Two small spheres with mass m = 14.4 g are hung by silk threads of length L = 1.12 m from a common point. When the spheres are given equal charges so that q1 = q2 = q = 1.83 µC each thread hangs at an angle 0 from the vertical. Draw a free-body diagram of the right sphere, then find the angle 0. 5.00⁰ 10.0⁰ 15.0⁰ 20.0⁰ 25.0⁰ L mass m charge q mass m charge q

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Chapter1: Units, Trigonometry. And Vectors
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**Two small spheres with mass \( m = 14.4 \, \text{g} \) are hung by silk threads of length \( L = 1.12 \, \text{m} \) from a common point. When the spheres are given equal charges so that \( q_1 = q_2 = q = 1.83 \, \mu\text{C} \), each thread hangs at an angle \( \theta \) from the vertical. Draw a free-body diagram of the right sphere, then find the angle \( \theta \).**

Options:

- 5.00°
- 10.0°
- 15.0°
- 20.0°
- 25.0°

**Diagram Explanation:**

The diagram depicts two small spheres, each with mass \( m \), suspended from a common point by silk threads of length \( L \). Each sphere carries a charge \( q \), and the threads form an angle \( \theta \) with the vertical. The spheres repel each other due to their identical charges.

**Free-Body Diagram of the Right Sphere:**

- **Tension (\( T \))**: Acts along the length of the thread.
- **Gravitational Force (\( mg \))**: Acts vertically downward.
- **Electrostatic Force (\( F_e \))**: Acts horizontally, pushing the spheres apart.

The angle \( \theta \) can be determined by analyzing the forces and using trigonometric relationships.
Transcribed Image Text:**Two small spheres with mass \( m = 14.4 \, \text{g} \) are hung by silk threads of length \( L = 1.12 \, \text{m} \) from a common point. When the spheres are given equal charges so that \( q_1 = q_2 = q = 1.83 \, \mu\text{C} \), each thread hangs at an angle \( \theta \) from the vertical. Draw a free-body diagram of the right sphere, then find the angle \( \theta \).** Options: - 5.00° - 10.0° - 15.0° - 20.0° - 25.0° **Diagram Explanation:** The diagram depicts two small spheres, each with mass \( m \), suspended from a common point by silk threads of length \( L \). Each sphere carries a charge \( q \), and the threads form an angle \( \theta \) with the vertical. The spheres repel each other due to their identical charges. **Free-Body Diagram of the Right Sphere:** - **Tension (\( T \))**: Acts along the length of the thread. - **Gravitational Force (\( mg \))**: Acts vertically downward. - **Electrostatic Force (\( F_e \))**: Acts horizontally, pushing the spheres apart. The angle \( \theta \) can be determined by analyzing the forces and using trigonometric relationships.
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