This rubber band's work in stretching from x = 0 to x = l is:
[tex]W=(\frac{aL^2}{2}+\frac{bL^3}{3}})[/tex]
Work is a measure of energy transfer that occurs when an object is moved over a distance by an external force that is applied in the direction of Work is a measure of energy transfer that occurs when an object is moved over a distance by an external force that is applied in the direction of displacement .
We say that work has been done whenever a force moves an object. When a ball rolls down a hill due to gravity, when you pick up your backpack from the ground, or when your car's internal engine applies a force to move your wheels, all of these events involve a force moving an object over a distance and thus involve some work. No work is done when a force is applied to an object but it does not move.
Given,
force , [tex]f=ax+bx^2[/tex]
work done can be determined by formula,
[tex]W=\int\limits^a_b F\, dx \\\\W=\int\limits^L_0(ax+bx^2)dx\\\\W=(\frac{ax^2}{2}+\frac{bx^3}{3}})|\limits^L_0\\\\W=(\frac{aL^2}{2}+\frac{bL^3}{3}})-0\\\\W=(\frac{aL^2}{2}+\frac{bL^3}{3}})[/tex]
Thus, the work done is [tex]W=(\frac{aL^2}{2}+\frac{bL^3}{3}})[/tex].
To learn more about work refer here
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