Answer
Please see the work below.
Work Step by Step
We know that force force is given as:
$F=-Kx+bx^2-cx^3$
And the energy is given as:
$W=-\int F dx$
$\implies W=-\int (-kx+bx^2-cx^3)dx$
$W=K(\frac{x^2}{2})-b(\frac{x^3}{3})+c(\frac{x^4}{4})$
We plug in the known values to obtain:
$W=(223)(\frac{(2.62)^2}{2})-(4.10)(\frac{(2.62)^3}{3})+(3.1)(\frac{(2.62)^2}{4})$
$W=778J$
Using the equation for percent difference, we have:
$ \dfrac{778-741}{741}$
$ 4.9 \% $
