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Parabolic Curve : Application to Buoyancy

You have been hired as a special consultant by u.s coast guards to evaluate some proposed new design for navigational aids buoys. The buoys are floating cans that need to be visible from some distance away without rising too far out of the water. Each buoy has a circular cross-section (viewed from below) and will be lifted with a superstructure that carries equipment such as lights and batteries. To be acceptable a fully equipped buoys must float with not less than 1.5 feet nor more than 3 feet of freeboard (the distance from the water to the top of the device).

1) A floating object will displace a volume of water whose weight equals the weight of the floating object. (This is Archimedes Principle)
2) Your devices will be floating in salt water whose density is 65.55 lb/ft^3
3) the buoys will be constructed of 1/2 inch thick sheet metal that weights 490lb/ft^3
4) You can estimate an additional 205 lb in weight attributable to welds bolts and so forth.
5) Each bouys will be fitted with a superstructure and equipment weighing a total of 2,000 pounds.
6) Each design will be presented in the form of a curve X = f(y), to be revolved around the Y-axis
Evaluate at least two seperate designs both of which are concave outward.
The graph should be a parabolic with floating cans could be cone shapes.

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Solution Summary

A problem involving buoyancy and parabolas is solved. The solution is detailed and well presented.