AP Physics Ladder Problem

Question

 A clerk is going up a ladder. The clerk's weight is 450N, and the ladder's weight is 200N. There is negligible friction between the ladder and the wall. The angle between the ladder and the floor is 45, and the coefficient of friction between the ladder and the floor is 0.7. Will the force of friction keep the ladder from moving?

Answer 1

Do a torque balance with the pivot at the foot of the ladder (torque balance is true everywhere for the ladder in equilibrium. The foot has two unknown forces.

The clockwise torques are Weight of ladder * L/2 * cos(θ) where theta is the floor angle. Using torque definition of FLsin(angle between) we find the torque to be weight *L/2 * sin(complement of theta

Weght of dude * .7L * cos(θ)

The CCL torque is Normal to wall * L * sin(θ)

Find Normal force by equating CL and CCL torques.

Horizontal force balance is Force of friction required = Normal force at wall

Vertical force balance is Normal force at the floor = weight of laddder + weight of dude

Compare F_f required to μ * normal force at floor