When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude
F = ax + bx² where a and b are constants. The work done in stretching the unstretched rubber-band by L is :

Question

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 rubber-band by L is :

Aicharya · Accepted Answer

$W = \int F dx$ $= \int (ax + bx^2) dx$ $= \frac{a}{2} \left[ x^2 \right]_0^L + \frac{b}{3} \left[ x^3 \right]_0^L$ $= \frac{aL^2}{2} + \frac{bL^3}{3}$

When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx 2…

Solution