What is the maximum angle for a ladder to lean against a wall without slipping?

[fifth0]

Homework Statement

A ladder or bar of length 1m with mass of 4 kg (39.2N), is leaning against a wall with angle alpha (this is the angle between the bar and the wall) and has coefficients of static friction of .3 between the floor and the wall. solve for maximum alpha for no slippage.

Homework Equations

sum forces X,Y force friction = mu(Fn)

The Attempt at a Solution

I summed forces in the X and in the Y and came up with a few relationships, but non of them actually relate to the angle, Which of course is where i am getting stuck.

I set the point where wall meets bar as point B and floor meets bar as point A. Then said there is a Fb +y Nb +x Fa -x Na +y and W-y(at the centroid)

 

[Shooting Star]

If you have actually done the summing of horz and vert forces correctly, then take moment about all the forces about a point, say A, and equate to zero. That'll immdtly involve the angle alpha.

 

[fifth0]

Solved. i did exactly that. i was just confused a little i guess when summing the moments. And figured out that the perpendicular distance related to the angle alpha.