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Re: [Phys-l] Separating inertial mass and g mass. Was: Re: adifferent kind of math background quiz

Hi all-
Gravitational mass and inertial mass are the same because Newton's gravitational constant is chosen to make them the same. Eotvos guarantees that the gravitational mass does not depend upon the material of which the mass is composeed.
Submerging a pendulum bob in a liquid does not alter the mass of the bob, be it gravitational or inertial. It does, of course, impose additional forces on the bob as the bob moves. (Unless the liquid has gravitational properties unknown to ordinary matter),

"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley

On Sat, 9 Jan 2010, John Clement wrote:

  Gravitational mass and inertial mass are the same only in the
gravitational field alone. All forces other than gravity tend to mask this
equivalence. One of the reasons of discrepancy with horological
corrections for a physical pendulum might be the dependence of the forces
involved on shape of moving object (a drag force on the swinging bob
depends on its velocity AND on its size, and even on degree of smoothness
of its surface if we go for high accuracy). An open parachute is a good
illustration. For a class demo I used sometimes a box with chalk and a
sheet of paper dropped together, and in the second trial did the same with
the same sheet thoroughly crumpled so that now both items hit the floor
simultaneously. By changing the shape of the sheet we could uncover the
equivalence of the inertial and gravitational mass. My personal feeling is
that the students were impressed by this simple demo.
But the equivalence between the gravitational and inertial masses is
actually very subtle, and it is doubtful that the simple demo impressed this
on the students. If they focus on anything, they will just say of course,
when you lower the air resistance the two fall at the same rate. I suspect
if you have them predict the results, they will predict the correct results.
Actually without a prediction, they will not remember the demo, and if it is
an obvious result, then it will not have much effect on their thinking.

Part of the problem with establishing this is that students always see
g=9.8m/s^2 used to calculate the gravitational force. So immediately the
distinction between the gravitational and inertial forces has been assumed.
But if g=9.8 N/kg where F_g = mg, then the inertial and gravitational forces
are not assumed to be the same. There is also the difficulty with this
equation that students find it difficult to understand because how can you
use an acceleration find the force on something that is not accelerating.

To bring up the issue of gravitation vs inertial mass one must establish
that they are initially different things and have students understand this
comes from 2 different equations. Since even students in an intro calculus
based course often do not really understand variables or equations, this is
a tall order. They sometimes know how to plug numbers into equations, but
understanding that equations are descriptions of relationships, and can have
meaning is something that the math teachers have been remiss in getting them
to comprehend.

I take it that horologists use an "effective inertial mass" rather than the
physics definition of inertial mass, to bundle the effect of the surrounding
fluid into the mass. Or do they use and "effective gravitational mass"?

John M. Clement
Houston, TX

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