bei48482_FM

EXERCISES

But be ye doers of the word, and not hearers only, deceiving your own selves. —James I:22

Exercises 49

Figure 1.26The world line of a particle in spacetime.

x=ct

ABSOLUTELY

UNRELATED

ABSOLUTELY

UNRELATED

ct

x

Here and now

World

line

x=−ct

ABSOLUTE FUTURE

ABSOLUTE PAST

6. An airplane is flying at 300 m/s (672 mi/h). How much time
   must elapse before a clock in the airplane and one on the
   ground differ by 1.00 s?


7. How fast must a spacecraft travel relative to the earth for each
   day on the spacecraft to correspond to 2 d on the earth?


8. The Apollo 11 spacecraft that landed on the moon in 1969
   traveled there at a speed relative to the earth of 1.08  104 m/s.
   To an observer on the earth, how much longer than his own day
   was a day on the spacecraft?


9. A certain particle has a lifetime of 1.00  10 ^7 s when meas-
   ured at rest. How far does it go before decaying if its speed is
   0.99cwhen it is created?

1.3 Doppler Effect

10. A spacecraft receding from the earth at 0.97ctransmits data at
    the rate of 1.00 104 pulses/s. At what rate are they received?


11. A galaxy in the constellation Ursa Major is receding from the
    earth at 15,000 km /s. If one of the characteristic wavelengths of
    the light the galaxy emits is 550 nm, what is the corresponding
    wavelength measured by astronomers on the earth?


12. The frequencies of the spectral lines in light from a distant
    galaxy are found to be two-thirds as great as those of the same
    lines in light from nearby stars. Find the recession speed of the
    distant galaxy.

1.1 Special Relativity

1. If the speed of light were smaller than it is, would relativistic
   phenomena be more or less conspicuous than they are now?


2. It is possible for the electron beam in a television picture tube
   to move across the screen at a speed faster than the speed of
   light. Why does this not contradict special relativity?

1.2 Time Dilation

3. An athlete has learned enough physics to know that if he meas-
   ures from the earth a time interval on a moving spacecraft,
   what he finds will be greater than what somebody on the
   spacecraft would measure. He therefore proposes to set a world
   record for the 100-m dash by having his time taken by an
   observer on a moving spacecraft. Is this a good idea?


4. An observer on a spacecraft moving at 0.700crelative to the
   earth finds that a car takes 40.0 min to make a trip. How long
   does the trip take to the driver of the car?


5. Two observers, Aon earth and Bin a spacecraft whose speed
   is 2.00  108 m/s, both set their watches to the same time
   when the ship is abreast of the earth. (a) How much time
   must elapse by A’s reckoning before the watches differ by
   1.00 s? (b) To A,B’s watch seems to run slow. To B, does A’s
   watch seem to run fast, run slow, or keep the same time as
   his own watch?

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