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but change the spring constant (k) of spring DB to 310 N/m

but change the spring constant (k) of spring DB to 310 N/m

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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but change the spring constant (k) of spring DB to 310 N/m
**Problem 3–11: Spring System Analysis** **Objective:** Determine the unstretched length of the spring \(DB\) required to hold a 40-kg crate in the given position. The spring constant \(k\) is given as 180 N/m. **Diagram Explanation:** - The diagram shows a static system where a crate (mass = 40 kg) is suspended by a system of cords and a spring. - The crate is labeled \(A\) and hangs from point \(D\). - Line \(CD\) is a cable with a length of 2 meters and extends horizontally left from point \(C\) (a fixed support) to point \(D\). - Line \(DB\) is attached to point \(B\), which is 3 meters horizontally to the right of point \(D\). - A spring is attached between points \(B\) and \(D\). The spring is depicted with coils, and it is at angle with line segment \(DB\). **System Dimensions:** - The vertical distance from point \(C\) to point \(D\) is 2 meters. - Horizontally, point \(C\) is 2 meters to the left of point \(D\), and point \(B\) is 3 meters to the right of point \(D\). **Parameters:** - Spring constant, \(k = 180 \, \text{N/m}\). - The weight of the crate creates a force due to gravity, \(W = mg = 40 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 392.4 \, \text{N}\). **Objective:** Calculate the unstretched length of the spring \(DB\) to maintain equilibrium in the described setup. (Note: Solve for the unstressed length of the spring using equilibrium equations related to forces and geometry of the system.)
Transcribed Image Text:**Problem 3–11: Spring System Analysis** **Objective:** Determine the unstretched length of the spring \(DB\) required to hold a 40-kg crate in the given position. The spring constant \(k\) is given as 180 N/m. **Diagram Explanation:** - The diagram shows a static system where a crate (mass = 40 kg) is suspended by a system of cords and a spring. - The crate is labeled \(A\) and hangs from point \(D\). - Line \(CD\) is a cable with a length of 2 meters and extends horizontally left from point \(C\) (a fixed support) to point \(D\). - Line \(DB\) is attached to point \(B\), which is 3 meters horizontally to the right of point \(D\). - A spring is attached between points \(B\) and \(D\). The spring is depicted with coils, and it is at angle with line segment \(DB\). **System Dimensions:** - The vertical distance from point \(C\) to point \(D\) is 2 meters. - Horizontally, point \(C\) is 2 meters to the left of point \(D\), and point \(B\) is 3 meters to the right of point \(D\). **Parameters:** - Spring constant, \(k = 180 \, \text{N/m}\). - The weight of the crate creates a force due to gravity, \(W = mg = 40 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 392.4 \, \text{N}\). **Objective:** Calculate the unstretched length of the spring \(DB\) to maintain equilibrium in the described setup. (Note: Solve for the unstressed length of the spring using equilibrium equations related to forces and geometry of the system.)
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Determine the unstretched length of DB to hold the 40-kg crate in the position shown. Take k = 310 N/m.

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