Floating Bed Problem: Calculate Volume Under Water

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To determine the fraction of a floating bed's volume submerged in seawater, the problem involves comparing the densities of the bed and seawater. The bed has a density of 765 kg/m^3, while seawater has a density of 1035 kg/m^3. By applying the principle of buoyancy, the equation 765 kg/m^3 * Volume * gravity = 1035 kg/m^3 * V * g is used to find the submerged volume fraction. The calculated fraction of the bed's volume under the water is approximately 0.739. This approach confirms that the buoyancy principle is correctly applied to solve the problem.
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Homework Statement


There is a large bed floating in sea with the density of 765 kg/m^3. What fraction of the bed's volume will be under the surface of the water? The density of sea water is 1035 kg/m^3.

Homework Equations


Fb = Density * v * gravity


The Attempt at a Solution


I know its a buoyancy problem, but i have no idea where to get started. i can't find the Fb b/c volume's not given. maybe i have to set them equal to each other?
so
765 kg/m^3 * Volume * gravity = 1035 kg/m^3 * V * g
so it woulbd be .739% of the volume.
It seems too easy or is this right?
Thank you!
 
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Call the fraction of the volume that is under water f.

Then the buoyant force is

BF = \rho_{water}f V g

where V is the entire volume of the bed. Then the weight of the bed in terms of its density and volume is ...

so for the bed to float ...
 

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