, it will of course become less bouyant.

jcsd
Gold Member
It's just that buoyancy is important to scuba divers (I got my advanced PADI qualification this Summer) and when you start to descend you find the deeper you go the faster you go down as you lose buoyancy.

ML
.

I appreciate these replies but i was focusing more on the actual force that the buoy would be capable of pulling upwards or an equation to help me determine it.

Integral
Staff Emeritus
Gold Member

Originally posted by ML
I appreciate these replies but i was focusing more on the actual force that the buoy would be capable of pulling upwards or an equation to help me determine it.
The boyuant force is the difference between the mass of water displaced and the mass of the object.

Integral
Staff Emeritus
Gold Member

Originally posted by ML
I appreciate these replies but i was focusing more on the actual force that the buoy would be capable of pulling up wards or an equation to help me determine it.
The buoyant force is the difference between the mass of water displaced and the mass of the object.

Your 1 m3 displaces 1000kg of water so experiences buoyant force equivalent to the weight of 1000kg of water B=mg= 9.8x103 N, the body has a weight of 9.8*20N. The difference is the weight required to keep the body submerged.

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