6) Bar BDE is attached to two links AB and CD. Knowing that at the instant shown link AB rotates with a constant angular velocity of 3 rad/s clockwise, determine the acceleration (a) of point D, (b) of point E. 19.1 cm 19.1 cm C -30.5 cm B OD

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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### Problem Statement:

**6)**

Bar **BDE** is attached to two links **AB** and **CD**. Knowing that at the instant shown, link **AB** rotates with a constant angular velocity of 3 rad/s clockwise, determine the acceleration:

(a) of point **D**, 
(b) of point **E**.

#### Detailed Diagram Description:

The diagram provided is a mechanical link system consisting of three points (A, B, and D) and two links (AB and CD). Here are the key measurements and components:

- **Link AB**: 
  - Length: 30.5 cm
  - Positioned horizontally with point **A** fixed and point **B** rotating.

- **Link CD**:
  - Two segments, both vertical:
    - The first segment is 19.1 cm in length from point **C** to point **D**.
    - The second segment is 19.1 cm from point **D** to point **E**.
  - Fixed at points **C** and **E**.

- **Bar BDE**:
  - Extends horizontally from point **B** (joint with link **AB**) to point **E** (at the end of link **CD**).

- The bottom horizontal distance from point **C** to **E** is 22.9 cm.

### Analytical Explanation:

#### Given:
- Angular velocity of link **AB** (ω): 3 rad/s (clockwise).

### Objective:
Calculate the acceleration of points **D** and **E**.

### Solution Approach:

1. **Angular Velocity and Acceleration Analysis**:
   - Compute linear velocities and accelerations of points based on given angular velocity.
   - Angular components contribution to accelerations.

2. **Point D and Point E Calculations**:
   - Use appropriate kinematic relationships for rotational motion to determine the absolute acceleration of both points taking into account the constraints provided by the bar and link system.

### Conclusion:

#### Understanding the Kinematics:
For each point:
- The acceleration of point **D** located midway on bar **BDE**.
- The acceleration of point **E** considering the entire motion constraints imposed by links **AB** and **CD**.

The precise computational steps involve physics principles such as angular velocity (ω), tangential acceleration, and rotational formulas.

**End of the Exercise Explanation**
Transcribed Image Text:### Problem Statement: **6)** Bar **BDE** is attached to two links **AB** and **CD**. Knowing that at the instant shown, link **AB** rotates with a constant angular velocity of 3 rad/s clockwise, determine the acceleration: (a) of point **D**, (b) of point **E**. #### Detailed Diagram Description: The diagram provided is a mechanical link system consisting of three points (A, B, and D) and two links (AB and CD). Here are the key measurements and components: - **Link AB**: - Length: 30.5 cm - Positioned horizontally with point **A** fixed and point **B** rotating. - **Link CD**: - Two segments, both vertical: - The first segment is 19.1 cm in length from point **C** to point **D**. - The second segment is 19.1 cm from point **D** to point **E**. - Fixed at points **C** and **E**. - **Bar BDE**: - Extends horizontally from point **B** (joint with link **AB**) to point **E** (at the end of link **CD**). - The bottom horizontal distance from point **C** to **E** is 22.9 cm. ### Analytical Explanation: #### Given: - Angular velocity of link **AB** (ω): 3 rad/s (clockwise). ### Objective: Calculate the acceleration of points **D** and **E**. ### Solution Approach: 1. **Angular Velocity and Acceleration Analysis**: - Compute linear velocities and accelerations of points based on given angular velocity. - Angular components contribution to accelerations. 2. **Point D and Point E Calculations**: - Use appropriate kinematic relationships for rotational motion to determine the absolute acceleration of both points taking into account the constraints provided by the bar and link system. ### Conclusion: #### Understanding the Kinematics: For each point: - The acceleration of point **D** located midway on bar **BDE**. - The acceleration of point **E** considering the entire motion constraints imposed by links **AB** and **CD**. The precise computational steps involve physics principles such as angular velocity (ω), tangential acceleration, and rotational formulas. **End of the Exercise Explanation**
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