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System in equilibrium

  • Thread starter laurids
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  • #1
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Homework Statement


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.

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??
 
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Answers and Replies

  • #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.
 
  • #3
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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.
 
  • #4
PhanthomJay
Science Advisor
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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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