The uniform pole has a weight of 30 lb and a length of 26 ft.Determine the maximum distance d it can be placed from the smoothwall and not slip. The coefficient of static friction between thefloor and the pole is

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s = 0.3.

EXPERT ANSWER

GIVEN:
AB = 26 ft
μs = 0.3
WAB = 30 lb

FIND:
d = ? (use are going to use θ)


First find the equations of equilibrium

ΣFx:
Bx – Ax = 0

ΣFy:
Ay – WAB = 0 ∴ Ay = 30 lb

In the x-direction we know that Ax cannot be greaterthan the static friction at that point. Therefore,
Fs,max = Ax = μsAy = (0.3) 30 = 9 lb ∴ Bx = 9 lb

ΣMA:
13 W cosθ – 26 Bx sinθ =0 ∴ tanθ= 13(30) / 9(26) ∴ θ = 59.036°

Finally we find d using basic trig

cosθ = d / AB ∴ d = 26 cos (59.036) = 13.377 ft