A worker places an aluminum ladder on a horizontal concrete slab against a vertical wooden wall at 30 degrees from the vertical. The ladder has length L=5m and m=30 kg. The ladder’s CM is at a third of the length up. Worker Bob has mass M=90 kg and intends to climb up the ladder. Simultaneously, worker Charlie has mass M=90 kg and operates a rope through a single pulley to hoist a pail of mass m=30 kg. The axle of the pulley is anchored to the ladder at A=0.3 m along the ladder from the top point. Charlie is pulling the rope down with enough force to hoist the pail at uniform velocity. The mass of the pulley and rope are negligible. The friction in the pulley axle is negligible. The ladder is equipped with rubber booties and a rubber top. The kinetic friction coefficients are: rubber on dry concrete 0.9, rubber on dry wood 0.9, aluminum on wet concrete 0.2, aluminum on wet wood 0.2. b) Repeated use has deteriorated the rubber coating of the ladder, exposing the aluminum under it. In addition, it rained the previous night and now both the wall and the concrete slab are wet. Calculate the safety limit in terms of maximal height off the ground that Bob can reach climbing up the ladder before the ladder starts sliding down.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A worker places an aluminum ladder on a horizontal concrete slab against a vertical wooden wall at 30 degrees from the vertical. The ladder has length L=5m and m=30 kg. The ladder’s CM is at a third of the length up. Worker Bob has mass M=90 kg and intends to climb up the ladder. Simultaneously, worker Charlie has mass M=90 kg and operates a rope through a single pulley to hoist a pail of mass m=30 kg. The axle of the pulley is anchored to the ladder at A=0.3 m along the ladder from the top point. Charlie is pulling the rope down with enough force to hoist the pail at uniform velocity. The mass of the pulley and rope are negligible. The friction in the pulley axle is negligible. The ladder is equipped with rubber booties and a rubber top. The kinetic friction coefficients are: rubber on dry concrete 0.9, rubber on dry wood 0.9, aluminum on wet concrete 0.2, aluminum on wet wood 0.2. b) Repeated use has deteriorated the rubber coating of the ladder, exposing the aluminum under it. In addition, it rained the previous night and now both the wall and the concrete slab are wet. Calculate the safety limit in terms of maximal height off the ground that Bob can reach climbing up the ladder before the ladder starts sliding down.

Expert Solution

Step 1

Given:

Length of ladder, L = 5 m

Mass of ladder, M = 30 kg

Mass of man, m = 90 kg

Coefficient of friction, $μ = 0.9$

To find:

Maximal height off the ground that Bob can reach climbing up the ladder before the ladder starts sliding down

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