homework 14 – KIM, JI – Due: Apr 27 2008, 4:00 am
1
Question 1, chap 36, sect 3.
part 1 of 3
10 points
A spaceship travels with a speed of 0
.
8
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 30 m.
0
.
8 c
Earth
Determine its length as measured by a per
son on Earth.
Correct answer: 18 m (tolerance
±
1 %).
Explanation:
Let :
L
0
= 30 m
and
v
= 0
.
8
c.
Applying length contraction,
L
=
L
0
γ
=
L
0
r
1
−
v
2
c
2
= (30 m)
R
1
−
(0
.
8
c
)
2
c
2
=
18 m
.
Question 2, chap 36, sect 3.
part 2 of 3
10 points
The pilot of the spaceship observes that the
spaceship travels for 8 years.
Determine how much time has passed ac
cording to a person on Earth.
Correct answer: 13
.
3333 years (tolerance
±
1
%).
Explanation:
Δ
T
=
Δ
T
0
γ
= 8 years
×
1
.
66667 =
13
.
3333 years
.
Question 3, chap 36, sect 3.
part 3 of 3
10 points
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 (tolerance
±
1
%).
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
.
Question 4, chap 36, sect 3.
part 1 of 2
10 points
Two Frecrackers explode at the same place
in a rest frame with a time separation of 14 s
in that frame.
±ind the time between explosions, as mea
sured in a frame moving with a speed 0
.
6 c
with respect to the rest frame according to
classical physics without the special theory of
relativity.
Correct answer: 14 s (tolerance
±
1 %).
Explanation:
According to classical physics:
t
=
t
0
= 14 s
.
Question 5, chap 36, sect 3.
part 2 of 2
10 points
±ind the time between explosions, as mea
sured in a frame moving with a speed 0
.
6 c
with respect to the rest frame according to
the special theory of relativity.
Correct answer: 17
.
5 s (tolerance
±
1 %).
Explanation:
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View Full Documenthomework 14 – KIM, JI – Due: Apr 27 2008, 4:00 am
2
According to the special theory of relativ
ity:
t
=
t
0
r
1
−
(
v
c
)
2
=
(14 s )
r
1
−
(
0
.
6 c
c
)
2
= 17
.
5 s
.
Question 6, chap 36, sect 4.
part 1 of 1
10 points
Rods
P
and
Q
are at rest in an inertial
reference frame and oriented as shown. Both
rods have length
L
in this reference frame.
A person moves at a relativistic speed in the
positive
x
direction.
x
y
Q
L
P
L
O
Which of the following would be the
lengths, as compared to
L
, observed for these
rods by the person?
P
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 Spring '08
 Turner
 Physics, Work, Special Relativity, Correct Answer

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