Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 16 - Vector Calculus - 16.2 Exercises - Page 1098: 45

Answer

$\approx 1.67 \times 10^{4} ft-lb$

Work Step by Step

The magnitude of the gravitational force acting on the man plus the can of paint is equal to $=160+25=185lbs$ Since we are moving in the upward direction: $F \cdot dr=185 dr$ Work done: $W=\int_C F\cdot dr=185 \int_C dr$ Since $C$ shows a vertical line segment connecting the bottom and top of the silo, we have: Work done, $W=\int_C F\cdot dr=185 \int_C dr=185(90)=16, 650 ft-lbs \approx 1.67 \times 10^{4} ft-lb$
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