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*From*: Jack Uretsky <jlu@hep.anl.gov>*Date*: Sat, 9 Jan 2010 22:13:22 -0600 (CST)

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),

Regards,

Jack

"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 theBut the equivalence between the gravitational and inertial masses is

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.

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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**Follow-Ups**:**Re: [Phys-l] Separating inertial mass and g mass. Was: Re: adifferent kind of math background quiz***From:*Bernard Cleyet <bernardcleyet@redshift.com>

**References**:**[Phys-l] Separating inertial mass and g mass. Was: Re: a different kind of math background quiz***From:*Bernard Cleyet <bernardcleyet@redshift.com>

**Re: [Phys-l] Separating inertial mass and g mass. Was: Re: a different kind of math background quiz***From:*Moses Fayngold <moshfarlan@yahoo.com>

**Re: [Phys-l] Separating inertial mass and g mass. Was: Re: adifferent kind of math background quiz***From:*"John Clement" <clement@hal-pc.org>

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