Please provide as much detail as possible I really appreciate the insight! The u

Question

Please provide as much detail as possible I really appreciate the insight!

The uniform ladder of weight W = 20 lbs rests on the rough floor for which the coefficient of static friction is mu s = 0.4 and against the smooth wall at B. The horizontal distance from the wall of the base to the ladder (i.e., b) is 6 ft, the vertical distance from the ground to the tip of the ladder (i.e., a) is 8 ft and distance c =5 ft (which is the distance from the location of force applied to point B). State your assumptions clearly. Determine the horizontal force P the man must on the ladder in order to cause it to move. Explain when will the ladder slip instead of tipping?

Explanation / Answer

a) when the ladder starts to move, NB = 0, NA = W, friction F = W = 0.4*20 = 8 lbs

horizontal net force = P - F = 0, so P = 8 lbs

b) In the figure shown, the torque of gravity about A = W*(b/2) = 20*3 = 60 lb-ft

the torque of P about A = P*h, where h is the distance of P to the floor, h = a*[1 - c/(a2 + b2)] = 4 ft

P*h = 8*4 = 32 lb-ft < torque of gravity, so it won't tip.

when it starts to tip about A, net moment about A = P*h - W(b/2) 0

h Wb/(2P) = 20*6/(2*8) = 7.5 ft, c (a2 + b2) * (1 - h/a),

c 0.625 ft

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