Discussion Forum

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

Answer:

Explanation:

 We know that change in potential  energy ofa  system corresponding to a conservative internal force as

$U_{f}-U_{i}=-W=-\int_{i}^{f} F.dr$

  Given,   $F= ax+bx^{2}$

We know that work done in stretching  the rubber band by L is

    |dW|= |F dx|

$|W|=\int_{0}^{L} (ax+bx^{2})dx$

   =   $\left[ \frac{ax^{2}}{2}\right]_0^L+\left[\frac{bx^{3}}{3}\right]_0^L$

    = $\left[ \frac{aL^{2}}{2}-\frac{a\times (0)^{2}}{2}\right]$ +  $\left[ \frac{bL^{3}}{3}-\frac{b\times (0)^{3}}{3}\right]$

            $|W|=\frac{aL^{2}}{2}+\frac{bL^{3}}{3}$