# Homework Help: Catenary - rope hanging between poles

1. Dec 28, 2009

### Jonnyb42

1. The problem statement, all variables and given/known data

Problem is regarding approximating the value of a in y= a cosh(x/a) using Newton's method, and then use a to find the length of the rope.
That equation represents the curve formed by a rope hanging with it's ends attached to poles at a distance 2b.
(cosh() = hyperbolic cosine)

distance between poles = 2b = 400 ft.
sag = S = 30 ft.

2. Relevant equations

(previously proven eqns)

L = 2 a sinh(b/a)
where L is the length of the rope
a is a physical constant
and 2b is the distance between the poles that the rope is hanging from

S = a cosh(b/a) - a
where S is the sag (vertical distance between highest and lowest points on the rope)
a is a physical constant
2b is distance between poles

3. The attempt at a solution

I am really not sure how to do this, as I do not know how/why Newton's method could be used to get a value for a.
Also, they gave a hint, a clip from the Calc book I am reading: "[Hint: First let u = 200/a]"

2. Dec 28, 2009

### JaWiB

Re: Catenary

How about f(a) = a cosh(b/a) - a - S

3. Dec 30, 2009

### Jonnyb42

Re: Catenary

Is that correct? I didnt put that under at attempted solution because I thought it was not even right since I tried newton's method on it and it wasn't really homing in on a particular number, or perhaps I messed up with something. I also thought I did it wrong because, first of all the book did not give a hint to how many iterations to do and my answer, after about 4 iterations, was 470 and the answer in the book was about 404 something.

Last edited: Dec 30, 2009
4. Dec 30, 2009

### JaWiB

Re: Catenary

Is that your answer for the value of a, or the value of L? Seems to me like it should work. Maybe you should post your attempt