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17-55. The 100-kg uniform crate C rests on the elevator floor where the coefficient of static friction is μ = 0.4. Determine the largest initial angular acceleration a, starting from rest at 0 = 90°, without causing the crate to slip. No tipping occurs. -0.6 m-- 1.2 m E 1.5 m A B 1.5 m

17-55. The 100-kg uniform crate C rests on the elevator floor where the coefficient of static friction is μ = 0.4. Determine the largest initial angular acceleration a, starting from rest at 0 = 90°, without causing the crate to slip. No tipping occurs. -0.6 m-- 1.2 m E 1.5 m A B 1.5 m

Elements Of Electromagnetics
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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### Problem 17-55: Maximum Initial Angular Acceleration of a Crate on an Elevator Floor A 100-kg uniform crate \(C\) rests on the elevator floor where the coefficient of static friction \(\mu_s = 0.4\). The task is to determine the largest initial angular acceleration \(\alpha\), starting from rest at \(\theta = 90^\circ\), without causing the crate to slip. It is specified that no tipping occurs. #### Objective: To find the maximum value of angular acceleration \(\alpha\) that does not lead to slipping. #### Given Data: - Weight of crate (C): 100 kg - Coefficient of static friction \(\mu_s\): 0.4 - Crate dimensions: 0.6 m (width), 1.2 m (height) - Distance between pivot points D, E, and A, B: 1.5 m - Initial angle \(\theta\): 90° #### Diagram Description: The provided diagram includes the following details: - A rigid crate labeled \(C\). - A supportive structure with arms connected at points \(D, E, A\), and \(B\). - The distance between connection points is labeled as 1.5 m on either side. - The arm sections protrude at an angle \(\alpha\) from the base points \(D\) and \(A\). The crate \(C\) is shown centered on a horizontal beam connected by supports at its midpoint, which is 1.2 m high and 0.6 m wide. #### Analysis: To determine the largest angular acceleration (\(\alpha\)) without causing the crate to slip, consider the following steps: 1. **Force Analysis**: Analyze the forces acting on the crate including gravitational force, normal force, and frictional force. 2. **Friction Calculation**: Use the coefficient of static friction to find the maximum static friction force (\(f_s = \mu_s \cdot N\)). 3. **Equilibrium Conditions**: Apply equilibrium conditions to ensure no slipping or tipping occurs which involves setting up equations for both translational and rotational equilibrium. 4. **Angular Motion Equations**: Relate the angular acceleration \(\alpha\) to the forces and moments acting on the crate. 5. **Solve for \(\alpha\)**: Solve the obtained equations to find the maximum allowable value of \(\
Transcribed Image Text:### Problem 17-55: Maximum Initial Angular Acceleration of a Crate on an Elevator Floor A 100-kg uniform crate \(C\) rests on the elevator floor where the coefficient of static friction \(\mu_s = 0.4\). The task is to determine the largest initial angular acceleration \(\alpha\), starting from rest at \(\theta = 90^\circ\), without causing the crate to slip. It is specified that no tipping occurs. #### Objective: To find the maximum value of angular acceleration \(\alpha\) that does not lead to slipping. #### Given Data: - Weight of crate (C): 100 kg - Coefficient of static friction \(\mu_s\): 0.4 - Crate dimensions: 0.6 m (width), 1.2 m (height) - Distance between pivot points D, E, and A, B: 1.5 m - Initial angle \(\theta\): 90° #### Diagram Description: The provided diagram includes the following details: - A rigid crate labeled \(C\). - A supportive structure with arms connected at points \(D, E, A\), and \(B\). - The distance between connection points is labeled as 1.5 m on either side. - The arm sections protrude at an angle \(\alpha\) from the base points \(D\) and \(A\). The crate \(C\) is shown centered on a horizontal beam connected by supports at its midpoint, which is 1.2 m high and 0.6 m wide. #### Analysis: To determine the largest angular acceleration (\(\alpha\)) without causing the crate to slip, consider the following steps: 1. **Force Analysis**: Analyze the forces acting on the crate including gravitational force, normal force, and frictional force. 2. **Friction Calculation**: Use the coefficient of static friction to find the maximum static friction force (\(f_s = \mu_s \cdot N\)). 3. **Equilibrium Conditions**: Apply equilibrium conditions to ensure no slipping or tipping occurs which involves setting up equations for both translational and rotational equilibrium. 4. **Angular Motion Equations**: Relate the angular acceleration \(\alpha\) to the forces and moments acting on the crate. 5. **Solve for \(\alpha\)**: Solve the obtained equations to find the maximum allowable value of \(\
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