The spring is initially in unstretched condition. It is first stretched by a length ' x ' and the work done is W 1 . Then again it is stretched by further length ' x ' when the w

Question

The spring is initially in unstretched condition. It is first stretched by a length ' x ' and the work done is W 1 ​ . Then again it is stretched by further length ' x ' when the work done is W 2 ​ . The value of W 2 ​ is given by

TestHub · Accepted Answer

Work done in stretching a spring from its natural length to an extension $x$ is given by $W_{1} = \frac{1}{2} k x^{2}$ .

When the spring is further stretched by a length $x$ , the total extension becomes $2 x$ .

Total work done from the natural length to an extension $2 x$ is $W = \frac{1}{2} k (2 x)^{2} = 4 (\frac{1}{2} k x^{2}) = 4 W_{1}$ .

Work done in the second step is $W_{2} = W - W_{1} = 4 W_{1} - W_{1} = 3 W_{1}$ .

Answer: $3 W_{1}$

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