Question

A steel wire of 2mm in diameter is stretched by applying a force of 72N. Stress in the wire is

Answer 1

diameter=2mm
radius=2/2=1mm
$radius = 1\times {10}^{ - 3} m$
$area \: of \: circle \: = \pi {r}^{2} \\ = 3.14 \times (1 \times { {10}^{- 3} }) ^{2} \\ = 3.14 \times {10}^{ - 6}$
$stress = \frac{force}{ area} \\ = \frac{72}{3.14 \times {10}^{ - 6} } \\ = 2.29 \times {10}^{7} \frac{n}{{m}^{2} }$

Answer 2

Stress in the wire is $2.29 \times 10^7\ N/m$.

Explanation:

Given:

Diameter = 2 mm

Force = 72 N

We need to find the stress in the wire.

First we will find the area of the wire.

Radius 'r' is half of the diameter 'D'.

$r =\frac{2}{2} = 1\ mm$

Since wire forms a circular shape we will find the area of circle.

Area of Wire is π times square of the radius.

framing in equation form we get;

Area of Wire = $\pi r^2 = 3.14 \times (1\times 10^{-3})^2= 3.14 \times 10^{-6}$

Now Stress is amount of force applied per unit area.

framing in equation form we get;

Stress σ = $\frac{Force\ (F)}{Area\ (A)}$

Substituting the value we get;

Stress σ = $\frac{72}{3.14\times 10^{-6}} = 2.29 \times 10^7\ N/m$

Hence Stress in the wire is $2.29 \times 10^7\ N/m$.