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The 64.4-lb crate slides down the curved path in the vertical plane. If the crate has a velocity of 3 ft∕sec down the incline at A and a velocity of 0 ft∕sec at B, compute the work Uƒ done on the crate by friction during the motion from A to B

The 64.4-lb crate slides down the curved path in the vertical plane. If the crate has a velocity of 3 ft∕sec down the incline at A and a velocity of 0 ft∕sec at B, compute the work Uƒ done on the crate by friction during the motion from A to B

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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The 64.4-lb crate slides down the curved path in the vertical plane. If the crate has a velocity of 3 ft∕sec down the incline at A and a velocity of 0 ft∕sec at B, compute the work Uƒ done on the crate by friction during the motion from A to B.

### Motion of a Block Down an Inclined Plane #### Diagram Illustration The diagram provided illustrates the motion of a block moving down an inclined plane. The key features and details of the diagram are as follows: 1. **Block A**: - Block A is positioned at the top of the inclined plane. - It begins its motion with an initial velocity of 3 feet per second (ft/sec) directed downward along the plane. 2. **Height of Inclined Plane**: - The vertical height of the inclined segment from the top to the bottom is 20 feet. 3. **Block B**: - Block B is located at the bottom right of the diagram, resting on a horizontal surface. 4. **Distance Between Blocks**: - The horizontal distance from the bottom of the inclined plane (where Block A reaches the flat surface) to Block B is 30 feet. #### Understanding the Diagram - The inclined plane and the path taken by Block A is depicted with a smooth curve transitioning to a flat surface where Block B is placed. - The motion of Block A is driven by gravitational force, starting from a height of 20 feet. - As Block A descends from the height of 20 feet with an initial velocity of 3 ft/sec, it transitions from the inclined path to the horizontal path. - The horizontal separation indicates that once Block A reaches the flat surface, it must cover an additional 30 feet to reach Block B. #### Applications This diagram can be studied to understand the principles of: - Kinematics: Describing the motion in terms of initial velocity, distance traveled, and acceleration due to gravity. - Dynamics: Analyzing the forces acting on Block A as it moves down the inclined plane. By studying such diagrams, students can gain insights into the mechanics of motion under the influence of gravity and the interplay of initial velocities, distances, and heights in determining the final positions and velocities of objects.
Transcribed Image Text:### Motion of a Block Down an Inclined Plane #### Diagram Illustration The diagram provided illustrates the motion of a block moving down an inclined plane. The key features and details of the diagram are as follows: 1. **Block A**: - Block A is positioned at the top of the inclined plane. - It begins its motion with an initial velocity of 3 feet per second (ft/sec) directed downward along the plane. 2. **Height of Inclined Plane**: - The vertical height of the inclined segment from the top to the bottom is 20 feet. 3. **Block B**: - Block B is located at the bottom right of the diagram, resting on a horizontal surface. 4. **Distance Between Blocks**: - The horizontal distance from the bottom of the inclined plane (where Block A reaches the flat surface) to Block B is 30 feet. #### Understanding the Diagram - The inclined plane and the path taken by Block A is depicted with a smooth curve transitioning to a flat surface where Block B is placed. - The motion of Block A is driven by gravitational force, starting from a height of 20 feet. - As Block A descends from the height of 20 feet with an initial velocity of 3 ft/sec, it transitions from the inclined path to the horizontal path. - The horizontal separation indicates that once Block A reaches the flat surface, it must cover an additional 30 feet to reach Block B. #### Applications This diagram can be studied to understand the principles of: - Kinematics: Describing the motion in terms of initial velocity, distance traveled, and acceleration due to gravity. - Dynamics: Analyzing the forces acting on Block A as it moves down the inclined plane. By studying such diagrams, students can gain insights into the mechanics of motion under the influence of gravity and the interplay of initial velocities, distances, and heights in determining the final positions and velocities of objects.
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