239
Chapter 39
Relativity
Conceptual Problems
1
•
[SSM]
The approximate total energy of a particle of mass
m
moving
at speed
u
<<
c
is (
a
)
mc
2
+
1
2
mu
2
, (
b
)
1
2
2
, (
c
)
cmu
, (
d
)
mc
2
, (
e
)
1
2
cmu
.
Determine the Concept
The total relativistic energy
E
of a particle is defined to
be the sum of its kinetic and rest energies.
The sum of the kinetic and rest
energies of a particle is given by:
2
2
2
1
2
mc
mu
mc
K
E
+
=
+
=
and
)
(
a
is correct.
2
•
A set of twins work in an office building. One twin works on the top
floor and the other twin works in the basement. Considering general relativity,
which twin will age more quickly? (
a
) They will age at the same rate. (
b
) The
twin who works on the top floor will age more quickly. (
c
) The twin who works
in the basement will age more quickly. (
d
) It depends on the speed of the office
building. (
e
) None of the above.
Determine the Concept
The gravitational field of Earth is slightly greater in the
basement of the office building than it is at the top floor. Because clocks run more
slowly in regions of low gravitational potential, clocks in the basement will run
more slowly than clocks on the top floor. Hence, the twin who works on the top
floor will age more quickly.
)
(
b
is correct.
3
•
True or false:
(
a
)
The speed of light is the same in all reference frames.
(
b
)
The time interval between two events is never shorter than the proper time
interval between the two events.
(
c
)
Absolute motion can be determined by means of length contraction.
(
d
)
The lightyear is a unit of distance.
(
e
)
Simultaneous events must occur at the same place.
(
f
)
If two events are not simultaneous in one frame, they cannot be
simultaneous in any other frame.
(
g
)
The mass of a system that consists of two particles that are tightly bound
together by attractive forces is less than the sum of the masses of the
individual particles when separated.
(
a
) True
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(
b
) True
(
c
) False. The shortening of the length of an object in the direction in which it is
moving is independent of the velocity of the frame of reference from which it is
observed.
(
d
) True
(
e
) False. Consider two explosions equidistant, but in opposite directions, from an
observer in the observer’s frame of reference.
(
f
) False. Whether events appear to be simultaneous depends on the motion of the
observer.
(
g
) True
4
•
An observer sees a system moving past her that consists of a mass
oscillating on the end of a spring and measures the period
T
of the oscillations. A
second observer, who is moving with the mass–spring system, also measures its
period. The second observer will find a period that is (
a
) equal to
T
, (
b
) less than
T
, (
c
) greater than
T
, (
d
) either (
a
) or (
b
) depending on whether the system was
approaching or receding from the first observer, (
e
) Not enough information is
given to answer the question.
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 Spring '12
 Goussiou
 Physics, Energy, Mass

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