physics problems
Mike Macallister
assigning problems from the text we use (Physics, Giancoli 3rd edition) for
my students to solve. I have also been getting increasingly dissatisfied
with this. The problems usually key in on a particular section of a chapter
with its narrow focus of possible concepts to be brought to bear on the
problem and their equation(s). I don't disparage this. I do, however, wish
there was more.
For example, I came across an interesting problem not too long ago which
simply asked the following: "If two galaxies passed through each other, what
is the probability that two stars would collide? Or one Neils Bohr once
proposed, "How many molecules does a car tire lose for each revolution of the
tire. To solve the problem there are estimates that have to be made and
relevant quantities researched. There is a strategy to solving the problem
that is not tacitly dictated by the section of the text the problem comes
from. And so on.
Anyhoo, I am not terribly creative at making up my own such problems like
this. I also have not found any good sources as yet. If you know of any
such source, or have pet problems like this you wouldn't mind sharing, could
you pass it along to me?
Thank you
Mike Macallister
Central Catholic High School
Portland, Oregon
Lowell Herr
The very best source of problems that I know of comes from Pat Canan of
Corvallis High School right here in the Great Northwest. My students
think it is an excellent way to learn physics.
Lowell
Project PHYSLab
The Catlin Gabel School
Portland, OR 97225
Donald E. Simanek
requiring analysis, synthesis and insight:
> Anyhoo, I am not terribly creative at making up my own such problems like
> this. I also have not found any good sources as yet. If you know of any
> such source, or have pet problems like this you wouldn't mind sharing, could
> you pass it along to me?
Mike,
This a very good suggestion, and such problems should be shared with the
entire group. About a month ago I solicited ideas for such problems, ones
which would focus on concepts as opposed to *mere* number-crunching. No
one took the bait, and none were submitted.
I have a few of my own, which I can post soon (soon enough for your final
exams? :-), once I reformat them for ASCII. You'll have to imagine any
diagrams. Till then, here's one I just used in an optics exam.
Dick and Jane are lab partners. They are doing the standard spectrometer
experiment, getting a spectrum from a prism. They know the formula for
index of refraction at minimum deviation: n = sin[(A+d)/2)]/sin(A/2) where
A is the angle between the prism faces and d is the minimum deviation
angle. They are given a prism with two 45 degree angles and one 90 degree
angle, with all three faces polished. Jane wants to use two faces which
make a 45 degree angle. Dick says that they'd get a greater deviation and
greater dispersion by using the faces making 90 degrees, and therefore get
better resolution of the spectral lines. Who is right, and why?
The answer is somewhere below:
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Answers:
(1) Larger angles do give greater deviation. Test 20, 45, 60, etc. Now
try 90 degrees.
(2) Larger angles give greater dispersion for the flint glass usually
used in these experiments (answer based on student experience and astute
observation).
(3) Greater dispersion and deviation do not result in greater resolution.
The Rayleigh criterion rules here, and the resolution is due to the
optics of the spectrometer, not on the prism.
(4) For a refractive index of 1.6 or 1.7 (typical, based again on student
experience with this experiment) the light wouldn't emerge from the
second face, it would have total internal reflection. Therefore useless
for the experiment (Jane is right, so long as she gave the right reason).
Note that this answer involved (1) lab experience, (2) understanding of
minimum deviation, (3) understanding of the Rayleigh criterion of
resolution, (5) some math, (5) synthesis of these, (6) ability to
brainstorm a problem, and (7) ability to express physical ideas in words.
This particular question is a bit *much* for elementary physics courses,
but does illustrate the kind of problem we seek: one which uses concepts,
insight, understanding, experience, *and* the ability to handle the math.
It's not merely 'plug and solve'.
I'm not sure the classic 'Fermi' problem is appropriate for exams, but
certainly is for homework. (I'm speaking of the "How many piano tuners
are there in New York City" type of problem.)
Another one from optics:
Someone once looked at the Van Gogh painting "Starry Night" (available in
a nice GIF on the internet) and some other of his paintings, and wondered
why he painted things in the sky (sun, moon, stars) as fuzzy, indistinct
swirls and blobs, while foreground objects, houses, trees, etc, were
painted with far more detail. He speculated that Van Gogh was nearsighted,
and did not wear glasses, therefore he'd never seen anything in the sky
clearly. But he could walk up to nearby objects and see their details, and
therefore painted them that way. Discuss.
And still another 'arty' one:
Look at some paintings by El Greco. Note how he painted people tall and
skinny. Some have suggested this is because he had uncorrected
astigmatism. Explain why this explanation is wrong. Use physics in your
discussion.
Are you ready for another? This is from Meyer-Arendt, _Introduction to
Classical and Modern Optics_ 3rd ed. Prentice-Hall, 1972.
The neo-impressionist painter Georges Seurat was a member of the
pointillist school His paintings consisted of an enormous number of
closely spaced small dots (approximately 1/10 inch) of pure pigment. The
illusion of additive color mixing was produced only in the eye of the
observer. How far from such a painting should one stand in order to
achieve the desired blending of Color?
Who was it here, Fred Bucheit, I think, who said we don't often enough
cross disciplinary boundaries in our teaching? Such boundary-crossing
questions are 'out there' if you only look for them.
The answer to these are interesting. See below, but don't peek till
you've thought about them for several days.
The Van Gogh problem came from a textbook I've forgotten, and from an
astronomy professor who quoted it straight-faced. I'm not sure this is a
good one to pose to physics students, for there's no physics to be
brought to bear on this. If Van was nearsighted all his life, and never
wore glasses (questionable assumptions crying out for library research),
and had never seen anyone else's paintings, drawings or photographs (Were
there photographs of these in Van Gogh's time? Back to the library) then
the conjecture might carry some weight. Most likely he painted them that
way because he liked the effect. Did he *always* paint that way (back to
the library).
Even if El Greco had a severe eye defect which elongated objects
vertically, his canvas would appear to him elongated as well, and *if* he
painted things 'as he saw them' the painting would look normal to everyone
else. Besides, astigmatism in the eye doesn't cause that much size
disparity, but mainly causes a resolution disparity. Again, he probably
simply liked the startling effect.
Seurat: The human eye has a pupil diameter of about D = 2mm in bright light.
With a wavelength of 550 nm (middle of visible spectrum) the smallest
resolvable angle is 1.22(wavelength)/D = 1.153 minute of arc. (1 minute
of arc is taken as a rough rule of thumb.) The eye's focal length is
about 20mm (in normal room light) so the resolution on the retina is 6700
nm. This is roughly twice the mean spacing between the receptors on the
retina. The human eye should therefore be able to resolve two points, an
inch apart, at a distance of some 2980 inches (about 1 in 3000, or 1 inch
at 100 yard). Answer: 1 part in 3000, 3000x(1/10 inch) = 300 inches = 25
feet = 8.33 yard.
This kind of homework problem encourages library research.
I found this in Janson, H. W. _History of Art_ Prentice-Hall, 1965: "In
Seurat's later works, such as _Side Show_, the flecks (of paint) become
tiny dots of brilliant color that were supposed to merge in the
beholder's eye and produce intermediary tints more luminous than those
obtainable from pigments mixed on the palette. This procedure was
variously known as Neo-Impressionism, Pointillism, or Divisionism (the
term preferred by Seurat). The actual result, however, did not conform to
the theory. Looking at _Side Show_ from a comfortable distance (...7' to
10' for the original), we find that the mixing of colors remains
incomplete; the dots do not disappear, but remain as clearly visible as
the tesserae of a mosaic... Seurat himself must have liked this
unexpected effect..."
Do we really want to go interdisciplinary?
A colleague at another school told of his experience teaching a "Physics
for Poets" type course. He expected the non-science students in the
course to know hardly any science, or even to have any initial interest
in it. But found, to his dismay, that they had no interest in liberal
arts content either. They simply had no interest in *anything* academic.
How many of your students have even heard of El Greco or Seurat, or can
remember seeing any specific pictures by them? How many will, on their
own initiative, use the library to seek out more information? Shouldn't
we be encouraging such habits, and such breadth of interests? How many
will use mathematics (as appropriate) in an 'essay' question?
-- Donald
Steve Hamersky
> Corvallis High School right here in the Great Northwest. My students
> think it is an excellent way to learn physics.
>
> Lowell
>
> Project PHYSLab
> The Catlin Gabel School
> Portland, OR 97225
>
Lowell,
Are these problems published
--
=============
Stephen Hamersky e-mail: hame...@bluejay.creighton.edu
Daniel J. Gross H.S. voice: (402) 734-2000
7700 So. 43rd St. The Lord prefers common people.
Omaha, NE 68147 That is why he made so many of us.
Matt Tuley
>Anyhoo, I am not terribly creative at making up my own such problems like
>this. I also have not found any good sources as yet. If you know of any
>such source, or have pet problems like this you wouldn't mind sharing, could
>you pass it along to me?
Two good books for this are _Thinking Physics_ (blanking on author, don't know
publisher, don't have it handy) and the quickly-becoming-a-classic _Flying
Circus of Physics, with Answers_ by Jearl Walker (published by John Wiley and
Sons).
Matt Tuley tu...@csn.org
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Making my own little dent in the infinite Spandex of the universe...
Lowell Herr
Pat is an outstanding physics teacher and I might add, very busy right
now. It might be better to contact him about the third week in June -
when school is over. Nevertheless, I am sending him a carbon copy of your
request.
Lowell Herr
Project PHYSLab
The Catlin Gabel School
Portland, OR 97225
Donald E. Simanek
> Two good books for this are _Thinking Physics_ (blanking on author, don't know
> publisher, don't have it handy)
Surely you must mean Paul G. Hewitt!
> and the quickly-becoming-a-classic _Flying
> Circus of Physics, with Answers_ by Jearl Walker (published by John Wiley and
> Sons).
Walker's book ought to be in every teacher's library. But few of the
things in there lend themselves to problems students in introductory
physics courses could be expected to handle (IMO). The first edition of
Walker's book did not have answers, but only library and literature
references. The fact that the publisher thought it necessary to add short
answers testifies to the fact that the answers are not that easy and
certainly not always obvious, even to those who know physics quite well.
To pose them to students as homeowrk might be intimidating. To urge them
to read the book and learn from it is entirely appropriate, and most
students find it fascinating.
I like to haunt used-book sales, and have found many out-of-print books
of great merit. One is:
Julius Sumner Miller _Millergrams_ (paperback)
-- Donald
gibson
It sounds like you are looking for Fermi questions. This was discussed
last year and lots of questions are probably in the archieves. I haven't
tried to get those but it is possible. Look in the info you recieved
when you first subscribed to find out how to get archieved info. Send a
message to me if you want me to send you a few of these.
Al
On Thu, 4 May 1995, Mike Macallister wrote:
> In my AP physics class for the last four years I have been dutifully
> assigning problems from the text we use (Physics, Giancoli 3rd edition) for
> my students to solve. I have also been getting increasingly dissatisfied
> with this. The problems usually key in on a particular section of a chapter
> with its narrow focus of possible concepts to be brought to bear on the
> problem and their equation(s). I don't disparage this. I do, however, wish
> there was more.
> For example, I came across an interesting problem not too long ago which
> simply asked the following: "If two galaxies passed through each other, what
> is the probability that two stars would collide? Or one Neils Bohr once
> proposed, "How many molecules does a car tire lose for each revolution of the
> tire. To solve the problem there are estimates that have to be made and
> relevant quantities researched. There is a strategy to solving the problem
> that is not tacitly dictated by the section of the text the problem comes
> from. And so on.
> Anyhoo, I am not terribly creative at making up my own such problems like
> this. I also have not found any good sources as yet. If you know of any
> such source, or have pet problems like this you wouldn't mind sharing, could
> you pass it along to me?
Donald E. Simanek
demonstrations, problems, and strategies of teaching. Many of these
are older books, found at used-book sales and used-book stores.
They are worth watching for. The comments in square brackets are
my own.
Thompson, N. _Thinking Like a Physicist, Physics Problems for
Undergraduates_ Adam Hilger, 1990. A collection of problems and
solutions, written by the staff of the Physics Department of the
University of Bristol, and Edited by N. Thompson, PhD, FInstP,
Emeritus Professor of Physics, University of Bristol. [Definitely
college level. Uses math and calculus freely.]
J. W. Warren _The Teaching of Physics_ Butterworths, 1965. From the
dust jacket: "The author, long dissatisfied with the falsities and
absurdities which have gradually come to be accepted by physics
teachers and examiners, cuts through the traditional interpretation
of elementary physics and offers constructive criticism."
Jargocki, Christopher P. _Science Brain-Twisters, Paradoxes, and
Fallacies_ Scribner's, 1976. [Good collection, useful at high
school or elementary college level.]
Jargocki, Christopher P. _More Science Brain-Twisters and
Paradoxes_, Van Nostrand, 1983.
Gardner, Martin. _Entertaining Science Experiments with Everyday
Objects_ Dover 1981. Reprint of _Science Puzzlers_, 1960, published
by Scholastic Book Service.
Gardner, Martin. _Encyclopedia of Impromptu Magic_ Magic Inc.,
1978, 1985, 1991. [Many of these are physics demos in disguise, in
the spirit of Martin's recent contributions to _The Physics
Teacher_.]
Gardner, Martin: There's a whole series of reprint books of
Gardner's columns _Mathematical Games_ from the Scientific
American. Many of these have useful ideas for physics demos, and
are just good reads to stretch the mind.
Miller, Julius Sumner. _Millergrams I_ Doubleday, 1970 (pb).
_Millergrams II_ (companion volume) [Physics puzzlers with answers,
but the answers suggest more puzzles. Designed to encourage
conceptual thinking.]
Miller, Julius Sumner. _Demonstrations in Physics_ Ure Smith,
Sydney, London, 1969. [A larger collection in the spirit of the
Millergrams books. This one was not readily available in the United
States.]
Lynde, Carleton John. _Science Experiences with Home Equipment_ D.
Van Nostrand, 1937, 1949.
Good, Arthur. Prolific author of many books on magic tricks,
puzzles and science demonstrations, often published under
pseudonyms. These remind us of earlier times when people,
especially young people, thought science was fun, and enjoyed doing
science with readily available objects and materials and home-made
apparatus. Definitely hands-on physics. These are frequently
reprinted under other titles, for example:
_100 Amazing Magic Tricks_ Pinnacle Books, 1977.
Lanners, Edi. _Secrets of 123 Old-Time Science Tricks and
Experiments_ TAB Books, 1981.
_Columbus' Egg_ [Several books have appeared under this title.
Lanners' book is from one such two-volume set, published in 1890.
-- Donald
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Dr. Donald E. Simanek Office: 717-893-2079
Prof. of Physics Internet: dsim...@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745 CIS: 73147,2166
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Paul Hickman
know
> publisher, don't have it handy)
"Surely you must mean Paul G. Hewitt!"
Actually, "Thinking Physics" is by L.C. Epstien not PG Hewitt although Paul
did do the illustrations.
Paul
Matt Tuley
>On Fri, 5 May 1995, Matt Tuley wrote:
>> Two good books for this are _Thinking Physics_ (blanking on author, don't know
>> publisher, don't have it handy)
>Surely you must mean Paul G. Hewitt!
Um, nope. :) That's _Conceptual Physics_. _Thinking Physics_ is a sort
of a "low-budget" paperback (though, if I'm going to use a movie analogy,
"independent production" would be more apt). It's a great book, and I can
see the guys photo on the back of the book plain as day (in my mind, that
is) but can't recall his name. I'll check when I get back to school on
Monday.
>> and the quickly-becoming-a-classic _Flying
>> Circus of Physics, with Answers_ by Jearl Walker (published by John Wiley
>>and Sons).
>Walker's book ought to be in every teacher's library. But few of the
>things in there lend themselves to problems students in introductory
>physics courses could be expected to handle (IMO). The first edition of
>Walker's book did not have answers, but only library and literature
>references. The fact that the publisher thought it necessary to add short
>answers testifies to the fact that the answers are not that easy and
>certainly not always obvious, even to those who know physics quite well.
>To pose them to students as homeowrk might be intimidating. To urge them
>to read the book and learn from it is entirely appropriate, and most
>students find it fascinating.
Good points. Some of the physics questions in there are, in fact, killer.
But there are quite a few that I think would be okay to ask, perhaps for a few
extra points... for an honors class... Okay okay. But every teacher should
have this.