I am still having a problem understanding why the gamma factor would be applied to the mass at the introductory level. If students are at the F=ma level, then the "m" that gives the reistance to acceleration is really m0/(1-v^2/c^2)^(3/2), as I had noted in another posting. The gamma factor is actually not the factor that gives the increased resistance to acceleration - so why use it? If the studets are at the Impulse=momentum_change level, then the use of the gamma factor as part of the momentum seems quite natural when exploring the dynamics of Relativity.
Bob at PC
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From: phys-l-bounces@carnot.physics.buffalo.edu on behalf of Rick Tarara
Sent: Tue 2/26/2008 1:35 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Invariant mass and relativist mass...
Not sure I see how attaching gamma to the momentum is more 'satisfying' to
intro students than attaching it to the mass. We have two fundamental
concepts--mass and velocity which can be reasonably 'understood' from
everyday experience. When we combine them, we have a new concept--somewhat
more abstract in my mind, but I know others would set momentum as primary
here. That concept, momentum, can be pretty well 'understood' again from
experience--I stress that we have good instincts about momentum.
Now we go to the relativistic realm. Momentum doesn't increase linearly as
we would deduce from our Newtonian experiences, but we can directly measure
the velocities which are limited by the speed of light. I guess I have an
easier time (I try always to put myself in the mind-set of my students, and
maybe after 30 years of teaching ONLY intro physics, I myself am pretty much
stuck in that mind set ;-) with the idea that the mass is increasing in the
high speed realm rather than that the momentum was really a lot more
complicated in the low speed realm. But as someone else wrote--it
ultimately is a matter of taste, at least at the level we are discussing.