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## Homework Statement

A uniform 7.7 m tall aluminum ladder is leaning against a friction-less vertical wall.

The ladder has a weight of 291 N.

The ladder slips when it makes a 59.0◦ angle with the horizontal ﬂoor.

Determine the coeﬃcient of static friction between the ladder and the ﬂoor.

## Homework Equations

τ = (r) (F) (sin(Θ))

r = (1/2)(h) (because it is a solid figure and force applies from the center of it)

τ

_{x}= τ cos(Θ)

F(friction max) = µ

_{s}* N

(so)

µ(static) = F(friction max) / N

## The Attempt at a Solution

h = 7.7

M=291

Θ=59◦

r = 3.85

so:

τ = (3.85) (291) (sin(59◦))

τ = 960.3274

τ

_{x}= 960.3247 * cos(59◦)

τ

_{x}= 494.6052

so if τ(x) is the amount of force moving in the x direction, then shouldn't τ

_{x}= Force(friction max) ?

µ

_{s}= F(friction max) / N

µ

_{s}= 494.6052 / 291 which is more than 1 so it is obviously wrong.

I am clearly going in the wrong direction and I would really appreciate any help that you could offer, even if you tell me i need to scrap this! If you could steer me in the right direction I would greatly appreciate it!