https://file.aiquickdraw.com/mathbot/file/17287348401590negl2iv.jpg

The problem asks to determine the magnitude of the moment about point \( B \) due to the force \( F_3 = 766 \, \text{N} \), neglecting the force \( F_1 \).

### Step-by-step approach:

1. **Identify the components of force \( F_3 \):**
   - \( F_3 \) makes an angle of \( 30^\circ \) with the horizontal.
   - The components of \( F_3 \) are:
     - Horizontal component: \( F_{3x} = F_3 \cdot \cos(30^\circ) \)
     - Vertical component: \( F_{3y} = F_3 \cdot \sin(30^\circ) \)

2. **Moment arm of each component:**
   The moment arm is the perpendicular distance from point \( B \) to the line of action of the force component.
   
   - For the horizontal component \( F_{3x} \), the moment arm is \( 0.05 \, \text{m} \) (vertical distance from point \( B \) to the line of action).
   - For the vertical component \( F_{3y} \), the moment arm is the horizontal distance from point \( B \) to the line of action of \( F_{3y} \), which is \( 0.5 \, \text{m} \).

3. **Moment calculation:**
   The moment \( M_B \) at point \( B \) is given by:

   \[
   M_B = F_{3x} \cdot d_{y} + F_{3y} \cdot d_{x}
   \]
   where:
   - \( d_y = 0.05 \, \text{m} \) (moment arm for \( F_{3x} \)),
   - \( d_x = 0.5 \, \text{m} \) (moment arm for \( F_{3y} \)).

   Now, let's compute:

   - \( F_{3x} = 766 \, \text{N} \cdot \cos(30^\circ) = 766 \cdot 0.866 = 663.96 \, \text{N} \)
   - \( F_{3y} = 766 \, \text{N} \cdot \sin(30^\circ) = 766 \cdot 0.5 = 383 \, \text{N} \)

   The moment at point \( B \) is:

   \[
   M_B = (663.96 \, \text{N}) \cdot (0.05 \, \text{m}) + (383 \, \text{N}) \cdot (0.5 \, \text{m})
   \]
   \[
   M_B = 33.198 \, \text{N} \cdot \text{m} + 191.5 \, \text{N} \cdot \text{m}
   \]
   \[
   M_B = 224.698 \, \text{N} \cdot \text{m}
   \]

### Final Answer:
The magnitude of the moment about point \( B \) due to the force \( F_3 \) is approximately **224.7 N·m**.

Would you like more details or have any further questions?

---

Here are some related questions for you to explore:
1. How does the angle of the applied force affect the moment?
2. What happens if the length from point \( B \) to the point of application of \( F_3 \) increases?
3. How would the moment change if the force \( F_3 \) were applied vertically?
4. Can you explain the physical meaning of the moment and its direction?
5. How does the moment arm influence the effectiveness of the applied force?

**Tip:** Always remember that moments depend on both the force magnitude and the perpendicular distance from the point of rotation to the line of action of the force!

Determine the magnitude of the moment about point B of the force F_3 = 766 N. Do not consider F_1. Give your answer in N·m.

Learn how to calculate the moment about point B in a truss system where force F3 = 766 N is applied at a 30-degree angle. This problem covers key concepts in statics, including force components and moment arms. Suitable for undergraduate engineering and physics students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation