Suppose that a box is being towed up an inclined plane as shown in the
figure. Find the force w needed to make the component of the force
parallel to the inclined plane equal to 2.3 lb.

To solve the problem, we need to find the force \( w \) such that its component parallel to the inclined plane equals 2.3 lb. This problem involves resolving the force \( w \) into components.

### Step-by-Step Solution:

1. **Identify the Components of Force \( w \):**
   - The force \( w \) acts along the direction indicated in the diagram.
   - The component of \( w \) parallel to the inclined plane is given by:
     \[
     w_{\parallel} = w \cos(\theta)
     \]
     where \( \theta \) is the angle between the force \( w \) and the direction parallel to the incline.

2. **Given Information:**
   - The parallel component of the force \( w \) is given to be 2.3 lb.
   \[
   w_{\parallel} = 2.3 \, \text{lb}
   \]

3. **Relate the Given Condition to the Components:**
   \[
   w \cos(\theta) = 2.3 \, \text{lb}
   \]

4. **Solve for the Force \( w \):**
   \[
   w = \frac{2.3 \, \text{lb}}{\cos(\theta)}
   \]

5. **Conclusion:**
   - To find the exact value of \( w \), you need the value of \( \theta \), the angle between the force and the direction parallel to the inclined plane.
   - If \( \theta \) is given or can be determined from the diagram, plug in the value to find \( w \).

### Example Calculation:

Assume the angle \( \theta \) is \( 30^\circ \) (just for illustration):

\[
w = \frac{2.3 \, \text{lb}}{\cos(30^\circ)}
\]
\[
w = \frac{2.3 \, \text{lb}}{0.866} \approx 2.66 \, \text{lb}
\]

Thus, the force \( w \) would be approximately 2.66 lb if \( \theta = 30^\circ \).

### Questions for Further Exploration:
1. What is the actual angle \( \theta \) in your problem?
2. Is there any additional force acting on the box (e.g., friction)?
3. What would the force \( w \) be if the angle \( \theta \) was different?
4. How would the calculation change if the force was applied at a different angle?
5. What is the total work done by the force \( w \) over a certain distance along the incline?

### Tip:
When working with inclined plane problems, always ensure you have the correct angle and understand which component of the force you need to resolve. This helps in setting up the correct equations.

Do you need help finding the angle \( \theta \) or would you like to go deeper into any other part of this problem?

Learn how to calculate the force \( w \) needed to make the component parallel to the inclined plane equal to 2.3 lb. This physics problem involves vectors and trigonometry, focusing on resolving forces along an inclined plane. Suitable for high school students studying physics.

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