Static Equilibrium

[BillytheKid]

One end of a uniform 4.00-m long rod of weight Fg is supported by a cable. The other end rests against the wall, where it is held by friction. The coefficient of static friction between the wall and the rod is = 0.500. Determine the minimum distance x from point A at which an additional weight Fg (the same as the weight of the rod) can be hung without causing the rod to slip at point A. Angle cable and beam make is 36 degrees

I'm just staring at the problem we have done a lot in class involving the tension in the cable and how far one could walk before the beam breaks but that involves the beam being at a hinge on the wall. I have seen one only involving friction. I could use some hints

[Andrew Mason]

One end of a uniform 4.00-m long rod of weight Fg is supported by a cable. The other end rests against the wall, where it is held by friction. The coefficient of static friction between the wall and the rod is = 0.500. Determine the minimum distance x from point A at which an additional weight Fg (the same as the weight of the rod) can be hung without causing the rod to slip at point A. Angle cable and beam make is 36 degrees

I'm just staring at the problem we have done a lot in class involving the tension in the cable and how far one could walk before the beam breaks but that involves the beam being at a hinge on the wall. I have seen one only involving friction. I could use some hints
What you describe appears to be a lever with a fulcrum at the cable end. The issue is how much torque can be applied to this lever arm. The maximum downward force at A (contact point between rod and wall) without slipping is a function of the horizontal component of the force at A times \mu_s.

Does that help?

AM