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A ladder of length L is supported at the wall and floor. Determine the greatest angle a such that the ladder does not slip. H₂ = 0.32 α 200 lb M = 0.25

A ladder of length L is supported at the wall and floor. Determine the greatest angle a such that the ladder does not slip. H₂ = 0.32 α 200 lb M = 0.25

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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### Problem Statement: A ladder of length \( L \) is supported at the wall and floor. Determine the greatest angle \( \alpha \) such that the ladder does not slip. ### Diagram Explanation: The diagram shows a ladder leaning against a wall. Key elements in the diagram include: - **Ladder**: Identified as length \( L \), leaning against a wall at an angle \( \alpha \). - **Angle \( \alpha \)**: The angle between the ladder and the floor. - **Weight**: A downward force of 200 lb is applied approximately in the middle of the ladder. - **Static Friction**: - At the **floor**, the coefficient of static friction \( \mu_s = 0.32 \). - Against the **wall**, the coefficient of static friction \( \mu_s = 0.25 \). The problem requires finding the maximum angle \( \alpha \) while ensuring the ladder does not slip due to the given frictional forces and weight.
Transcribed Image Text:### Problem Statement: A ladder of length \( L \) is supported at the wall and floor. Determine the greatest angle \( \alpha \) such that the ladder does not slip. ### Diagram Explanation: The diagram shows a ladder leaning against a wall. Key elements in the diagram include: - **Ladder**: Identified as length \( L \), leaning against a wall at an angle \( \alpha \). - **Angle \( \alpha \)**: The angle between the ladder and the floor. - **Weight**: A downward force of 200 lb is applied approximately in the middle of the ladder. - **Static Friction**: - At the **floor**, the coefficient of static friction \( \mu_s = 0.32 \). - Against the **wall**, the coefficient of static friction \( \mu_s = 0.25 \). The problem requires finding the maximum angle \( \alpha \) while ensuring the ladder does not slip due to the given frictional forces and weight.
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