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Unformatted text preview: MAE 101: Homework 1 Solution October 5, 2011 Problem 4 The light fixture of weight W is suspended from a circular arch by a large number N of equally spaced cables. The tension T in each cable is the same. Show that T = πW 2 N . Strategy: Consider an element of the arch defined by an angle dθ measured from the point where the cables join: Since the total angle described by the arch is π radians, the number of cables attached to the element is (N/ pi ) dθ . You can use this result to write the equilibrium equations for the part of the cable system where the cables join. Solution: The angle between any cable and the positive x axis is kδθ , where k = 0 , 1 , 2 , 3 ...K , where K = ( π δθ ) is the number of intervals, one less than the number of cables. The tension in the k th cable is T k =  T k  ( i cos kδθ + j sin kδθ ). The weight is W = 0 i  W  j . The equilibrium conditions are X F = W + K X k =0 T k = 0 where N is the number of cables....
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 Spring '08
 ORIENT
 Statics, Force, Sin, tk, sin kδθ

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