Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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The problem presented involves a pavement compactor descending an inclined plane. The compactor has an initial velocity of \( v_G = 5 \, \text{ft/s} \) when its motor is disengaged. The task is to calculate the angular velocity of the roller \( B \) after the compactor has traveled 20 feet down the plane. 

Key data include:

- **Compactor Body**: Excluding the rollers, the body weighs 8000 lb and has its center of gravity at \( G \).

- **Rear Rollers**: Each of the two rear rollers weighs 400 lb with a radius of gyration \( k_A = 3.3 \, \text{ft} \).

- **Front Roller**: This roller weighs 800 lb with a radius of gyration \( k_B = 1.8 \, \text{ft} \).

- **Non-slip Condition**: The rollers roll without slipping as they rotate.

### Diagram Explanation:

- The diagram depicts the compactor on a \( 30^\circ \) incline. Measurements are as follows:
  - Distance from the center of gravity \( G \) to the point of contact with the rear roller on the incline is 5 ft.
  - Horizontal distance from \( G \) to the front roller \( B \) is 10 ft.
  - Vertical distance from the plane to the center of gravity \( G \) is 4.5 ft.
  - The radius of the rear roller \( A \) is 3.8 ft.
  - The point of contact of the front roller \( B \) is shown 2.2 ft above the ground on the incline.

The compactor's motion involves both translational and rotational dynamics, requiring an understanding of moments of inertia and kinematics.
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Transcribed Image Text:The problem presented involves a pavement compactor descending an inclined plane. The compactor has an initial velocity of \( v_G = 5 \, \text{ft/s} \) when its motor is disengaged. The task is to calculate the angular velocity of the roller \( B \) after the compactor has traveled 20 feet down the plane. Key data include: - **Compactor Body**: Excluding the rollers, the body weighs 8000 lb and has its center of gravity at \( G \). - **Rear Rollers**: Each of the two rear rollers weighs 400 lb with a radius of gyration \( k_A = 3.3 \, \text{ft} \). - **Front Roller**: This roller weighs 800 lb with a radius of gyration \( k_B = 1.8 \, \text{ft} \). - **Non-slip Condition**: The rollers roll without slipping as they rotate. ### Diagram Explanation: - The diagram depicts the compactor on a \( 30^\circ \) incline. Measurements are as follows: - Distance from the center of gravity \( G \) to the point of contact with the rear roller on the incline is 5 ft. - Horizontal distance from \( G \) to the front roller \( B \) is 10 ft. - Vertical distance from the plane to the center of gravity \( G \) is 4.5 ft. - The radius of the rear roller \( A \) is 3.8 ft. - The point of contact of the front roller \( B \) is shown 2.2 ft above the ground on the incline. The compactor's motion involves both translational and rotational dynamics, requiring an understanding of moments of inertia and kinematics.
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