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unit. Take g = 32.2 ft/s². P 30° 1.5 ft

unit. Take g = 32.2 ft/s². P 30° 1.5 ft

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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The problem involves calculating the maximum force \( P \) that can be applied to a roller without causing it to slip on the ground. This is an application of static friction concepts in physics. ### Problem Statement: A man applies force \( P \) through a handle attached to the central axle of a 43-pound roller. The static friction coefficient \( \mu_s \) between the roller and the floor is 0.16. The roller is assumed to be a uniform cylinder and must roll on the ground without slipping. You are required to determine the maximum force \( P \) while ensuring your answer includes two decimal places and proper units. The gravitational acceleration \( g \) is given as 32.2 ft/s². ### Diagram Explanation: - The diagram depicts a man pushing the roller. - The handle makes a 30° angle with the horizontal. - The length from the roller’s center to where the force \( P \) is applied is 1.5 feet. ### Requirements: - Calculate the force \( P \) such that the roller does not slip. - Consider static friction and the given coefficient to find the maximum force. - Ensure calculations reflect appropriate precision and units. ### Solution: To solve the problem, consider the physical principles of friction and rotational motion. Calculate the frictional force required to prevent slipping and determine \( P \) based on force equilibrium analysis. Your Answer: \[ \boxed{\text{Your answer here}} \] Make sure your final answer accounts for all calculations and constraints provided.
Transcribed Image Text:The problem involves calculating the maximum force \( P \) that can be applied to a roller without causing it to slip on the ground. This is an application of static friction concepts in physics. ### Problem Statement: A man applies force \( P \) through a handle attached to the central axle of a 43-pound roller. The static friction coefficient \( \mu_s \) between the roller and the floor is 0.16. The roller is assumed to be a uniform cylinder and must roll on the ground without slipping. You are required to determine the maximum force \( P \) while ensuring your answer includes two decimal places and proper units. The gravitational acceleration \( g \) is given as 32.2 ft/s². ### Diagram Explanation: - The diagram depicts a man pushing the roller. - The handle makes a 30° angle with the horizontal. - The length from the roller’s center to where the force \( P \) is applied is 1.5 feet. ### Requirements: - Calculate the force \( P \) such that the roller does not slip. - Consider static friction and the given coefficient to find the maximum force. - Ensure calculations reflect appropriate precision and units. ### Solution: To solve the problem, consider the physical principles of friction and rotational motion. Calculate the frictional force required to prevent slipping and determine \( P \) based on force equilibrium analysis. Your Answer: \[ \boxed{\text{Your answer here}} \] Make sure your final answer accounts for all calculations and constraints provided.
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