Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 16 - Vector Calculus - 16.2 Line Integrals - 16.2 Exercises - Page 1126: 46


$16, 245 ft-lbs $

Work Step by Step

The magnitude of gravitational force acting on the man +Can of paint $=(160+m)lbs$ In the upward direction, we get $F \cdot dr=(185-\dfrac{9r}{s}) dr$ $W=\int_C F\cdot dr= \int_0^s (185-\dfrac{9r}{s}) dr$ Here, $C$ shows a vertical line segment connects the bottom and top part of the silo. Now, we have $W=\int_C F\cdot dr=[185r-\dfrac{9r^2}{2s}]_0^s=185 s-4.5 s =16, 245 ft-lbs $
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