Complete the table below. (Measure all angles between 0° and 360°, counterclockwise from the +x-axis.) Data Table 1 Force Mass (kg) Force (N) Angle (degrees) |x-component (N) y-component (N) F₁ 0.150 1.47 60 0.735 1.273 ✓ F₂ 0.150 1.47 300 0.735 -1.273 R = F₁+F₂ Resultant = 1.47 0 ✓ Equilibrant = -1.47 ✔ What is the calculated value of F3 (equilibrant) needed to balance the two forces F₁ and F₂? magnitude F3,calc = 1.47 N direction 03,calc = 180 What is the experimental value of F3 (equilibrant) needed to balance the two forces F₁ and F2? magnitude F3,exp = direction 03,exp = What is the percent difference between the calculated and experimental values of the magnitude of F3? (Percent differences should not be rounded to one significant HINT figure.) percent difference = % What is the percent difference between the calculated and experimental values of 03? (Percent differences should not be rounded to one significant figure.) HINT percent difference = % 0

To approach the problem, we need to analyze and understand the following aspects:

1. **Given Information**:
   - The table provides data for forces \( F_1 \) and \( F_2 \).
   - The resultant force \( R \) is also given, along with the equilibrant.

2. **Force Analysis**:
   - The resultant force \( R \) is the vector sum of \( F_1 \) and \( F_2 \).
   - The equilibrant force \( F_3 \) is equal in magnitude but opposite in direction to \( R \). It balances the system.

3. **Data Summary**:

| Force | Mass (kg) | Force (N) | Angle (degrees) | x-component (N) | y-component (N) |
|-------|-----------|-----------|----------------|-----------------|-----------------|
| \( F_1 \) | 0.150     | 1.47      | 60°            | 0.735           | 1.273           |
| \( F_2 \) | 0.150     | 1.47      | 300°           | 0.735           | -1.273          |
| \( R = F_1 + F_2 \) | -         | 1.47      | 0°             | 1.47            | 0               |
| \( F_3 \) (Equilibrant) | -         | 1.47      | 180°           | -1.47           | 0               |

4. **Calculated Value for \( F_3 \)**:
   - Magnitude: \( F_{3,\text{calc}} = 1.47 \, \text{N} \)
   - Direction: \( \theta_{3,\text{calc}} = 180^\circ \)

5. **Experimental Value of \( F_3 \)**:
   - Magnitude: \( F_{3,\text{exp}} = \) (This value needs to be provided from experimental data.)
   - Direction: \( \theta_{3,\text{exp}} = \) (This value also needs to be experimentally determined.)

6. **Percent Differences**:
   - **Magnitude Difference**:
     \[
     \text{Percent Difference} = \frac{|F_{3,\text{exp}} - F_{3,\text{calc}}|}{\frac{F_{3,\text{exp}} + F_{3,\text{calc}}}{2}} \times 100
     \]

   - **Angle Difference**:
     \[
     \text{Percent Difference} = \frac{|\theta_{3,\text{exp}} - \theta_{3,\text{calc}}|}{\frac{\theta_{3,\text{exp}} + \theta_{3,\text{calc}}}{2}} \times 100
     \]

### Completing the Table:

The missing experimental values and the percent differences can be filled in as follows:

1. **Magnitude \( F_{3,\text{exp}} \)**: (Use the experimental measurement.)
2. **Angle \( \theta_{3,\text{exp}} \)**: (Use the experimental measurement.)
3. **Percent Difference for Magnitude**: Calculate using the formula.
4. **Percent Difference for Angle**: Calculate using the formula.

### Follow-up Questions:

1. What are the x- and y-components of the resultant force \( R \)?
2. How would changing the mass affect the forces \( F_1 \) and \( F_2 \)?
3. Why is the direction of \( F_3 \) opposite to that of \( R \)?
4. How do experimental errors affect the calculation of \( F_3 \)?
5. What role does the angle play in determining the components of a vector?

**Tip**: Always double-check your calculations, especially when dealing with percent differences, as small changes can lead to significant percentage differences.

Learn how to balance forces using vector addition and calculate the equilibrant force. Explore the calculation of percent differences between calculated and experimental values. Suitable for high school students studying physics and trigonometry.

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