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A band brake has a = 100 mm, r= 140 mm and a coefficient of friction of 0.35 between the band and wheel. If P = 100 N, the maximum moment M that the brake can hold is best given by P 3a a. 337 N*m b. 30.8 N*m c. 112 N*m d. 84.1 N*m

A band brake has a = 100 mm, r= 140 mm and a coefficient of friction of 0.35 between the band and wheel. If P = 100 N, the maximum moment M that the brake can hold is best given by P 3a a. 337 N*m b. 30.8 N*m c. 112 N*m d. 84.1 N*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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### Transcription and Explanation for Educational Use #### Problem Statement A band brake has \( a = 100 \, \text{mm}, \, r = 140 \, \text{mm} \) and a coefficient of friction of 0.35 between the band and wheel. If \( P = 100 \, \text{N} \), the maximum moment \( M \) that the brake can hold is best given by: - a. \( 337 \, \text{N} \cdot \text{m} \) - b. \( 30.8 \, \text{N} \cdot \text{m} \) - c. \( 112 \, \text{N} \cdot \text{m} \) - d. \( 84.1 \, \text{N} \cdot \text{m} \) #### Diagram Explanation The diagram shows a schematic of a band brake mechanism: - **Components:** - A horizontal rod where force \( P \) is applied at a distance of \( 3a \) from the pivot point. - A band wraps around a wheel with radius \( r \). - The band is connected to a lever, and the lever length is denoted as \( a \). - **Variables:** - \( a \): Distance from the pivot to where the band is attached on the lever (100 mm). - \( r \): Radius of the wheel (140 mm). - Friction coefficient between band and wheel: 0.35. - \( M \): Resulting moment about the wheel. Understanding how the mechanism operates reveals that the force \( P \) applied to the lever causes a tension in the band, exerting a frictional force on the wheel, which ultimately creates a moment \( M \). The problem asks to determine which choice correctly represents this maximum moment. Make sure to apply the principles of torque and friction to solve for \( M \) using the given parameters and understand the physical diagram representation in helping to solve this problem.
Transcribed Image Text:### Transcription and Explanation for Educational Use #### Problem Statement A band brake has \( a = 100 \, \text{mm}, \, r = 140 \, \text{mm} \) and a coefficient of friction of 0.35 between the band and wheel. If \( P = 100 \, \text{N} \), the maximum moment \( M \) that the brake can hold is best given by: - a. \( 337 \, \text{N} \cdot \text{m} \) - b. \( 30.8 \, \text{N} \cdot \text{m} \) - c. \( 112 \, \text{N} \cdot \text{m} \) - d. \( 84.1 \, \text{N} \cdot \text{m} \) #### Diagram Explanation The diagram shows a schematic of a band brake mechanism: - **Components:** - A horizontal rod where force \( P \) is applied at a distance of \( 3a \) from the pivot point. - A band wraps around a wheel with radius \( r \). - The band is connected to a lever, and the lever length is denoted as \( a \). - **Variables:** - \( a \): Distance from the pivot to where the band is attached on the lever (100 mm). - \( r \): Radius of the wheel (140 mm). - Friction coefficient between band and wheel: 0.35. - \( M \): Resulting moment about the wheel. Understanding how the mechanism operates reveals that the force \( P \) applied to the lever causes a tension in the band, exerting a frictional force on the wheel, which ultimately creates a moment \( M \). The problem asks to determine which choice correctly represents this maximum moment. Make sure to apply the principles of torque and friction to solve for \( M \) using the given parameters and understand the physical diagram representation in helping to solve this problem.
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