# w03 - x = 0 on the x-axis(a ±ind the work done in moving a...

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Math 152 Workshop #3 Spring 2011 1. A homogeneous liquid whose density is 300 kg/m 3 flls three buried containers. Each container, illustrated below, is 10 meters tall. The top oF each container is at ground level. All three containers have the same volume. The middle container is a cylinder, and the other two are circular cones. Which container needs the least amount oF work to empty (that is, to pump the liquid to ground level)? Which container needs the most work to empty? JustiFy your assertions by computing the work necessary in each case (Suggestion: Try the cylinder frst). 3 m. 10 m. ground level Note: the volume oF a circular cylinder with base radius r and height h is πr 2 h ; the volume oF a circular cone with base radius r and height h is πr 2 h/ 3. 2. Electrons repel each other with a Force which is inversely proportional to the square oF the distance between them; call the proportionality constant k in the units to be used. Suppose one electron is fxed at

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Unformatted text preview: x = 0 on the x-axis. (a) ±ind the work done in moving a second electron along the x-axis From the point x = 10 to the point x = 1. (b) ±ind the work done in moving the second electron along the x-axis From the point x = M to the point x = 1. (c) What happens to your answer in b) (which should depend on M ) as M → + ∞ ? 3. Compute the work necessary to raise a triangular sail 13 feet wide, 20 feet high, and 75 lb of weight from the boom (horizontal pole) to its maximum extent (20 feet high). 4. Water is pumped into a spherical tank of radius 5 ft from a source located 2 ft below a hole at the bottom (Fgure to the right). The density of water is 62.4 lb/ft 3 . a) Calculate the work required to Fll the tank. b) Calculate the work F ( h ) required to Fll the tank to a height h ft from the bottom of the sphere. c) Graph the function F ( h ) for 0 ≤ h ≤ 10. Water source 2 5...
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w03 - x = 0 on the x-axis(a ±ind the work done in moving a...

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