---### 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 kg2. **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 Solution1. **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

Mass of the crate = m= 40kgSpring constant= k = 180N/mFree body diagram:-

In (Figure 1), k = 180 N/m. Figure Tc- 2 m- -3 m- wwwww 1 of 1 > Part A Determine the unstretched length of DB to hold the 40-kg crate in the position shown. Express your answer to three significant figures and include the appropriate units. 1= Value Submit HÅ Provide Feedback Request Answer Units ?

In (Figure 1), k = 180 N/m. Figure Tc- 2 m- -3 m- wwwww 1 of 1 > Part A Determine the unstretched length of DB to hold the 40-kg crate in the position shown. Express your answer to three significant figures and include the appropriate units. 1= Value Submit HÅ Provide Feedback Request Answer Units ?

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

5th Edition

ISBN:9781305084766

Author:Saeed Moaveni

Publisher:Saeed Moaveni

Chapter18: Mathematics In Engineering

Section: Chapter Questions

Problem 1P

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