03 Brownian And Energy After Class

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This is lecture 3, more about Brownian motion, and introduction to energy, conservation of energy.

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03 Brownian And Energy After Class

  1. 1. Today: Brownian motion, energy, kinds of energy, conservation of energy http://www.flickr.com/photos/davewilliams/ “Wind farm”
  2. 2. Quizzes <ul><li>Quiz #1 posted tonight, due before class Thursday. </li></ul><ul><li>You can take the quizzes more than once </li></ul><ul><li>One recommended strategy: </li></ul><ul><ul><li>Do all assignments / readings / problems related to quiz. </li></ul></ul><ul><ul><li>Take the quiz…note which ones were tricky </li></ul></ul><ul><ul><li>Study those topics, go to office hours, surf the web, re-read book, etc. </li></ul></ul><ul><ul><li>Re-take quiz after studying </li></ul></ul><ul><ul><li>Before exam – You can take all the quizzes again as review </li></ul></ul>
  3. 3. Answer to Question 12, Chapter 11 <ul><li>&quot;Why is Brownian motion apparent only for microscopic particles?“ </li></ul>Melody: “…as the size of the particles increases, the speed at which the particles move decreases because they have a larger mass . This was clearly demonstrated in both experiments we did in class. When we added larger plastic balls to the container, they moved slower than the smaller balls. &quot; Astara: Atoms are always bouncing around, and pushing the tiny particles that surround them. Any momentum that is gained by one of these particles, however, is quickly reversed as it gets bumped back in the opposite direction - Giving the particle a net displacement very near to zero . To our eyes, the particles appear to not be moving because their movement is so little (at a life size view). There were MANY excellent student answers! I will collect these and post them on WebCT
  4. 4. Answer to Question 12, Chapter 11 <ul><li>&quot;Why is Brownian motion apparent only for microscopic particles?“ </li></ul><ul><li>Author’s answer (confusing): </li></ul><ul><ul><li>Brownian motion is apparent only for microscopic particles because of their small mass. Against a large particle, the random bumps exert nearly steady forces on each side that average to zero, but for a small particle there are moments when appreciably more hits occur on one side than the other, producing motion visible in a microscope. </li></ul></ul><ul><li>I say: A decent answer, but incomplete </li></ul>
  5. 5. <ul><ul><li>A) The larger radius particles will undergo more Brownian motion </li></ul></ul><ul><ul><li>B) The smaller radius particles will undergo more Brownian motion </li></ul></ul><ul><ul><li>C)The amount of Brownian motion is unaffected by the radius </li></ul></ul>Clicker Question Say we have a mixture of two tiny plastic microspheres in water made of the same material one kind has a larger radius than the other. Which is true?
  6. 6. Answer to Question 12, Chapter 11 <ul><li>Author’s answer (confusing): </li></ul><ul><ul><li>Brownian motion is apparent only for microscopic particles because of their small mass. Against a large particle, the random bumps exert nearly steady forces on each side that average to zero, but for a small particle there are moments when appreciably more hits occur on one side than the other, producing motion visible in a microscope. </li></ul></ul><ul><li>My answer (probably confusing also): </li></ul>A larger particle has more mass and requires more force to accelerate. At the same time, a larger particle gets many more collisions with water molecules. Inertia  r 3 (volume) Force  r 2 (surface area) (note: because opposite sides almost cancel, it’s even less than this) “ Inertia is proportional to cube of radius” “ Force is proportional to square of radius” As things get bigger, the volume beats the surface area Play around with the Brownian motion applet!
  7. 7. The “math” of Brownian motion (“is proportional to”) Einstein’s formula in 1905: (Too complicated for us!) Avogadro’s number Amount of movement Time interval Gas constant Temperature viscosity Particle radius This is the take home message for us: Amount of Brownian Motion  Temperature Particle radius  Avogadro’s Number  viscosity
  8. 8. <ul><ul><li>A) As you increase the temperature, particles will undergo more Brownian motion </li></ul></ul><ul><ul><li>B) As you increase the temperature, particles will undergo less Brownian motion </li></ul></ul><ul><ul><li>C) Brownian motion only depends on the particle size, not temperature!!! </li></ul></ul>Clicker Question Say we are looking at Brownian motion of tiny plastic microspheres. First at room temperature, then we increase the temperature. Which is true?
  9. 9. <ul><ul><li>A) As you increase the temperature, particles will undergo more Brownian motion </li></ul></ul><ul><ul><li>B) As you increase the temperature, particles will undergo less Brownian motion </li></ul></ul><ul><ul><li>C) Brownian motion only depends on the particle size, not temperature!!! </li></ul></ul>Clicker Question Say we are looking at Brownian motion of tiny plastic microspheres. First at room temperature, then we increase the temperature. Which is true?
  10. 10. Brownian motion simulation on the web Tim’s: http://www.physics.uq.edu.au/people/mcintyre/applets/brownian/brownian.html http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/applet.html Let’s try some experiments with this one: “Tim’s Brownian Motion Applet” Scientists create simplified models that they can simulate on computers This is a powerful way of gaining understanding of nature
  11. 11. Take home messages for Brownian motion (“is proportional to”) At room temperature, atoms have a lot of kinetic energy! Amount of Brownian Motion  Temperature Particle radius  Avogadro’s Number  viscosity What? Remember the (failed) molecular motion demo last week? What is transferred between the ball bearings when they collide?
  12. 12. What is energy???
  13. 13. Let’s brainstorm on different kinds of energy Radiation Potential energy Solar energy Heat Kinetic Gravitational Convection energy Elastic Electrical Mechanical Nuclear Thermal Mass, chemical, dark
  14. 14. There is no in-a-nutshell definition of “energy”… But that’s not a big problem! <ul><li>Simple definitions are very misleading: </li></ul><ul><ul><li>“ Energy is the capacity to do work” </li></ul></ul><ul><ul><li>True: some form of energy is required to do work But some energy cannot be used for work (crackpots) </li></ul></ul><ul><li>This is like saying: </li></ul><ul><ul><li>“ A vegetable is a potato” (http://home.pacifier.com/~ppenn/whatswrong.html) </li></ul></ul><ul><li>We can know recognize something without being able to succinctly define it: </li></ul><ul><ul><li>What is economic value? </li></ul></ul><ul><ul><li>“ Value is money?” </li></ul></ul><ul><ul><li>What is love? </li></ul></ul><ul><ul><li>“ Love is affection?” </li></ul></ul>--Anyone know the source? “ Nature gives us shapeless shapes: clouds and waves and flame. But human expectation is that love remains the same.”
  15. 15. Clicker Question – Total Energy <ul><li>Consider two baseballs (of identical material and mass) traveling in straight lines, with the same spin, at the same height above the ground. One is traveling at 98 mph, the other at 101 mph. Which one has more total energy? </li></ul><ul><ul><li>Baseball @ 98 mph </li></ul></ul><ul><ul><li>Baseball @ 101 mph </li></ul></ul><ul><ul><li>Same…it only depends on the height </li></ul></ul><ul><ul><li>Impossible to determine </li></ul></ul>i.e., there is no difference except their speeds
  16. 16. Clicker Question – Total Energy <ul><li>Consider two baseballs (of identical material and mass) traveling in straight lines, with the same spin, at the same height above the ground. One is traveling at 98 mph, the other at 101 mph. Which one has more total energy? </li></ul><ul><ul><li>Baseball @ 98 mph </li></ul></ul><ul><ul><li>Baseball @ 101 mph </li></ul></ul><ul><ul><li>Same…it only depends on the height </li></ul></ul><ul><ul><li>Impossible to determine </li></ul></ul>What kind of energy does the 101 mph baseball have more of?
  17. 17. Clicker Question – Total Energy 2 <ul><li>A one kilogram chunk of ordinary steel (iron alloy) is sitting next to a kilogram chunk of enriched uranium. Both are stationary . Which has more total energy? </li></ul><ul><li>kilogram of steel </li></ul><ul><li>kilogram of enriched uranium </li></ul><ul><li>Same, they are both at rest and at the same height . </li></ul><ul><li>Impossible to determine. </li></ul>
  18. 18. Clicker Question – Total Energy 2 <ul><li>A one kilogram chunk of ordinary steel (iron alloy) is sitting next to a kilogram chunk of enriched uranium. Both are stationary . Which has more total energy? </li></ul><ul><li>kilogram of steel </li></ul><ul><li>kilogram of enriched uranium </li></ul><ul><li>Same, they are both at rest and at the same height . </li></ul><ul><li>Impossible to determine. </li></ul>What kind of energy does the uranium have more of? This was supposed to be though-provoking Exam questions will not be this ambiguous or tricky (hopefully!)
  19. 19. Kinetic and Potential Energy KINETIC ENERGY “ Energy of Motion” Potential Energy “ Energy of position” Objects moving in straight line Objects spinning Random motion of molecules Position of object in gravitational field Chemical Nuclear Elastic
  20. 20. Dennis’ little blocks – Energy is in the bookkeeping (mathematics) <ul><li>We know how to write down the equations for the many forms of energy…but unlike with Dennis, we have no blocks to look at </li></ul><ul><li>ALL calculations of energy have the same “units”: </li></ul><ul><li>Joules (J) Calories (calories or Calories (kilocalories)) kilowatt-hours </li></ul><ul><li>kg m 2 / s 2 ; Newton-meters; N-m </li></ul><ul><li>Work (transfer of “macroscopic” mechanical energy) and Heat (transfer of “internal energy”) have units of energy </li></ul>
  21. 21. For now, don’t worry about all the different formulas for energy. <ul><li>But, notice that many are not too complicated! </li></ul>K.E. = ½ mv 2 P.E = mgh Kinetic energy of object = ½ mass * speed squared Gravitational potential energy = mass * gravitational acceleration * height E = mc 2 Mass Energy = mass * speed of light squared P.E = ½ k x 2 Energy in a spring = ½ spring constant * stretch squared E = h f Photon (light) energy = constant * frequency
  22. 22. Nose basher
  23. 23. Conservation of Energy “ Energy can flow from one form to another, but cannot be created or destroyed” For example: Macroscopic Kinetic Energy Potential Energy Microscopic K.E. Heat flow This concept is more amazing the more you think about it What about conservation of energy related to body weight / weight loss?
  24. 24. Rattleback—Flow of energy from one form to another <ul><li>The behavior can be complicated and fun! </li></ul>
  25. 25. ENERGY – Take home messages <ul><li>Energy is hard to define! </li></ul><ul><li>Energy flows from one form to another </li></ul><ul><ul><li>Always has the same mathematical “units” </li></ul></ul><ul><li>Potential Energy & Kinetic Energy—important for waves </li></ul><ul><li>And… </li></ul>Energy is absolutely conserved!

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