A mobile is formed by supporting four metal butterflies of equal mass m from a s

Question

A mobile is formed by supporting four metal butterflies of equal mass m from a string of length L. The points of support are spaced evenly at a distance l apart as shown in the figure. The string forms an angle 1 with the ceiling at each end point. The center section of the string is horizontal.

a) Find the tension in each section of the string in terms of 1, m, and g.
b) Find the angle 2 in terms of 1, that the sections of the string between the outside butterflies and the inside butterflies form with the horizontal.
c) Show that the distance D between the end points of the string is:

Explanation / Answer

T1=2mg / sin(theta_1)
T2=mg/sin(tan^-1(tan( (theta_1)/ 2 )))
T3=2mg/tan(theta_1)
T4=mg/sin(tan^-1(tan( (theta_1)/ 2 )))
T5=2mg / sin(theta_1)

Part B

tan^-1(tan(theta_1)/2)

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