What Are the Forces in Equilibrium for a Weight Hanging on a Rod?

[laurids]

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

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,
$$\sum F_x = F_c - T cos(45) = 0$$
$$\sum F_y = T sin(45) - W_r - mg = 0$$

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

But trying to solve for e.g. $$F_c$$ now gives me
$$F_c = cos(45) \frac{F_c - mg}{sin(45)} = F_c - mg$$,
which is kinda bad. What am I doing wrong??

 

[PhanthomJay]

Since it is given that the rod is light, you can ignore W_r. But you are forgetting the vertical reaction at O.

 

[laurids]

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.

 

[PhanthomJay]

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).