Question

When a rubber-band is stretched by a distance $x$, it exerts a restoring force of magnitude $F=ax+b{x}^2$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber band by $L$ is

• A. $\frac{a{L}^2}{2}+\frac{b{L}^3}{3}$
• B. $\frac{1}{2}(\frac{a{L}^2}{2}+\frac{b{L}^3}{3})$
• C. $a{L}^2+b{L}^3$
• D. $\frac{1}{2}(a{L}^2+b{L}^3)$

Answer 1

The correct option is A $\frac{a{L}^2}{2}+\frac{b{L}^3}{3}$

$F=ax+b{x}^2$

$dw=Fdx$

$W={\int }_0^L(ax+b{x}^2)dx$

$W=\frac{a{L}^2}{2}+\frac{b{L}^3}{3}$