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Mechanical equilibrium

An artist friend of yours needs help hanging a 500 lb sculpture from the ceiling. For artistic reasons, she wants to use just two ropes. One will be 30 degrees from vertical, the other 60 degrees. She needs you to determine the smallest diameter rope that can safely support this expensive piece of art. On a visit to the hardware store you find that rope is sold in increments of 1/8 of an inch diameter and that the safety rating is 4000 pounds per square inch of cross section.

What size (diameter) rope should you buy?


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The solution is 3 pages long including a diagram and full derivations of the equations.