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1.5 m -3 m/s wwww k = 100 N/m B

1.5 m -3 m/s wwww k = 100 N/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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The 5-kg smooth collar has a speed of 3 m/sm/s when it is at s = 0. The spring has an unstretched length of 1 mm. 

Determine the maximum distance ss the collar travels before it stops momentarily.

This diagram represents a mechanical system involving a spring and a vertical motion element. Here is a detailed description of the components and measurements: 1. **Spring Connected to a Wall:** - The spring is attached to a fixed wall on one end and connects to point \( A \) on the other end. The spring has a stiffness constant \( k = 100 \, \text{N/m} \). 2. **Mechanical Structure:** - A vertically oriented rod is shown, with point \( A \) connected to the spring. - Point \( B \) is marked on the rod below point \( A \). 3. **Displacement and Velocity:** - The distance from the wall to point \( A \) where the spring is attached is \( 1.5 \, \text{m} \). - The rod is moving vertically downward with a velocity of \( 3 \, \text{m/s} \). - The vertical displacement from point \( A \) towards a reference point below is denoted by \( s \). **Graphical Explanation:** - **Spring Representation:** The spring is illustrated as a coiled line, with a stiffness constant labeled as \( k = 100 \, \text{N/m} \). The spring is horizontal and appropriately compressed or stretched. - **Rod and Movement:** The rod is shown in a vertical position with both ends connected to fixed horizontal surfaces. The significant points \( A \) and \( B \) are highlighted along the rod. - **Measurements:** - Horizontal measurement from the wall to the attachment point \( A \) of the spring is given as \( 1.5 \, \text{m} \). - The downward velocity of the rod at point \( A \) is indicated as \( 3 \, \text{m/s} \). - The variable \( s \) indicates the measure of vertical displacement at point \( A \). This system can be used in various educational contexts, such as explaining the principles of mechanical oscillations, the behavior of springs under load, and the dynamics of vertically moving bodies. The combination of spring stiffness, displacement, and velocity introduces topics like Hooke's Law, kinetic energy, and potential energy in mechanical systems.
Transcribed Image Text:This diagram represents a mechanical system involving a spring and a vertical motion element. Here is a detailed description of the components and measurements: 1. **Spring Connected to a Wall:** - The spring is attached to a fixed wall on one end and connects to point \( A \) on the other end. The spring has a stiffness constant \( k = 100 \, \text{N/m} \). 2. **Mechanical Structure:** - A vertically oriented rod is shown, with point \( A \) connected to the spring. - Point \( B \) is marked on the rod below point \( A \). 3. **Displacement and Velocity:** - The distance from the wall to point \( A \) where the spring is attached is \( 1.5 \, \text{m} \). - The rod is moving vertically downward with a velocity of \( 3 \, \text{m/s} \). - The vertical displacement from point \( A \) towards a reference point below is denoted by \( s \). **Graphical Explanation:** - **Spring Representation:** The spring is illustrated as a coiled line, with a stiffness constant labeled as \( k = 100 \, \text{N/m} \). The spring is horizontal and appropriately compressed or stretched. - **Rod and Movement:** The rod is shown in a vertical position with both ends connected to fixed horizontal surfaces. The significant points \( A \) and \( B \) are highlighted along the rod. - **Measurements:** - Horizontal measurement from the wall to the attachment point \( A \) of the spring is given as \( 1.5 \, \text{m} \). - The downward velocity of the rod at point \( A \) is indicated as \( 3 \, \text{m/s} \). - The variable \( s \) indicates the measure of vertical displacement at point \( A \). This system can be used in various educational contexts, such as explaining the principles of mechanical oscillations, the behavior of springs under load, and the dynamics of vertically moving bodies. The combination of spring stiffness, displacement, and velocity introduces topics like Hooke's Law, kinetic energy, and potential energy in mechanical systems.
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