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So during my particle physics years, I decided that the teaching of the
“relativist mass” concept was (at best) confusing and unhelpful.
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).