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Recitation ClassWork 11 solutions
Physics 204 evening summer 2008
1.
CONCEPT QUESTIONS
a.
The Martian measures the proper time interval
Δ
t
0
, because the Martian 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.
b.
The given distance between Mars and Venus is the distance as measured by a person on earth.
That person
is at rest relative to the two planets and, hence, measures the proper length.
The Martian, who is moving
relative to the planets, does not measure the proper length, but measures a contracted length.
c.
According to the Martian, the time of the trip
Δ
t
0
is equal to the contracted length that he measures divided
by the speed
v
of the spaceship.
SOLUTION
a.
The contracted length
L
measured by the Martian is related to the proper length
L
0
by Equation 28.2 as
()
2
2
11
10
0
22
0.80
1
1.20 10
m
1
7.2 10
m
c
v
LL
cc
=−
=
×
−
=
×
b.
The time of the trip as measured by the Martian is
11
2
0
8
0.72 10 m
3.0 10 s
0.80 3.00 10 m/s
L
t
v
×
Δ= =
= ×
×
2.
CONCEPT QUESTIONS
a.
The passengers would measure a length for the spaceships that does not match the constructed length if
the two ships have a nonzero relative speed.
This would mean that the ships are moving with respect to one
another.
If so, the phenomenon of length contraction would occur.
b.
If the passengers in either ship are moving with respect to the other ship, they would measure a
contracted length.
c.
To calculate the contracted length
L
, the length contraction formula must be used, as given in
Equation 28.2:
2
AB
0
2
1
v
c
(28.2)
where
L
0
is the proper length of the spaceships, that is, the length measured by an observer at rest with
respect to them.
In other words, the proper length is the constructed length.
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 Spring '09
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 Physics

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