9. A 75 N crate is at rest on an incline that is inclined a 25° above the horizontal. The coefficient of static friction between the crate and the incline is 0.25 and the coefficient of kinetic friction between the crate and the incline is 0.15. (a) What is the minimum magnitude of a force parallel to the incline that will prevent the crate from sliding down the incline? (b) What is the minimum magnitude of the force parallel to the incline that will start the crate to move up the incline? (c) Include a force (or free body) diagram of each situation.

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**Problem 9: Incline and Friction Analysis**

A 75 N crate is at rest on an incline that is inclined at 25° above the horizontal. The coefficient of static friction between the crate and the incline is 0.25, and the coefficient of kinetic friction between the crate and the incline is 0.15.

(a) What is the minimum magnitude of a force parallel to the incline that will prevent the crate from sliding down the incline?

(b) What is the minimum magnitude of the force parallel to the incline that will start the crate to move up the incline?

(c) Include a force (or free body) diagram of each situation.

**Explanation of Diagrams:**

While the image does not provide the specific diagrams, for educational purposes, here's a description of what the diagrams should include:

1. **Diagram for Part (a):**
   - Display the incline at a 25° angle with the horizontal.
   - Show the gravitational force acting downward on the crate (75 N).
   - Illustrate the static frictional force acting up the incline.
   - Include the normal force perpendicular to the incline.
   - Indicate the applied force parallel to the incline required to prevent sliding.

2. **Diagram for Part (b):**
   - Display the incline at a 25° angle with the horizontal.
   - Show the gravitational force acting downward on the crate (75 N).
   - Illustrate the kinetic frictional force acting opposite to the direction of the applied force.
   - Include the normal force perpendicular to the incline.
   - Indicate the applied force parallel to the incline required to move the crate up the incline.
Transcribed Image Text:**Problem 9: Incline and Friction Analysis** A 75 N crate is at rest on an incline that is inclined at 25° above the horizontal. The coefficient of static friction between the crate and the incline is 0.25, and the coefficient of kinetic friction between the crate and the incline is 0.15. (a) What is the minimum magnitude of a force parallel to the incline that will prevent the crate from sliding down the incline? (b) What is the minimum magnitude of the force parallel to the incline that will start the crate to move up the incline? (c) Include a force (or free body) diagram of each situation. **Explanation of Diagrams:** While the image does not provide the specific diagrams, for educational purposes, here's a description of what the diagrams should include: 1. **Diagram for Part (a):** - Display the incline at a 25° angle with the horizontal. - Show the gravitational force acting downward on the crate (75 N). - Illustrate the static frictional force acting up the incline. - Include the normal force perpendicular to the incline. - Indicate the applied force parallel to the incline required to prevent sliding. 2. **Diagram for Part (b):** - Display the incline at a 25° angle with the horizontal. - Show the gravitational force acting downward on the crate (75 N). - Illustrate the kinetic frictional force acting opposite to the direction of the applied force. - Include the normal force perpendicular to the incline. - Indicate the applied force parallel to the incline required to move the crate up the incline.
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