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Equilibrium of a particle

  1. Feb 23, 2009 #1
    1. The problem statement, all variables and given/known data
    Determine the maximum weight W of the block that can be suspended in the position shown if each cord can support a max tension of 80lb. also what is the angle [tex]\theta[/tex] for equilibrium?


    Untitled-2.jpg


    2. Relevant equations



    3. The attempt at a solution
    the free body diagram should be:
    -force A to B is 60[tex]^{o}[/tex] from the positive x axis
    -force from the block is in the negative y direction
    -tension is in the third quadrant at and angle of [tex]\theta[/tex] from the negative y axis

    putting the forces in their respected x and y components:
    **note: i'm using 30[tex]^{o}[/tex] instead of the 60 from the x axis**

    F[tex]_{x}[/tex] = 80sin30 - Wsin[tex]\theta[/tex] = 0
    F[tex]_{y}[/tex] = 80cos30 - Wcos[tex]\theta[/tex] - W = 0

    from F[tex]_{x}[/tex] : W = [tex]\frac{80sin30}{sin\theta}[/tex]

    sub into F[tex]_{y}[/tex]:

    0=80cos30 - [tex]\frac{80sin30}{sin\theta}[/tex]cos[tex]\theta[/tex] - [tex]\frac{80sin30}{sin\theta}[/tex]

    then i get:
    cot30 = [tex]\frac{cos\theta - 1}{sin\theta}[/tex]
    form here i'm not sure how to solve for [tex]\theta[/tex]. the angle should b 60 deg, but from the solution, it seems to me lyk a random guess....

    any help would b appreciated.
    cheers
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 26, 2009 #2
    any1????
     
  4. Feb 26, 2009 #3

    LowlyPion

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    Homework Helper

    Is θ constrained to be less than 90°?

    Because at greater than 90° more weight can be supported it seems, because the Tension of the rope no longer has a negative y component.
     
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