Question

A wire of length 7 𝑚 and radius 2.37 𝑚𝑚 is stretched by a load of 12370 𝑔𝑚 and increased by 1.78% of the original length. Find the stress, strain, and Young’s modulus of the material of the wire. 

Answer 1

Determine the required values: stress $\sigma$, strain $\epsilon$, and Young's modulus $Y$:

$$\sigma=\frac{F}{A}=\frac {mg}{\pi r^2}=6.87\text{ MPa}.\\\space\\ \epsilon=1.78/100=0.0178.\\\space\\ E=\frac{\sigma}{\epsilon}=386\text{ MPa}.$$