Given the hydraulic cylinder AB shortens at a constant rate of 0.15 m/s so that girder G of a bascule bridge is raised. Find the angular velocity of the bridge girder when Theta =60°.

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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**Problem Statement:**

Given the hydraulic cylinder AB shortens at a constant rate of 0.15 m/s so that girder G of a bascule bridge is raised. Find the angular velocity of the bridge girder when Theta = 60°.

**Diagram Explanation:**

The image depicts a mechanical system of a bascule bridge where:
- A hydraulic cylinder (AB) is connected to point A on the ground and point B on the girder G.
- The girder G is modeled as a rigid body pivoting counterclockwise about point C.
- The initial setup includes a horizontal distance of 5 meters from point A to point C, and a vertical height of 3 meters for the girder's position.
- An angle θ is marked at point C, showing the inclination of the girder.
- The girder is represented with an angled surface, and the angle θ is specified as 60°.

This scenario models a real-world problem where the rate of contraction of the hydraulic cylinder is used to determine the angular velocity of the bridge girder. The analysis involves the use of kinematics to find the relationship between linear speed and angular motion.
Transcribed Image Text:**Problem Statement:** Given the hydraulic cylinder AB shortens at a constant rate of 0.15 m/s so that girder G of a bascule bridge is raised. Find the angular velocity of the bridge girder when Theta = 60°. **Diagram Explanation:** The image depicts a mechanical system of a bascule bridge where: - A hydraulic cylinder (AB) is connected to point A on the ground and point B on the girder G. - The girder G is modeled as a rigid body pivoting counterclockwise about point C. - The initial setup includes a horizontal distance of 5 meters from point A to point C, and a vertical height of 3 meters for the girder's position. - An angle θ is marked at point C, showing the inclination of the girder. - The girder is represented with an angled surface, and the angle θ is specified as 60°. This scenario models a real-world problem where the rate of contraction of the hydraulic cylinder is used to determine the angular velocity of the bridge girder. The analysis involves the use of kinematics to find the relationship between linear speed and angular motion.
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