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: [Phys-l] g...



On 11/19/2006 08:58 AM, Herb Gottlieb wrote:

According the American Institute of Physics Handbook, Page 2-93,
the acceleration of gravity is given as 9.78 at sea level at the earth's
equator.

OK, but that's not the whole story.

... New York City
(Where the acceleration of gravity is not 9.81 N/kg)

Actually in NYC the acceleration of gravity is 9.8023(5) m/s^2.

Hint: There is a nifty formula to be found at
http://www.npl.co.uk/mass/faqs/gravity.html

You can check selected sites against the table near the end of
http://www.andweighing.com/and.nsf/html/WEBB6853UH/$FILE/HC-i_IM.pdf


Therefore 9.81, while nothing to be proud of, is a better approximation
than 9.78.

For the vast majority of locations in NY State, 9.80 would be a better
approximation than 9.81. The latter value is marginally better in the
far north corner, e.g. Ogdensburg and Plattsburgh and points north.

Similarly, in the vast majority of locations in the continental US,
9.80 is a better approximation than 9.81.

I assume that the 9.81 figure comes not from local observation nor from
decent physics-based theory, but from mindlessly rounding off the "standard"
value, namely 9.80665±0.
http://physics.nist.gov/cgi-bin/cuu/Value?gn

If you wrote that g has a value of 9.8 N/kg at the Earth's surface,
I would agree. But is it correct to add the additional significant
figure and make it 9.81 here??

1) Significant figures are an abomination. People who care about
their data do not use significant figures.
http://www.av8n.com/physics/uncertainty.htm

2) Nobody knows what uncertainty attaches to a number like 9.81.
It could mean
a) 9.81 ± 0
b) 9.81 ± .01
c) 9.81 ± .05
*) or ..... ????

In cases (b) and (c), the uncertainty is such that the precise
value 9.8023(5) is consistent with the stated value 9.81(?).

Similarly 9.78 could mean
a) 9.78 ± 0
b) 9.78 ± .01
c) 9.78 ± .05
*) or ..... ????

In case (c), the uncertainty is such that the precise value is
consistent with the stated value.


What, if anything, will happen if you do not conform , and use a correct
value for the acceleration of gravity in your course and while grading
the students' regents examination in June?

Using 9.8 instead of 9.81 is within the error bars under the most-common
guesses as to what 9.81 might mean ... especially if there are other
contributions to the bottom-line uncertainty ... so if the test has any
consistency at all, nothing "should" happen.

But I cannot guarantee what "should" happen will happen. Many years ago
the Regents' was definitely a first-class operation, but lately I'm not
so sure. There is some chance that they would test for rote regurgitation
of the 9.81 number. Sigh.

FWIW once I took a federally-standardized test in which we were obliged
to use pi=3. Using pi=3.14 produced answers that would be marked wrong.
(Fortunately I figured this out /before/ taking the test.)



On 11/24/2006 03:13 PM, Jeffrey Schnick wrote:
Suppose you are given a value and you have reason to believe that the
provider of the value used significant figures conventions in deciding
how many significant figures to write in the value.

Again: Significant figures are an abomination. People who care about
their data do not use significant figures.
http://www.av8n.com/physics/uncertainty.htm