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The image shows a system of cables carrying a bucket with weight \( W = 2.5 \, \text{N} \), and we are asked to find the tension in cable \( ED \). The diagram includes angles of \( 30^\circ \) for the cables connected to the bucket. Let's solve this step by step using static equilibrium principles.

### Step 1: Free Body Diagram (FBD) at point \( E \)
- The bucket's weight \( W = 2.5 \, \text{N} \) acts directly downward.
- Cables \( EB \) and \( ED \) are making angles with the horizontal of \( 30^\circ \).
- We need to break the forces into horizontal and vertical components and apply equilibrium conditions (since the system is in static equilibrium).

### Step 2: Write the equilibrium equations

- **Vertical equilibrium:**
  The sum of the vertical forces must be zero. 
  \[
  T_{EB} \sin(30^\circ) + T_{ED} \sin(30^\circ) = W
  \]
  Substituting \( \sin(30^\circ) = 0.5 \):
  \[
  0.5 T_{EB} + 0.5 T_{ED} = 2.5
  \]
  Simplifying:
  \[
  T_{EB} + T_{ED} = 5 \, \text{N} \quad \text{(Equation 1)}
  \]

- **Horizontal equilibrium:**
  The sum of the horizontal forces must also be zero. 
  \[
  T_{EB} \cos(30^\circ) = T_{ED} \cos(30^\circ)
  \]
  Since \( \cos(30^\circ) = \frac{\sqrt{3}}{2} \), the equation simplifies to:
  \[
  T_{EB} = T_{ED}
  \]
  This tells us that the tensions in cables \( EB \) and \( ED \) are equal.

### Step 3: Solve for tension
From the horizontal equilibrium, we know \( T_{EB} = T_{ED} \). Substituting this into Equation 1:
\[
T_{ED} + T_{ED} = 5
\]
\[
2T_{ED} = 5
\]
\[
T_{ED} = 2.5 \, \text{N}
\]

### Final Answer:
The tension in cable \( ED \) is **2.5 N**, but none of the provided choices matches this directly. It seems we must reassess the options or double-check if any rounding or other factors were involved.

Would you like more details or further clarification on any step?

Here are five related questions for deeper understanding:
1. What role do equilibrium equations play in solving tension problems?
2. How do we break forces into components?
3. What if the angles in the cables were different?
4. Why is it important to check both horizontal and vertical equilibrium?
5. How could we verify the results experimentally?

**Tip:** In problems involving tension, always begin by resolving forces into their components and using equilibrium conditions.

The system of cables shown are used to carry a bucket of weight W=2.5 N. What is the tension in cable ED?

Learn how to find the tension in cable ED for a system supporting a 2.5 N weight using static equilibrium principles. This problem involves resolving forces into components and applying equilibrium equations, suitable for students in Grades 11-12.

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