Question

The work done in extending a spring by x is w. find the work done in further extension x​

Answer 1

Answer:

  3w

Explanation

see the attacment

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Answer 2

Given :-

Work done in extending x = W

W =$\int\:Fdx$

As we know that in spring,

F = Kx

W = $\int\: Kxdx$

W = Kx²/2

For further extension,

x' = 2x

W' = $\int^{2x}_{x}\:Fdx$

W' = $\int^{2x}_{x}\:kxdx$

W' = K/2[(2x)²-(x)²]

W' = 3Kx²/2

Again,

W'/W = 3Kx²/2 × 2/Kx²

W'/W = 3

W' = 3W

Hence,

The work done in further extension = W' = 3W.