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!

Homework Help: Determine the length of l (equilibrium)

  1. Sep 23, 2007 #1
    A ring of negligible size is subjected to vertical force P. Determine the required length l of the cord AC such that tension acting in AC is TAC. Also, what is the force acting in cord AB?

    P = 300N, d = 0.2m (distance between A & B), angle ABC = 45 degrees, TAC = 250N

    The graph basically looks like a "Y" with C & B at the tops, A at the centre and P the downward force.

    Fx = 0; Fab(cos45) - 250cosx = 0
    Fy = 0; Fab(sin45) + 250sinx - 300 = 0

    Fab = (250cosx/cos45)

    (250cosx/cos45)sin45 + 250sinx - 300 = 0

    This is about as far as I get before I start mucking it up. Can some one help me through the steps to solve for "x" so I can eventually find l?
    Last edited: Sep 23, 2007
  2. jcsd
  3. Sep 23, 2007 #2
    okay, if you're sure that's the equation you want to solve, then you should realise it's a pretty nasty beast. You're unlikely to get an exact answer, but you can tidy it up so it looks a lot nicer.
    First, try dividing through by 50.
    then, think what sin 45/cos 45 is (hint - trig identities)
    in the end you've still got an equation that looks like this:
    a cosx +b sin x +c = 0
    this is an absolute pig to solve, your only chance is to do it numerically, or "translate" one of the functions into the other - do you know how to do this?? i.e cos(a)=sin(a+x)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook