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Unformatted text preview: PHY3063 Spring 2007 R. D. Field Exam 1 Solutions Page 1 of 6 February 1, 2007 PHY 3063 Exam 1 Solutions Problem 1 (20 points): Circle true or false for the following 5 questions (1 point each): (a) (True or False,) The laws of physics are invariant under a change in inertial frame. (b) (True or False,) The speed of light in a vacuum is independent of the velocity of the source of the light, but depends on the velocity of the observer. (c) (True or False, The mass and charge of a particle depends on its speed. (d) (True or False,) Light has no rest mass, but it has momentum and energy. (e) (True or False) The energy of a photon increases with increasing wavelength. Write in the answer to the following 5 questions (3 points each): (f) What is the speed = v/c of a proton with momentum p = 1 GeV/c? Answer: = 0.729 Solution: We know that 729 . ) GeV 93828 . ( ) 1 ( 1 ) ( ) ( 2 2 2 2 2 + = + = = GeV GeV c m pc pc E pc p (g) What is the Kinetic Energy of a proton with momentum p = 1 GeV/c? Answer: (in MeV) = 432.44 MeV Solution: We know that MeV MeV c m KE p 44 . 432 ) 28 . 938 )( 1 461 . 1 ( ) 1 ( 2 = = . (h) What is the speed = v/c at which the kinetic energy of a particle (with rest mass m ) is equal to its rest mass energy? Answer: = 0.866 Solution: Setting the kinetic energy equal to the rest mass energy gives 2 2 ) 1 ( c m RME c m KE = = = . Thus, 1 1 = , and = 2 and 866 . 2 3 4 3 4 1 1 1 1 2 = = = = . (i) What is the speed = v/c at which a the relativistic mass of an electron is equal to the rest mass of a meson? Answer: = 0.9999928 Solution: We see that 2 2 c m c m o e = and 1096 . 264 511 . 134.96 2 2 = = c m c m e o . Hence, 9999928 . 1 1 2 = . PHY3063 Spring 2007 R. D. Field Exam 1 Solutions Page 2 of 6 February 1, 2007 (j) What is the wavelength of light ( i.e. a photon) which has a relativistic mass equal to the rest mass of an electron? Answer: (in fm) = 2,426.32 fm Solution: The relativist mass of an electron is given by m = E/c 2 and hence fm MeV fm MeV c m hc E hc pc hc p h e 32 . 426 , 2 511 . 85 . 239 , 1 2 = = = = = . Problem 2 (40 points) Suppose Jim, John, and Rick were all born simultaneously in the Earth frame ( i.e. O-frame ). Jim and Rick were born at the origin at t = 0 and John was born on planet Zilch 49 light- years from Earth ( as measured in the O-frame ). Rick is put in a rocket ship at the moment of birth heading for John at speed = V/c = 0.98. Let the O'-frame be the rocket frame ( i.e....
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