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A wrench is used to loosen a nut as shown below by applying a force 14 N. Determine the torque (magnitude and direction: + for CCW and – for CW) about the nut joint. Express your answer in SI units with 3 or more significant figures.

To calculate the torque about the nut joint, we use the formula for torque:

\[
\tau = r \cdot F \cdot \sin(\theta)
\]

where:
- \( r = 0.28 \, \text{m} \) (the length from the point of force application to the nut joint),
- \( F = 14 \, \text{N} \) (the applied force),
- \( \theta = 50^\circ \) (the angle between the force vector and the lever arm).

### Step 1: Substitute the values into the torque formula.

\[
\tau = 0.28 \, \text{m} \cdot 14 \, \text{N} \cdot \sin(50^\circ)
\]

### Step 2: Calculate \(\sin(50^\circ)\).

\[
\sin(50^\circ) \approx 0.7660
\]

### Step 3: Complete the calculation.

\[
\tau = 0.28 \cdot 14 \cdot 0.7660
\]
\[
\tau \approx 3.003 \, \text{N} \cdot \text{m}
\]

### Direction:
Since the force is applied in such a way as to loosen the nut, we assume this direction is clockwise (CW). Therefore, we assign a negative sign to the torque.

\[
\tau \approx -3.003 \, \text{N} \cdot \text{m}
\]

### Final Answer:
The torque about the nut joint is approximately:

\[
\tau = -3.003 \, \text{N} \cdot \text{m}
\]

This torque is in the clockwise (CW) direction.

Would you like further clarification on any step, or do you have any other questions?

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Here are five questions to deepen understanding:

1. What would happen to the torque if the angle were increased or decreased?
2. How would the torque change if the force applied were increased to 20 N?
3. Why is the sine function used in the calculation of torque here?
4. How would reversing the direction of the force affect the torque calculation?
5. What is the significance of specifying the torque direction as clockwise or counterclockwise?

**Tip:** Always remember to use the angle between the force and the lever arm when calculating torque; it helps in determining the correct component of the force that contributes to rotation.

A wrench is used to loosen a nut as shown below by applying a force 14 N. Determine the torque (magnitude and direction: + for CCW and – for CW) about the nut joint. Express your answer in SI units with 3 or more significant figures.

Learn how to calculate the torque required to loosen a nut using a wrench, given a force of 14 N applied at a 50° angle and a 0.28 m lever arm. This problem demonstrates torque calculation with trigonometric concepts. Suitable for advanced high school physics or introductory college-level physics students.

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