An Intro to Special Relativity

1) A
high-speed train (a very high-speed train) is rolling toward you at half the
speed of light, 0.5c. What do you measure as the speed of the light emitted
from the train's headlights? How fast would you measure the light to be moving if
the train were rolling away from you at 0.5c?

2) A
question the young Einstein asked himself was “Could I see myself in a mirror
if I held it in my hands and ran at the speed of light?” How would you answer?

3) As you’re
floating peacefully in outer space, a spaceship zips past you at a tremendous
speed. If one second passes on your clocks, will you measure more or less than
one second on their clocks?

4) You see a
train pass you at close to the speed of light. From your reference frame, will
you or the people on the train measure proper time? In other words, which of
you is in the rest frame?

5) Consider
again the train from Problem 4. From the frame of the people on board the
train, which of you is in the rest frame?

6) Time is measured
to increase by a factor γ (“gamma”) when the clock is moving. What is the
value for γ if a friend in a spaceship flies past you at 0.750c? Give your
answer to three significant figures.

7) You are standing
by the side of the road when a car drives past at 0.500c. If you measure 1.00 s
to pass *inside the car* how much time
passes on *your* watch? Again, give
your answer to three significant figures.

8) A
spaceship flies past you one afternoon, and you measure its speed to be 0.650c.
If the folks in the ship measure 1.55 minutes to pass *on their ship* how many minutes would *they* measure to pass for you? (Three sig figs, please.)

9) How fast
would an object need to be moving for you to measure its value for γ to be
1.39?

10) Is it
THEORETICALLY possible for a space traveler to leave Earth at close to light
speed and return younger than when he left?