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When Time Flies.It Runs More Slowly Learning Goal: To understand length contraction and time dilation.

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When Time Flies...It Runs More Slowly
Learning Goal: To understand length contraction and time dilation.
In classical physics, and in your everyday experience, lengths and times
seem to be the same no matter who measures them. In fact, the notion
that lengths or time intervals might be different depending on who
measures them can seem profoundly disturbing (or just plain silly),
because measuring space and time are two of the most fundamental ideas
in physics. However, Einstein's special theory of relativity shows that
space and time are not as fundamental or as absolute as you are
accustomed to believing.
To discuss measurements more precisely, you must consider both the thing
being measured and the person (technically the frame of reference) doing
the measuring. An inertial frame of reference is a frame of reference
(i.e., a consistent way of measuring distances and times) that is not
accelerating. An inertial frame of reference moves at a constant speed,
relative to other inertial frames of reference.
between the two frames. The measured length and time are given by the
following two equations:
,
is the measured length in the direction of motion.
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Part A
?
in meters to three significant figures.
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Part B
passes on the clock?
Express your answer in seconds to three significiant figures.
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.
Part C
will the captain of ship B measure to have passed between the firing of
the two missiles?
Express your answer in seconds to three significant figures.
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Part D
of the missile, relative to ship B?
.
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). Your calculator may not be able to store enough digits to work these
problems accurately, so you may need to use the approximations from the
binomial expansion:
Part E
)? The answer is small but nonzero. You will need to find an expression
for the time difference using the approximation given in this problem
before you substitute in the numbers; otherwise your calculator will
just give zero.
.
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Part F
(a reasonable proper length for a car)? Use a similar procedure to the
one you used in the previous part.
.
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