m FIGURE 9-45 The angle 0 is 30° and the mass m is 200 kg. Find the tension in the two cords shown

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### Tension in Cords - Problem Analysis

**Figure 9-45:**

The diagram shows a system consisting of a mass \( m \) suspended by two cords. One cord is attached horizontally to a vertical support, while the other cord is inclined at an angle \( \theta \) to the horizontal and attached to a horizontal support.

**Given:**
- The angle \( \theta \) is \( 30^\circ \).
- The mass \( m \) is \( 200 \) kg.

**Objective:**
Determine the tension in each of the two cords.

**Detailed Breakdown:**

- **Inclined Cord (with angle \( \theta \)):**
    - This cord is at an angle \( 30^\circ \) with the horizontal. The tension in this cord will have both horizontal and vertical components.
    
- **Horizontal Cord:**
    - This cord is horizontal and will counteract only the horizontal component of the tension in the inclined cord.

**Steps for Problem Solving:**

1. **Analyze Forces:**
    - Resolve forces into their components:
      - Horizontal components.
      - Vertical components.
      
2. **Equilibrium Conditions:**
    - Utilize the equilibrium conditions for the system:
      - Sum of the horizontal forces should be zero.
      - Sum of the vertical forces should be zero.
    
3. **Formulate Equations:**
    - Use trigonometric functions to relate the tensions in the cords to the given angle and mass.

Please proceed with solving the equilibrium equations to find the tension in each cord.
Transcribed Image Text:### Tension in Cords - Problem Analysis **Figure 9-45:** The diagram shows a system consisting of a mass \( m \) suspended by two cords. One cord is attached horizontally to a vertical support, while the other cord is inclined at an angle \( \theta \) to the horizontal and attached to a horizontal support. **Given:** - The angle \( \theta \) is \( 30^\circ \). - The mass \( m \) is \( 200 \) kg. **Objective:** Determine the tension in each of the two cords. **Detailed Breakdown:** - **Inclined Cord (with angle \( \theta \)):** - This cord is at an angle \( 30^\circ \) with the horizontal. The tension in this cord will have both horizontal and vertical components. - **Horizontal Cord:** - This cord is horizontal and will counteract only the horizontal component of the tension in the inclined cord. **Steps for Problem Solving:** 1. **Analyze Forces:** - Resolve forces into their components: - Horizontal components. - Vertical components. 2. **Equilibrium Conditions:** - Utilize the equilibrium conditions for the system: - Sum of the horizontal forces should be zero. - Sum of the vertical forces should be zero. 3. **Formulate Equations:** - Use trigonometric functions to relate the tensions in the cords to the given angle and mass. Please proceed with solving the equilibrium equations to find the tension in each cord.
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