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Homework 13 solutions
Physics 204, morning summer 2008
Chapter 28
Problems 10,13,34,31
10.
REASONING
The distance between earth and the center of the galaxy is the proper length
L
0
, because
it is the distance measured by an observer who is at rest relative to the earth and the center of the galaxy.
A
person on board the spaceship is moving with respect to them and measures a contracted length
L
that is related
to the proper length by Equation 28.2 as
( )
22
0
1/
LL
vc
=−
.
The contracted distance is also equal to the
product of the spaceship’s speed
v
the time interval measured by a person on board the spaceship.
This time
interval is the proper time interval
Δ
t
0
because the person on board the spaceship measures the beginning and
ending events (the times when the trip starts and ends) at the same location relative to a coordinate system fixed
to the spaceship.
Thus, the contracted distance is also
L
=
v
Δ
t
0
.
By setting the two expressions for
L
equal to each other, we can find the how long the trip will take
according to a clock on board the spaceship.
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 Spring '09
 rollino
 Physics

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