The top of a ladder of length L and mass m is connected to a wall by a horizonta
ID: 1316094 • Letter: T
Question
The top of a ladder of length L and mass m is connected to a wall by a horizontal cable, as shown below. The ladder makes angle ? = 60o with the horizontal. A woman of mass 2m finds that as she climbs the ladder, the ladder begins to slip when she is one-third of the way up the ladder. Draw a free-body diagram for the ladder. Label all forces and introduce a coordinate system. Find the coefficient of static friction between the ladder and the ground. (Hint: First find expressions for the tension in the cable and the normal force from the ground.)
Explanation / Answer
along vertical Fynet = 0
N - mg - 2mg = 0
N = 3mg
along horizantal T - f = 0
T = f = u*N = u*3*m*g
net torque about the point in contact with the ground = 0
T*L*sin60 = mg*(L/2)*cos60 + 2mg*(L/3)*cos60
u*3*m*g*sin60 = (m*g*1/2 + 2mg(1/3) ) *cos60
3utan60 = (7/6)
u = 7/(18*tan60)
u = 0.225
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