Question

The potential energy of a certain spring when stretched through a distance x is 100J The amount of work done on the spring to stretch it through an additional distance will be​

Answer 1

Answer:

we know the potential energy is u = 1/2 ks^2

So, on Substituting we have = 100 = 1/2 ks ^2

Work done, w = 1/2k (2s) ^2' - 1/2 ks^2

W = 2ks^2 - 1/2ks^2

= 3/2 ks^2

Thus, W = 3*100 = 300 joules

Answer 2

Complete Question: The potential energy of a certain spring when stretched through a distance 'x' is 100 J. The amount of work done on the spring to stretch it through an additional distance 'x' will be?

The amount of work done on the spring to stretch it through an additional distance 'x' will be 300 J.

Given:

The potential energy of spring stretched through a distance 'x' = 100 J

To Find:

Work done to stretch it through an additional distance 'x'.

Solution:

The Potential energy of a spring is given by  $\frac{1}{2} KX^{2}$, where 'X' is the distance up to which it is stretched from its original unstretched position. Here 'K' denotes the spring constant of the spring.

Let us assume the spring constant of the given spring is equal to 'k'.

The initial potential energy of the spring:

                                         $Ui=\frac{1}{2}kx^{2} = 100 J$

If the spring is stretched through an additional distance 'x' then the total distance stretched from the original position would be equal to 2x.

The final potential energy of the spring:

                            $Uf =\frac{1}{2} k(2x)^{2} =4(\frac{1}{2}kx^{2} )=4(100)=400J$

The amount of work done will be equal to the change in potential energy.

                        $Work (W) = Uf - Ui = 400 - 100 = 300 J$

                            ∴ Work done (W) = 300 J

Hence, the amount of work done on the spring to stretch it through an additional distance 'x' will be 300 J.

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