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18-58. The slender 6-kg bar AB is horizontal and at rest and the spring is unstretched. Determine the stiffness k of the spring so that the motion of the bar is momentarily stopped when it has rotated clockwise 90° after being released. 1.5 m 2 m B

18-58. The slender 6-kg bar AB is horizontal and at rest and the spring is unstretched. Determine the stiffness k of the spring so that the motion of the bar is momentarily stopped when it has rotated clockwise 90° after being released. 1.5 m 2 m B

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 18-58: **Given:** A slender 6-kg bar \( AB \) is initially horizontal and at rest. The spring attached to the bar is unstretched in this configuration. **Objective:** Determine the stiffness \( k \) of the spring so that the motion of the bar is momentarily stopped when it has rotated clockwise 90° after being released. **Diagram Explanation:** - The diagram consists of a setup with a horizontal bar \( AB \) of length 2 meters. - Point \( A \) is fixed, and point \( B \) is free to move. - A spring is attached to the bar at point \( B \) and extends vertically upward to a fixed support at point \( C \). - The spring is denoted by the letter \( k \) to indicate its stiffness coefficient. - The vertical distance between point \( B \) and the spring’s fixed support \( C \) is 1.5 meters. ### Detailed Breakdown of the Diagram: - **Bar \( AB \):** - Length = 2 meters - Mass = 6 kg - Initially positioned horizontally - **Spring \( BC \):** - Initially unstretched - Fixed at point \( C \) and attached to point \( B \) - Length between \( B \) and fixed point \( C \) is 1.5 meters ### Conditions and Motion: - At the initial position, the bar \( AB \) is horizontal, and the spring is untensioned. - After release, the bar is expected to rotate clockwise. - The desired condition is that the bar comes to a momentary halt after rotating 90° (when point \( B \) is directly below point \( A \), making the spring fully stretched). This problem involves principles of rotational motion, energy conservation, and spring mechanics to determine the appropriate spring stiffness \( k \) that meets the given condition.
Transcribed Image Text:### Problem 18-58: **Given:** A slender 6-kg bar \( AB \) is initially horizontal and at rest. The spring attached to the bar is unstretched in this configuration. **Objective:** Determine the stiffness \( k \) of the spring so that the motion of the bar is momentarily stopped when it has rotated clockwise 90° after being released. **Diagram Explanation:** - The diagram consists of a setup with a horizontal bar \( AB \) of length 2 meters. - Point \( A \) is fixed, and point \( B \) is free to move. - A spring is attached to the bar at point \( B \) and extends vertically upward to a fixed support at point \( C \). - The spring is denoted by the letter \( k \) to indicate its stiffness coefficient. - The vertical distance between point \( B \) and the spring’s fixed support \( C \) is 1.5 meters. ### Detailed Breakdown of the Diagram: - **Bar \( AB \):** - Length = 2 meters - Mass = 6 kg - Initially positioned horizontally - **Spring \( BC \):** - Initially unstretched - Fixed at point \( C \) and attached to point \( B \) - Length between \( B \) and fixed point \( C \) is 1.5 meters ### Conditions and Motion: - At the initial position, the bar \( AB \) is horizontal, and the spring is untensioned. - After release, the bar is expected to rotate clockwise. - The desired condition is that the bar comes to a momentary halt after rotating 90° (when point \( B \) is directly below point \( A \), making the spring fully stretched). This problem involves principles of rotational motion, energy conservation, and spring mechanics to determine the appropriate spring stiffness \( k \) that meets the given condition.
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