Quiz1 - PHYSICS 2D PROF HIRSCH QUIZ 1 FALL QUARTER 2008 L = Lp c = 3 10 8 m s Formulas Time dilation Length contraction"t ="t $"t p

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Unformatted text preview: PHYSICS 2D PROF. HIRSCH QUIZ 1 FALL QUARTER 2008 OCTOBER 10, 2008 L = Lp /# ; c = 3 % 10 8 m / s ! Formulas: Time dilation; Length contraction : "t = #"t ' $ # "t p ; Lorentz transformation : x ' = " ( x # vt ) 1 y' = y , z' = z "= 1 # v 2 /c 2 t ' = " ( t # vx / c 2 ) x = " ( x ' + vt ' ) y = y', z = z' t = " ( t ' + vx ' / c 2 ) ! ! Velocity transformation : ux ! v ux' +v ux' = ux = 2 1 ! ux v / c 1 + ux ' v / c 2 uy uy ' uy' = uy = 2 " (1 ! ux v / c ) " (1 + ux ' v / c 2 ) Spacetime interval : ("s) 2 = (c"t ) 2 - ["x 2 + "y 2 + "z 2 ] 1+ v / c Relativistic Doppler shift : fobs = f (approaching) 1 ! v / c source r r 1 Momentum : p = " m u ; " = ; E = p 2c 2 + m 2c 4 2 2 1 # u /c Kinetic energy : K = (" # 1) mc 2 Total energy : E = " mc 2 Rest energy : E 0 = mc 2 Electron : me = 0.511 MeV / c 2 Proton : mp = 938.26 MeV / c 2 Neutron : mn = 939.55 MeV / c 2 ! ! Atomic mass unit : 1 u = 931.5 MeV / c 2 Justify all your answers to all problems Problem 1 (10 points) C B A ; electron volt : 1eV = 1.6 " 10 -19 J ! ! v=0.6c A spaceship moves at speed v=0.6c with respect to the ground. An observer on the ground (point A) measures the time interval between the front of the spaceship (point B) and the back of the spaceship (point C) flying by him to be 1µs (10-6s). (a) As measured on the spaceship, how much time passed since the instant the front of the spaceship (B) passed by A and the back of the spaceship (C) passed by A? (b) How long (in m) is this spaceship as measured by an observer on the ground? (c) How long (in m) is this spaceship as measured by an observer on the spaceship? PHYSICS 2D PROF. HIRSCH Problem 2 (10 points) QUIZ 1 FALL QUARTER 2008 OCTOBER 10, 2008 hen lays egg chicken is born 100m An egg is laid and a chicken is born on earth, simultaneously, at distance 100m apart. (a) Find a reference frame seen from which the egg came first, 0.1 µs before the chicken. (b) Find a reference frame seen from which the chicken came first, 0.1 µs before the egg. Hint: Use Lorentz transformation. Even if you don't find a quantitative answer give a qualitative answer explaining clearly the difference between (a) and (b). Problem 3 ( 10 points) Initial 2m v v m Final M v' Particles of masses 2m and m are moving towards each other in the horizontal direction, each at speed v=0.8c with respect to the ground. They undergo an inelastic collision and the resulting particle of mass M moves at speed v' in the horizontal direction. (a) Find v' (b) Find M in terms of m. (c) Explain why there is a difference between the total initial mass and the final mass. Justify all your answers to all problems ...
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This note was uploaded on 12/07/2009 for the course PHYS phys 2d taught by Professor Hirsch during the Fall '08 term at UCSD.

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