I made an argument that depended on the assertion
"Momentum is conserved".
That was wrong. I should rather have said "momentum is the
same before and after".
Let's be clear:
-- Constant means change = zero.
-- Conserved means change = flow across the boundary.
In context, conservation of momentum is neither necessary nor
sufficient to make the point I needed to make. In particular,
as others have pointed out, if m2 is initially non-stationary,
the argument falls apart. In this case momentum is conserved
(momentum is /always/ conserved) but the momentum of interest
would have been non-constant due to advection across the boundary.
There are lots of lame excuses I could offer, but let's not go
there. I just blew it, OK? And this is not a nitpick. The
distinction between conservation and constancy is important.
Bad things happen when people get sloppy about this. Sorry.