1- A 60 lb box is held on a smooth incline by a rope passing over the surface of contact with the coefficients of static friction of 0.25. Find (a) the tension on the rope and (b) the magnitude and location of the normal force exerted on the box by the plane. 40° 15 in. 60 lb 12 in. 30°

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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### Problem Statement

A 60 lb box is held on a smooth incline by a rope passing over the surface of contact with the coefficient of static friction of 0.25. 

**Tasks:**
- (a) Find the tension on the rope.
- (b) Find the magnitude and location of the normal force exerted on the box by the plane.

### Diagram Explanation

The diagram illustrates a 60 lb box positioned on a smooth inclined plane. Key features include:

- The incline angle is 30 degrees.
- The box is a rectangular object with dimensions: 15 inches along the incline and 12 inches perpendicular to the incline.
- The incline depicts the 60 lb force (weight of the box) acting downwards.
- An arrow is shown pointing parallel to the incline, indicating the direction of the tension in the rope.
- The normal force is depicted as perpendicular to the contact surface between the box and the inclined plane.

### Considerations

- The angle of incline and the dimensions of the box are critical for calculating the components of the gravitational force.
- The coefficient of static friction (0.25) will affect the calculations related to the rope tension and the normal force.

### Additional Notes

- Use trigonometric functions to resolve forces into components parallel and perpendicular to the inclined surface.
- Apply Newton's laws to solve for unknowns using equilibrium conditions, as the box is not moving.
Transcribed Image Text:### Problem Statement A 60 lb box is held on a smooth incline by a rope passing over the surface of contact with the coefficient of static friction of 0.25. **Tasks:** - (a) Find the tension on the rope. - (b) Find the magnitude and location of the normal force exerted on the box by the plane. ### Diagram Explanation The diagram illustrates a 60 lb box positioned on a smooth inclined plane. Key features include: - The incline angle is 30 degrees. - The box is a rectangular object with dimensions: 15 inches along the incline and 12 inches perpendicular to the incline. - The incline depicts the 60 lb force (weight of the box) acting downwards. - An arrow is shown pointing parallel to the incline, indicating the direction of the tension in the rope. - The normal force is depicted as perpendicular to the contact surface between the box and the inclined plane. ### Considerations - The angle of incline and the dimensions of the box are critical for calculating the components of the gravitational force. - The coefficient of static friction (0.25) will affect the calculations related to the rope tension and the normal force. ### Additional Notes - Use trigonometric functions to resolve forces into components parallel and perpendicular to the inclined surface. - Apply Newton's laws to solve for unknowns using equilibrium conditions, as the box is not moving.
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