The image shows a roller with weight \( W \) and diameter \( R \) being pushed to the left over a tile of thickness \( \delta \). The roller is in a state of momentary mechanical equilibrium as it rolls over the sharp corner of the tile.### Diagram Explanation- The roller is depicted with a horizontal surface underneath and a deviation at the point of the tile edge.- A force \( P \) is applied at an angle \( \theta \) to the horizontal.- The weight \( W \) acts vertically downward at the roller’s center.- The radius from the center of the roller to the contact point with the tile edge is labeled \( r \).- Two angles are indicated within the roller: - \( \alpha \), the angle between the vertical line through \( W \) and the radius \( r \). - \( \theta \), the angle of the force \( P \) from the horizontal. ### Tasksa. **Free Body Diagram**: - Sketch a free body diagram showing all the forces acting on the roller at this moment of equilibrium.b. **Force Triangle Sketch**: - Illustrate the closed force vector triangle that represents the equilibrium condition. Note that this sketch is not to scale.c. **Interior Angles of Force Triangle**: - Express each angle in the force triangle in terms of \( \alpha \) and \( \theta \), and label each force vector and angle.d. **Relation Establishment**: - Derive a relationship between \( \alpha \), \( \delta \), and \( r \).e. **Expression for Force \( P \)**: - Use static equilibrium and the law of sines to derive an expression for \( P \) in terms of \( W \), \( r \), \( \delta \), and \( \theta \).

Answered: 8 0 P | bartleby

Engineering

Mechanical Engineering

8 0 P

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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Concept explainers

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provide resistance in changing its state of velocity or motion for coming to a state of rest. In other words, Newton's first law of motion describes the law of inertia of a rigid body.

Question

The image shows a roller with weight \( W \) and diameter \( R \) being pushed to the left over a tile of thickness \( \delta \). The roller is in a state of momentary mechanical equilibrium as it rolls over the sharp corner of the tile.

### Diagram Explanation
- The roller is depicted with a horizontal surface underneath and a deviation at the point of the tile edge.
- A force \( P \) is applied at an angle \( \theta \) to the horizontal.
- The weight \( W \) acts vertically downward at the roller’s center.
- The radius from the center of the roller to the contact point with the tile edge is labeled \( r \).
- Two angles are indicated within the roller:
- \( \alpha \), the angle between the vertical line through \( W \) and the radius \( r \).
- \( \theta \), the angle of the force \( P \) from the horizontal.

### Tasks
a. **Free Body Diagram**:
- Sketch a free body diagram showing all the forces acting on the roller at this moment of equilibrium.

b. **Force Triangle Sketch**:
- Illustrate the closed force vector triangle that represents the equilibrium condition. Note that this sketch is not to scale.

c. **Interior Angles of Force Triangle**:
- Express each angle in the force triangle in terms of \( \alpha \) and \( \theta \), and label each force vector and angle.

d. **Relation Establishment**:
- Derive a relationship between \( \alpha \), \( \delta \), and \( r \).

e. **Expression for Force \( P \)**:
- Use static equilibrium and the law of sines to derive an expression for \( P \) in terms of \( W \), \( r \), \( \delta \), and \( \theta \).

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