Answer to Question #304212 in Physics for lea

Question

A steel rod 4 m long and 0.5 cm2

in cross sectional area is found to stretch 0.2

cm under a tension of 12000 N. Under these conditions, determine

(a) The stress

(b) The strain; and

(c) Young’s modulus for the material

Answer 1

Given:

$l_0=4\:\rm m$

$A=0.5*10^{-4}\:\rm m^2$

$\Delta l=0.002\:\rm m$

$F=12000\:\rm N$

(a) The stress

$$\sigma=\frac{F}{A}=\frac{12000}{0.5*10^{-4}}=2.4*10^8\:\rm Pa$$

(b) The strain

$$\varepsilon=\frac{\Delta l}{l_0}=\frac{0.002}{4}=5*10^{-4}$$

(c) The Young’s modulus for the material

$$E=\frac{\sigma}{\varepsilon}=\frac{2.4*10^8}{5*10^{-4}}=4.8*10^{11}\:\rm Pa$$