Calculus (3rd Edition)

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

Chapter 9 - Further Applications of the Integral and Taylor Polynomials - 9.2 Fluid Pressure and Force - Exercises - Page 475: 19


$$940,800 \mathrm{N}$$

Work Step by Step

A horizontal strip at depth $y$ has length 6 and width $$ \frac{\Delta y}{\sin 30^{\circ}}=2 \Delta y $$ Thus, \begin{align*} F&=2 \rho g \int_{0}^{4} 6 y d y\\ &=6\rho g y^2\bigg|_{0}^{4}\\ &=96 \rho g \end{align*} If distances are in feet, then $\rho g=w=62.5 \mathrm{lb} / \mathrm{ft}^{3}$ and $F=6000 \mathrm{lb}$; if distances are in meters, then $\rho g=9800 \mathrm{N} / \mathrm{m}^{3}$ and $$F=940,800 \mathrm{N}$$
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