Exam 27: Relativity

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A satellite, initially at rest in deep space, separates into two pieces, which move away from each other. One piece has a rest mass of 190 kg and moves away with a speed 0.280c, and the second piece moves in the opposite direction with a speed 0.600c. What is the rest mass of the second piece?

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A tracking station on Earth observes a rocket move away at 0.370c. This rocket is designed to launch a projectile at 0.505c relative to the rocket. What speed (in terms of the speed of light) does the tracking station measure for the projectile if it is fired (a) straight ahead of the rocket or (b) backward from the rocket?

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From the Earth, the Earthlings see the Enterprise approaching from the west at 0.800c and the Klingons approaching from the east at 0.900c. What speed, in terms of the speed of light, does the crew of the Enterprise measure for the Klingon ship?

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A spaceship with a constant speed of 0.800c relative to Earth travels to a star that is 4.30 light-years from Earth. How much time for this trip would elapse on a clock on Earth?

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Someone in Earth's rest frame says that a spaceship's trip between two planets took 10.0 y, while an astronaut on the space ship says that the trip took 5.78y5.78 \mathrm { y } What is the speed of the spaceship, assuming the planets are at essentially at rest?

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A particle physicist observes cosmic rays creating a new particle high in the atmosphere, and the speed of this particle is measured at 99.7% the speed of light. It is unstable, and is observed to decay in an average 37.0 μs. If this particle were at rest in the laboratory, what would be its average lifetime?

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Suppose one twin takes a ride in a spaceship traveling at a very high speed to a distant star and then back again, while the other twin remains on Earth. Compared to the twin who remained on Earth, the astronaut twin is

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A spaceship leaves Earth at a steady forward speed of 70% the speed of light. How fast relative to the ship must the spaceship launch a shuttlecraft in the forward direction so that it will be moving away from Earth at 98.7% the speed of light?

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An electron-volt is the energy gained by an electron if it is accelerated through a potential difference of one volt. What is the equivalent to an electron-volt in kilograms? (c = 3.00 × 108 m/s, e = 1.60 × 10-19C)

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A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light. The length of the train, as measured by a stationary observer on the ground,

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A person in a rocket ship traveling past the earth at a speed of 0.500c fires a laser gun in the forward direction. With what speed does an observer on Earth measure for the light pulse?

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What is the total energy of an electron moving with a speed of 0.950c? (c = 3.0 × 108 m/s, mel = 9.11 × 10-31 kg)

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A really high-speed train moves in a direction parallel to its length with a speed that approaches the speed of light. The height of the train, as measured by a stationary observer on the ground,

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One of the first atomic explosion released approximately 1.0 × 1014 J of energy. How much matter had to be changed into energy to produce this yield? (c = 3.0 × 108 m/s)

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How fast (in terms of the speed of light) should a moving clock travel if it is to be observed by a stationary observer as running at one-half its normal rate?

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A spaceship with a constant velocity of 0.800c relative to Earth travels to the star that is 4.30 light-years from Earth. What distance does the space ship travel as measured by a passenger on the ship?

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Two spaceships are approaching one another, each at a speed of 0.31c relative to a stationary observer on Earth. What speed, in terms of the speed of light, does an observer on one spaceship record for the other approaching spaceship?

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If you were in a spaceship traveling close to the speed of light with respect to Earth, you would notice that

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A 30-year-old astronaut goes off on a long-term mission in a spacecraft that travels at speeds close to that of light. The mission lasts exactly 20 years as measured on Earth. Biologically speaking, at the end of the mission, the astronaut's age would be

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A rocket is traveling away from Earth at 90% the speed of light. The captain turns on a laser light. What is the speed of the light as measured by an Earth-based astronomer if the captain aims the laser (a) directly forward or (b) directly backward?

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