# Min. angle at which ladder will not slip

1. Apr 9, 2010

### lockedup

1. The problem statement, all variables and given/known data
A uniform ladder of mass, m, and length, l, leans at an angle, $$\theta$$, against a frictionless wall. If the coefficient of static friction between the ladder and the ground is $$\mu_{s}$$, what is the minimum angle at which the ladder will not slip?

2. Relevant equations

3. The attempt at a solution
I've attached my FBD.

SFx = mg - N = 0
SFy = $$\mu$$mg - Fw = 0
St = FwL - mg(L/2) = 0

mg = N
$$\mu$$mg = Fw
FwL = mg(L/2)
L/2 = $$\mu$$

Where do I go from here?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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2. Apr 9, 2010

### PhanthomJay

Your FBD is good, and your sum of forces = 0 equations are good, but your sum of torques equation is incorrect. L, for example, is not the lever arm for the wall force moment about the base. You need to calculate that arm as a function of L and theta. L is the length of the ladder as measured along the incline.