Title: Maximum Mass Calculation in Tension Cord System**Problem Statement:**Find the nearest maximum mass of the lamp that the cord system can support so that no single cord develops a tension exceeding 400 N.**Diagram Description:**The diagram shows a lamp suspended by a system of cords. The arrangement includes the following points:- Point A is attached to the wall.- Two cords extend from the wall to a central point C. - The cord from point A to point C is inclined and follows a 3-4-5 triangle. - The cord from point B to point C forms a 45° angle with the wall.- A horizontal cord extends from point C to point D.- A vertical cord extends from point D downward to point F, where the lamp is attached.- Another cord extends from point D to point E at a 30° angle with the horizontal and is attached to the wall.**Objective:**Determine the maximum mass of the lamp (at point F) that ensures none of the cords exceed a tension of 400 N.### Solution Approach:1. **Analyze the forces:** - The tension in each cord must be evaluated to ensure it does not exceed 400 N. - Calculate the vertical and horizontal components of the tension force in each segment.2. **Set up the equilibrium equations:** - For point C: Use horizontal and vertical force balance. - For point D: Use horizontal and vertical force balance.3. **Use trigonometric relations:** - For angled cords, decompose the forces into their components using trigonometric functions (sine and cosine). - Apply the Pythagorean theorem where necessary.4. **Calculate the resultant forces:** - Ensure that the sum of forces in horizontal and vertical directions equals zero (equilibrium). - Solve for the mass that results in the maximum permissible tension in any cord.By systematically applying these steps, the exact value of the maximum permissible mass can be derived while ensuring that the tension in no single cord exceeds the 400 N limit. This calculation requires careful consideration of both static equilibrium and the geometric relationships between cord lengths and angles.

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Description: Title: Maximum Mass Calculation in Tension Cord System**Problem Statement:**Find the nearest maximum mass of the lamp that the cord system can support so that no single cord develops a tension exceeding 400 N.**Diagram Description:**The diagram show

GivenMass of lamp, Standard Quantities

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Find the nearest maximum mass of the lamp that the cord system can support so that no single cord develops a tension exceeding 400 N. B 45° C F 30° E

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Title: Maximum Mass Calculation in Tension Cord System

**Problem Statement:**
Find the nearest maximum mass of the lamp that the cord system can support so that no single cord develops a tension exceeding 400 N.

**Diagram Description:**
The diagram shows a lamp suspended by a system of cords. The arrangement includes the following points:

- Point A is attached to the wall.
- Two cords extend from the wall to a central point C.
- The cord from point A to point C is inclined and follows a 3-4-5 triangle.
- The cord from point B to point C forms a 45° angle with the wall.
- A horizontal cord extends from point C to point D.
- A vertical cord extends from point D downward to point F, where the lamp is attached.
- Another cord extends from point D to point E at a 30° angle with the horizontal and is attached to the wall.

**Objective:**
Determine the maximum mass of the lamp (at point F) that ensures none of the cords exceed a tension of 400 N.

### Solution Approach:

1. **Analyze the forces:**
- The tension in each cord must be evaluated to ensure it does not exceed 400 N.
- Calculate the vertical and horizontal components of the tension force in each segment.

2. **Set up the equilibrium equations:**
- For point C: Use horizontal and vertical force balance.
- For point D: Use horizontal and vertical force balance.

3. **Use trigonometric relations:**
- For angled cords, decompose the forces into their components using trigonometric functions (sine and cosine).
- Apply the Pythagorean theorem where necessary.

4. **Calculate the resultant forces:**
- Ensure that the sum of forces in horizontal and vertical directions equals zero (equilibrium).
- Solve for the mass that results in the maximum permissible tension in any cord.

By systematically applying these steps, the exact value of the maximum permissible mass can be derived while ensuring that the tension in no single cord exceeds the 400 N limit. This calculation requires careful consideration of both static equilibrium and the geometric relationships between cord lengths and angles.

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