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Understanding Work and Fluid Pressure: Concepts and Applications

This lesson explores the fundamentals of work and fluid pressure, highlighting key principles such as Hooke's Law. It covers the work done in various scenarios, including stretching springs, winding cables, and pumping liquids. Students will learn to apply integration to calculate work done by continuous forces, understand the relationship between force, distance, and pressure in fluids. Practical examples and exercises will enhance comprehension, ensuring a solid grasp of the material. Ideal for students seeking a deeper understanding of physics concepts.

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Understanding Work and Fluid Pressure: Concepts and Applications

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  1. Work and Fluid Pressure Lesson 7.7

  2. 50 Work • DefinitionThe product of • The force exerted on an object • The distance the object is moved by the force • When a force of 50 lbs is exerted to move an object 12 ft. • 600 ft. lbs. of work is done 12 ft

  3. a b x Hooke's Law • Consider the work done to stretch a spring • Force required is proportional to distance • When k is constant of proportionality • Force to move dist x = k • x = F(x) • Force required to move through i thinterval, x • W = F(xi) x

  4. Hooke's Law • We sum those values using the definite integral • The work done by a continuous force F(x) • Directed along the x-axis • From x = a to x = b

  5. Hooke's Law • A spring is stretched 15 cm by a force of 4.5 N • How much work is needed to stretch the spring 50 cm? • What is F(x) the force function? • Work done?

  6. Winding Cable • Consider a cable being wound up by a winch • Cable is 50 ft long • 2 lb/ft • How much work to wind in 20 ft? • Think about winding in y amt • y units from the top  50 – y ft hanging • dist = y • force required (weight) =2(50 – y)

  7. Pumping Liquids • Consider the work needed to pump a liquid into or out of a tank • Basic concept: Work = weight x dist moved • For each V of liquid • Determine weight • Determine dist moved • Take summation (integral)

  8. r b a Pumping Liquids – Guidelines • Draw a picture with thecoordinate system • Determine mass of thinhorizontal slab of liquid • Find expression for work needed to lift this slab to its destination • Integrate expression from bottom of liquid to the top

  9. Pumping Liquids 4 • Suppose tank has • r = 4 • height = 8 • filled with petroleum (54.8 lb/ft3) • What is work done to pump oil over top • Disk weight? • Distance moved? • Integral? 8 (8 – y)

  10. Fluid Pressure • Consider the pressure of fluidagainst the side surface of the container • Pressure at a point • Density x g x depth • Pressure for a horizontal slice • Density x g x depth x Area • Total force

  11. 2.5 - y Fluid Pressure • The tank has cross sectionof a trapazoid • Filled to 2.5 ft with water • Water is 62.4 lbs/ft3 • Function of edge • Length of strip • Depth of strip • Integral (-4,2.5) (4,2.5) (2,0) (-2,0) y = 1.25x – 2.5x = 0.8y + 2 2 (0.8y + 2) 2.5 - y

  12. Assignment • Lesson 7.7a • Page 307 • Exercises 1 – 13 odd, 21 • Lesson 7.7b • Page 307 • Exercises 23 – 35 odd

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