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

[arguellodw]

Homework Statement

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.

Homework Equations

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

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?

 

[Doc Al]

What am I missing here?

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.