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
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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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 Spring '05
 GeorgeKocur
 Coaxial cable, cable TV cables

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