- #1

djeitnstine

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## Homework Statement

A styrofoam slab has a thickness h and density [tex]\rho_{s}[/tex]. When a swimmer of mass m is resting on it, the slab floats in fresh water with its tip at the same level as the water surface. Find the area of the slab.

## Homework Equations

[tex]\Sigma F=F_{buoyant}-Mg=0[/tex]

[tex]F_{buoyant}=Mg[/tex]

[tex]F_{buoyant} = \rho_{f}ghA[/tex]

(Archimedes Principal: Any object completely or partially submerged in a fluid experiences an upward buoyant force whose magnitude is equal to the weight of the fluid displaced by the object)

When totally submerged [tex]\Sigma F= (\rho_{f}-\rho_{o})V_{o}g[/tex]

Where [tex]\rho_{o}[/tex] is the density of the object

## The Attempt at a Solution

I don't even know. I wrote out a bunch of stuff. I know the density of water is [tex]1.00 (10^{3} \frac{kg}{m^{3}})[/tex]. Of course I tried substituting and that gets me no where. I tried making a free body diagram and all that says is that the Buoyant force is equal to weight of the swimmer and the board (duh).

[tex]\Sigma F= F_{buoy} - F_{board} - F_{swimmer} = 0[/tex]

Also a simple manipulation showed that [tex](\rho_{f}-\rho_{s}) \Delta h A = m_{s}[/tex]. I think is right?

Honestly I think some more numbers are missing :S