(Edmiston) Furthermore, you can measure and/or feel the individual
forces that add
to zero using spring scales or load cells with strain gauges. You do
not measure any individual accelerations that add to zero. Each of the
three forces adding to zero can be made manifest. Three accelerations
adding to zero cannot each be made manifest. (Edmiston)
Al Bachman said:
(Bachman) Spring scales, load cells and strain gauges are single axis
devices,
therefore they will only measure a component of the force acting
on the particle. (Bachman)
Edmiston replies:
For each individual sensor, Bachman's statement is true, but I don't see
this has any bearing on my original statement. If the net force is zero
such that the acceleration is zero, and if the lab-frame velocity is
zero, it can be a piece of cake to measure the forces adding to zero.
The type of demonstration I had in mind is the typical force-table
experiment in which three forces are experimentally balanced. If three
forces are obtained from weights with strings going over pulleys, the
force magnitudes can be calculated from Newton's law of gravity, and the
force directions are observed from the string positions. If you want a
more direct measure of the force magnitudes without invoking the law of
gravity, that's when you can insert force transducers into the picture.
Anyway, in the zero acceleration, zero velocity case it is easy to
measure the individual forces that add as vectors to make zero net
force, but it is not possible to measure three non-zero accelerations
that add as vectors to provide zero net acceleration.
A further coment...
I am an experimentalist, not a theorist. Perhaps experimentalists view
equations differently than theorists. When I view F = ma I don't see
the two sides as experimentally equal. From an experimental viewpoint,
we often see that which side of an equation is more easily measured
depends on the circumstances. On the force table with zero acceleration
we might say the right side of F= ma is easiest to measure. We directly
observe a = 0, how could it get easier?. It takes more effort to
measure the three individual forces..
On the other hand, if we view the inner most portion of F(net) = (F1 +
F2 + F3) = m(a1 + a2 + a3) = ma(net) we run into an experimental
problem. Each individual force can be measured in many circumstances,
especially the zero acceleration zero velocity case. But I cannot
imagine any way to measure the individual accelerations that (multiplied
by m) equate to the individual forces, because the object has only one
manifest acceleration to measure.
Perhaps theoretically it is not appropriate to think of F = ma as
anything other than an equality. But I think there is a world of
difference when equations are viewed experimentally. One of the things
that I have been trying to say, and I think John Clement has been trying
to say the same, is that a big goal of science education these days is
to connect the equations and text to real-world observation an
experiment. In my mind this is what science has always been about, but
budget and time constraints have eroded hands-on laboratory and other
"discovery" methods of teaching. When we connect equations and
experiments, students are typically going to make some cause-effect
assumptions that might not be rigorously true, or even some cause-effect
assumptions for which the physicists are still debating. I think we
must be careful not to throw this theoretical debate at them too soon.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu