# Min. angle at which ladder will not slip

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## Homework Statement

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?

## 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?

## The Attempt at a Solution

#### Attachments

• 12b.jpg
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