segovia (cs39966) – Homework 9 – Spurlock – (14441)
1
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printout
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20
questions.
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001(part1of3)10.0points
A spaceship travels with a speed of 0
.
1
c
as
it passes by the Earth on its way to a distant
star, as shown in the diagram below.
The
pilot of the spaceship measures the length of
the moving ship as 40 m.
0
.
1 c
Earth
Determine its length as measured by a per
son on Earth.
Correct answer: 39
.
7995 m.
Explanation:
Let :
L
0
= 40 m
and
v
= 0
.
1
c .
Applying length contraction,
L
=
L
0
γ
=
L
0
radicalBigg
1

v
2
c
2
= (40 m)
radicalbigg
1

(0
.
1
c
)
2
c
2
=
39
.
7995 m
.
002(part2of3)10.0points
The pilot of the spaceship observes that the
spaceship travels for 2 years.
Determine how much time has passed ac
cording to a person on Earth.
Correct answer: 2
.
01008 years.
Explanation:
Δ
T
=
Δ
T
0
γ
=
2 years
0
.
994987
=
2
.
01008 years
.
003(part3of3)10.0points
Some time after passing the Earth, the pilot
shoots a laser pulse backward at a speed of
3
×
10
8
m
/
s with respect to the spaceship.
Determine the speed of the laser pulse as
measured by a person on Earth.
Correct answer: 3
×
10
8
m
/
s.
Explanation:
A laser pulse travels at the speed of light, in
dependent of the frame in which it is measured
( the key point of special relativity). Thus the
Earth observer sees the pulse traveling at the
same speed as the pilot,
3
×
10
8
m
/
s
.
004
10.0points
A spaceship is measured to be 183 m long
while at rest relative to the observer.
If this spaceship now flies by the observer
with a speed 0
.
967 times the speed of light,
what length does the observer measure?
Correct answer: 46
.
6241 m.
Explanation:
Let :
L
p
= 183 m
and
v
= 0
.
967
c .
If
L
p
is the proper length of the moving
object, the length of the spacecraft measured
by the observer is
L
=
L
p
radicalbigg
1

v
2
c
2
= (183 m)
radicalBig
1

(0
.
967)
2
=
46
.
6241 m
.
005
10.0points
A passenger on an interplanetary express bus
traveling at
v
= 0
.
95
c
takes a 3 minute cat
nap by his watch.
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segovia (cs39966) – Homework 9 – Spurlock – (14441)
2
How long does the nap last from your van
tage point on a fixed planet?
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 Fall '11
 HOFFMAN
 Work, Special Relativity, Correct Answer, Spurlock, Segovia

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