e with a speed of VA = ft/s increasing at The dimensions are LAB = 1.5 ft and LBC = instant shown A = 60° and 0c = 60°. ngular velocity and acceleration of link BC.
e with a speed of VA = ft/s increasing at The dimensions are LAB = 1.5 ft and LBC = instant shown A = 60° and 0c = 60°. ngular velocity and acceleration of link BC.
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 2**
The [Redacted] Mechanisms Lab is operating a hydraulic cylinder to drive the linkage with a speed of \( v_A = 4 \, \text{ft/s} \) increasing at \( a_A = 3 \, \text{ft/s}^2 \). The dimensions are \( L_{AB} = 1.5 \, \text{ft} \) and \( L_{BC} = 0.75 \, \text{ft} \). At the instant shown \( \theta_A = 60^\circ \) and \( \theta_C = 60^\circ \).
Determine the angular velocity and acceleration of link BC.
**Diagram Explanation:**
The provided diagram shows a mechanism consisting of a linkage system operated by a hydraulic cylinder. The linkage system involves two links, \( L_{AB} \) and \( L_{BC} \), connected at point B with point A and C being fixed supports.
- Link \( L_{AB} \) has a length of 1.5 feet, and link \( L_{BC} \) has a length of 0.75 feet.
- Point A is moving horizontally with a velocity \( v_A = 4 \, \text{ft/s} \) to the right and an acceleration \( a_A = 3 \, \text{ft/s}^2 \) to the right.
- The angles between the horizontal ground and links \( L_{AB} \) and \( L_{BC} \) are \( \theta_A = 60^\circ \) and \( \theta_C = 60^\circ \) respectively.
**Steps to Solve:**
1. **Determine Linear Velocities:**
- Use trigonometric relationships to determine the motion of point B using the known motion of point A.
2. **Calculate Angular Velocity (\(\omega\)) of BC:**
- Utilize the relationship between linear velocity and angular velocity, \( v_B = \omega_{BC} L_{BC} \).
3. **Determine Linear Accelerations:**
- Again, use the acceleration of point A and relationships between points within the linkage to find the acceleration of point B.
4. **Calculate Angular Acceleration (\(\alpha\)) of BC:**
- Use the relationship \( a_B = \alpha_{BC} L_{BC} \) considering tangential and centripetal components.
**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7b1f94a-aeb1-4e21-a353-b14674dcbf02%2F48220a48-64a1-4184-85ca-530d8acb0d05%2Fg52naf_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 2**
The [Redacted] Mechanisms Lab is operating a hydraulic cylinder to drive the linkage with a speed of \( v_A = 4 \, \text{ft/s} \) increasing at \( a_A = 3 \, \text{ft/s}^2 \). The dimensions are \( L_{AB} = 1.5 \, \text{ft} \) and \( L_{BC} = 0.75 \, \text{ft} \). At the instant shown \( \theta_A = 60^\circ \) and \( \theta_C = 60^\circ \).
Determine the angular velocity and acceleration of link BC.
**Diagram Explanation:**
The provided diagram shows a mechanism consisting of a linkage system operated by a hydraulic cylinder. The linkage system involves two links, \( L_{AB} \) and \( L_{BC} \), connected at point B with point A and C being fixed supports.
- Link \( L_{AB} \) has a length of 1.5 feet, and link \( L_{BC} \) has a length of 0.75 feet.
- Point A is moving horizontally with a velocity \( v_A = 4 \, \text{ft/s} \) to the right and an acceleration \( a_A = 3 \, \text{ft/s}^2 \) to the right.
- The angles between the horizontal ground and links \( L_{AB} \) and \( L_{BC} \) are \( \theta_A = 60^\circ \) and \( \theta_C = 60^\circ \) respectively.
**Steps to Solve:**
1. **Determine Linear Velocities:**
- Use trigonometric relationships to determine the motion of point B using the known motion of point A.
2. **Calculate Angular Velocity (\(\omega\)) of BC:**
- Utilize the relationship between linear velocity and angular velocity, \( v_B = \omega_{BC} L_{BC} \).
3. **Determine Linear Accelerations:**
- Again, use the acceleration of point A and relationships between points within the linkage to find the acceleration of point B.
4. **Calculate Angular Acceleration (\(\alpha\)) of BC:**
- Use the relationship \( a_B = \alpha_{BC} L_{BC} \) considering tangential and centripetal components.
**
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