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I'll help you solve these questions by breaking them down one by one.

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### Question 22.2
**Problem:**  
A wrench is 9 inches long, and 30 pounds of force are applied to the end of the wrench. Calculate the amount of torque at the other end of the wrench.

**Solution:**  
Torque (\( \tau \)) is given by the formula:
\[
\tau = r \times F
\]
where:
- \( r \) is the distance (length of the wrench), and
- \( F \) is the force applied.

Given:
- \( r = 9 \) inches (convert to feet: \( 9 \, \text{inches} = \frac{9}{12} = 0.75 \) feet)
- \( F = 30 \) pounds

Now, calculate the torque:
\[
\tau = 0.75 \, \text{ft} \times 30 \, \text{lbs} = 22.5 \, \text{foot-pounds}
\]

**Answer for 22.2:**  
The torque at the other end of the wrench is **22.5 foot-pounds**.

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### Question 22.3
**Problem:**  
A ratchet with a socket is 3 inches long, and 60 pounds of force are applied to the end of the ratchet. Calculate the amount of torque at the other end of the ratchet.

**Solution:**  
Again, use the torque formula:
\[
\tau = r \times F
\]

Given:
- \( r = 3 \) inches (convert to feet: \( 3 \, \text{inches} = \frac{3}{12} = 0.25 \) feet)
- \( F = 60 \) pounds

Calculate the torque:
\[
\tau = 0.25 \, \text{ft} \times 60 \, \text{lbs} = 15 \, \text{foot-pounds}
\]

**Answer for 22.3:**  
The torque at the other end of the ratchet is **15 foot-pounds**.

---

### Question 22.4
**Problem:**  
The torque needed to loosen a bolt is 130 Newton-meters. The length of a torque wrench is 0.8 meters. Calculate the amount of force required to loosen this bolt.

**Solution:**  
Rearrange the torque formula to solve for force:
\[
F = \frac{\tau}{r}
\]

Given:
- \( \tau = 130 \) Newton-meters
- \( r = 0.8 \) meters

Calculate the force:
\[
F = \frac{130 \, \text{Nm}}{0.8 \, \text{m}} = 162.5 \, \text{Newtons}
\]

**Answer for 22.4:**  
The force required to loosen the bolt is **162.5 Newtons**.

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Would you like a detailed explanation on any of these steps, or do you have any questions?

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### Additional Practice Questions

1. If the length of a wrench is doubled, how does that affect the torque if the same force is applied?
2. How much torque is produced if 45 pounds of force is applied to a 10-inch wrench?
3. Convert 130 Newton-meters to foot-pounds. (1 Nm ≈ 0.7376 ft-lbs)
4. If the force applied to a ratchet is increased by 50%, what happens to the resulting torque?
5. What is the required force to produce 200 Newton-meters of torque with a 0.5-meter wrench?

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### Tip:
Remember, torque is directly proportional to both the distance from the pivot point and the force applied. Increasing either will increase the torque produced.

22.2 A wrench is 9 inches long, and 30 pounds of force are applied to the end of the wrench. Calculate the amount of torque at the other end of the wrench.

22.3 A ratchet with a socket is 3 inches long, and 60 pounds of force are applied to the end of the ratchet. Calculate the amount of torque at the other end of the ratchet.

22.4 The torque needed to loosen a bolt is 130 Newton-meters. The length of a torque wrench is 0.8 meters. Calculate the amount of force required to loosen this bolt.

Step-by-step solutions for calculating torque and force using wrench and ratchet problems. Understand how to apply the torque formula, convert distance units, and solve practical physics problems related to mechanics. Suitable for students in Grades 9-12.

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