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Static Equilibrium please help

  1. Dec 9, 2008 #1
    1. The problem statement, all variables and given/known data

    One end of a uniform 4.00-m-long rod of weight Fg is supported by a cable. The other end rests against the wall, where it is held by friction, as in Figure below. The coefficient of static friction between the wall and the rod is s = 0.500. Determine the minimum distance x from point A at which an additional weight Fg (the same as the weight of the rod) can be hung without causing the rod to slip at point A.

    [​IMG]




    2. Relevant equations

    TORQUEnet = (F)1(d)1 + (F)2(d)2 + ...

    3. The attempt at a solution

    Assuming fulcrum is at the right tip of the bar
    TORQUEnet = 2Fg + 4Ff - x Fg
     

    Attached Files:

  2. jcsd
  3. Dec 9, 2008 #2

    Doc Al

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    Staff: Mentor

    Redo this: How far is the hanging weight from the pivot? In what direction do the torques act?

    What other conditions for equilibrium must be satisfied? (And will give you additional equations.)
     
  4. Dec 9, 2008 #3
    okay so 0 = 2Fg + 4Ff - xFg

    N = Tension in X direction

    Ff = N (Mu) = (tension in X)(Mu)

    I dont get how to calculate tension =/
     
  5. Dec 9, 2008 #4

    Doc Al

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    As I said, you'll need to redo this.

    What forces act on the beam? At the left end? At the right end?

    What's the net force in any direction?
     
  6. Dec 9, 2008 #5
    there's weight of beam, weight of sphere, tension, normal, friction.
    Friction is at the left, tension at the right.
    Isnt the pivot at the right end, so TORQUEnet = 0(Tension) - 2Fg + 4Ff - x Fg and TORQUEnet = 0 so that it is in equillibrium?
     
  7. Dec 9, 2008 #6

    Doc Al

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    Good. Set up equations for the vertical and horizontal forces to equal zero.
    x is measured from the left end.
     
  8. Dec 9, 2008 #7
    so,

    0 = -2Fg + 4Ff - (4-x)(Fg)

    0 = Tx - N
    0 = Ty + Ff - 2Fg

    Are these correct? I have no idea where I'm going with this... should it end with a finite number or will it have variables in it?
     
  9. Dec 9, 2008 #8

    Doc Al

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    Staff: Mentor

    Good.
    Good. Instead of using Tx & Ty, use some trig and the given angle to express it just in terms of T.

    Hint: How does Ff relate to N?

    By solving all these equations together, you should get a numerical answer for x.
     
  10. Dec 9, 2008 #9

    turin

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    Homework Helper

    Since this is a static problem, you can put the pivot whereever you want. I chose to put mine at the point where the rod touches the wall. Any idea why I chose it here? (There are actually two reasons.)
     
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