In some of my early readings of John D's messages, I think I was misreading
him, and it may be others are still doing a thing similar to what I was
doing.
I was thinking we had to have the spring scale provide the same reading for
a particular force as we would measure if we also used F=ma, or F=Gmm/r^2,
or some other method for measuring that force.
But then I realized that was not what John was trying to say. If the spring
scale would be the primary standard, and when it is stretched to its mark
that would be the definition of one newton, then this would always be
correct... if we can idealize the spring and pointer and hook to have
insignificant mass.
We could make it so that when we are in a nearly inertial reference frame at
a location on earth where g = 9.81 that the scale reads 1 newton when a
0.10194 kg mass is hung on it. But if we do that, and then take the scale
to the moon and find that the 0.10194 kg mass doesn't bring the pointer
anywhere close to the 1 newton mark, the scale is not wrong. In fact, it is
correct, we don't have a one newton force on it. We're not supposed to be
trying to measure mass with the scale. We're trying to measure force. The
scale will do that properly whether it is in earth's g, or moon's g, or zero
g, or accelerating, or moving with constant velocity, or whatever... as long
as the spring's mass and pointer's mass are small enough to be of no
concern.
If the spring's mass, pointer's mass, hook's mass are indeed significant,
then it seems to me we would have a problem in various g fields or various
non-inertial frames because some of the spring deflection would be caused by
the scale's internal components as opposed to the externally applied force.
Maybe everyone has already agreed to this, and you are all discussing
something different. But this was a problem for me. Once I idealized a
massless frictionless mechanism then I think I started agreeing with John.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817