If the coefficient of static friction between the mans shoes

If the coefficient of static friction between the man\'s shoes and the pole is mu_s = 0.60, determine the minimum coefficient of static friction required between the belt and the pole at A in order to support the man. The man has a weight of 150 lb and a center of gravity at G.

Solution

Forces in the X-direction

Nc = Na

Forces in the Y direction

Fa + Fc = W

Fa = aNa

and

Fc = sNc

Let the clockwise be positive moment

Then

Fc = sNc

585 = sNc(0.75) + Nc(4)
585 = Nc (s(0.75) + (4))
585 = Nc (0.6(0.75) + (4))
585 = Nc 4.45
Nc = 131.5 lbf

Fc = sNc
Fc = 0.6(131.5)
Fc = 78.9 lbf


Fa + Fc = W
W - Fc = Fa
150 - 78.9 = 71.1 lbf

Fa = Na(a)
(a) = Fa / Na
as Na = Nc
(a) = 71.1 / 131.5
(a) = 0.54