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Conservation of Momentum

Conservation of Momentum. -v. v. -v. v. Conservation of Momentum. v’. v. -v’. -v. Moving with Top Particle. -v. v. v”. v’. What is conserved?. Transform velocities:. Top ball:. Bottom ball:. “old” momentum is not conserved. New Momentum Definition.

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Conservation of Momentum

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  1. Conservation of Momentum -v v -v v Conservation of Momentum v’ v -v’ -v

  2. Moving with Top Particle -v v v” v’ What is conserved? Transform velocities: Top ball: Bottom ball: “old” momentum is not conserved

  3. New Momentum Definition This g is associated with the particle. Particle 1: Orthogonal component of this momentum does not change when changing frames!

  4. New Momentum Definition (continued) Particle 2: Same as 1 Momentum is conserved!

  5. Is Definition Right? Implies momentum can increase indefinitely even though velocity reaches a limit of c. Must do an experiment: Magnetic Field Velocity Selector ExB Fields R

  6. Bending a Proton Fermilab accelerates protons until their g=1000. What is the radius of the circle that they will follow in a 5 Tesla magnet?

  7. Kinetic Energy Try:

  8. Energy Identify Mass is Energy Quantity is independent of frame!

  9. Small Velocity Limit Relativistic Classical Limit

  10. Speed Limit = c As a object moves closer and closer to the speed of light, it takes more and more energy to accelerate it. No massive particle can ever reach the speed of light. Massless particle (photons, neutrinos, gravitons) can only go the speed of light.

  11. Momentum-Energy Four Vector Define: In particle rest frame: Invariant!

  12. Is Energy Conserved? In boxcar problem, as long as the magnitudes of the momenta before and after do not change, then energy is conserved. How about other problems? Does mc2 represent an energy? Do you get the experimental answer for different masses and relative velocities? Must compare calculations with experiments!

  13. Radioactive Decays Masses: If a mole decayed, how much energy is released?

  14. Nuclear Fission Binding potential energy is mass!

  15. Nuclear Fusion Masses: If a mole of helium is produced, how much energy is released?

  16. Fermilab Accelerator Complex KE E(MeV) g p(MeV/c) Machine b Cockroft -Walton 750 keV 938.75 1.0008 37.5 .04 Linac 400 MeV 1338 1.426 954 .71 8 GeV 8938 9.5 8884 .994 Booster 120938 128.9 120934 .99997 Main Injector 120 GeV Tevatron 1 TeV 106+938 1.067E3 ~E 1-4.4E-7

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