How much will a 30m steel tape 1 cm wide and 0.05 cm thick stretch unde a pull of a force of 300N if Young's modulus of steel is `2 xx 10^(11) Nm^(-2)`

Explanation

To solve the problem of how much a 30m steel tape will stretch under a pull of 300N, we can use the concept of Young's modulus. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Length of the steel tape, \( L = 30 \, \text{m} \)
- Width of the tape, \( w = 1 \, \text{cm} = 0.01 \, \text{m} \)
- Thickness of the tape, \( t = 0.05 \, \text{cm} = 0.0005 \, \text{m} \)
- Force applied, \( F = 300 \, \text{N} \)
- Young's modulus of steel, \( Y = 2 \times 10^{11} \, \text{N/m}^2 \)

### Step 2: Calculate the cross-sectional area \( A \)
The cross-sectional area \( A \) of the tape can be calculated using the formula for the area of a rectangle:
\[ A = w \times t \]
Substituting the values:
\[ A = 0.01 \, \text{m} \times 0.0005 \, \text{m} = 0.000005 \, \text{m}^2 = 5 \times 10^{-6} \, \text{m}^2 \]

### Step 3: Use the formula for extension \( \Delta L \)
The formula for extension \( \Delta L \) in terms of Young's modulus is given by:
\[ \Delta L = \frac{F \cdot L}{A \cdot Y} \]

### Step 4: Substitute the values into the formula
Now, substituting the values we have calculated and given:
\[ \Delta L = \frac{300 \, \text{N} \cdot 30 \, \text{m}}{5 \times 10^{-6} \, \text{m}^2 \cdot 2 \times 10^{11} \, \text{N/m}^2} \]

### Step 5: Calculate the extension
Calculating the numerator:
\[ 300 \, \text{N} \cdot 30 \, \text{m} = 9000 \, \text{N m} \]
Calculating the denominator:
\[ 5 \times 10^{-6} \, \text{m}^2 \cdot 2 \times 10^{11} \, \text{N/m}^2 = 1 \times 10^{6} \, \text{N} \]
Now substituting these into the extension formula:
\[ \Delta L = \frac{9000 \, \text{N m}}{1 \times 10^{6} \, \text{N}} = 0.009 \, \text{m} \]

### Step 6: Convert the extension to centimeters
To express the extension in centimeters:
\[ \Delta L = 0.009 \, \text{m} \times 100 = 0.9 \, \text{cm} \]

### Final Answer
The extension of the 30m steel tape under a pull of 300N is **0.009 m** or **0.9 cm**.

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