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Announcements 4/11/11

Announcements 4/11/11. Prayer Wednesday: Project Show & Tell. The lucky winners are: Michael Meehan & Nick Prestwich – Doppler effect Conrad Rosenbrock & Mike Abrahamson – evaporative cooling Matt Pitts, Marcus Holden, Cody Petrie – refraction of light

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Announcements 4/11/11

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  1. Announcements 4/11/11 • Prayer • Wednesday: Project Show & Tell. The lucky winners are: • Michael Meehan & Nick Prestwich – Doppler effect • Conrad Rosenbrock & Mike Abrahamson – evaporative cooling • Matt Pitts, Marcus Holden, Cody Petrie – refraction of light • Alan Snow – demos: air & water “whirlpools” You will present in that order; a 10 minute cut-off for each group. • Final exam: Sat, Apr 16 – Wed Apr 20, in Testing Center • Final exam review – On Thurs or Friday. Vote for times! FoxTrot, by Bill Amend

  2. HW 37-3: Elastic Collision 1 kg 2 kg 1 kg 2 kg v1,after = ? 9 m/s v2,after = ? 0 m/s 3 m/s 6 m/s ? Check: (1)(9) + (2)(0) = -(1)(3) + (2)(6) 9 = 9  5 m/s 2 kg 2 kg 1 kg 1 kg 1 m/s 8 m/s 5 m/s 4 m/s ? Check: (1)(4) - (2)(5) = -(1)(8) + (2)(1) -6 = -6 

  3. Elastic Collision 1 kg 2 kg 1 kg 2 kg 0.3 c 0.9 c 0.6 c 0 m/s ? Check: (1)(0.9) + (2)(0) = -(1)(0.3) + (2)(0.6) 0.9 = 0.9  Is momentum conserved??? 0.5 c 2 kg 2 kg 1 kg 1 kg 0.14 c 0.70 c 0.5 c 0.73 c ? Check: (1)(0.73) - (2)(0.5) = -(1)(0.70) + (2)(0.14) -0.27 = -.41 Х

  4. Relativistic Momentum • “The Truth”:

  5. Momentum, Sgmv, is conserved in every reference frame!!! (disclaimer: has to be elastic collision) Elastic Collision 1 kg 2 kg 1 kg 2 kg 0.78 c 0.9 c 0 m/s 0.40 c g = 2.29 g = 1.09 g = 1.60 ? Check: (2.29)(1)(0.9) + 0 = -(1.09)(1)(0.4) + (1.60)(2)(0.78) 2.06 = 2.06  0.5 c 1 kg 2 kg 1 kg 2 kg 0.73 c 0.5 c 0.46 c 0.75 c g = 1.46 g = 1.15 g = 1.51 g = 1.13 ? Check: (1.46)(1)(0.73) – (1.15)(2)(0.5) = -(1.51)(1)(0.75) + (1.13)(2)(0.46) -0.095 = -0.095 

  6. Thought Question • What is the maximum momentum that a particle with mass m can have? • p = mc • p = 2 mc • p = 0.5 mc • There is no maximum momentum • None of the above

  7. Momentum vs. Velocity Why do they agree at small velocities?

  8. Reading Quiz • If m is the rest mass of an object, what does mc2 equal? • The gravitational energy of an object • The kinetic energy of an object • The potential energy of an object • The rest energy of an object • The total energy of an object

  9. Relativistic Energy • Momentum  Force (F = dp/dt) • Force  Work (W =  Fdx) • Work  Energy (Ebef + W = Eaft) For mass = 1 kg Result: Correct KE KE (joules) ½ mv2 v/c Why can’t anything go faster than c?

  10. A Word About Units • eV • MeV • MeV/c2

  11. Thought Question • Hydrogen atoms consist of one electron which is bound to a proton by electromagnetic forces. If I very carefully weigh a hydrogen atom, what will I get? • The mass of an electron plus the mass of a proton • Something a little BIGGER than (a) • Something a little SMALLER than (a) • Something entirely different from (a) Ebef + W = Eaft

  12. Thought Question • A nuclear power plant generates 10 million Watts of power nonstop for a day. How much less do the fuel rods weigh at the end of the day? • around 0.0001 grams • around 0.01 grams • around 1 gram • around 0.1 kg • around 10 kg Nuclear power is not alone in converting mass to energy, ALL power sources do this!

  13. Elastic Collision 1 kg 2 kg 1 kg 2 kg 0.40 c 0.9 c 0 m/s 0.78 c g = 2.2942 How did I find out the two speeds after the collision? Conservation of momentum: Conservation of energy:

  14. Elastic Collision 1 kg 2 kg 1 kg 2 kg 0.40 c 0.9 c 0 m/s 0.78 c g = 2.2942

  15. Relationship between E and p • Classical: KE = ½ mv2 = ? (in terms of p) • Relativistic: E = gmc2 = ? (in terms of p) What if m=0? ? Proof:

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