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Relativistic Mass as described by Kenneth Krane in 'Modern Physics'

  1. Jan 5, 2012 #1
    1. The problem statement, all variables and given/known data
    Mr. Krane describes this scenario in a presentation of relativistic mass in his book
    Modern Physics
    John Wiley & Sons, Inc. 1983
    p. 36-37

    According to one observer, two balls of equal mass, m1 and m2, are approaching each other at equal speed, v. The proper mass of each is m0. They collide inelastically for a final speed of V = 0 and mass M = m1 + m2.

    2. Relevant equations

    m' = m0 / sqrt(1 - u^2/c^2)

    3. The attempt at a solution

    The conclusion is that the final the final mass of the two balls (stuck together) is:

    M = m1 + m2 = m0/sqrt(1-v^2/c^2) + m0/sqrt(1-(-v)^2/c^2) = 2m0 / sqrt(1-v^2/c^2)

    Instead, I argue that since two balls are now at rest in the reference frame of the observer, the mass of the two stuck balls is

    M = 2m0

    What am I missing here?
  2. jcsd
  3. Jan 5, 2012 #2

    Doc Al

    User Avatar

    Staff: Mentor

    What happened to the kinetic energy of the masses? (The so-called 'relativistic mass' includes the kinetic energy of the masses.) Since the collision was totally inelastic, presumably all the energy goes into the rest mass of the two stuck balls.
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