Robin Hood, who weighs 800 N, is assaulting a castle by climbing a uniform ladde

Question

Robin Hood, who weighs 800 N, is assaulting a castle by climbing a uniform ladder that is 5.0 m long and weighs 180 N. The bottom of the ladder rests on a ledge and leans across the moat in equilibrium against a frictionless, vertical castle wall. The ladder makes an angle of 53.1 degree with the horizontal. Robin pauses one-third of the way up the ladder. A) Find the normal and friction forces on the base of the ladder. B) Find the minimum coefficient of static friction needed to prevent the base. C) Find the magnitude and direction of the contact force on the base of the ladder.

Explanation / Answer

at the base

along vertical

n1 - Wladder - Wrobin = 0

normal force , n1 = 800 + 180 = 980 N

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net torque about the base = 0

WRobin*L/3*cos53.1 + Wladder*L/2*cos53.1 = n2*L*sin53.1

800*(1/3)*cos53.1 + (180*(1/2)*cos53.1) = n2*sin53.1

n2 = 268 N

along horizontal

f - n2 = 0

friciton f = 268 N

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B)

friction f = u*n1

u = f/n1 = 268/980 = 0.273 <<<--------answer

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(C)

at the base

along vertical n1 = 980 N

along horizontal f = 268 N

magnitude F = sqrt(980^2+268^2) = 1016 N   <<<--------answer

direction tan^-1(n1/f)

direction = tan^-1(980/268) = 74.7 degrees wth horizontal <<<<--------answer

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