An 80-cm-long, 1.0-mm-diameter steel guitar string must be tightened to a tension of 2000 N by turning the tuning screws.

**Part A**

By how much is the string stretched?

Express your answer with the appropriate units.


To calculate how much the steel guitar string is stretched, we have already used the following formula based on **Hooke's Law** for elastic deformation:

\[
\Delta L = \frac{F L_0}{A Y}
\]

Where:
- \( \Delta L \) is the change in length,
- \( F = 2000 \, \text{N} \) is the tension in the string,
- \( L_0 = 0.80 \, \text{m} \) is the original length,
- \( A = 7.85 \times 10^{-7} \, \text{m}^2 \) is the cross-sectional area of the string (calculated using the diameter \(1.0 \, \text{mm}\)),
- \( Y = 2.0 \times 10^{11} \, \text{N/m}^2 \) is the Young's modulus for steel.

The result for the stretch is:

\[
\Delta L \approx 0.0102 \, \text{m} = 1.02 \, \text{cm}
\]

This means the steel string is stretched by **1.02 cm** when a tension of 2000 N is applied.

Would you like to dive deeper into the physics behind this, or have more questions? Here are some related questions for practice:

1. How does the frequency of a vibrating string depend on its length and tension?
2. What would happen if the tension in the string were doubled?
3. How does the cross-sectional area affect the amount of stretch for a given force?
4. How does Young's modulus vary between different materials?
5. What are the practical limits of stretching a guitar string before it breaks?

**Tip:** Always check the units when solving physics problems—converting to SI units upfront simplifies your calculations!

Discover how much a steel guitar string stretches under 2000 N tension with this physics problem solution. Use Hooke's Law to find the change in length, considering the string's original length, diameter, and Young's modulus of steel.

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