Imagine that your spaceship is lying on a truck
bed, waiting to be hoisted into position on the launch pad. You
and some friends measure its length while it’s lying motionless
(which is called its rest length, L_{0}),
and you find that it’s 10 meters long.
But then you fly off to the party at 86.6 percent of the speed
of light, or 0.866c. Your friends, who’ve been following
your progress with telescopes, decide to try to measure your ship
while it’s in flight. They find that its length, L, is
shorter than its rest length. It turns out that it’s shorter
by a factor you can calculate if you know the speed v of
the ship. This factor is known as gamma ():
If you do the calculation, you’ll find that when v =
0.866c, = 2 .
Once you know the value of gamma, you can solve the equation for
length contraction, L = L_{0}/.
L =
10 m/2
L =
5 m
To your friends on Earth, then, your ship appears to be half its
rest length, or 5 meters long.
Try This!
Enter two values into the calculator—a fraction of the
speed of light (from 0 to 0.999 999 999) and the rest length of
an object of your choice. You’ll find out what fraction of
its rest length the object would be at that speed.
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