Find the tension on each of the two cable holding the mass. C 30° 40 kg B Draw a free body diagram. Label the horizontal cable, T₁, and the other cable, T2.

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**Title: Tension Calculation in Cables**

**Objective:** 
Determine the tension in each of the two cables supporting the mass.

**Description:**

In the given diagram, a mass of 40 kg (labeled as C) is suspended and held by two cables. The system includes:

- **Point A:** The junction where the mass connects to both cables.
- **Cable AD:** A horizontal cable attached to point D.
- **Cable AB:** An angled cable attached to point B, forming a 30-degree angle with the horizontal.
- **Mass (C):** Weighing 40 kg, suspended from point A.

**Problem Statement:**
- Calculate the tension in each cable (AD and AB) that holds the mass.

**Instructions:**
1. Draw a free body diagram.
2. Label the horizontal cable as \( T_1 \).
3. Label the angled cable as \( T_2 \).

**Analysis:**
The system requires balancing forces along both the horizontal and vertical axes to maintain equilibrium. Consider applying Newton’s second law and trigonometric identities to solve for tensions \( T_1 \) and \( T_2 \).

**Note:** 
Remember the gravitational force acting on the mass, \( W = mg = 40 \, \text{kg} \times 9.8 \, \text{m/s}^{2} \).
Transcribed Image Text:**Title: Tension Calculation in Cables** **Objective:** Determine the tension in each of the two cables supporting the mass. **Description:** In the given diagram, a mass of 40 kg (labeled as C) is suspended and held by two cables. The system includes: - **Point A:** The junction where the mass connects to both cables. - **Cable AD:** A horizontal cable attached to point D. - **Cable AB:** An angled cable attached to point B, forming a 30-degree angle with the horizontal. - **Mass (C):** Weighing 40 kg, suspended from point A. **Problem Statement:** - Calculate the tension in each cable (AD and AB) that holds the mass. **Instructions:** 1. Draw a free body diagram. 2. Label the horizontal cable as \( T_1 \). 3. Label the angled cable as \( T_2 \). **Analysis:** The system requires balancing forces along both the horizontal and vertical axes to maintain equilibrium. Consider applying Newton’s second law and trigonometric identities to solve for tensions \( T_1 \) and \( T_2 \). **Note:** Remember the gravitational force acting on the mass, \( W = mg = 40 \, \text{kg} \times 9.8 \, \text{m/s}^{2} \).
Expert Solution
Step 1

Given data: 

Mass (m) = 40 kh

Required:

The free body diagram, the tension in horizontal cable (T1) and tension in other cable (T2

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