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EEJ MAIN Physics QUESTION #7026
Question 1
When a specific rubber band is elongated by a distance $x$, it produces a restorative force of $F = ax + bx^2$, where $a$ and $b$ are constants. Find the total work done in stretching this rubber band from its equilibrium position to a length $L$.
  • $\frac{aL^{2}}{2}+\frac{bL^{3}}{3}$✔️
  • $\frac{1}{2}(\frac{aL^{2}}{2}+\frac{bL^{3}}{3})$
  • $aL^{2}+bL^{3}$
  • $\frac{1}{2}(aL)^{2}+bL^{3}$
Correct Answer Explanation
Work done $W$ is calculated by integrating the force over the distance: $W = \int_{0}^{L} (ax + bx^2) dx$. Performing the integration gives $[\frac{ax^2}{2} + \frac{bx^3}{3}]_0^L$, which simplifies to $\frac{aL^2}{2} + \frac{bL^3}{3}$.