The increase of length of a wire under a load is equal to its initial length. What is the stress in the wire equal to?

Answer

To solve the problem, we need to understand the relationship between stress, strain, and Young's modulus. Here’s the step-by-step solution:

### Step 1: Understand the Definitions
- **Stress (σ)** is defined as the force (F) applied per unit area (A) of the material:
\[ \sigma = \frac{F}{A} \]

- **Strain (ε)** is defined as the change in length (ΔL) divided by the original length (L):
\[ \epsilon = \frac{\Delta L}{L} \]

- **Young's Modulus (Y)** relates stress and strain:
\[ Y = \frac{\sigma}{\epsilon} \]

### Step 2: Given Information
- The increase in length (ΔL) of the wire is equal to its initial length (L). Therefore:
\[ \Delta L = L \]

### Step 3: Calculate Strain
Using the definition of strain:
\[ \epsilon = \frac{\Delta L}{L} = \frac{L}{L} = 1 \]

### Step 4: Relate Stress and Young's Modulus
From the formula for Young's modulus:
\[ Y = \frac{\sigma}{\epsilon} \]

Substituting the value of strain (ε = 1):
\[ Y = \frac{\sigma}{1} \]
Thus,
\[ \sigma = Y \]

### Step 5: Conclusion
The stress in the wire is equal to the Young's modulus (Y) of the material.

### Final Answer
The stress in the wire is equal to the Young's modulus of the material.

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