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homework02 (1) - Introduction to Computers and Engineering...

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Introduction to Computers and Engineering Problem Solving Spring 2005 Problem Set 2: Telephone cable height Due: 12 noon, Session 8 1. Problem statement Telephone, electrical and cable TV cables are hung from utility poles in most areas. The figure below shows an example: y y min Pole Pole Cable (0,0) x The cable has a uniform weight w (Newtons/meter or N/m or kg/sec 2 ) per unit length. The differential equation, derived from force balance in the x and y directions, for the height y of the cable as a function of x is: 1 2 d 2 dy y w (1) + = 2 T dx dx where T= tension force along the cable (Newtons). The solution to the differential equation is: 1.00 Spring 2005 1/5 Problem Set 2
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y = T w cosh wx T + y min T w (2) where the hyperbolic cosine, cosh(x), is defined as x x ) cosh( x ) = ( 5 . 0 e + e (3) 2. Problem objective Your program will compute the tension T in a cable that is strung between two poles at positions +x and –x, each having a height of y. Since the geometry is symmetric, we only need to consider the pole at +x; the solution for x<0 will be the same. Your program must compute T from the following equation, obtained by rewriting equation (2) above: T f ) ( = y T w cosh wx T y min + T w (4) By finding a zero or root of f(T) (The value of T for which f(T) == 0), we will find a value of T that is consistent with the input values of x, y, w and y min . Details are given in section 3 below; you will use the bisection method to find the root.
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