### Educational Content: Free-Body Diagram on an Inclined Plane#### Scenario Description:A block of mass \( m \) rests on a rough inclined plane. The task is to identify the correct free-body diagram for this situation.#### Diagram Explanation:- **Inclined Plane Diagram:** - The block is shown on an inclined plane with angle \( \theta \). - The forces acting on the block include gravitational force, normal force, and frictional force (due to roughness).- **Free-Body Diagrams:** - **Option 1:** - Normal force \( \mathbf{N} \) is perpendicular to the plane. - Frictional force \( \mathbf{f} \) is parallel to the plane, pointing up the incline. - Gravitational force \( m \mathbf{g} \) acts vertically downward. - **Option 2:** - Normal force \( \mathbf{N} \) is perpendicular to the plane. - Frictional force \( \mathbf{f} \) is parallel but misaligned (not on the incline). - Gravitational force \( m \mathbf{g} \) acts vertically downward. - **Option 3:** - Normal force \( \mathbf{N} \) is perpendicular to the plane. - Frictional force \( \mathbf{f} \) is parallel to the plane, pointing up the incline. - Gravitational force \( m \mathbf{g} \) acts vertically downward. - **Option 4 (Correct Answer):** - Normal force \( \mathbf{N} \) is perpendicular to the plane. - Frictional force \( \mathbf{f} \) is parallel to the plane, pointing up the incline. - Gravitational force \( m \mathbf{g} \) acts vertically downward.#### Answer Identification:The correct free-body diagram is the one labeled with a red X, showing the forces properly oriented with respect to the inclined plane: normal force perpendicular, frictional force parallel up the incline, and gravitational force vertically downward.

The given problem is based on the free-body diagram of a mass on an inclined plane. To solve the…

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Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Question

### Educational Content: Free-Body Diagram on an Inclined Plane

#### Scenario Description:
A block of mass \( m \) rests on a rough inclined plane. The task is to identify the correct free-body diagram for this situation.

#### Diagram Explanation:

- **Inclined Plane Diagram:**
- The block is shown on an inclined plane with angle \( \theta \).
- The forces acting on the block include gravitational force, normal force, and frictional force (due to roughness).

- **Free-Body Diagrams:**
- **Option 1:**
- Normal force \( \mathbf{N} \) is perpendicular to the plane.
- Frictional force \( \mathbf{f} \) is parallel to the plane, pointing up the incline.
- Gravitational force \( m \mathbf{g} \) acts vertically downward.

- **Option 2:**
- Normal force \( \mathbf{N} \) is perpendicular to the plane.
- Frictional force \( \mathbf{f} \) is parallel but misaligned (not on the incline).
- Gravitational force \( m \mathbf{g} \) acts vertically downward.

- **Option 3:**
- Normal force \( \mathbf{N} \) is perpendicular to the plane.
- Frictional force \( \mathbf{f} \) is parallel to the plane, pointing up the incline.
- Gravitational force \( m \mathbf{g} \) acts vertically downward.

- **Option 4 (Correct Answer):**
- Normal force \( \mathbf{N} \) is perpendicular to the plane.
- Frictional force \( \mathbf{f} \) is parallel to the plane, pointing up the incline.
- Gravitational force \( m \mathbf{g} \) acts vertically downward.

#### Answer Identification:
The correct free-body diagram is the one labeled with a red X, showing the forces properly oriented with respect to the inclined plane: normal force perpendicular, frictional force parallel up the incline, and gravitational force vertically downward.

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