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

[Hairy Biped]

Homework Statement

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."

Homework Equations

Density of object=mass/volume
Density of fluid= mass fluid/volume fluid

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.

 

[Hairy Biped]

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

 

[Redbelly98]

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Welcome to Physics Forums

Homework Statement

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."

Homework Equations

Density of object=mass/volume
Density of fluid= mass fluid/volume fluid

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.

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

Yes, F_b would have to equal mg if the ball is at rest (i.e. not accelerating). And, as you said, F_b is g times the mass of the displaced fluid.

 

[Hairy Biped]

so if buoyant 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)?