## Buoyancy problem: Deriving an equation for volume of a floating object

1. The problem statement, all variables and given/known data
The problem consists of a ball almost completely submerged. The exact question is:
"An object with density ρO and mass m is floating in a pool of fluid with density ρF. Derive an expression for the volume of the object that is above the fluid."

2. Relevant equations
Density of object=mass/volume
Density of fluid= mass fluid/volume fluid

3. The attempt at a solution
I have no idea where to begin.
I know this looks like i'm just fishing for a free answer, but I am not. I tried setting the buoyant force to the (mass of the fluid displaced) * (g) but I don't know how to relate this to the other variables. Any help is greatly appreciated, thanks.

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 would the buoyant force equal the downward force? ie, would Fb=mg?

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 Quote by Hairy Biped 1. The problem statement, all variables and given/known data The problem consists of a ball almost completely submerged. The exact question is: "An object with density ρO and mass m is floating in a pool of fluid with density ρF. Derive an expression for the volume of the object that is above the fluid." 2. Relevant equations Density of object=mass/volume Density of fluid= mass fluid/volume fluid 3. The attempt at a solution I have no idea where to begin. I know this looks like i'm just fishing for a free answer, but I am not. I tried setting the buoyant force to the (mass of the fluid displaced) * (g) but I don't know how to relate this to the other variables. Any help is greatly appreciated, thanks.
 Quote by Hairy Biped would the buoyant force equal the downward force? ie, would Fb=mg?
Yes, Fb would have to equal mg if the ball is at rest (i.e. not accelerating). And, as you said, Fb is g times the mass of the displaced fluid.

## Buoyancy problem: Deriving an equation for volume of a floating object

so if bouyant force equals mg, then the mass of the displaced fluid equals the mass of the ball? If so then (density water)(Volume displaced)=(density ball)(volume ball)?

 Tags buoyancy, density, volume