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Unformatted text preview: Homework 6.5 Extra Solutions Problem 9 A heavy rope, 50 feet long, weighs . 5 lbs foot and hangs over a building 120 feet high. (a) How much work is done in pulling the rope to the top of the building? Adding up the weights of each little piece of rope and how far this must be lifted we get for the total work: . 5 integraldisplay 50 (50 y ) dy = 0 . 5 parenleftBigg 50 y y 2 2 parenrightBiggvextendsingle vextendsingle vextendsingle vextendsingle vextendsingle y =50 y =0 = 0 . 5 parenleftBigg 50 2 50 2 2 parenrightBigg = 625ftlbs (b) How much work is done in half the rope to the top of the building? In this case, the portion of the rope from y = 25 to y = 50 is lifted to the top of the building as before. The portion of the rope from y = 0 to y = 25 is simply raised 25 feet. This piece of rope weighs 0 . 5 25 = 12 . 5 lbs and so lifting it 25 feet requires 25 12 . 5 = 312 . 5 ftlbs. Thus the total work required is 312 . 5 + 0 . 5 integraldisplay 50 25 (50 y ) dy = 312 . 5 + 0...
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 Spring '08
 Keppelmann

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