hw9 - Physics 1C Homework 9 --- Chapters 37: Special Theory...

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Unformatted text preview: Physics 1C Homework 9 --- Chapters 37: Special Theory of Relativity g. (I), A spaceship passes you at a speed of 0.750 c. You measure its length to be 28.2 m. How long would it be when at rest? 7 ($7 WK 3‘ (l) A certain type of elementary particle travels at a speed of 2.70 X 108 m/s. At this speed. the averagelife— be 4.76 X 10'“ s. What is the particle’s (a. (II) A frlend of yours travels by you in her fast sports car at a speed of 0.660c. It is measured in your frame to be 4.80 m long and 1.25 m high. (a) What will be its length and height at rest? (b) How many seconds would you say elapsed on your friend’s watch when 20.05 passed on yours? (c) How fast did you appear to be traveling according to your friend? (d) How many seconds would she say elapsed on your watch when she saw 20.0 5 pass on hers? A; time is measured to lifetime at rest? l 6. (II) A spaceship leaves Earth traveling at 0.71 c. A second spaceship leaves the first at a speed of 0.87c with respect to the first. Calculate the speed of the second ship with respect to Earth if it is fired (a) in the same direction the first space- ship is already moving, (b) directly backward toward Earth. v- :E“?, (I 441) If you were to travel to a star 100 light-years from Earth at a speed of 2.50 X 108 m/s. what would you measure this distance to be? ' ' M (II) A stick of length L0, at rest in reference frame S, makes ' an angle 0 with the x axis. In reference frame 8’, which moves to the right with velocity v = vi with respect to S, determine (a) the length L of the stick, and (b) the angle 0’ itflrnakes with the xLaxis. W N V 7 fl 7 7 i 7 W 8 4‘ (11) Suppose a news report stated that starship Enterprise had just returned from a 5—year voyage while traveling at 0.84 c. (a) If the report meant 5.0 years of Earth time, how much time elapsed on the ship? (b) If the report meant 5.0 years of ship time. how much time passed on Earth? V 7 4+ - 4'59 ' x 7 (II) A certain star is 95.0 light-years away. How long ‘ would it take a spacecraft traveling 0.960c to reach that star from Earth, as measured by observers: (a) on Earth, (b) on the spacecraft? (c) What is the distance traveled 38 (II) Calculate the kinetic energy and momentum of a pro. ‘ ton traveling 2.60 X 108 m/s. : according to observers on the spacecraft? (d) What will the spacecraft occupants compute their speed to be from the P c Mr m ‘ & results of (b) and (c)? J ' V ) 7 \r i v by?“ 5‘74” K '3 E - Mac ~ W 11%; t? 1/ / Mo:[.6}x(0 (Li.- ' v: ’ 1 _. f L '21 E 4M C ( Hwfipfifap‘) I. 6"” o 1 7% Show analytically that a particle with momentUm . ( P éga) What is the speed of an electron whose kinetic energy is . energy E has a speed glven by 10,000 times its rest energy? Such speeds are reached in the Stanford Linear Accelerator, SLAC. (b) If the electrons travel in the lab through a tube 3.0 km long (as at SLAC), how long is this tube in the electrons’ reference frame? 45. I": E « /m262 + pz '1} Bonus Problems 4'6. (11) Suppose a spacecraft of mass 27,000 kg is accelerated to 0.21‘c. (a) How much kinetic energy would it have? (b) If you used the classical formula for kinetic energy, by what ’ percentage would you be in error? 7 J t 7:; ‘1/ 7/, '____,_..r “C Mac / Md (’w/v' C l v kccaflsc/ : ) Mow ‘1 The nearest star to Earth is Proxima Centauri, 4.3 light- “ years away. (a) At what constant velocity must a spacecraft travel from Earth if it is to reach the star in 4.0 years, as measured by travelers on the spacecraft? (b) How long does the trip take according to Earth observers? 2 7!. Two protons, each having a speed of 0.935 c in the laboratory, are moving toward each other. Determine (a) the momen— tum of each proton in the laboratory, (b) the total momen- tum of the two protons in the laboratory, and (c) the momentumfiof one proton as seen by the other proton. \ OBI—9' «ado?» ...
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hw9 - Physics 1C Homework 9 --- Chapters 37: Special Theory...

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