Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculating parabola of drooping chain

  1. Mar 25, 2004 #1
    Hi,

    I was giving a pub quiz type quesstion the other day, which I managed to solve without the use of formulae/mathematics, but it got me thinking about how to solve it mathematically too.

    Imagine a chain stretched between two posts, that then droops in the middle, and forms a natural parabola. What are the variables involved and what is the relationship that determines the curve?

    I guess that it would mean calculating for all positions on the chain (using calculus?), in order to give a final curve, but this would require a basic starting formulae stating the relationship.

    So variable would be, for any specific point on the chain:
    Chain tension
    Chain weight
    Chain angle (tangent to curve)

    Any others?
    Any idea on the relationship?

    looking forward to hearing your comments

    thanks,
    Martin
     
  2. jcsd
  3. Mar 25, 2004 #2

    Integral

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You are on the right track. Trouble is the shape is not a parabola, it is a catenary.

    I cannot help you off the top of my head, but this type of analysis can be found in books on Partial Differential equations.
     
  4. Mar 25, 2004 #3

    Chi Meson

    User Avatar
    Science Advisor
    Homework Helper

  5. Mar 25, 2004 #4
    thanks guys, that's great!
     
  6. Mar 25, 2004 #5
    Molydood
    How so?
     
  7. Mar 26, 2004 #6
    Hi,

    'Solve' is perhaps the wrong word. I'll give you the problem then post the answer a little later if required:
    two posts of 4 metre height support a chain of length 6 metres. The chain hangs 1 metre from the floor at its lowest point. How far apart are the posts?
     
  8. Mar 26, 2004 #7

    Chi Meson

    User Avatar
    Science Advisor
    Homework Helper

    AHA! THis is a brain teaser that does not require any knowledge of the catenary! (I've heard this one before, and I never got the chance to discover it for myself, so I won't give it away)
     
  9. Mar 26, 2004 #8
    As Chi Meson said this has nothing to do with physics... but if the said chain hung 2 meters from the floor you couldn't solve it. :smile:
     
  10. Mar 26, 2004 #9

    chroot

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Yeah that brain teaser's pretty dumb... hehe.

    - Warren
     
  11. Mar 26, 2004 #10

    Integral

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I can't believe that I did not see the solution instantly, had to think about it for a few minutes.
     
  12. Mar 28, 2004 #11
    Nice brain teaser. I'll challenge my friends at school. I bet it'll drive them crazy!
     
  13. Mar 28, 2004 #12

    ShawnD

    User Avatar
    Science Advisor

    So how is it solved without using the caternary formula?
     
  14. Mar 28, 2004 #13
    Here's a hint: Draw it to scale.

    cookiemonster
     
  15. Mar 28, 2004 #14

    ShawnD

    User Avatar
    Science Advisor

    It's a tad hard to draw something that fits this equation

    [tex]y = \frac{e^{ax} + e^{-ax}}{2a}[/tex]

    Besides, it aparently can be done without using that formula.
     
  16. Mar 28, 2004 #15
    Heh, start with the posts. Then add in the minimum height off the ground. Calculate a distance or two, like how far the chain is drooping and how long the chain is. The rest comes pretty naturally.

    cookiemonster
     
  17. Mar 28, 2004 #16

    Integral

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    LOL, come on.... Think man.

    Consider the problem statement.

    You are going to hate yourself when the solution pops into your head.
     
  18. Mar 28, 2004 #17

    ShawnD

    User Avatar
    Science Advisor

    The only thing I can think of doing is breaking the length of the chain into little triangles then integrating it.
     
  19. Mar 28, 2004 #18

    Integral

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Let it all hang out!
     
  20. Mar 28, 2004 #19
    You're working way too hard here, Shawn.

    cookiemonster
     
  21. Mar 28, 2004 #20

    ShawnD

    User Avatar
    Science Advisor

    Well what's the answer? I've asked a 3rd year chem honors student as well as a 2nd year mechanical engineer and neither of them can figure it out. I'm stumped as well.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Calculating parabola of drooping chain
  1. Shot parabola (Replies: 2)

Loading...