12. LO: 5, 6 Draw and find the normal force in each case. Select a set of coordinate axes and set-up Newton's Second Law along each axis assuming that the mass is at rest. L 0 N 10kg mg (a) F-SN 10kg (b) 13. LO: 6 - Find the components of weight parallel and perpendicular to the incline. Write Newton's Laws along each axis assuming that the mass is accelerating down the incline. F=5N 10kg (c)

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Chapter1: Units, Trigonometry. And Vectors
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**Problem 12:**

**Learning Objectives (LO):** 5, 6

- **Task:** Draw and find the normal force in each case. Select a set of coordinate axes and set up Newton’s Second Law along each axis assuming that the mass is at rest.

**Diagram Analysis:**

The diagram displays three cases of a 10 kg block with different external forces:

- **Case (a):** No external force applied on the block.
- **Case (b):** A horizontal force of 5 N applied downward on the block.
- **Case (c):** A vertical force of 5 N applied upward on the block.

**Problem 13:**

**Learning Objective (LO):** 6

- **Task:** Find the components of weight parallel and perpendicular to the incline. Write Newton’s Laws along each axis assuming that the mass is accelerating down the incline.

**Diagram Analysis:**

The diagram features a block on an inclined plane:

- **Incline:** Angle with the horizontal is denoted as θ.
- **Forces:**
  - \( mg \): The gravitational force acting downward.
  - \( N \): The normal force perpendicular to the surface of the incline.
  - Coordinate axes \( x \) and \( y \): \( x \) parallel and \( y \) perpendicular to the surface.

**Instructions:** Analyze each setup to determine the normal force and apply Newton’s Second Law to delineate the forces and accelerations in the specified directions.
Transcribed Image Text:**Problem 12:** **Learning Objectives (LO):** 5, 6 - **Task:** Draw and find the normal force in each case. Select a set of coordinate axes and set up Newton’s Second Law along each axis assuming that the mass is at rest. **Diagram Analysis:** The diagram displays three cases of a 10 kg block with different external forces: - **Case (a):** No external force applied on the block. - **Case (b):** A horizontal force of 5 N applied downward on the block. - **Case (c):** A vertical force of 5 N applied upward on the block. **Problem 13:** **Learning Objective (LO):** 6 - **Task:** Find the components of weight parallel and perpendicular to the incline. Write Newton’s Laws along each axis assuming that the mass is accelerating down the incline. **Diagram Analysis:** The diagram features a block on an inclined plane: - **Incline:** Angle with the horizontal is denoted as θ. - **Forces:** - \( mg \): The gravitational force acting downward. - \( N \): The normal force perpendicular to the surface of the incline. - Coordinate axes \( x \) and \( y \): \( x \) parallel and \( y \) perpendicular to the surface. **Instructions:** Analyze each setup to determine the normal force and apply Newton’s Second Law to delineate the forces and accelerations in the specified directions.
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