Question

a wire of cross sectional area of 6x10m and length 50cm stretches by 0.2mm under a load of 3000N. Calculate the youngs modulus for the wire

Answer 1

Question 32000

We are given $S = 6 \cdot 10^{-5} m^2$ ; $l = 50 \, \text{cm} = 0.5 \, \text{m}$ ; $x = 0.2 \, \text{mm}$ ; $F = 3000 \, \text{N}$ .

By definition, mechanical stress is $\sigma = \frac{F}{S}$ , which from the other side might be written as $\sigma = \epsilon E$ , where $E$ - Youngs modulus and $\epsilon = \frac{x}{l}$ - is the engineering strain (Cauchy strain), which is the ratio of total deformation to the initial dimension of the body. Combining last three equations, obtain $\frac{F}{S} = \frac{x}{l} \cdot E \Rightarrow E = \frac{Fl}{Sx} = 125000 \, \text{MPa}$ .