Question

a steel wire of length 2m diameter 2mm is suspended from a regid support . calculate extension in the wire (mm) if aload of 314kg Is attached at its lower end (g = 10ms ,y = 2 × 10Nm​

Answer 1

Answer:

A steel wire of length 2m diameter 2mm is suspended from a rigid support. if a load of 314kg Is attached at its lower end (g = 10ms ,y = 2 × 10Nm​, the extension is $10^{-2}m$

Explanation:

• The Young's modulus (Y) is the ratio of longitudinal stress by corresponding strain

                   $Y= stress /strain$

• The stress is the force by area and the strain is the ratio of change in length divided by its original length

                  $stress=F/A$

                  $strain=l/L$

From the question,

the length of the copper wire $L=2m$

diameter of the wire $d=2mm=2*10^{-3}m$

the radius $r=d/2=10^{-3}m$

cross-sectional area $A=\pi r^{2} =3.14*10^{-6}m^{2}$

here force is due to the weight of the body suspended at the end

weight $W=mg$

mass of the body $m=314kg$

acceleration due to gravity $g=10m/s^{2}$

⇒ weight $W=314*10=3140N$

the stress is $=\frac{3140}{3.14*10^{-6} } =10^{9} N/m^{2}$

and strain $l/2$

the young's modulus $Y=2*10^{11}$

put all the given values

⇒

the elongation $l=\frac{10^{9}*2 }{2*10^{11}}=10^{-2}m$