First slide

Elastic Modulie

Question

A wire of length /and cross-sectional area A is made of a material of Young's modulus Y. If the wire is stretched by an amount x, the work done is

Moderate

A

$\frac{{YAx}^{2}}{2 L}$
B

$\frac{YAX}{2 L^{2}}$
C

$\frac{YAx}{2 L}$
D

$\frac{{YAx}^{2}}{L}$

Solution

$\begin{array}{l} Y = \frac{FL}{Al} or F = \frac{YAl}{L} \\ dW = Fdl = \frac{YA}{L} ldl \\ ∴ W = \int_{0}^{x} \frac{YA}{L} ldl = \frac{YA}{L} {[\frac{l^{2}}{2}]}_{0}^{X} = \frac{{YAx}^{2}}{2 L} \end{array}$

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