1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to Express the Curve of a String Hung Between Two Columns

  1. Aug 22, 2014 #1
    1. Imagine two columns between which is hung a string. The hung string may be expressed graphically and mathematically as a parabola whose nature is exponential. If these columns are moved closer together or farther apart, the hung string becomes more loose or taut according to a trigonometric function both of the length of the string and the distance between the two columns. 1. What is this trigonometric function? 2. Create a general equation which can anticipate the mathematical expression of the parabola based on any combination of string lengths and column distances.



    2. I am not sure of the relevant equations but I believe the nature of the string behaves according to a hyperbolic trigonometric function.



    3. I lack the mathematical aptitude and relevant physics knowledge to provide an attempted solution. Thank you for your help and guidance. Please see my attached photo showing my attempt to visually reproduce this phenomenon.
     

    Attached Files:

  2. jcsd
  3. Aug 22, 2014 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Why do you believe so? I am not saying it is wrong, it would just be of help to know how you argue to come to this conclusion.

    It would also help to know how much physics and maths you do know. The physical principle is not very difficult - the string takes the shape that minimizes its energy. The mathematics involve variational calculus with given constraints. I assume we are considering the string to be non-elastic so that it does not stretch under its own weight (although this could be taken into account for added complexity).
     
  4. Aug 22, 2014 #3

    NascentOxygen

    User Avatar

    Staff: Mentor

    Hi techjumper. Welcome to the famous Physics Forums. :approve:

    Much has been written about wires strung between supports. http://en.m.wikipedia.org/wiki/Catenary
     
  5. Aug 22, 2014 #4

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    I'm not sure the solver is expected to go through that. The OP states that it is a parabola. From the further remark
    it would appear that the ends of the string are to be taken to be at the same height.
    That should be enough to solve the problem without calculus.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: How to Express the Curve of a String Hung Between Two Columns
Loading...