0.4 m E 0.3 m k = 500 N/m D B 0.15 m

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Problem Description:**

The 20-kg sphere \( C \) is released from rest when \( \theta = 0^\circ \) and the tension in the spring is \( F = 100 \, \text{N} \).

**Objective:**

Determine the speed of the sphere at the instant \( \theta = 90^\circ \). Neglect the mass of rod \( AB \) and the size of the sphere.

Express your answer to three significant figures and include the appropriate units.

**Input Fields:**
- \( v = \) [Value] [Units]
  
**Options:**
- Submit
- Request Answer
- Provide Feedback

**Figure Explanation:**

The diagram illustrates a setup involving:
- A horizontal rod labeled \( AB \) with a 20-kg sphere labeled \( C \) at point \( B \).
- A spring with a constant \( k = 500 \, \text{N/m} \) attached to a fixed point \( E \) vertically above point \( A \), the spring is initially at an angle \( \theta \).
- The rest position of the spring when \( \theta = 0^\circ \).
- Distance \( AB = 0.3 \, \text{m} \) and distance \( BD = 0.15 \, \text{m} \).
- Vertical height \( AE = 0.4 \, \text{m} \).

**Instructions:**

- Calculate the speed of the sphere \( C \) as it reaches \( \theta = 90^\circ \).
- Consider energy conservation and equations of motion for accurate results.
  
**Next Steps:**
- Proceed to the next problem or review the calculations done.
Transcribed Image Text:**Problem Description:** The 20-kg sphere \( C \) is released from rest when \( \theta = 0^\circ \) and the tension in the spring is \( F = 100 \, \text{N} \). **Objective:** Determine the speed of the sphere at the instant \( \theta = 90^\circ \). Neglect the mass of rod \( AB \) and the size of the sphere. Express your answer to three significant figures and include the appropriate units. **Input Fields:** - \( v = \) [Value] [Units] **Options:** - Submit - Request Answer - Provide Feedback **Figure Explanation:** The diagram illustrates a setup involving: - A horizontal rod labeled \( AB \) with a 20-kg sphere labeled \( C \) at point \( B \). - A spring with a constant \( k = 500 \, \text{N/m} \) attached to a fixed point \( E \) vertically above point \( A \), the spring is initially at an angle \( \theta \). - The rest position of the spring when \( \theta = 0^\circ \). - Distance \( AB = 0.3 \, \text{m} \) and distance \( BD = 0.15 \, \text{m} \). - Vertical height \( AE = 0.4 \, \text{m} \). **Instructions:** - Calculate the speed of the sphere \( C \) as it reaches \( \theta = 90^\circ \). - Consider energy conservation and equations of motion for accurate results. **Next Steps:** - Proceed to the next problem or review the calculations done.
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