Shown in the figure below is a 5 meter, 10 kg uniform ladder leaning on a fricti

Question

Shown in the figure below is a 5 meter, 10 kg uniform ladder leaning on a frictionless wall at an angle of 60 degrees to the floor. The COM for the ladder is located half-way up the ladder. The floor has a static coefficient of friction equal to 0.42. A person climbs the ladder and above some point the ladder slips out and falls. Calculate the following at the point where the person is at the maximum distance up along the ladder before it slips. Calculate the normal force of the floor on the ladder with the person a distance d along the length of the ladder. Calculate the normal force of the wall on the ladder with the person a distance d along the length of the ladder. Calculate the greatest distance, d, along the length of the ladder a person can climb without the ladder slipping.

Explanation / Answer

let

m = 10 kg

L = 5 m

M = 85 kg

mue_s = 0.42

a) N = (m+M)*g

= (10 + 85)*9.8

= 931 N <<<<<<<<--------------Answer

b) Apply, Fnetx = 0

Nw - N*mue_s = 0

Nw = N*mue_s

= 931*0.42

= 391 N <<<<<<<<--------------Answer

c)

Apply net torque about the bottom is zero.

m*g*(L/2)*sin(30) + M*g*d*sin(30) - Nw*L*sin(60) = 0

m*g*L/4 + M*g*d/2 - Nw*L*sin(60) = 0

M*g*d/2 = Nw*L*sin(60) - m*g*L/4

d = (2/(M*g))*(Nw*L*sin(60) - m*g*L/4)

= (2/(85*9.8))*(391*5*sin(60) - 10*9.8*5/4)

= 3.77 m <<<<<<<<--------------Answer

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