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194. Problem 3.41 (R) An electron moves in the positive x-direction
in frame S at a speed v = 0.8 c. (a) We have
to find its momentum and its energy in frame S. (b) Consider a
frame
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moving
to the right of S with a speed 0.6 c. We have to find the momentum
and energy of the electron in the frame
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Solution: Click For PDF Version (a) We will solve this problem by considering that under Lorentz transformations
In the frame S electron is observed to be moving with speed u = 0.8 c in the x-direction. Its momentum will therefore be
Energy of the electron in the frame S will be
(b) Using the Lorentz transformations for energy and momentum, we will determine
their values in
And energy
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transforms like ct and p transforms like x. If in the frame
S the energy and momentum are E and p, then in the frame
and
will
be 
with
respect to S. We have
will be