The problem with using "relativistic mass" is a matter of which "relativistic mass" you are going to use: longitudinal, or transverse. The usual formula with the square root in the denominator is really for forces perpendicular to the motion. To correct a pendulum, and use the concept of force and mass, requires a 3/2 power in the denominator - better to stick with non-scalar momentum, total relativistic energy, and rest mass.
Bob at PC
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From: phys-l-bounces@carnot.physics.buffalo.edu on behalf of Jacques Rutschmann
Sent: Sun 2/24/2008 4:15 PM
To: phys-l@carnot.physics.buffalo.edu
Subject: [Phys-l] Invariant mass and relativist mass...
But now, many years later, I am not sure about this. Let's say I wanted
to compute the gravitational pull of a car (coasting by my lab) on a
very sensitive pendulum (the pendulum does not swing: I apply a small
force on it to keep it steady). The rest mass of the car is know.
I am tempted to use the car "relativistic mass" in my computation (This
is very natural: I believe that most non GR versed people would do the
same).
Is this a good idea? Is this a bad idea? Is it referential dependent?