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Measuring masses and momenta

Measuring masses and momenta. Measuring charged particle momenta. Momentum and Special Relativity. Kinetic energy in a simple accelerator. Total energy, mass and momentum. Measuring masses. v. B-field. F. Motion of Charged Particle in a Magnetic Field.

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Measuring masses and momenta

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  1. Measuring masses and momenta • Measuring charged particle momenta. • Momentum and Special Relativity. • Kinetic energy in a simple accelerator. • Total energy, mass and momentum. • Measuring masses.

  2. v B-field F Motion of Charged Particle in a Magnetic Field • Charge Q, magnetic field strength B. • Velocity v, normal to magnetic field. • Lorentz force F, normal to directions of B and v. • Magnitude of force • Circular path.

  3. Measuring momentum • Centripetal force • Equate Lorentz and centripetal forces

  4. electron momentum (kg m/s) electron velocity (1/c) Momentum and Special Relativity • Measurementof momentumagainst speedfor an electron • Must redefine momentum to keep conservation of momentum • Relativistic momentum:

  5. Kinetic energy in a simple accelerator • Remember two rules: • Work done = _____ x ________. • Change in K.E. = work done. • Build an accelerator to check this: electron gun accelerator plates velocity measurement

  6. v2 (1/c2) work done (mc2) Kinetic energy cont. • More measurements: • If want to keep K.E. = work done, define: where

  7. Energy and mass • Have seen:so know E = mc2 (ignoring K.E.). • Putting it all together: • Rememberingcan show that and

  8. An aside, units • We have • Multiply p by c to get energyBut Q = 1.6x10-19 C for e,  etc. • Now c = 3x108 ms-1 so: • Finally, express p in units of GeV/ c:

  9. PC Exercise 2 • Use PC to do following experiment: Side viewEnd view +, +, K+ or p E known e+ e- B field -, -, K- or p +, +, K+ or p Measure r, hence get p -, -, K- or p

  10. PC exercise 2 cont. • Using known energy (from energy conservation) and momentum (from r measurement) calculate mass: • Compare with known particle masses, can you identify the particles?

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