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Unformatted text preview: 7.5 part 1 Work and Pumping Liquids Greg Kelly, Hanford High School, Richland, Washington 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 30 W x dx = ∫ 3 2 15 W x = 135 newtonmeters W = → Over a very short distance, even a nonconstant 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 = ∫ → 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 ftlb ⋅ = 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, x F = = Check: 20 ( 29 b a W F x dx = ∫ 20 4 16 x 5 dx = ∫ → A leaky 5 lb bucket is raised 20 feet...
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This note was uploaded on 03/10/2008 for the course MATH 214 taught by Professor Riggs during the Fall '05 term at Cal Poly Pomona.
 Fall '05
 Riggs
 Differential Calculus

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