a box is at rest on an inclined surface. which diagram correctly illustrates all forces, including any component forces? assume the x - axis is parallel to the surface.

Question

Accepted Answer

# Brief Explanations:
To determine the correct force diagram for a box at rest on an inclined surface, we analyze the forces:
1. **Gravitational Force ($F_g$)**: Acts vertically downward. For inclined planes, we resolve $F_g$ into two components:
   - $F_{gx}$ (parallel to the incline, causing the box to slide down).
   - $F_{gy}$ (perpendicular to the incline, pressing the box into the surface).
2. **Normal Force ($F_N$)**: Acts perpendicular to the incline (opposing $F_{gy}$).
3. **Frictional Force ($F_f$)**: Acts parallel to the incline, opposing $F_{gx}$ (since the box is at rest, it is static friction).

Now, we evaluate the diagrams:
- **First diagram**: $F_N$ is vertical (incorrect, as $F_N$ must be perpendicular to the incline).
- **Second diagram**: $F_g$ is parallel to $F_N$ (incorrect, as $F_g$ is vertical and $F_N$ is perpendicular to the incline).
- **Third diagram**: $F_g$ is parallel to the incline (incorrect, as $F_g$ is vertical).
- **Fourth diagram**: $F_g$ is resolved into $F_{gx}$ (parallel to incline) and $F_{gy}$ (perpendicular to incline). $F_N$ opposes $F_{gy}$, and $F_f$ opposes $F_{gx}$ (consistent with static equilibrium).

# Answer: The fourth diagram (with $F_g$ resolved into $F_{gx}$ and $F_{gy}$, $F_N$ perpendicular to the incline, and $F_f$ parallel to the incline).

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Answer: