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PHY 113 C General Physics I 11 AM-12:15 P M TR Olin 101 Plan for Lecture 19:

PHY 113 C General Physics I 11 AM-12:15 P M TR Olin 101 Plan for Lecture 19: Chapter 14: The physics of fluids Density and pressure Variation of pressure with height Buoyant forces. Comment on exam. iclicker question:. Exam 2 feedback iclicker question

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PHY 113 C General Physics I 11 AM-12:15 P M TR Olin 101 Plan for Lecture 19:

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  1. PHY 113 C General Physics I 11 AM-12:15 PM TR Olin 101 Plan for Lecture 19: Chapter 14: The physics of fluids Density and pressure Variation of pressure with height Buoyant forces PHY 113 C Fall 2013 -- Lecture 19

  2. PHY 113 C Fall 2013 -- Lecture 19

  3. Comment on exam iclicker question: PHY 113 C Fall 2013 -- Lecture 19

  4. Exam 2 feedback • iclicker question • For Exam 3 would you prefer: • To have an in class exam only. • To have both in class and take-home components. PHY 113 C Fall 2013 -- Lecture 19

  5. toward away Webassign questions: A driver travels northbound on a highway at a speed of 30.0 m/s. A police car, traveling southbound at a speed of 34.0 m/s, approaches with its siren producing sound at a frequency of 2500 Hz. (a) What frequency does the driver observe as the police car approaches?(b) What frequency does the driver detect after the police car passes him?(c) Repeat parts (a) and (b) for the case when the police car is traveling northbound. PHY 113 C Fall 2013 -- Lecture 19

  6. toward away Webassign questions -- continued: A driver travels northbound on a highway at a speed of 30.0 m/s. A police car, traveling southbound at a speed of 34.0 m/s, approaches with its siren producing sound at a frequency of 2500 Hz. (a) What frequency does the driver observe as the police car approaches? Police vs Driver vo PHY 113 C Fall 2013 -- Lecture 19

  7. Webassign question: A violin string has a length of 0.400 m and is tuned to concert G, with fG = 392 Hz.(a) How far from the end of the string must the violinist place her finger to play concert A, with fA = 440 Hz? cm from the bridge(b) If this position is to remain correct to one-half the width of a finger (that is, to within 0.270 cm), what is the maximum allowable percentage change in the string tension? • Assuming the tension remains the same: lAfA=lGfG LAfA=LGfG PHY 113 C Fall 2013 -- Lecture 19

  8. The physics of fluids. • Fluids include liquids (usually “incompressible) and gases (highly “compressible”). • Fluids obey Newton’s equations of motion, but because they move within their containers, the application of Newton’s laws to fluids introduces some new forms. • Pressure: P=force/area 1 (N/m2) = 1 Pascal • Density: r =mass/volume 1 kg/m3 = 0.001 gm/ml Note: In this chapter Ppressure (NOT MOMENTUM) PHY 113 C Fall 2013 -- Lecture 19

  9. Pressure Note: since P exerted by a fluid acts in all directions, it is a scalar parameter PHY 113 C Fall 2013 -- Lecture 19

  10. Example of pressure calculation • High heels (http://www.flickr.com/photos/moffe6/3771468287/lightbox/) F PHY 113 C Fall 2013 -- Lecture 19

  11. Pressure exerted by air at sea-level • 1 atm = 1.013x105 Pa • Example: What is the force exerted by 1 atm of air pressure on a circular area of radius 0.08m? • F = PA = 1.013x105 Pa x p(0.08m)2 • = 2040 N Patm PHY 113 C Fall 2013 -- Lecture 19

  12. Density = Mass/Volume PHY 113 C Fall 2013 -- Lecture 19

  13. Relationship between density and pressure in a fluid Effects of the weight of a fluid: P(y+Dy) rgDy = mg/A y P(y) Note: In this formulation +y is defined to be in the up direction. PHY 113 C Fall 2013 -- Lecture 19

  14. For an “incompressible” fluid (such as mercury): r = 13.585 x 103 kg/m3 (constant) Example: r = 13.595 x 103 kg/m3 PHY 113 C Fall 2013 -- Lecture 19

  15. Barometric pressure readings • Historically, pressure was measured in terms of inches of mercury in a barometer r = 13.595 x 103 kg/m3 PHY 113 C Fall 2013 -- Lecture 19

  16. Weatherreport: PHY 113 C Fall 2013 -- Lecture 19

  17. Question: Consider the same setup, but replace fluid with water (r = 1000 kg/m3). What is h? • iclicker equation: • Will water barometer have h: • Greater than mercury. • Smaller than mercury. • The same as mercury. r = 1000kg/m3 PHY 113 C Fall 2013 -- Lecture 19

  18. Question: Consider the same setup, but replace fluid with water (r = 1000 kg/m3). What is h? r = 1000kg/m3 PHY 113 C Fall 2013 -- Lecture 19

  19. iclicker question: • A 0.5 m cylinder of water is inverted over a piece of paper. What will happen • The water will flow out of the cylinder and make a mess. • Air pressure will hold the water in the cylinder. PHY 113 C Fall 2013 -- Lecture 19

  20. General relationship between P and r: PHY 113 C Fall 2013 -- Lecture 19

  21. Approximate relation of pressure to height above sea-level y-y0(mi) P (atm) PHY 113 C Fall 2013 -- Lecture 19

  22. iclicker question: • Have you personally experienced the effects of atmospheric pressure variations? • By flying in an airplane • By visiting a high-altitude location (such as Denver, CO etc.) • By visiting a low-altitude location (such as Death Valley, CA etc.) • All of the above. • None of the above. PHY 113 C Fall 2013 -- Lecture 19

  23. Example: Hydraulic press incompressible fluid A1Dx1=A2Dx2 F1/A1=F2/A2 PHY 113 C Fall 2013 -- Lecture 19

  24. Buoyant forces in fluids • (For simplicity we will assume that the fluid is incompressible.) Image from the web of a glass of ice water Image from the web of a floating iceberg. PHY 113 C Fall 2013 -- Lecture 19

  25. Buoyant force for fluid acting on a solid: FB=rfluidVdisplacedg FB - mg = 0 rfluidVsubmergedg -rsolidVsolidg = 0 A Dy mg PHY 113 C Fall 2013 -- Lecture 19

  26. Summary: Some densities: ice r = 917 kg/m3 fresh water r= 1000 kg/m3 salt water r = 1024 kg/m3 PHY 113 C Fall 2013 -- Lecture 19

  27. iclicker question: • Suppose you have a boat which floats in a fresh water lake, with 50% of it submerged below the water. If you float the same boat in salt water, which of the following would be true? • More than 50% of the boat will be below the salt water. • Less than 50% of the boat will be below the salt water. • The submersion fraction depends upon the boat's total mass and volume. • The submersion fraction depends upon the barometric pressure. PHY 113 C Fall 2013 -- Lecture 19

  28. Archimede’s method of finding the density of the King’s “gold” crown Wwater Wair PHY 113 C Fall 2013 -- Lecture 19

  29. Summary: Application of Newton’s second law to fluid (near Earth’s surface) PHY 113 C Fall 2013 -- Lecture 19

  30. Review of equations describing static fluids in terms of pressure P and density r: PHY 113 C Fall 2013 -- Lecture 19

  31. Buoyant force Ftop A Dy Fbottom PHY 113 C Fall 2013 -- Lecture 19

  32. Scale reading due to buoyant force: T FB mg PHY 113 C Fall 2013 -- Lecture 19

  33. Scale reading due to buoyant force: T FB mg PHY 113 C Fall 2013 -- Lecture 19

  34. Fluid dynamics (for incompressible fluids) PHY 113 C Fall 2013 -- Lecture 19

  35. Approximate energy conservation in fluid dynamics  Bernoulli’s equation PHY 113 C Fall 2013 -- Lecture 19

  36. Bernoulli’s equation: PHY 113 C Fall 2013 -- Lecture 19

  37. Bernoulli’s equation: PHY 113 C Fall 2013 -- Lecture 19

  38. Possibilities: Fire extinguisher P>>P0 PHY 113 C Fall 2013 -- Lecture 19

  39. Possibilities: Open top: P=P0 PHY 113 C Fall 2013 -- Lecture 19

  40. iclicker question: • Notice that if P<<P0, v1could become very small. How might this happen? • Put an air-tight lid on the top. • Remove the lid on the top. • This will never happen. PHY 113 C Fall 2013 -- Lecture 19

  41. Siphon PHY 113 C Fall 2013 -- Lecture 19

  42. Simplistic statement: v1, P1 v2, P2 PHY 113 C Fall 2013 -- Lecture 19

  43. Webassign question: The gravitational force exerted on a solid object is 5.30 N. When the object is suspended from a spring scale and submerged in water, the scale reads 3.50 N (figure). Find the density of the object. PHY 113 C Fall 2013 -- Lecture 19

  44. PHY 113 C Fall 2013 -- Lecture 19

  45. Dy Dz PHY 113 C Fall 2013 -- Lecture 19

  46. PHY 113 C Fall 2013 -- Lecture 19

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