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

s = 0.3.

EXPERT ANSWER

GIVEN:
AB = 26 ft
μ_s = 0.3
W_AB = 30 lb

FIND:
d = ? (use are going to use θ)

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First find the equations of equilibrium

ΣF_x:
B_x – A_x = 0

ΣF_y:
A_y – W_AB = 0 ∴ A_y = 30 lb

In the x-direction we know that A_x cannot be greaterthan the static friction at that point. Therefore,
F_s,max = A_x = μ_sA_y = (0.3) 30 = 9 lb ∴ B_x = 9 lb

ΣM_A:
13 W cosθ – 26 B_x 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