## Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson

# Chapter 7 - Exercises and Problems - Page 126: 33

#### 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: $\dfrac{778-741}{741}$ $4.9 \%$

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