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To determine if this system is in equilibrium, we need to evaluate the following two conditions:

1. **Sum of forces in the vertical direction must be zero:**
   \[
   \Sigma F_y = 0
   \]
   The vertical forces in the diagram include:
   - A 10 kN force acting upwards.
   - A 4 kN force acting downwards.
   - A 6 kN force acting downwards.

2. **Sum of moments around any point must be zero:**
   \[
   \Sigma M = 0
   \]
   A moment is the product of the force and the perpendicular distance to the point around which we calculate the moment. The moments in the diagram include:
   - An 80 kNm clockwise moment applied at the center.
   - The moments generated by the 10 kN, 4 kN, and 6 kN forces about the central point.

### Step 1: Vertical Force Equilibrium

Let's sum all vertical forces. Taking upward forces as positive and downward forces as negative:
\[
\Sigma F_y = 10 \, \text{kN} - 4 \, \text{kN} - 6 \, \text{kN} = 10 - 4 - 6 = 0
\]
The sum of the vertical forces is zero, so the system satisfies vertical equilibrium.

### Step 2: Moment Equilibrium

Now, we calculate the moment about the center point. The clockwise moment is positive, and the counterclockwise moment is negative.

- **10 kN force**: The force is 5 meters to the left of the center, generating a counterclockwise moment:
  \[
  M_1 = 10 \, \text{kN} \times 5 \, \text{m} = 50 \, \text{kNm} \, (\text{counterclockwise})
  \]
  
- **4 kN force**: This force acts at the center, so it produces no moment.

- **6 kN force**: This force is 5 meters to the right of the center, generating a clockwise moment:
  \[
  M_2 = 6 \, \text{kN} \times 5 \, \text{m} = 30 \, \text{kNm} \, (\text{clockwise})
  \]

- **80 kNm moment**: There is a direct 80 kNm clockwise moment applied at the center.

Now, summing the moments:
\[
\Sigma M = 80 \, \text{kNm} + 30 \, \text{kNm} - 50 \, \text{kNm} = 60 \, \text{kNm}
\]
Since the sum of the moments is **not zero** (\(\Sigma M = 60 \, \text{kNm}\)), the system is **not in rotational equilibrium**.

### Conclusion:
The system is **not in equilibrium** because the sum of the moments around the center point is not zero, even though the vertical forces are balanced.

---

Would you like further details on this? Here are five related questions to explore further:

1. How would adding a horizontal force affect the equilibrium?
2. What happens if the clockwise moment is changed to 50 kNm?
3. Can equilibrium be achieved by adjusting the positions of the forces?
4. What role does the distance between forces play in calculating moments?
5. How would the equilibrium change if the 6 kN force was removed?

**Tip:** When solving for equilibrium in 2D systems, always ensure that both the sum of forces and the sum of moments are balanced to achieve full equilibrium.

This problem involves determining whether a system of forces and moments is in equilibrium. The analysis includes evaluating the sum of vertical forces and the sum of moments around a point. Explore how to check for equilibrium using statics principles. Suitable for university engineering students.

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