nylon tennis string

[logistic_guy]

A nylon tennis string on a racket is under a tension of \(\displaystyle 250 \ \text{N}\). If its diameter is \(\displaystyle 1.00 \ \text{mm}\), by how much is it lengthened from its untensioned length of \(\displaystyle 30.0 \ \text{cm}\)?

 

[khansaheb]

A nylon tennis string on a racket is under a tension of \(\displaystyle 250 \ \text{N}\). If its diameter is \(\displaystyle 1.00 \ \text{mm}\), by how much is it lengthened from its untensioned length of \(\displaystyle 30.0 \ \text{cm}\)?

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[logistic_guy]

This problem is one of the most beautiful problems of all time where it combines stress and strain in a fascinating way.

We are experts in solving beams, so we have a pretty good idea of how to relate stress and strain in one equation.

The Young's modulus

\(\displaystyle \sigma = \epsilon E\)

\(\displaystyle \frac{F}{A} = \frac{\Delta L}{L} E\)

A \(\displaystyle \textcolor{green}{\bold{nylon}}\) - by how much is it lengthened from its untensioned length of \(\displaystyle 30.0 \ \text{cm}\)?

\(\displaystyle \Delta L = \frac{FL}{A\textcolor{green}{E}} = \frac{250(0.3)}{\pi(0.0005)^2 \cdot \textcolor{green}{5 \times 10^{9}}} = 0.0191 \ \text{m} = \textcolor{blue}{1.91 \ \text{cm}}\)