A 5.00-m-long uniform ladder, weighing 200 N, rests against a smooth vertical wall with its base on a horizontal rough floor, a distance of 1.20 m away from the wall. The coefficient of static
Friction between the ladder and the floor is 0.200. How far up the ladder, measured along the
Ladder, can a 600-N person climb before the ladder begins to slip?
A) 4.56 m
B) 3.95 m
C) 1.26 m
D) 1.05 m
E) 1.50 m

Question

Quizplus · Accepted Answer

The correct answer is A because the ladder will begin to slip when the force of friction between the ladder and the floor is less than or equal to the force of static friction. The force of friction is given by f = μN, where μ is the coefficient of static friction and N is the normal force. The normal force is equal to the weight of the ladder plus the weight of the person, which is 200 N + 600 N = 800 N. Therefore, the force of friction is f = 0.200 * 800 N = 160 N. The ladder will begin to slip when the force of friction is less than or equal to 160 N. The force of friction is equal to the force of the person's weight times the sine of the angle between the ladder and the floor. The angle between the ladder and the floor is given by tan θ = 1.20 m / 5.00 m = 0.240. Therefore, the force of friction is equal to f = 600 N * sin 0.240 = 144 N. Since the force of friction is less than 160 N, the ladder will begin to slip when the person is 4.56 m up the ladder.

A 500-M-Long Uniform Ladder, Weighing 200 N, Rests Against a Smooth