physics - A structural steel rod has a radius of 10 mm and a length of 1.0 m. A 100 kN force stretches it along its length. Calculate (a) stress, (b) elongation, and (c) strain on the rod. Young’s modulus, of structural steel is 2.0 * 10^{11} N m^{-2} .

Sangeetha Pulapaka (last edited 1 year ago) (Expert, Educator @Qalaxia)

Young's modulus or elastic modulus, is the essence of the stiffness of a material. It is how easily it is bent or stretched. It depends on temperature and pressure.

Young's modulus = Stress/Strain

Stress = F/A, where F is the force acting , A is the area of the cross-sectional area.

Strain = Change in length/original length = \frac{\Delta L}{L_{0}}

So, the formula of young's modulus Y = \frac{FL_{0}}{A\Delta L}

A) Stress = F/A =\frac{F}{\pi \cdot r^{2}} = \frac{100 \times 10^{3} N}{3.14 \times (10^{-2} m)^{2}} =3.18 \times 10^{8} N m^{-2}

B) Elongation = \Delta L = \frac{FL_{0}}{AY} = \frac{(3.18 \times 10^{8} N m^{-2})( 1m)}{2 \times 10^{11} N m^{-2}} = 1.59 \times 10^{-3} m

C) Strain = \frac{\Delta L}{L_{0}}= \frac{1.59 \times 10^{-3}m}{1m} =1.59 \times 10^{-3}