# Bouyancy Force

Discussion in 'MCAT Study Question Q&A' started by vapremed, May 29, 2008.

1. ### vapremed 2+ Year Member

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Hi

Fb=p(fluid)V(displaced)g

What if the object isn't submerged? In this case the volume displaced is equal to mg of the object. So is it Fb=p(fluid)m*g(object)*g again?

sorry I think im just confusing myself!

2. ### Kaustikos Archerize It 10+ Year Member

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I am not exactly sure what you meant by V = mg. But if the object isn't submerged, it still exhibits a buoyant force. The only thing, is that the buoyant force isn't at a maximum.

I guess you mean if none of the volume is displaced? then the buoyant force is 0 and the only force is due to gravity. Fb = pVg; Fnet = Fg-Fb. Since V = 0, Fb = 0 and Fnet = Fg = mg.

3. ### Doctor D 10+ Year Member

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Knowing that mg displaced = mg of the object when it is floating will allow you to calculate the volume displaced if you know the density of the fluid. I dont think you can just substitute mg in for volume though. You must convert to volume using the density of the fluid.

4. ### Doctor D 10+ Year Member

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The volume displaced is not equal to the mg of the object. The mg of the object = the mg of fluid displaced.

5. ### auroraboy 2+ Year Member

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In case the object is not submerged:

Buoyant force = (density of fluid)*(volume of submerged object)*g

This should make sense intuitively since total weight of object, W = m*g

m here should be equal to (density of object)*(total volume),

so W = (density of object)*(total volume)*g

when submerged, the object is floating... buoyant force = weight of object(W)

thus implying,
(density of fluid)*(volume of submerged object)*g = (density of object)*(total volume)*g

simplifying this,
(volume of submerged object)/(total volume) = (density of object)/(density of fluid)

example: if an object is 50% submerged, left hand side is reduced to (1/2), thus implying (density of object)/(density of fluid) = .5 or the object is half as dense as the fluid its floating in...

In case the object is fully submerged:

if density of object is equal to density of fluid,
using following force representation,
(density of fluid)*(volume of submerged object)*g = (density of object)*(total volume)*g,
simplifying this,

(volume of submerged object)/(total volume) = 1
Entire object is in the fluid and it could be anywhere within the fluid since densities are exactly same.

if density of object is greater than density of fluid,

the buoyant force would not be enough to support weight of the object, hence the object sinks down.

Bottom line, its always a matter of difference in densities...
object is less dense than fluid => floats
object is more dense than fluid => sinks down

hope this helps!