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Re: F=ma; new strain...



No, no, no! (see below)


On Fri, 14 Nov 2003, Nathaniel Davis wrote:

I asked about a year ago about the same time a question that still vexes me;
but for which I have no reasonable solution beyond some categorical response
I received that involved Einstein's theory of General Relativity, which I
could hardly provide for students as a rationale.

I would like to pose the question again...

Mass (the "amount" of something) is directly connected to the force of
gravitational attraction: Weight.

We also define mass according to the measure of inertia, i.e., more massive
objects "carry" more inertia.

I remember my college professors constantly alluding the fact that inertial
mass is always equal to gravitational mass. But why is this true? Wherein
lies the equivalency? The "inertial mass" should be completely independent
of a gravitational field, right?

Take two iron balls and a spring. Use the spring to measure the
mass of each ball in some units, by measuring the mass-spring
HORIZONTAL oscillation frequency on a smooth table. Now do a Cavendish
(or Eotvos) experiment to measure the gravitational force between the
balls in your favorite units. Calculate Newton's constant G from the
relationship: F= Gm_1m_2/r^{2}. Note that you have <defined> G so that
gravitational mass = inertial mass.
What Eotvos showed was that this definition of G does not depend
upon the material from which the balls were constructed, so
that the ratio gravitational mass/inertial mass is independent of the
material that constitutes the mass. G may therefore be chosen to make the
ratio unity. This is discussed in Weinberg's book on gravitation, I'll
give you the page if you don't find it in the index under "equivalence".




How can I explain this to my high-school students?


--
"Don't push the river, it flows by itself"
Frederick Perls