Question

A man stretches and stores a potential energy of 10j in a spring. if he wants to further stretch the spring by an equal additional amount, how much work will he need to do

Answer 1

Given:

A man stretches and stores a potential energy of 10j in a spring.

To find:

Total work done if he wants to for that stretch the string by an equal additional amount.

Calculation:

Let the initial stretch be x.

So, initial work done be W_(0):

$\therefore \: W_{0} = \dfrac{1}{2} k {x}^{2} = 10 \: joule \: \: ......(1)$

Now , addition stretch of x is given , so total stretch becomes (x + x) = 2x.

Now work be W_(1):

$\therefore \: W_{1} = \dfrac{1}{2} k {(2x)}^{2}$

$= > \: W_{1} =4 \times \dfrac{1}{2} k {x}^{2}$

$= > \: W_{1} =4 \times W_{0}$

$= > \: W_{1} =4 \times 10$

$= > \: W_{1} =40 \: joule$

So, work done is 40 Joules.