A wire of length 2.00 m and radius 1.0 mm is stretched by 25.0 mm on application of a force of 103 N. Calculate the Young's modulus for the wire.
Question 1 Report
A wire of length 2.00 m and radius 1.0 mm is stretched by 25.0 mm on application of a force of 103 N. Calculate the Young's modulus for the wire.
Answer Details
Young's modulus \(Y = \dfrac{\text{stress}}{\text{strain}} = \dfrac{F/A}{e/L} = \dfrac{FL}{Ae}\).
Data: \(L = 2.00\ \text{m}\), radius \(r = 1.0\ \text{mm} = 1.0\times10^{-3}\ \text{m}\), extension \(e = 25.0\ \text{mm} = 2.5\times10^{-2}\ \text{m}\), force \(F = 103\ \text{N}\).
Cross-sectional area:
\[ A = \pi r^2 = \pi (1.0\times10^{-3})^2 = 3.14\times10^{-6}\ \text{m}^2. \]Therefore
\[ Y = \frac{FL}{Ae} = \frac{103 \times 2.00}{3.14\times10^{-6} \times 2.5\times10^{-2}} = \frac{206}{7.85\times10^{-8}}. \] \[ Y = 2.62\times10^{9}\ \text{N m}^{-2}. \]Young's modulus \(\approx 2.6\times10^{9}\ \text{N m}^{-2}\).
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