An alternative derivation of the mass-energy formula E, = mɑc² also given by
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Transcribed Image Text:Initial center of mass
M/2
-M/2
-Burst of radiation is emitted
L.
New center of mass
s K-
Radiation is
-absorbed and
box stops
Transcribed Image Text:2. An alternative derivation of the mass-energy formula E, = moc² also given by
Einstein, is based on the principle that the location of the center of mass (CM) of
an isolated system cannot be changed by any process that occurs inside the
system. The Figure below shows a rigid box of length L that rests on a frictionless
surface; the mass M of the box is equally divided between its two ends. A burst of
electromagnetic radiation of energy E, is emitted by one end of the box. According
to classical physics, the radiation has the momentum p = "0%c , and when it is
emitted, the box recoils with the speed v z
Eo/
so that the total momentum of
Mc
the system remains zero. After a time t z L/c the radiation reaches the other end
of the box and is absorbed there, which brings the box to a stop after having moved
the distance S. If the CM of the box is to remain in its original place, the radiation
must have transferred mass from one end to the other. Show that this amount of
mass is m, =
c2.
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