Question

Calculate the force which will produce an extension of 0.30mm in a steel wire with a length of 4.0m and a cross section area of 2.0 x 10^(-6) m^2Youngs modulus of steel is 2.1 x 10 ^11 Pa

Answer 1

Given data:

* The extension of the steel wire is 0.3 mm.

* The length of the wire is 4 m.

* The area of cross section of wire is,

`A=2*10^(-6)m^2`

* The young modulus of the steel is,

`Y=2.1*10^(11)\text{ Pa}`

Solution:

The young modulus of the steel in terms of the force and extension is,

`Y=(F* l)/(A* dl)`

where F is the force acting on the steel wire,, l is the original length of the wire, dl is the extension of the wire, and A is the area,

Substituting the known values,

`\begin{gathered} 2.1*10^(11)=(F*4)/(2*10^(-6)*0.3*10^(-3)) \\ F=0.315*10^2\text{ N} \\ F=31.5\text{ N} \end{gathered}`

Thus, the force which produce the extension of 0.3 mm of the steel wire is 31.5 N.