https://file.aiquickdraw.com/mathbot/file/1726164865245w1568mu4.jpg

It looks like you are working through a mechanical or statics problem involving equilibrium equations and moments. Here's a breakdown of what I can interpret from the image:

1. **\( F_B \)**:
   \[
   F_B = \frac{82.7}{9.60} = 8.61458 \, \text{kN}
   \]

   This seems to be the reaction force \( F_B \), computed by dividing 82.7 by 9.60.

2. **Moment equation**:
   The equation starts with \( \Sigma M = 0 \), implying it's the sum of moments about a point (likely point \( B \)).
   \[
   0 = (1 \cdot 4) + (3.5 \cdot 3) + (6.1 \cdot 1.8) + (9.6 \cdot 2.5)
   \]
   You are summing moments due to forces at distances from a pivot point.

3. **\( F_A \)**:
   Below the moment equation, there is another equation for \( F_A \). You have the fraction:
   \[
   F_A = \frac{9.60}{?}
   \]
   The value for \( F_A \) hasn't been computed yet, but the setup suggests this force will also be solved based on equilibrium conditions.

Would you like me to solve the moment equation or provide further clarification on the statics problem?

Here are 5 related questions you might find useful:
1. How do you determine the correct moment arm for each force?
2. What is the role of a free-body diagram in solving statics problems?
3. How do you ensure that the sum of forces in the vertical direction equals zero?
4. Can you explain the significance of using equilibrium equations in structural analysis?
5. What steps should be taken to solve for unknown forces in a beam problem?

**Tip:** Always check your units to ensure consistency, particularly when dealing with moments and forces.

Calculate reaction forces FA and FB using moment equations and equilibrium conditions.

Learn how to solve a statics problem involving reaction forces FA and FB by applying the sum of forces and sum of moments equilibrium equations. This problem covers core concepts of moments and equilibrium in mechanical engineering, suitable for college-level students.

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