160 Elastic Potential Energy Formula Derivation
A derivation of the elastic potential energy formula that is used to obtain \(U_{\mathrm{Sp}} = \dfrac{1}{2}k(\Delta s)^{2}\) from the spring force.
The elastic potential energy is
\[ U_{\mathrm{Sp}} = \dfrac{1}{2}k(\Delta s)^{2} \]
where
- \(U_{\mathrm{Sp}}\) is the elastic potential energy.
- \(k\) is the spring constant.
- \(\Delta s\) is the displacement from equilibrium.
160.1 References
- Logan, J. D. A First Course in Differential Equations. Springer, 2015. — \(V(x)=-\int(-kx)\,dx=\dfrac{1}{2}kx^{2}\).
- Knight, R. D. Physics for Scientists and Engineers: A Strategic Approach with Modern Physics. Pearson, 2023. — \(U_{\mathrm{Sp}}=\dfrac{1}{2}k(\Delta s)^{2}\) from \(\Delta U_{\mathrm{Sp}}=-W\).
- Annihilation
- Constancy of the Speed of Light
- Contracted Length
- Coordinate Transformations
- Elastic Potential Energy Formula Derivation
- Electromagnetic Field Transformations
- Energy-Momentum Relation
- Events
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- Potential Energy Formula Derivation
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