Question

1. Thinking Process We know that change in potential energy of a system corresponding to a conservative internal force as
Given,
[
begin{array}{c}
U_{f}-U_{i}=-W=-int_{i}^{f} mathrm{F} cdot d mathrm{r}
F=a x+b x^{2}
end{array}
]
We know that work done in stretching the rubber band by ( L ) is ( |d W|=|F d x| )
[
begin{aligned}
|W| &=int_{0}^{L}left(a x+b x^{2}right) d x
&=left[frac{a x^{2}}{2}right]_{0}^{L}+left[frac{b x^{3}}{3}right]_{0}^{L}
&=left[frac{a L^{2}}{2}-frac{a times(0)^{2}}{2}right]+left[frac{b times L^{3}}{3}-frac{b times(0)^{3}}{3}right]
&=|W|=frac{a L^{2}}{2}+frac{b L^{3}}{3}
end{aligned}
]

# 1. When a rubber band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx, where a and b are constants. The work done in stretching the unstretched rubber band by L is (2014 Main) (a) al? + bĽ (b)(a + b)

Solution