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System in equilibrium

  1. Mar 2, 2009 #1
    1. The problem statement, all variables and given/known data
    A light rod is holding a weight with mass m in equilibrium. The rod is attached to the wall with a hinge and a wire as shown on the figure.

    http://sveskekat.dk/files/uploads/phys_4.PNG [Broken]

    Problem:
    Draw a force diagram of the rod and determine the force with which the hinge affects the rod and the tension force in the wire.

    3. The attempt at a solution
    I did the force diagram as shown on the figure, with the green arrows as the forces.
    I want to determine
    The force with which the hinge affects the rod, Fc.
    The tension force in the wire, T.

    I have that Ww = mg.

    I wrote up the conditions for equilibrium,
    [tex]\sum F_x = F_c - T cos(45) = 0[/tex]
    [tex]\sum F_y = T sin(45) - W_r - mg = 0[/tex]

    I do torque around the attachment point on the wall,
    [tex]\sum \tau = 2amg + aW_r - aF_c = 0[/tex]

    But trying to solve for e.g. [tex]F_c[/tex] now gives me
    [tex]F_c = cos(45) \frac{F_c - mg}{sin(45)} = F_c - mg[/tex],
    which is kinda bad. What am I doing wrong??
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 2, 2009 #2

    PhanthomJay

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    Since it is given that the rod is light, you can ignore W_r. But you are forgetting the vertical reaction at O.
     
  4. Mar 2, 2009 #3
    Hi Jay, thanks. I will ignore W_r then. How should the vertical reaction at O look like? Should it be another component, or should it be part of F_c?

    Thanks.
     
  5. Mar 2, 2009 #4

    PhanthomJay

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    Call it a component O_y, acting vertical, perpendicular to F_c (which you probably should be referring to as O_x instead of F_c).
     
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