Re: [Phys-l] Invariant mass and relativist mass...

[Tom Sandin <sandint@ncat.edu>]

Look at my
Subject: [Phys-l] Non-existence of Transverse and Longitudinal Relativistic
 Mass
post.

If the students are at the |F| = m|a| level, they need to be told 
that version of Newton's second law is true only for constant mass.

When the force and velocity are perpendicular, the speed and 
therefore the relativistic mass are constant--and F/a equals the 
relativistic mass.

When the force and velocity are parallel, the speed and therefore the 
relativistic mass are not constant and F is not equal to ma.

(F, p, v, and a are vectors in this paragraph.) For a particle in an 
inertial reference frame, the net force equals the time rate of 
change of its linear momentum, F = dp/dt = d(mv)/dt. Only if m is 
constant does this give F = m dv/dt = ma. If m is not constant, you 
have a second (dm/dt)v term.

John Denker's reply is from the perspective of an relativistic mass opponent.

Tom Sandin

At 7:06 PM -0500 2/26/08, LaMontagne, Bob wrote:
> 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