55 ### Problem 17-55: Maximum Initial Angular Acceleration of a Crate on an Elevator FloorA 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 \(\

Given data as per the question Mass of crate =100 kg coefficient of friction =0.40

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

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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