Question

The work done in stretching a certain spring, through a distance‘d’ is 20 J. The amount of work done to stretch this spring through an additional distance 2 d will be​

Answer 1

Given

work done = 20 J,

i.e u=20 J,

We know that Potential energy (work done)  is u = $\frac{1}{2} Kd^{2}$

So, on substituting we have, $20=\frac{1}{2} Kd^{2}$,

When stretched through additional distance d,

work done due to additional distance d will be ,

$U'=\frac{1}{2} K(d=d)^{2} \\ =4*\frac{1}{2} Kd^{2} \\ =4*20J$

$= 80 J$

Therefore work done will be

=$U'-U\\= 80-20\\=60J$

This work done for distance d for 2d it will ,

= 30 J

Answer 2

Given:

The work done in stretching a certain spring, through a distance‘d’ is 20 J.

To find:

Amount of work done to stretch it by 2d ?

Calculation:

• Work done to stretch string will be stored in string as the POTENTIAL ENERGY.

Initial work :

$W = \dfrac{1}{2} k {d}^{2} = 20 \:J$

• New stretch distance = d + 2d = 3d

Now, final work :

$W_{2} = \dfrac{1}{2} k {(3d)}^{2}$

$\implies W_{2} = 9 \times \dfrac{1}{2} k {d}^{2}$

$\implies W_{2} = 9 \times 20$

$\implies W_{2} =180 \: J$

So, the additional work done is 180-20 = 160 Joule