A mass of 11.0 kg is suspended from a rigid support by an aluminum wire of length 2.0 m, diameter 2.0 mm and Young's modulus 7.0 x 10\(^{11}\) Nm\(^{-2}\). Determine the extension produced. [g = 10 ms\(^{-2}\); \(\pi\) = 3.142]
Explanation
E = \(\frac{Fl}{Ae}\) E = 7.0 x 10\(^{-11}\) Nm\(^{-2}\); F = mass x acceleration due to gravity = 11 x 10 = 110N l = 2.0m A = \(\pi\) r\(^2\) d = 2.0 mm \(\implies\) r = 1.0 mm A = 3.142 x \((\frac{10}{1000})^2\) e = \(\frac{Fl}{EA} = \frac{110 \times 20}{7.0 \times 10^{11} \times 3.142(\frac{10}{1000})^2}\) = 1.0 x 10\(^{-5}\)m
