Question

How does the work required to stretch a spring 2 cm compare with the work required to stretch it 1 cm

Answer 1

Answer:

The work done required is $W_{1}=4W_{2}$

Explanation:

Given that,

Stretch spring = 2 cm

Stretch spring = 1 cm

We need to calculate the work done

Using formula of work done

$W_{1}=\dfrac{1}{2}kx_{1}^2$

Put the value into the formula

$W_{1}=\dfrac{1}{2}\timesk\times0.02^2$.....(I)

We need to calculate the work done

Using formula of work done

$W_{2}=\dfrac{1}{2}kx_{2}^2$

Put the value into the formula

$W_{1}=\dfrac{1}{2}\timesk\times0.01^2$.....(II)

We need to calculate the work done

Using equation (I) and (II)

$\dfrac{W_{1}}{W_{2}}=\dfrac{\dfrac{1}{2}\timesk\times0.02^2}{\dfrac{1}{2}\timesk\times0.01^2}$

$\dfrac{W_{1}}{W_{2}}=\dfrac{0.02^2}{0.01^2}$

$W_{1}=4W_{2}$

Hence, The work done required is $W_{1}=4W_{2}$