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18-38. The spool has a mass of 50 kg and a radius of gyration of ko = 0.280 m. If the 20-kg block A is released from rest, determine the distance the block must fall in order for the spool to have an angular velocity w = 5 rad/s. Also, what is the tension in the cord while the block is in motion? Neglect the mass of the cord.

18-38. The spool has a mass of 50 kg and a radius of gyration of ko = 0.280 m. If the 20-kg block A is released from rest, determine the distance the block must fall in order for the spool to have an angular velocity w = 5 rad/s. Also, what is the tension in the cord while the block is in motion? Neglect the mass of the cord.

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 Statement:** The spool has a mass of 50 kg and a radius of gyration of \( k_O = 0.280 \, \text{m} \). If the 20-kg block \( A \) is released from rest, determine the distance the block must fall in order for the spool to have an angular velocity \( \omega = 5 \, \text{rad/s} \). Also, what is the tension in the cord while the block is in motion? Neglect the mass of the cord. **Diagram Explanation:** The image illustrates a spool with a rope wound around it. The following key components and measurements are noted in the diagram: 1. **Spool:** - Total mass: \( 50 \, \text{kg} \) - Radius of Gyration: \( k_O = 0.280 \, \text{m} \) - Two radii labeled: - Radius from the center \( O \) to the point where the rope reaches the spool: \( 0.3 \, \text{m} \) - Radius from the center \( O \) to the point where the block is initially hanging from the spool: \( 0.2 \, \text{m} \) 2. **Block \( A \):** - Mass: \( 20 \, \text{kg} \) - The block is hanging from the cord wound around the spool. - The position of block \( A \) indicates it will descend vertically when released. To solve this problem, consider the following physics and mechanics principles to relate angular velocity, distance fallen by the block, and tension in the cord: 1. **Energy Conservation Principles:** - Potential energy of block \( A \) converting into rotational kinetic energy of the spool. 2. **Rotational Kinematics and Dynamics** - Angular velocity and angular acceleration. - Tension in the cord generating torque on the spool. ### Required Steps for Solution: 1. **Find the Distance the Block Must Fall:** - Use conservation of energy: - Initial potential energy of the block. - Final rotational kinetic energy of the spool. 2. **Determine the Tension in the Cord:** - Use Newton's second law for rotational motion: - Torque generated by the tension in the cord. - Relation between linear and angular quantities to
Transcribed Image Text:**Problem Statement:** The spool has a mass of 50 kg and a radius of gyration of \( k_O = 0.280 \, \text{m} \). If the 20-kg block \( A \) is released from rest, determine the distance the block must fall in order for the spool to have an angular velocity \( \omega = 5 \, \text{rad/s} \). Also, what is the tension in the cord while the block is in motion? Neglect the mass of the cord. **Diagram Explanation:** The image illustrates a spool with a rope wound around it. The following key components and measurements are noted in the diagram: 1. **Spool:** - Total mass: \( 50 \, \text{kg} \) - Radius of Gyration: \( k_O = 0.280 \, \text{m} \) - Two radii labeled: - Radius from the center \( O \) to the point where the rope reaches the spool: \( 0.3 \, \text{m} \) - Radius from the center \( O \) to the point where the block is initially hanging from the spool: \( 0.2 \, \text{m} \) 2. **Block \( A \):** - Mass: \( 20 \, \text{kg} \) - The block is hanging from the cord wound around the spool. - The position of block \( A \) indicates it will descend vertically when released. To solve this problem, consider the following physics and mechanics principles to relate angular velocity, distance fallen by the block, and tension in the cord: 1. **Energy Conservation Principles:** - Potential energy of block \( A \) converting into rotational kinetic energy of the spool. 2. **Rotational Kinematics and Dynamics** - Angular velocity and angular acceleration. - Tension in the cord generating torque on the spool. ### Required Steps for Solution: 1. **Find the Distance the Block Must Fall:** - Use conservation of energy: - Initial potential energy of the block. - Final rotational kinetic energy of the spool. 2. **Determine the Tension in the Cord:** - Use Newton's second law for rotational motion: - Torque generated by the tension in the cord. - Relation between linear and angular quantities to
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