Re: Mass

[Bernard Cleyet <anngeorg@PACBELL.NET>]

"Yeh, I agree, but you could place the balance in a evacuated chamber to
get rid of buoyancy effects.  You can't do much to get rid of the
gravitational effects.  Displacing the center of mass by delta r causes
a change in gravitational force equal to:
  d(GMm/r^2)/dr (delta r) = GMm (-2/r^3) (delta r)
                          = GMm/r^2 (-2/r) (delta r)
or a fractional change of 2*(delta r)/r.  For 1 cm difference in center
of mass, this causes a relative difference in measured mass of
2e-2/6.37e6 ~ 3e-9. So, for a 1-kg standard, the difference is 3
micrograms.  I know this seems tiny and for almost all practical
purposes irrelevant but I thought it was pertinent to the discussion
about measuring inertial vs. gravitational mass.  I also think balances
are available that can measure with a precision exceeding 1e-9.  If you
happen to be using one, it helps to know if you're measuring inertial
mass or not."


Please check my reading:  Is the problem due to differences in the
distance from the earth of the CofM between the std. and the measured?
If so, I'd think one can easily (compared to the other problems) reduce
this to < one mm.

This I think would bring this problem to about the sensitivity of
commonly available microbalances.

http://www.cielec.com/microbalance.html

note at this sensitivity they are (some) vacuum balances.

I didn't read completely, but I think position of CofM is ignored as the
use is for changes, not absolute mass.

bc


Robert Cohen wrote:

> I asked:
>
>
> > > I'm
> > > asking how I would know that the mass of sample is 1 kg.  It just
> > > appears to me that we don't count the number of atoms but
> > rather the

cut