Question

calculate work done to pull a spring​

Answer 1

Let's start with the derivation of the above equation.

Let the spring be stretched through a small distance d x dx dx.

Then work done in stretching the spring through a distance d x dx dx is d W = F d x , dW=Fdx, dW=Fdx, where F is the force applied to stretch the spring.

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Answer 2

To find :

Work done in pulling a spring ?

Solution:

Let's assume that a spring has been pulled by distance of "x" from its mean, unstretched position.

So, the magnitude of spring force at that stretched position :

$\therefore \: |F| = kx$

• "k" is spring constant.

Now, the net work done :

$\therefore \: dW = F \times dx$

$\implies\: dW = (kx) \times dx$

Integrating on both sides:

$\displaystyle \implies\: \int_{0}^{W} dW = k \int_{0}^{x} x \times dx$

$\displaystyle \implies\: W = k \times \dfrac{ {x}^{2} }{2}$

$\displaystyle \implies\: W = \dfrac{1}{2} k{x}^{2}$

So, net work done is:

$\boxed{ \bold{\: W = \dfrac{1}{2} k{x}^{2}}}$