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Mechanics: 1. A rope of constant density  (mass per unit length) hangs in the gravitational...

Mechanics:

1. A rope of constant density  (mass per unit length) hangs in the gravitational field between two points A(x1,y1) and B(x2,y2). The length of the rope is not subject to any length constraints. Find the shape of the curve, assuming that the potential energy of the rope takes a minimum.

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Answer #1

In equilibrium, the rope takes such a shape that minimizes its potential energy in the gravitational field. Using the calculus of variations,Lets determine the equilibrium shape of the rope y(x) in a general form.

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