l5 - Review Conservation of momentum Photon mass Invariants...

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Unformatted text preview: Review Conservation of momentum Photon mass Invariants Collisions LHC Review: momentum and forces We found that relativistic momentum goes like p 1 = m v 2 For perpendicular forces ( vector F vector v ) we found vector F = m vector a The centripetal force for uniform circular motion is F = mv 2 / r . For parallel forces ( vector F bardbl vector v ) we found vector F = 3 m vector a Review Conservation of momentum Photon mass Invariants Collisions LHC Review: relativistic energy Relativistic kinetic energy is E k = ( 1 ) m c 2 . Classical limit reduces to E k = 1 2 mv 2 Suggests total energy of E tot = E + E k = m c 2 + ( 1 ) m c 2 = m c 2 (1) Common unit for energies in modern physics: electron Volt, where 1 eV=1 . 602 10- 19 Joules. Chemical bonds are typically 36 eV. Can describe particle masses in energy units. Electron: m e = 511 10 3 eV/ c 2 or just 511 keV. Proton: m p = 939 10 6 eV/ c 2 or just 939 MeV. Review Conservation of momentum Photon mass Invariants Collisions LHC Relativistic conservation of momentum Classically, kinetic energy is p 2 / 2 m . Consider p 2 in relativity: ( pc ) 2 = ( m vc ) 2 = ( m c 2 ) 2 . (2) If we then use E = m c 2 and 2 = 1 1 2 , we obtain p 2 c 2 = 2 ( 1 1 2 ) E 2 = ( 2 1 ) E 2 = 2 E 2 E 2 . (3) However, since we found before that the total energy is E = E , we have p 2 c 2 = E 2 E 2 or E 2 = E 2 + p 2 c 2 . (4) Therefore if E k E we have E k ,relativistic pc . Review...
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This note was uploaded on 05/28/2011 for the course PHY 251 taught by Professor Rijssenbeek during the Fall '01 term at SUNY Stony Brook.

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l5 - Review Conservation of momentum Photon mass Invariants...

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