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djeitnstine
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This (textbook) question seems so simple yet I have been having the hardest time solving it :S I know there's something completely obvious I'm missing.
A styrofoam slab has a thickness h and density \rho_{s}. 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.
\Sigma F=F_{buoyant}-Mg=0
F_{buoyant}=Mg
F_{buoyant} = \rho_{f}ghA
(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 \Sigma F= (\rho_{f}-\rho_{o})V_{o}g
Where \rho_{o} is the density of the object
I don't even know. I wrote out a bunch of stuff. I know the density of water is 1.00 (10^{3} \frac{kg}{m^{3}}). 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).
\Sigma F= F_{buoy} - F_{board} - F_{swimmer} = 0
Also a simple manipulation showed that (\rho_{f}-\rho_{s}) \Delta h A = m_{s}. I think is right?
Honestly I think some more numbers are missing :S
Homework Statement
A styrofoam slab has a thickness h and density \rho_{s}. 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
\Sigma F=F_{buoyant}-Mg=0
F_{buoyant}=Mg
F_{buoyant} = \rho_{f}ghA
(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 \Sigma F= (\rho_{f}-\rho_{o})V_{o}g
Where \rho_{o} 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 1.00 (10^{3} \frac{kg}{m^{3}}). 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).
\Sigma F= F_{buoy} - F_{board} - F_{swimmer} = 0
Also a simple manipulation showed that (\rho_{f}-\rho_{s}) \Delta h A = m_{s}. I think is right?
Honestly I think some more numbers are missing :S