Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 6: Applications of Definite Integrals - Section 6.5 - Work and Fluid Forces - Exercises 6.5 - Page 347: 3


$0.08 j$ or 0.08 N-m

Work Step by Step

Hooke's Law states that $F=k x$ or, $k=\dfrac{F}{x}=\dfrac{2}{(0.02)}= 100$ N-m When we stretch the rubber band, the limits for $x$ become from $0$ to $x=\dfrac{4}{100}=0.04 m$ The work done can be found as: $W=\int_0^{(0.04)} (100 x) dx$ Use formula: $\int x^n=\dfrac{x^{n+1}}{n+1}+C$ This implies that $W= 100[ \dfrac{x^2}{2}]_0^{(0.04)}=50 (0.04)^2 =0.08 J$ or 0.08 N-m
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