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Catenary - rope hanging between poles

  1. Dec 28, 2009 #1
    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. jcsd
  3. Dec 28, 2009 #2
    Re: Catenary

    How about f(a) = a cosh(b/a) - a - S
  4. Dec 30, 2009 #3
    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
  5. Dec 30, 2009 #4
    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
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