Question

A 5mm diameter string has original lenght of 2.2m. The string is pulled by a force of 220N. If the length of the string is 2.22m, calculate the stress, strain, and young's modulus of the string

Answer 1

(a) We can find the stress of the string as follows:

$$\sigma=\dfrac{F}{A}=\dfrac{F}{\pi r^2},$$ $$\sigma=\dfrac{220\ N}{\pi\times(2.5\times10^{-3}\ m)^2}=1.12\times10^7\ \dfrac{N}{m^2}.$$

(b) We can find the strain of the string as follows:

$$\epsilon=\dfrac{\Delta l}{l}=\dfrac{2.22\ m-2.2\ m}{2.2\ m}=9.1\times10^{-3}.$$

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

$$E=\dfrac{\sigma}{\epsilon}=\dfrac{1.12\times10^7\ \dfrac{N}{m^2}}{9.1\times10^{-3}}=1.23\times10^9\ \dfrac{N}{m^2}.$$