   Chapter 8, Problem 88AP

Chapter
Section
Textbook Problem

A painter climbs a ladder leaning against a smooth wall. At a certain height, the ladder is on the verge of slipping, (a) Explain why the force exerted by the vertical wall on the ladder is horizontal, (b) 11 the ladder of length L leans at an angle ft with the horizontal, what is the lever arm for this horizontal force with the axis of rotation taken at the base of the ladder? (c) If the ladder is uniform, what is the lever arm for the force of gravity acting on the ladder? (d) Let the mass of the painter be 80 kg, L = 4.0 m, the ladder’s mass be 30 kg, θ = 53% and the coefficient of friction between ground and ladder be 0.45. Find the maximum distance the painter can climb up the ladder.

(a)

To determine
Reason for the force exerted by the vertical wall on the ladder is horizontal.

Explanation

The wall is smooth which means the friction between wall and ladder is negligible.

Since there is no friction between wall and ladder, the vertical force from the vertical wall on the ladder is absent that is since the wall is frictional less there will not be any forc...

(b)

To determine
The magnitude of lever arm for the horizontal force exerted by the wall.

(c)

To determine
The magnitude of lever arm for the horizontal force exerted by the wall.

(d)

To determine
The magnitude of maximum distance that the painter can climb up the ladder.

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