https://file.aiquickdraw.com/mathbot/file/1726868499764dgiwoo91.jpg

To determine if the system is in equilibrium, we need to check if the following conditions for equilibrium are satisfied:

1. **Sum of forces in the horizontal direction (\( \Sigma F_x = 0 \)):** There are no horizontal forces in this system based on the diagram, so this condition is trivially satisfied.

2. **Sum of forces in the vertical direction (\( \Sigma F_y = 0 \)):** The sum of the vertical forces must be zero.

3. **Sum of moments about any point (\( \Sigma M = 0 \)):** The moments about any point must also sum to zero.

### Step 1: Sum of vertical forces

We have three forces acting vertically:
- A 10 kN force acting upwards.
- A 5 kN force acting downwards at 5 m from the 10 kN force.
- Another 5 kN force acting downwards 15 m from the 10 kN force.

Summing the vertical forces:

\[
\Sigma F_y = 10 \, \text{kN} \, (\text{up}) - 5 \, \text{kN} \, (\text{down}) - 5 \, \text{kN} \, (\text{down})
\]

\[
\Sigma F_y = 10 - 5 - 5 = 0
\]

So, the sum of the vertical forces is zero.

### Step 2: Sum of moments about any point

We'll take the moment about the point where the 10 kN force is applied. The moment is the force multiplied by the perpendicular distance from the point.

- The 10 kN force creates no moment about this point because its distance is zero.
- The 5 kN force at 5 m creates a clockwise moment: \( M_1 = 5 \, \text{kN} \times 5 \, \text{m} = 25 \, \text{kN}\cdot\text{m} \) (clockwise).
- The 5 kN force at 15 m creates a clockwise moment: \( M_2 = 5 \, \text{kN} \times 15 \, \text{m} = 75 \, \text{kN}\cdot\text{m} \) (clockwise).

Summing the moments:

\[
\Sigma M = 25 \, \text{kN}\cdot\text{m} + 75 \, \text{kN}\cdot\text{m} = 100 \, \text{kN}\cdot\text{m}
\]

The sum of the moments is not zero, so the system is **not** in rotational equilibrium.

### Conclusion:

While the system satisfies the condition for the sum of vertical forces, it does not satisfy the condition for the sum of moments. Therefore, the system is **not in equilibrium**.

Would you like more details, or do you have any questions?

---

Here are 5 related questions to expand your understanding:

1. How would the system change if we added another force to balance the moments?
2. What is the definition of static equilibrium in a physical system?
3. How do we calculate the center of mass in a system of forces?
4. What role do clockwise and counterclockwise moments play in determining rotational equilibrium?
5. How would this system behave if friction forces were involved?

**Tip:** When calculating moments, always ensure to consider both the magnitude of the force and its distance from the chosen point of rotation.

Analyze whether a system with multiple forces is in equilibrium by summing vertical forces and calculating moments. This problem involves key static equilibrium concepts and is suitable for high school physics or engineering 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