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

In summary: And c+s = 1. Solve for c and s and then you know what the volume ratio is.In summary, a floating bridge pontoon can be constructed using concrete and Styrofoam, with a desired volume ratio to achieve a specific percentage of the overall volume above water. The density of the pontoon must be around 657 kg/m^3 to have 34.3% of its volume above water. The volume ratio of concrete to Styrofoam can be calculated by solving a system of equations using the densities and the desired percentage of volume above water.
  • #1
sona1177
173
1

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?
 
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  • #2
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.
 

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

1. How do you calculate the volume ratio of concrete and styrofoam for a floating bridge pontoon?

The volume ratio of concrete and styrofoam for a floating bridge pontoon can be calculated by dividing the total volume of styrofoam needed by the total volume of concrete needed. This can be determined by first calculating the total volume of the pontoon and then determining the volume of styrofoam and concrete needed to fill that space.

2. What is the importance of calculating the volume ratio of concrete and styrofoam for a floating bridge pontoon?

Calculating the volume ratio of concrete and styrofoam is important because it helps determine the buoyancy and stability of the pontoon. The right ratio ensures that the pontoon will be able to support the weight of the bridge and any additional loads without sinking or tilting.

3. How do you determine the volume of the pontoon?

The volume of the pontoon can be determined by multiplying its length, width, and height. This will give the total volume of the space that needs to be filled with concrete and styrofoam.

4. What factors should be considered when calculating the volume ratio of concrete and styrofoam?

When calculating the volume ratio, factors such as the weight of the bridge, water conditions, and desired buoyancy should be taken into account. The type and density of the styrofoam and concrete used should also be considered.

5. Can the volume ratio of concrete and styrofoam be adjusted for different pontoon sizes?

Yes, the volume ratio can be adjusted for different pontoon sizes. The ratio will be influenced by the size of the pontoon and the weight it needs to support. However, it is important to maintain a balance between the amount of concrete and styrofoam used to ensure the pontoon's stability and buoyancy.

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