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Calc07_5day1 - 7.5 part 1 Work and Pumping Liquids Greg...

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7.5 part 1 Work and Pumping Liquids Greg Kelly, Hanford High School, Richland, Washington
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Review: Hooke’s Law: F kx = A spring has a natural length of 1 m . A force of 24 N stretches the spring to 1.8 m . a Find k : F kx = ( 29 24 .8 k = 30 k = 30 F x = b How much work would be needed to stretch the spring 3m beyond its natural length? ( 29 b a W F x dx = 3 0 30 W x dx = 3 2 0 15 W x = 135 newton-meters W =
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Over a very short distance, even a non-constant force doesn’t change much, so work becomes: ( 29 F x dx If we add up all these small bits of work we get: ( 29 b a W F x dx =
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A leaky 5 lb bucket is raised 20 feet The rope weighs 0.08 lb/ft. The bucket starts with 2 gal (16 lb) of water and is empty when it just reaches the top. Work: Bucket: 5 lb 20 ft 100 ft-lb = Water: The force is proportional to remaining rope. ( 29 20 16 20 x F x - = 5 4 4 16 5 x = - At 0, 16 x F = = At 20, 0 x F = = Check: 0 20 ( 29 b a W F x dx = 20 0 4 16 x 5 dx = -
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A leaky 5 lb bucket is raised 20 feet The rope weights 0.08 lb/ft.
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