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 θ1 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 θ1, m, and g.
b) Find the angle θ2 in terms of θ1, that the sections of the string between the outside butterflies and the inside butterflies form with the horizontal.

Answer 1

figure?

Answer 2

Part (b) seems a bit too easy. The horizontal components of the tensions the outermost masses are given by \(l\cos\theta_1\). The horizontal component of the tension between the leftmost and second leftmost masses is \(l\cos\theta_2\), so you have
\[l\cos\theta_1=l\cos\theta_2~~\iff~~\cos\theta_1=\cos\theta_2~~\iff~~\theta_2=\cos^{-1}(\cos\theta_1)\]
Whether this means \(\theta_1=\theta_2\), I'm not sure...

Answer 3

since cosine of the angles are equal, \(\theta_1=\theta_2\). It is pretty sure it pass thru' criteria of similar triangles... http://www.mathsisfun.com/geometry/triangles-similar-finding.html