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### Problem Summary:
- The wrench in the figure has **six forces** (A through F) of **equal magnitude** acting on it.
- You need to **rank these forces based on the torque** they apply to the wrench.
- The **torque** depends on two factors:
  1. **Magnitude** of the force (which is equal for all forces here).
  2. **Perpendicular distance** (lever arm) from the axis (center of the bolt) to the line of action of each force.

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### Key Idea:
The **torque (τ)** is given by the formula:
\[
\tau = F \cdot r \cdot \sin(\theta)
\]
- **\(F\)** is the force (equal for all).
- **\(r\)** is the perpendicular distance from the axis to the line of force.
- **\(\theta\)** is the angle between the force and the lever arm.

The force that acts:
- **Perpendicular** to the lever arm (90°) generates the **maximum torque**.
- **Closer to the bolt** or aligned along the lever arm (0° or 180°) results in **less or zero torque**.

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### Analysis of the Figure:
- Force **C**: Far away from the bolt and acts almost **perpendicular** to the wrench → **High torque**.
- Force **D**: Close to the bolt but still has a perpendicular component.
- Force **A**: Acts **horizontally**, close to the bolt → Generates **low torque**.
- Forces **B** and **F**: Act in a similar fashion (midway along the wrench) → Moderate torque.
- Force **E**: Acts along the axis of the wrench, resulting in **no torque** (since it's aligned with the bolt's center).

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### Ranking of Torques (Largest to Smallest):
1. **C** (farthest and nearly perpendicular).
2. **D** (perpendicular but closer to the bolt).
3. **B** and **F** (mid-range distance with some perpendicular components).
4. **A** (near the bolt with a small perpendicular component).
5. **E** (aligned with the bolt’s center → Zero torque).

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Does this answer help? If you have further questions or need more clarifications, feel free to ask!

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Here are 5 related questions:
1. What is the role of the lever arm in torque calculations?
2. How does the angle between force and lever arm affect torque?
3. Why does force E produce zero torque in this setup?
4. Can two forces at different distances produce the same torque?
5. What happens if the wrench handle is shortened—how does it affect torque?

**Tip:** Always look for **perpendicular components** of the force to quickly assess torque without calculations.

Rank the forces (A through F) on the wrench based on the magnitude of the torque they apply to the wrench, measured about an axis centered on the bolt. Forces have equal magnitude.

Analyze the forces acting on a wrench and rank them based on the torque generated. Explore how force magnitude, perpendicular distance, and angles affect the torque calculations. Includes a step-by-step breakdown with the formula τ = F * r * sin(θ).

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