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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

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
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 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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