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mhw3 - Problems Due 9/30 7.10(Graded(1 1(easy Suppose one...

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Problems: Due 9/30 7 . 10 ( Graded ) (1) 1. (easy) Suppose one photon has an energy of 200 MeV and is traveling along the x axis. Suppose another has an energy of 100 MeV and is traveling along the y axis. (a) What is the total energy of this system? (b) If a single particle had this same energy and moemntum, what would be its mass? (c) In what direction would it be traveling? (d) With what speed? 2. (medium, Graded ) A particle as observed in a certain reference frame (i.e. observer A ) has a total energy of 5 GeV and a momentum of 3 GeV /c (i.e. cp which has the dimension of energy, is equal to 3 GeV ) (a) What is the energy in the frame in which its momentum is equal to 4 GeV / c, i.e. an observer B moving with velocity v relative to A measures a momentum of 4 GeV / c. (b) What is its rest mass in GeV/c 2 and what is the ratio between this mass and the proton mass? (c) What is the relative velocity of the two frames? 3. ( medium ) A neutral π meson ( π o ) decays into two γ rays (and nothing else). If a π o (whose rest mass is 135 MeV is moving with a kinetic energy of 1 GeV: (a) What are the energies of the γ rays if the decay process causes them to be emitted in opposite directions along the pion’s original direction.
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