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.
τ = (r) (F) (sin(Θ))
r = (1/2)(h) (because it is a solid figure and force applies from the center of it)
τx = τ cos(Θ)
F(friction max) = µs * N
µ(static) = F(friction max) / N
The Attempt at a Solution
h = 7.7
r = 3.85
τ = (3.85) (291) (sin(59◦))
τ = 960.3274
τx = 960.3247 * cos(59◦)
τx = 494.6052
so if τ(x) is the amount of force moving in the x direction, then shouldn't τx = Force(friction max) ?
µs = F(friction max) / N
µs = 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!