Question

A spring is stretched by distance x by applying a force F. What will be the

new force required to stretch the spring by 3x? Calculate the work done in

increasing the extension?

Answer 1

Given that,

A spring is stretched by distance x by applying a force F.

Stretch the string by new force = 3x

We know that,

Applied force on the spring is

$F=kx$...(I)

We need to calculate the new force

Using hooke's law

$F'=kx'$

Put the value of x'

$F'=k(3x)$

$F'=3kx$

From equation (I)

$F'=3F$

The new force is 3F.

We need to calculate the work done in  increasing the extension

Using formula of work done

$W=\dfrac{1}{2}\times k(x'^2-x^2)$

Put the value into the formula

$W=\dfrac{1}{2}\times k((3x)^2-x^2)$

$W=\dfrac{1}{2}\times k(9x^2-x^2)$

$W=\dfrac{1}{2}\times k\times 8x^2$

$W=4kx^2$

Hence, The new force is 3F.

The work done in  increasing the extension is 4kx² .