# A spring 40 mm long spring is stretched by applying a force. If 10 N force is required to stretch the spring through one mm, then work done in stretching the spring through 40 mm is :

Answer:

F = 10 N

x = 1mm = 0.001

Force contant

⇒$k=\frac{F}{x}$

⇒ $k=\frac{10}{0.001}= 10^{4}N/m$

Now the spring is stretched through a distance, x1 = 40 mm = 0.04 m

The force required to stretch it through x, is

F1 =  kx1

work done is given by the formula

⇒ $W=\frac{1}{2}kx^{2}$

⇒ $W=\frac{1}{2}\times 10^{4}\times (\frac{40}{1000})^{2}$

⇒ $W=\frac{1}{2}\times 10^{4}\times (\frac{16}{40^{4}}) = 8J$

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