6-6 Work by a Variable Force 215 LE.4 A conical tank with a circular cross section and vertex at the SOLVING A WORD PROBLEM ■EXAMP bottom has a vertical axis. The radius of the top is 4.00 m, and the depth is 5.00 m. The tank is filled with water. Find the work required to pump out all the water over the top. The force of gravity on each cubic meter of water is 9800 N. See Fig. 6-64. 4.00 m Each horizontal layer of water is a circular disk dh meters thick (just as in finding volumes by use of disk elements). This means that the weight of each disk of water is 9800[π(radius)(thickness)]. From similar triangles in the figure, we see that 5.00 m dh /h 4.00/5.00 or 0.800h The distance each disk must be raised in order to empty the tank is 5.00 h me- ters. Therefore, summing the products of weight and distance, we find the work done. Fig. 6-64 5.00 5.00 W | (9800m" dh)(5.00 _ h,-9800m | (0.800h)-(5.00-h) dh 0 25.00 5.00 5.00,3 6270m(52.1) - 1.03 x 10 N m 1.03 MJ EXERCISES O-

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.