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A 0.8 lb roll of paper is suspended from a wire hanger so that it rests against the wall. The hanger has a negligible weight and the bearing O can be considered as frictionless. The two ends of the hanger can be treated as pin joints. Determine the force P required to start turning the roll if theta = 37 degrees and the coefficient of static friction is 0.29.

A 0.8 lb roll of paper is suspended from a wire hanger so that it rests against the wall. The hanger has a negligible weight and the bearing O can be considered as frictionless. The two ends of the hanger can be treated as pin joints. Determine the force P required to start turning the roll if theta = 37 degrees and the coefficient of static friction is 0.29.

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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A 0.8 lb roll of paper is suspended from a wire hanger so that it rests against the wall.  The hanger has a negligible weight and the bearing O can be considered as frictionless.  The two ends of the hanger can be treated as pin joints.  Determine the force P required to start turning the roll if theta = 37 degrees and the coefficient of static friction is 0.29.

 

 

### Image Description for Educational Context #### Diagram Explanation: Mechanics and Forces The diagram displays a mechanical setup involving a pulley, cable, and forces at play. Here is a detailed breakdown of the components and angles depicted: 1. **Pulley Specifications**: - The pulley is shown as a circular object with a radius of 3 inches, denoted by a circle with a centered hub labeled 'O'. 2. **Cable Orientation and Force**: - A cable is attached to the center of the pulley ('O') and is oriented at an angle of 30 degrees from the vertical. - The cable is connected to a wall or fixed point labeled 'A'. 3. **Angled Force Application**: - There is a tension force applied to the cable running tangentially to the pulley and directed downward, represented by the letter 'P'. - The force 'P' acts at an angle θ from the horizontal direction. 4. **Annotations and Dimensions**: - The radius of the pulley (3 inches) is clearly labeled. - The angle between the cable and the vertical line is depicted as 30 degrees. - The diagram uses arrows to indicate the direction of force and the orientation of the cable. This visual aids in understanding the concept of mechanical advantage provided by pulleys, the interaction of forces at angles, and the tension in the cables.
Transcribed Image Text:### Image Description for Educational Context #### Diagram Explanation: Mechanics and Forces The diagram displays a mechanical setup involving a pulley, cable, and forces at play. Here is a detailed breakdown of the components and angles depicted: 1. **Pulley Specifications**: - The pulley is shown as a circular object with a radius of 3 inches, denoted by a circle with a centered hub labeled 'O'. 2. **Cable Orientation and Force**: - A cable is attached to the center of the pulley ('O') and is oriented at an angle of 30 degrees from the vertical. - The cable is connected to a wall or fixed point labeled 'A'. 3. **Angled Force Application**: - There is a tension force applied to the cable running tangentially to the pulley and directed downward, represented by the letter 'P'. - The force 'P' acts at an angle θ from the horizontal direction. 4. **Annotations and Dimensions**: - The radius of the pulley (3 inches) is clearly labeled. - The angle between the cable and the vertical line is depicted as 30 degrees. - The diagram uses arrows to indicate the direction of force and the orientation of the cable. This visual aids in understanding the concept of mechanical advantage provided by pulleys, the interaction of forces at angles, and the tension in the cables.
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