Question

A wire of length 𝟑𝟓𝟎 𝒄𝒎 and radius 𝟏. 𝟓 𝒎𝒎 is stretched by load of 𝟏𝟎 𝒌𝒈 and increased by 𝟐. 𝟓% of the original length. Find the stress, strain and Young’s modulus of the material of the wire

Answer 1

We can find the stress as follows:

$$\sigma=\dfrac{F}{A}=\dfrac{mg}{\pi r^2},$$ $$\sigma=\dfrac{10\ kg\times9.8\ \dfrac{m}{s^2}}{\pi\times(1.5\times10^{-3}\ m)^2}=1.38\times10^7\ \dfrac{N}{m^2}.$$

We can find the strain as follows:

$$\epsilon=\dfrac{\Delta l}{l}=\dfrac{3.5\ m\times0.025}{3.5\ m}=0.025.$$

We can find the Young’s modulus of the material of the wire as follows:

$$E=\dfrac{\sigma}{\epsilon}=\dfrac{1.38\times10^7\ \dfrac{N}{m^2}}{0.025}=5.52\times10^8\ \dfrac{N}{m^2}.$$