University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 6 - Section 6.5 - Work - Exercises - Page 380: 2

Answer

a) $200$ lb/in b) $400$ lb-in $\approx 33.3$ ft-lb c) 8 in

Work Step by Step

a) Since, we know $F=k x$ Then, $k=\dfrac{F}{x}=\dfrac{800}{4}= 200$ lb/in b) Now, integrate. From part (a) $k =200$ $\int_0^2 kx dx= 200[ \dfrac{x^2}{2}]_0^2$ or, $100[ 2^2-0] =400 lb- in \approx 33.3 ft -lb$ c) Since, we know $F=k x$ and here, F=1600 N Then, $1600=(200) (x) \implies x=\dfrac{1600}{200}$ $x=8$ inches
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