Question

Out of a pair of two springs of spring constant 240 N/m, one is compressed by 10cm and the other is stretched by 10cm. What is the difference in the potential energies stored in the two springs.

Answer 1

$$\begin{gathered} \mathrm{Given}, \\ \mathrm{Spring}\mathrm{constant},\mathrm{k}=240\mathrm{N}/\mathrm{m} \\ \mathrm{Compression}\mathrm{of}\mathrm{spring},\mathrm{x}=10\mathrm{cm} \\ \mathrm{Potential}\mathrm{energy}\mathrm{of}\mathrm{spring}\left(U_1\right)\mathrm{during}\mathrm{compression}\mathrm{is}\mathrm{given}\mathrm{by} \\ {U}_{\mathit{1}}=\frac{1}{2}k{\left(-x\right)}^2 \\ \Rightarrow U_1=\frac{1}{2}k{x}^2=\frac{1}{2}\times 240\times {\left(10\right)}^2 \\ \Rightarrow U_{\mathit{1}}=12000\mathrm{J} \\ \mathrm{Potential}\mathrm{energy}\mathrm{of}\mathrm{the}\mathrm{spring}\mathrm{during}\mathrm{expansion}\left(U_2\right)\mathrm{is}\mathrm{given}\mathrm{by} \\ {U}_2=\frac{1}{2}k{\left(x\right)}^2 \\ \mathit{\Rightarrow }{U}_{\mathit{2}}=\frac{1}{2}\times 240\times {\left(10\right)}^2=12000\mathrm{J} \\ \mathrm{Now},\mathrm{difference}\mathrm{in}\mathrm{potential}\mathrm{energy}\left(U\right)\mathrm{is}\mathrm{given}\mathrm{by} \\ U=U_1-U_2 \\ =12000-12000=0 \end{gathered}$$