What Is the Volume Ratio of Concrete to Styrofoam for a Floating Bridge Pontoon?

[sona1177]

Homework Statement

In many locations, such as Lake Washington in Seattle, floating bridges are preferable to conventional bridges. Such a bridge can be constructed out of concrete pontoons, which are essentially concrete boxes filled with air, Styrofoam, or another extremely low-density material. Suppose a floating bridge pontoon is constructed out of concrete and Styrofoam, which have densities of 2200 kg/m3 and 50.0 kg/m3. What must the volume ratio of concrete to Styrofoam be if the pontoon is to float with 34.3% of its overall volume above water?

Homework Equations

Fbuoyancy-mg=o

The Attempt at a Solution

Fbuoy-mg=o
p(fluid)gV(displaced fluid)=p(platoon)g(Vplatoon)
Vfluid/Vplatoon=p(platoon)/p(fluid)=.343
so p(platoon)/p(fluid)=.343
p(plattoon)=p(fluid) *.343
1000 * .343=343 kg/m^3=density of platoon.

Where do i go from here?

 

[Delphi51]

I didn't understand that! But I think something has gone wrong.
Say the density was half that of water. Then 50% of the pontoon would stick out above the water. If you want a little less to stick out (34%), it would be a little more dense then that. More than half the density of water (1000) - probably 657 rather than 343.

Say you have 1 cubic meter of pontoon. Let c be the volume of the concrete and s the volume of styrafoam. Then
c*2200 + s*50 = 657.