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. c) Alarmed by the unsafety of the worn-out ladder in wet conditions, Bob decides to “stabilize” it by suspending a second pail of mass m=30 kg off the ladder at a point at D=0.3m up the ladder length from the bottom. What is the new safety limit of the worn-out ladder for Bob in terms of maximal height off the ground in wet conditions?
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. c) Alarmed by the unsafety of the worn-out ladder in wet conditions, Bob decides to “stabilize” it by suspending a second pail of mass m=30 kg off the ladder at a point at D=0.3m up the ladder length from the bottom. What is the new safety limit of the worn-out ladder for Bob in terms of maximal height off the ground in wet conditions?
International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter9: Moments And Products Of Inertia Of Areas
Section: Chapter Questions
Problem 9.46P
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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.
c) Alarmed by the unsafety of the worn-out ladder in wet conditions, Bob decides to “stabilize” it by suspending a second pail of mass m=30 kg off the ladder at a point at D=0.3m up the ladder length from the bottom. What is the new safety limit of the worn-out ladder for Bob in terms of maximal height off the ground in wet conditions?
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