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

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 newton-meters W = → 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 = ∫ → 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, 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...
View Full Document

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.

Page1 / 12

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online