|Chronology||Current Month||Current Thread||Current Date|
|[Year List] [Month List (current year)]||[Date Index] [Thread Index]||[Thread Prev] [Thread Next]||[Date Prev] [Date Next]|
A spaceship has a length of 200m in its own reference
frame. It is traveling at 0.95c relative to Earth.
Suppose that the tail of the spaceship emits a flash
of light. (a)In the reference frame of the spaceship,
how long does the light take to reach the nose?
(b)In the reference frame of the Earth, how long does
this take? Calculate the time directly from the motions of
the spaceship and the flash of light, and explain
why you cannot obtain the answer by applying the
time-dilation factor to the result from Part (a).
(from Ohanian's Principles of Physics)
The answers listed in the book are (a)6.67E-7s and (b)2.13E-6s I have no
difficulty with (a) as being simple v=d/t using c and the
non-length-contracted 200m since the observers are at rest relative to
the ship. It is part (b) that I am having trouble with. As I understand
it, observers that see the ship fly by will see its length contracted.
(It is actually contracted to 62.4m) So, since the speed of light is the
same in all reference frames, I figured this observer would see the light
travel 62.4m at a speed of c. Using v=d/t this gave me 2.08E-7s.
WRONG! I though about it, and I figured that this was wrong because not
only does the light pulse have to travel the length of the ship, but also
the distance that the ship travels while it is headed towards the nose.
Setting this up (which I think I set it up right) and solving still gave
me a wrong answer (4.16E-6).