In many locations, such as Lake Washington in Seattle, floating bridges are pref

Question

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 64.1% of its overall volume above water?

Explanation / Answer

Archimedes' principle is the law of buoyancy. It states that "any body partially or completely submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body." The weight of an object acts downward, and the buoyant force provided by the displaced fluid acts upward. If these two forces are equal, the object floats.

Hence, wt. of water displaced = (1-0.641)*(Vc+Vs)*1000*g          [density of water=1,000 kg/m

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