Question

A structural steel rod has a radius of 10mm and a length of 1m . A 100km force stretches it along its length calculate
1.Stress
2.elongation
3.strain on the rod
Young's modulus , of structural steel is 2x10^11 N/m^2

Answer 1

I hope it will help you

Answer 2

Given that,

Radius = 10 mm

Length = 1 m

Force = 100 kN

(1). We need to calculate the stress

Using formula of stress

$\sigma=\dfrac{F}{A}$

Put the value into the formula

$\sigma=\dfrac{10^{5}}{\pi(10^{-2})^2}$

$\sigma=3.18\times10^{8}\ N/m^2$

(2). We need to calculate the elongation

Using formula of Young's modulus

$y=\dfrac{\sigma}{\epsilon}$

$\epsilon=\dfrac{\sigma}{y}$

Put the value into the formula

$epsilon=\dfrac{3.18\times10^{8}}{2\times10^{11}}$

$epsilon=0.00159$

$epsilon=1.59\times10^{-3}$

(3). We need to calculate the strain on the rod

Using formula of elongation

$\epsilon=\dfrac{\Delta l}{l}$

$\Delta l=epsilon\times l$

Put the value into the formula

$\Delta l=1.59\times10^{-3}\times1$  

$\Delta l=1.59\times10^{-3}$

$\Delta l=1.59\ mm$

Hence, (1). The stress is $3.18\times10^{8}\ N/m^2$

(2). The elongation is $1.59\times10^{-3}$

(3). The strain on the rod is 1.59 mm.