### Determining Forces in Cables BC and BD with a Spring System**Problem Statement:**The spring has a stiffness of \( k = 800 \, \text{N/m} \) and an unstretched length of 200 mm. Determine the force in cables BC and BD when the spring is held in the position shown.**Given Data:**- Stiffness of spring \( k = 800 \, \text{N/m} \)- Unstretched length of spring: 200 mm- Horizontal distance from point A to point B: 500 mm (AB)- Distance from point B to the wall along the horizontal direction: 400 mm (BC)- Vertical distance from point C to point B: 400 mm (BC)- Vertical distance from point D to point B: 300 mm (BD)**Diagram Description:**The illustration shows a spring connected between points A and B. The spring has a noted stiffness of 800 N/m. Point B is connected to two cables, BC and BD, which support it vertically.- Point A is fixed to the left boundary.- The spring is extended to point B on the horizontal, which is 500 mm from A.- Point B is vertically supported by cable BC extending 400 mm upwards to point C, and cable BD extending 300 mm downwards to point D.### Steps to Solve:1. **Calculate the extended length of the spring AB:** Use the given coordinates to find the actual length of AB using the Pythagorean Theorem.2. **Determine the elongation of the spring:** \[ \Delta L = L_{AB} - L_0 \] where \( L_0 \) is the original length (200 mm).3. **Find the force in the spring from Hooke's Law:** \[ F = k \Delta L \] 4. **Resolve forces in horizontal and vertical directions:** The forces in cables BC and BD need to be found by analyzing the equilibrium of forces at point B.5. **Set up equilibrium equations:** \[ \sum F_x = 0 \quad \text{(horizontal equilibrium)} \] \[ \sum F_y = 0 \quad \text{(vertical equilibrium)} \]### Solution:Following these steps involves detailed calculations of trigon

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The spring has a stiffness of k = 800 N/m and an unstretched length of 200 mm. Determine the force in cables BC and BD when the spring is held in the position shown. A k = 800 N/m www -500 mm -400 mm- D 400 mm 300 mm

The spring has a stiffness of k = 800 N/m and an unstretched length of 200 mm. Determine the force in cables BC and BD when the spring is held in the position shown. A k = 800 N/m www -500 mm -400 mm- D 400 mm 300 mm

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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