(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A light rod is holding a weight with massmin 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??

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# System in equilibrium

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