George , Romeo \'s not often heard about older brother, was also quite in love w

Question

George, Romeo's not often heard about older brother, was also quite in love with Juliet. One night he tried to climb a 10 m long , 25 kg ladder to her window. He put the base of the ladder 2.5 m from the wall, which was frictionless. Unfortunately for George, who was a considerable 120 kg, it had rained earlier that evening and the grass was wet. When he was but 1/4 of the way up to Juliet's window, his ladder began to slip. What was the coecient of friction between the ladder and the grass that evening?

Explanation / Answer

a) normal force exerted by floor N = (M+m)*g

b) force exerted by wall on ladder Nw = u*N

net torque = 0

h = sqrtL^2-d^2) = (10^2 - 2.5^2)^.5 = 9.68

Nw*h = (M*g*(L/4)*costheta + m*g*(L/2)*costheta

u (M+m)*g*h = M*g*(L/4)*(d/L)+ m*g*(L/2)*(d/L)

u(25+120)*9.8*9.68 = (120*9.8*(2.5/4))+(25*9.8*(2.5/2))

u = 0.0757 = 0.08

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