Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Inertial vs gravitational mass



Hi Nathaniel-
In part, it's trivial. In part, it's mysterious. Here's a
summary of the easy part:
Use a standard spring to measure the masses of a couple of lead spheres
by measuring the periods of oscillation. Call these masses m1 and m2.
These are clearly inertial masses.

Now do the Cavendish experiment to determine the value of G from Newton's
law: F=Gm1m2/r^{2} (LaTeX notation). Your value (and units) for G were
determined in terms of the inertial masses, so you have defined G to make
inertial mass equal to gravitational mass - but only for lead spheres. So
the first answer is that we have defined the two kinds of mass to be equal
by making the "right" choice for the value of G.

Now comes a somewhat more difficult proposition. Eotvos asked whether the
value of G that we got from lead spheres would be the same if we
substituted other kinds and shapes of material (his work is still going on
at the University of Washington and elsewhere). So far as anyone can
tell, the answer is a resounding "Yes."

This is about as much of the subject that I can discuss without getting
into relativity.


Regards,
Jack

On Tue, 21 Jan 2003, Nathaniel Davis wrote:

My students and I (Honors College Prep.) were having a discussion of mass...
and the qualities of inertial mass vs. gravitational mass. And then came
the question I feared, because I could not rationalize an answer, even
having spent some time looking back at my college Mechanics textbook.

Why is inertial mass always equal to gravitational mass?

My students were keen on the fact that mass and weight were not synonymous,
but nevertheless related. Weight is how hard earth pulls on an object,
which can be readily measured using a spring scale. Graphing weights of
objects vs. their mass will readily yield (small) g as the slope.

However, one can also use an inertial balance (measuring period as a
function of mass) to find the mass of an unknown, given the mass of a known
and its period.

Students understand a relationship HAS to exist; and yet, what is the
rationale?

I would be most appreciative for a response. Please forgive my ignorance if
this query sounds trivial.

-nate.

--
Nathaniel Wayne Davis
Physics Teacher
Mountain View High School
haphaestus@earthlink.net


--
"What did Barrow's lectures contain? Bourbaki writes with some
scorn that in his book in a hundred pages of the text there are about 180
drawings. (Concerning Bourbaki's books it can be said that in a thousand
pages there is not one drawing, and it is not at all clear which is
worse.)"
V. I. Arnol'd in
Huygens & Barrow, Newton & Hooke