Classical Mechanics Level 5

Consider an n - pod consisting of \(n\) uniform bars (legs) of length \(a\) and mass \(m = 0.8 kg\) , freely jointed at point A. The middle points of the legs of the n-pod are joined by \(n\) massless strings of length \(b\) . The n-pod rests on a smooth surface while supporting a camera of mass \(M = 1 Kg\) . For \(n=3\), figure is:

For \(\frac{a}{b} = \eta\), find an expression for tension in the strings. Considering this expression for \(\eta = 4\), let the maximum value of \(n\) for which tension \(T\) in the strings is real be \(N\), and the tension in the strings for \(n=N\) be \(T\) (in newtons) , find \(T \times N\) rounded to the nearest integer.

Details and assumptions:-

  • \(g = 9.8 m/s^2\)

  • The arrangement is symmetric , i.e. the points where legs meet floor form a regular n-gon

  • This problem has been inspired by a past brilliant problem Tripod


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