Re: Scientific method was physical pendulums/ an opportunity
From: "JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@HEP.ANL.GOV>
Date: Fri, 24 Sep 1999 06:55:07 -0500
Hi all-
Leigh writes:
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Another way to look at this "independence of g" phenomenon in
mechanics problems that David Bowman and I see is to recognize
that the trajectories are unique, and the time evolution of
the motions is just different. Low-g means slower motion,
that's all.
The ironic thing about the problem I quoted is that the person
who made it up felt it necessary to specify the value of g. If
the student is guided by that he will solve the problem somewhat
inelegantly, but I can't make my students (who must already have
done such problems in high school) see that there is merit and
beauty in the elegant solution. It gives insight which the high
school student won't see.
The sliding-off-the-hemisphere problem is very closely related
to the meter stick falling from rest after standing against a
wall problem. I beieve the answers to both problems are
the same, something like arccos 2/3.
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Yeh! Even more blatant, I think, is that gravity problems are independent
of mass. But getting the students to do algebra, and watch the mass cancel out
(or leaving only mass ratios) is an impossibility. It makes me wonder about the
big push, currently, to introduce algebra in the lower grades. Yes, you can teach
them to mouth the words (or write down symbols), but doesn't it take maturity to
understand the meaning (or use the symbols to solve problems)?
Regards,
Jack
"I scored the next great triumph for science myself,
to wit, how the milk gets into the cow. Both of us
had marveled over that mystery a long time. We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
Mark Twain, Extract from Eve's
Autobiography