Question

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

Answer 1

The youngs modulus for steel is \(200 \times 10^{9}\)

stress \(=y^{*}\) strain

or

\(\frac{\text { force }}{\text { area }}=\frac{Y \Delta L}{L}\)

\(\Delta L=\frac{\mathrm{LF}}{\mathrm{AY}}=\frac{\mathrm{LF}}{\pi r^{2} y}\)

\(=\frac{0.80 * 2000}{\pi^{*} 0.0005^{2} * 200 \times 10^{9}}\)

\(=0.0102 \mathrm{~m}\)

\(=1.02 \mathrm{~cm}\)