58 ### 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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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

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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