Dave Van Domelen (2007) in his PhysLrnR post of 21 Sep 2007 titled
"The Swinging Bucket Problem" wrote [bracketed by lines "DDDDD. . .
."; my insert at ". . . .[insert]. . . .":
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
I'm curious as to whether anyone knows of research that's been done
on. . . . ["The Swinging Bucket Problem"]. . . . (I'll go journal
hunting if no one knows, but it's the sort of thing that I suspect
might be hard to find by name).
When introducing centripetal force, one of the classic examples is
the "how fast do I have to spin a bucket in a vertical circle to
avoid water spilling out?" problem. It's got plenty of subtleties to
help divide those who really understand the situation from the plug
and chuggers (for instance, anyone who draws tension in as a force on
the water is probably not thinking too carefully about the situation).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pretty consistently, almost everyone in my sections gets things
correct from the "mg = mv^2/r" point onward. . . . . . . . . . . . .
However, almost no one even comes close to setting it up correctly.
Centripetal force is usually included as one of the component forces
(often pointing outward!) and the acceleration is taken to be zero.
Other combinations of incorrect or misdirected forces show up, such
as tensions, or outward-directed normal forces. But no matter how
off-track they start, they always get to "mg = mv^2/r" from it. Only
a handful had explanations that came close to sketching out why
centripetal force is equal to weight, and explicit mention of how the
Normal force is zero at the minimum speed almostnever comes up.
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Although the above student difficulties are well known to most
physics teachers, I know of no research that's been published that's
specifically on the "Swinging Bucket Problem."
However, if one wished to undertake such research, a possible
starting point is the section "Water Bucket Swing" on page 10 of the
online version of "Socratic pedagogy in the introductory physics lab"
[Hake (1992)].
For further ideas on the swinging bucket problem go to the powerful
but seldom used PhysLrnR search engine
<http://listserv.boisestate.edu/cgi-bin/wa?S1=physlrnr&X=->, and type
"bucket" (without the quotes) into the "Search for" slot, to obtain
13 hits (as of 21 Sep 2007 15:27:00 -0700. To access the archives of
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REFERENCES
Hake, R.R. 1992. "Socratic pedagogy in the introductory physics lab,"
Phys. Teach. 30: 546-552; updated version (4/27/98) online at
<http://www.physics.indiana.edu/~sdi/SocPed1.pdf>
(88 kB). See also Hake (1998, 2002, 2003)
Hake, R.R. 1998. Socratic Dialogue Inducing (SDI) Lab #3 "Circular
Motion and Frictional Forces," online at
<http://www.physics.indiana.edu/~sdi>. A Teacher's Guide for SDI Lab
#3 <sdi3gTchAll.pdf> (764 kB) will be transmitted as an attachment in
an email to those who request it from <rrhake@earthlink.net>.
Hake. R.R. 2002. "Socratic Dialogue Inducing Laboratory Workshop,"
"Proceedings of the UNESCO-ASPEN Workshop on Active Learning in
Physics," Univ. of Peradeniya, Sri Lanka,
2-4 Dec 2002; online at
<http://www.physics.indiana.edu/~hake/Hake-SriLanka-SDIb.pdf>
(44 kB) [ASPEN = ASian Physics Education Network.]
Hake, R.R. 2003. "Re: Uniform Circular Motion Lab," online at
<http://tinyurl.com/33n6xr>. Post of 15 Jan 2003 21:11:05-0800 to
AP-Physics, Physhare, Phys-L, & PhysLrnR.
Van Domelen, D. 2007. "The Swinging Bucket Problem," PhysLrnR post of
21 Sep 2007 08:55:40-0700; online at <http://tinyurl.com/2uk46x>.