Question

The elastic limit of steel is 8 × 108 N m−2 and its Young modulus 2 × 1011 N m−2. Find the maximum elongation of a half-metre steel wire that can be given without exceeding the elastic limit.

Answer 1

Maximum elongation of a half-metre steel wire that can be given without exceeding the elastic limit is 2 millimetre.

Explanation:

1. Given data is

   Elastic limit of steel $(\sigma)=8\times 10^{8}(\frac{N}{m^{^{2}}})$

   Young modulus of elasticity (Y) = $2\times 10^{11}(\frac{N}{m^{^{2}}})$

   Length of wire (L) = 0.5 (m)

2. From relation

    $\Delta L=\frac{\sigma L}{Y}$     ...1)

   where $\Delta L$ = change in length of wire

3. So from equation 1) and given data

  $\Delta L=\frac{8\times 10^{8}\times 0.5}{2\times 10^{11}}$

 after calculate

  Change in length of wire ($\Delta L$)= 0.002(m)= 2 (mm)

Answer 2

Required Elongation of Steel Wire is 2 mm

Explanation:

Elastic Limit of Steel $\frac {F}{A} = 8\times10^5 N/m^2$

Young's Modulus of Steel $Y = 2 \times 10^1^1 N/m^2$

Length of Steel Wire $L = \frac {1}{2} m$

The elastic limit of steel indicates the maximum pressure that steel will be able to bear.

Let maximum elongation of steel wire be $\Delta L$

$Y = \frac {F \times L}{A \times\Delta L}$

$\Delta L = \frac {8\times10^5\times(0.5)}{2\times10^1^1}$

$= 2\times10^-^3 m = 2 mm$

So, Required Elongation of Steel Wire is 2 mm.