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

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The discussion focuses on calculating the maximum angle (alpha) at which a ladder can lean against a wall without slipping, given its length, mass, and static friction coefficient. The problem involves summing forces in both horizontal and vertical directions, as well as taking moments around specific points to derive relationships involving the angle. The key challenge lies in correctly applying these equations to relate them to alpha. Participants emphasize the importance of considering the perpendicular distance in relation to the angle when summing moments. Ultimately, the solution requires a clear understanding of the forces at play and their geometric relationships.
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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)
 
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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.
 
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.
 

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