Question

A 5cm² cord has original length of 120cm is pulled by a 20N force. The change in length in the cord is 5mm. Find the strain, stress and elastic modulus.

Answer 1

By definition, the stress is the ratio of a force to a cross-sectional area:

$$\sigma = \dfrac{F}{A} = \dfrac{20N}{5\times 10^{-4}m^2} = 4\times 10^4Pa$$

The strain is the ratio of a length change to the original length:

$$\varepsilon = \dfrac{\Delta L}{L} = \dfrac{0.5cm}{120cm} \approx 4.17\times 10^{-3}$$

The Hook's law states that:

$$\sigma = E\varepsilon$$

where $E$ is the elastic modulus. Thus:

$$E = \dfrac{\sigma}{\varepsilon} = \dfrac{4\times 10^4Pa}{4.17\times 10^{-3}} = 9.6\times 10^6Pa = 9.6\space GPa$$

Answer. stress = $4\times 10^4Pa$, strain = $4.17\times 10^{-3}$, elastic modulus = $9.6\times 10^6Pa$.