Three strings are tied together. They lie on top of a circular table and the kno

Question

Three strings are tied together. They lie on top of a circular table and the knot is exactly in the center of the table, as shown in the figure (top view). Each of the strings hangs over the edge of the table, and a weight is supported from it. The masses m1 = 3.90 kg and m2 = 5.20 kg are known. The angle ? = 81.2 degrees between strings 1 and 2 is also known. What is the angle ? between strings 1 and 3? (Please specify your answer in degrees.)

Three strings are tied together. They lie on top of a circular table and the knot is exactly in the center of the table, as shown in the figure (top view). Each of the strings hangs over the edge of the table, and a weight is supported from it. The masses m1 = 3.90 kg and m2 = 5.20 kg are known. The angle ? = 81.2 degrees between strings 1 and 2 is also known. What is the angle ? between strings 1 and 3?

Explanation / Answer

equating forces,

m3g cos(?+? -180) = m2g + m1g cos?

m3g sin(?+? -180) = m1sin?

substituting values

m3g(cos(?-98.8)) = 50.96 + 5.85 = 56.81

m3g(sin(?-98.8)) = 3.85

dividing both we get,

tan(?-98.8) = 3.85/56.81 = 0.067769

so (?-98.8) = 3.877 degrees

so ? = 102.677 degrees

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