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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18-50. The pavement compactor is traveling down the incline at VG = 5 ft/s when the motor is disengaged. Determine the angular velocity of the roller B when the compactor has traveled 20 ft down the plane. The body of the compactor, excluding the rollers, has a weight of 8000 lb and a center of gravity at G. Each of the two rear rollers weighs 400 lb and has a radius of gyration of k= 3.3 ft. The front roller has a weight of 800 lb and a radius of gyration of kg = 1.8 ft. The rollers do not slip as they rotate. 3.8 ft 5 GT- 5 ftl 12.2 ft 10 ft 30° B

18-50. The pavement compactor is traveling down the incline at VG = 5 ft/s when the motor is disengaged. Determine the angular velocity of the roller B when the compactor has traveled 20 ft down the plane. The body of the compactor, excluding the rollers, has a weight of 8000 lb and a center of gravity at G. Each of the two rear rollers weighs 400 lb and has a radius of gyration of k= 3.3 ft. The front roller has a weight of 800 lb and a radius of gyration of kg = 1.8 ft. The rollers do not slip as they rotate. 3.8 ft 5 GT- 5 ftl 12.2 ft 10 ft 30° B

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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