determine A 15ft ladder has a uniform weight of 50 lb and rests against the wall

Question

determine

A 15ft ladder has a uniform weight of 50 lb and rests against the wall at B. Ole, who weighs 150 lb. wishes to freely stand on the 10 rung of the ladder 10-ft from the bottom as depicted. If the coefficient of static friction between the ladder and the ground at A is mu 5 = .3 and the coefficient of static friction between the ladder and the wall at B is mu 5 = .2. determine the minimum angle (or maximum distance A is from the wall) the ladder doesn't slip so that Ole doesn't fall and injure himself

Explanation / Answer

Minimum angle => max friction acting

Let normal reaction at wall be N1

At ground be N2

Let friction at wall be F1

at ground be F2

Force balance:

Horizontal:

N1 = F2

Vertical:

200 = N2 + F1

Moment

about wall point:

50*7.5*CosA + 150*5*CosA + F2*15SinA = N2*15 CosA

=> (15*N2 - 1125)CosA = 15*F2*SinA

=> F1 + F2 tan A = 125

tanA = (125 - F1)/F2

for A to be minimum: F1 is max and F2 is max

F1 = 0.2N1

F2 = 0.3N2

From all the equations:

F1 = 11.3

F2 = 56.6

=> tanA = 2.0=> A = 63.54 degree

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