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Question

A spring of force constant $$800$$ N/m has an extension of $$5$$ cm. Find work done in extending it from $$5$$ cm to $$15$$ cm.


Solution

$$\textbf{Step 1: Expression for Work done by spring}$$ 
Work done in stretching spring from length $$x_{1}$$ to  $$x_{2}$$ is given by:
                        $$W = \dfrac{1}{2} k (x_{2}^{2} - x^{2}_{1})$$ 
Where $$k$$ is the spring constant

$$\textbf{Step 2: Calculations}$$ 
Putting given values, we get:
                       $$W = \dfrac{1}{2} \times 800N/m [(0.15m)^{2} - (0.05m)^{2}] $$ 
                             $$ = 8\ J$$ 

Hence the work done in extending the spring from $$5cm$$ to $$15cm$$  is $$8\ J.$$ 

Physics

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