# Angle at which a ladder begins to slip

## Homework Statement

Consider the ladder in the figure. Assume there is friction between the verticle wall and the ladder, with the coeffecient of static friction=0.30. Find the angle at which the ladder just begins to slip.

## Homework Equations

$$\Sigma$$$$\tau$$=0=NwLsin$$\Theta$$-mg(L/2)sin(90-$$\Theta$$)
0=+NwLsin$$\Theta$$-mg(L/2)cos$$\Theta$$

$$\Sigma$$Fx[/=0=-Nw+Ffriction
$$\Sigma$$Fy=0=NF-mg

Ffriction=$$\mu$$sNF=$$\mu$$
smg

tan$$\Theta$$=1/2$$\mu$$s

## The Attempt at a Solution

tan$$\Theta$$=1/2(0.30)
tan-1(1.667)=$$\Theta$$
59=$$\Theta$$

I got 59 but the answer given by the book is 40

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