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# Problems on relativity

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9-The Tevatron accelerator at the Fermi National Accelerator Laboratory (Fermilab) outside Chicago actually consists of 5 stages to sequentially boost protons to 1 TeV (1000 GeV). What is the speed of the proton at the end of each stage? Note: the numbers given in parentheses represent the total kinetic energy at the end of each stage.
Cockcroft-Walton (750 keV)

Linac (400 MeV)

Booster (8 GeV)

Main ring or injector (150 GeV) (express to at least 5 decimal places)

Tevatron itself (1 TeV) (express to at least 7 decimal places)

10-The International Space Federation constructs a new spaceship that can travel at a speed of 0.920c. Mary, the astronaut, boards the spaceship to travel to Barnard's star, which is the second nearest star to our solar system after Alpha Centauri and is 5.98 ly away. After reaching Barnard's star, the spaceship travels slowly around the star system for 5 years doing research before returning back to Earth.
(a) How much time does the journey take?

(b) How much older is her twin Frank when she returns?

11-Calculate the momentum p, kinetic energy K, and total energy E of an electron traveling at each of the speeds tabulated below.

(a) 0.03c

(b) 0.3c

(c) 0.8c

12-A muon has a mass of 106 MeV/c2. Calculate the speed, momentum, and total energy of a 197 MeV muon.