College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![### Problem Description:
A wrecking ball is suspended below two cables, each at an angle with the horizontal. The left cable has tension \( T1 \) and forms an angle \( α \) of 42 degrees with the horizontal. The right cable has tension \( T2 \) and forms an angle \( β \) of 26 degrees with the horizontal. The wrecking ball has a mass of 120 kg.
**Objective:**
Find the magnitude of tension \( T1 \).
### Detailed Diagram Explanation:
The diagram illustrates a rectangular structure from which a wrecking ball is suspended. Two cables attach the wrecking ball to the rectangular structure, one on the left and one on the right.
- The left cable makes an angle \( \alpha \) of 42 degrees with the horizontal and has a tension represented by \( \overrightarrow{T1} \).
- The right cable makes an angle \( \beta \) of 26 degrees with the horizontal and has a tension represented by \( \overrightarrow{T2} \).
### Key Elements in the Diagram:
1. **Rectangular Structure:**
- The point of attachment for both cables.
2. **Cables:**
- Left Cable (\( \overrightarrow{T1} \)) forms an angle \( \alpha \) (42 degrees) with the horizontal.
- Right Cable (\( \overrightarrow{T2} \)) forms an angle \( \beta \) (26 degrees) with the horizontal.
3. **Wrecking Ball:**
- Mass of 120 kg.
### Required Calculation:
To find the magnitude of tension \( T1 \):
1. **Identify Forces:**
- The gravitational force acting downward on the wrecking ball: \( F_g = m \cdot g \), where \( m \) is 120 kg and \( g \) is the acceleration due to gravity (9.8 m/s²).
\[
F_g = 120 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 1176 \, \text{N}
\]
2. **Establish Equilibrium Conditions:**
- For horizontal components: \(\sum F_x = T1 \cos(\alpha) - T2 \cos(\beta) = 0\)
- For vertical components: \(\sum F_y = T](https://content.bartleby.com/qna-images/question/c0f85ff8-2ea0-4d43-a0c0-84de96cc63b8/af564bf8-9c93-4ed2-91cb-93a2bff44271/0gmu8w_processed.png)
Transcribed Image Text:### Problem Description:
A wrecking ball is suspended below two cables, each at an angle with the horizontal. The left cable has tension \( T1 \) and forms an angle \( α \) of 42 degrees with the horizontal. The right cable has tension \( T2 \) and forms an angle \( β \) of 26 degrees with the horizontal. The wrecking ball has a mass of 120 kg.
**Objective:**
Find the magnitude of tension \( T1 \).
### Detailed Diagram Explanation:
The diagram illustrates a rectangular structure from which a wrecking ball is suspended. Two cables attach the wrecking ball to the rectangular structure, one on the left and one on the right.
- The left cable makes an angle \( \alpha \) of 42 degrees with the horizontal and has a tension represented by \( \overrightarrow{T1} \).
- The right cable makes an angle \( \beta \) of 26 degrees with the horizontal and has a tension represented by \( \overrightarrow{T2} \).
### Key Elements in the Diagram:
1. **Rectangular Structure:**
- The point of attachment for both cables.
2. **Cables:**
- Left Cable (\( \overrightarrow{T1} \)) forms an angle \( \alpha \) (42 degrees) with the horizontal.
- Right Cable (\( \overrightarrow{T2} \)) forms an angle \( \beta \) (26 degrees) with the horizontal.
3. **Wrecking Ball:**
- Mass of 120 kg.
### Required Calculation:
To find the magnitude of tension \( T1 \):
1. **Identify Forces:**
- The gravitational force acting downward on the wrecking ball: \( F_g = m \cdot g \), where \( m \) is 120 kg and \( g \) is the acceleration due to gravity (9.8 m/s²).
\[
F_g = 120 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 1176 \, \text{N}
\]
2. **Establish Equilibrium Conditions:**
- For horizontal components: \(\sum F_x = T1 \cos(\alpha) - T2 \cos(\beta) = 0\)
- For vertical components: \(\sum F_y = T
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