Structural Analysis
Structural Analysis
6th Edition
ISBN: 9781337630931
Author: KASSIMALI, Aslam.
Publisher: Cengage,
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Collection Systems
The collection systems form a part of sanitary engineering, which is a sub-branch of civil engineering. It is also known as public health engineering and wastewater engineering. It is a methodology followed to remove and properly dispose of human waste, …
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--- ### Physics Problem: Determining the Unstretched Length of a Spring System In this problem, we are tasked with finding the unstretched length of the spring \(DB\) to hold a 40-kg crate in the position depicted in the diagram. The spring constant, \(k\), is provided as 180 N/m. 1. **Given Data:** - Spring constant, \(k\) = 180 N/m - Mass of crate = 40 kg 2. **Diagram Explanation:** - The diagram displays a system with a crate \(A\) suspended and connected to point \(D\). - Point \(D\) is connected to points \(B\) and \(C\) by a spring and a rigid rod, respectively. - The coordinates for points are given: - \(D\) is located at the origin. - \(C\) is at a horizontal distance of 2 meters to the left of \(D\) and a vertical distance of 2 meters above \(D\). - \(B\) is at a horizontal distance of 3 meters to the right of \(D\) and the same vertical distance of 2 meters above \(D\). 3. **Objective:** - Determine the unstretched length \(l\) of the spring \(DB\) in order to balance the system as illustrated. --- ### Steps to Solution 1. **Calculate the Weight of the Crate:** - Weight = mass \(\times\) gravitational acceleration - Weight \(W = 40 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 392.4 \, \text{N}\) 2. **Analyze the Geometry:** - The distances are relative to the initial position \(D\). - Length of \(CD = 2 \, \text{m}\) - Length of \(BD = \sqrt{3^2 + 2^2} = \sqrt{13} \, \text{m}\) 3. **Determine the Unstretched Length \(l\):** - Applying equilibrium conditions and utilizing Hooke's Law for springs will be necessary for deriving the solution. Express your answer to three significant figures and include the appropriate units by inputting it in the provided solution box. --- ### Solution Input Format ```markdown
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Transcribed Image Text:--- ### Physics Problem: Determining the Unstretched Length of a Spring System In this problem, we are tasked with finding the unstretched length of the spring \(DB\) to hold a 40-kg crate in the position depicted in the diagram. The spring constant, \(k\), is provided as 180 N/m. 1. **Given Data:** - Spring constant, \(k\) = 180 N/m - Mass of crate = 40 kg 2. **Diagram Explanation:** - The diagram displays a system with a crate \(A\) suspended and connected to point \(D\). - Point \(D\) is connected to points \(B\) and \(C\) by a spring and a rigid rod, respectively. - The coordinates for points are given: - \(D\) is located at the origin. - \(C\) is at a horizontal distance of 2 meters to the left of \(D\) and a vertical distance of 2 meters above \(D\). - \(B\) is at a horizontal distance of 3 meters to the right of \(D\) and the same vertical distance of 2 meters above \(D\). 3. **Objective:** - Determine the unstretched length \(l\) of the spring \(DB\) in order to balance the system as illustrated. --- ### Steps to Solution 1. **Calculate the Weight of the Crate:** - Weight = mass \(\times\) gravitational acceleration - Weight \(W = 40 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 392.4 \, \text{N}\) 2. **Analyze the Geometry:** - The distances are relative to the initial position \(D\). - Length of \(CD = 2 \, \text{m}\) - Length of \(BD = \sqrt{3^2 + 2^2} = \sqrt{13} \, \text{m}\) 3. **Determine the Unstretched Length \(l\):** - Applying equilibrium conditions and utilizing Hooke's Law for springs will be necessary for deriving the solution. Express your answer to three significant figures and include the appropriate units by inputting it in the provided solution box. --- ### Solution Input Format ```markdown
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Step 1: Given data:-
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Step 2: Calculation of forces in cable and spring:-
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Step 3: Unstretch length of DB:-
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