MASSACHUSETTS INSTITUTE OF TECHNOLOGY
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Physics 8*02T
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2 March 1966
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ASSIGNMENT NO. 4
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Reading:
Problems:
IV-1
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Text, Chapter 4 (finish); Chapter 5, pages 1-18.
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A 10 meter pole is carried
so fast by a super-athlete
that it would measure only
9 m long to a stationary
observer. The athlete holds
the pole horizontal and runs
toward the door of a barn.
The barn is 9.5 m wide and
has a door on its other side
^_ 9 v5m _j
just opposite to the first
one* Is it possible to close the first door behind the
athlete before the second door has to be opened to let him
out the other side? (And how fast, incidentally, is he
running?) Describe the sequence of events in the rest-•
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• - of
. . the barn and
. . in the
> ^ rest-frame
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• of , the runner.
IV-2 We observe that a flash of light is emitted at position x.
on the x-axis and is absorbed at position x^ ** *i + ^ •
To observers moving with velocity v « PC alSng tne x-axis:
(a) What would have been the spatial separation JL* between
the point of emission and the point of absorption of
the light? (The answer is not ^ f * //V •)
(b) How much time would have elapsed between emission and
absorption of the light?
Ans: (1 - 0)
IV- 3
An atomic clock is mounted in an earth satellite that is
circling the earth at a height of 300 Xm above the earth's
surface. How many years would it have to remain in orbit
before being 1 second -^ low, relative to a similar clock
on earth, as a result of time dilation? (Strictly speaking,
general relativity should also be taken into account, but
for the orbit assumed here its effects would be fairly
small.)
Ans: about ibo years
IV-4 A beam of unstable particles (K* mesons) traveling at a
speed of c >/3/2, passes through two counters 9m apart. Hie
particles suffer a negligible loss of speed and energy in
passing through the counters, bvit give electrical pulses
that can be counted. It is observed that 1000 counts are
recorded in the first counter, and 250 in the second.
Assuming that this whole decrease is due to decay of the
particles in flight, what is their half -1 ife as measured in
their own rest-frame?
Ans: about 0.9 x 10"b sec
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(Continued on reverse side of paper.)
IV-5
At hoon a rocket ship passes the Earth at a speed 4c/5.
Observers on the ship and on Earth agree that it is noon.
(a) At 12:30 p.m. as read by a rocket-ship clock, the
ship passes an interplanetary navigational station
that is fixed relative to the Earth and whose clocks
read Earth time. What time is it at the station?
Ans: 12:50 p.m.
(b) At 12:30 (rocket time) the rocket ship reports by
radio back to Earth. When, by Earth time, does the
Earth receive the signal?
Ans: 1:30 p.m.
IV-6
A K meson at rest decays into two IT mesons each having a
speed of about 0.85 c." If a K+ ibeson is traveling at a
speed of 0.9 c through the laboratory when it decays, what
is the greatest and what is the lea art speed that one of
the TT mesons could have?
Ans: 0.991 c; 0.21 c
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IV-7
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Some observations reported on a recently discovered astro­
nomical object (Quasar 3C-9) suggest that, when it emitted
the li^it that has just readied the^earth, it was moving
away from the earth at a speed of about 0.8 cJ
(a) One of the lines identified in its spectrum (the Lymanalpha line of hydrogen) has a wavelength of about
1200 A when emitted from a stationary source. At what
wavelength must this line have appeared on the observed
spectrum of the quasar?
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Ans: ' 3600
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(b) Quasars emit energy at such a huge rate that astronomers
believe they must burn out in a relatively short time.
? If the lifetime of 3C-9 were assumed to be 106 years
as measured in its own rest-frame* over what total
span of earth-time would radiation from it be received
at the earth? (Assume that its velocity relative to
the earth remains constant.)
Ans: 3 x 10° years
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IV-8
(Optional) Verify the statement about clock readings at
the foot of p£^e 4-18 of the text.
IV-9
(Optional) two rockets afe A connected by an inextensible
string of proper length L . At time t « 0 the ro<3cets
start out from rest with exactly equal constant accelerations
as measured in S. At time t - t^ the acceleration ceases
and the rockets coast with equal constant velocities as
string
S. Why
in
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^^ -_ • break?
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_•. * the
w - *^_ difil
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1V-10 (Optional) A rocket starts at rest in a system -^ and thereafter maintains a constant acceleration 9*ftn/secr as mea­
sured in the rocket's instantaneous rest frame. After 1
year has elapsed in the fr£tae in which it was originally
f at rest> how far has it gone in~. that* frame?
(c)
The station on Earth replies immediately.
rocket time) is ithe reply received?
Ans: 4:30 p.m.
When (by