Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 6 - Applications of the Integral - 6.5 Work and Energy - Exercises - Page 318: 23

Answer

$2.94 \times 10^{6} \ J$

Work Step by Step

The force of one layer is equal to: $\ Force= \ Mass \times \ gravity = 9.8 \times (1000) \times 32 \Delta y \ N=313600 \Delta y \ N$ Therefore, the work done against can be computed as: $ W=\int_{2.5}^{5} 313600 y \ dy \\=313600 [\dfrac{y^2}{2}]_{2.5}^{5} \\ =156800 [y^2]_{2.5}^{5} $ By using a calculator, the required result is: $W \approx 2.94 \times 10^{6} \ J$
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