From: "JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@HEP.ANL.GOV>
Date: Tue, 24 Aug 1999 11:56:31 -0500
Hi Bob-
In answer to:
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Hi Jack,
I am intrigued by your post cuz I follow everything but your conclusion.
I agree that if the acceleration goes as t to the power b, then it follows
that v goes as t to the power (b+1) and x goes as t to the power (b+2).
From this it follows that x(v) goes as v to the power (b+2)/(b+1) = 1 +
1/(b+1).
So what? Where's the conundrum? I don't get the point!
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I am addressing the difficulty of making real measurements with real
errors. We teach the student that the "expected value (I curse the expression)"
of b is zero. Now put it (the student) in a lab and let it demonstrate that
result. How accurately must you measure v in order to show that b is less
than, say, 0.1?
More broadly, change your experiments from measurements of g to
investigations of whether there exists a constant "g"? That is much harder to
do, given the uncertainties that arise in every experiment.
Stated another way, the constancy of the acceleration of a falling
body close to the earth is not a fact determined by any experiment, but
an idealization that harmonizes the results of many experiments. A subtle
point, but one that I think is worth teaching, because such idealizations
are part of the process of physics.
Regards,
Jack
"These several facts prove nothing, for one cannot deduce a principle from so
few examples, but they do at least indicate that the ability to learn to spell
correctly is a gift; that it is born in a person, and that it is a sign of
intellectual inferiority. By parity of reasoning, its absence is a sign of
great mental power."
Mark Twain, "Extract from Eve's Diary'.