Mail Time: Waves on a snakey demonstration

Deidre Higgins, of Corbin Kentucky and veteran of my 2009 APSI at Morehead State University, writes:

I was trying to do some lesson planning over the break to get caught up & I was wondering if you could help me with a wave demo. I have in my notes from this summer something about showing interference using paper cups set up two "tiles" away and starting with an amplitude of one "tile," but that's about all I have. (Apparently I need to improve my note-taking skills!) I was wondering if you could give me a brief description of how to do this demo--I remember it being really good to show interference, I just don't remember the details.

Happy to help, Deidre. After I’ve shown the class all the relevant definitions for waves (i.e. amplitude, transverse wave, longitudinal wave, etc.), the class takes a field trip to the tiled floor of the hallway. I bring along a “snakey,” which is like a smaller-diameter slinky with the coils very close together. One student holds an end of the slinky on the floor, while I hold the other on the floor about 5 yards away. The setup is similar to what you see in the picture above, but with the slinky aligned parallel to and on top of a line between tiles. And my kiddies are somewhat older.

I place a line of paper cups on each side of the snakey, parallel to the snakey but about 1.5 tiles away from the snakey’s resting location. I send a wave pulse along the string. If this wave pulse has an amplitude equal to one tile, then the cups aren’t knocked over. (A two-tile-amplitude pulse knocks over all of the cups.)

But when I have the student holding the other end of the snakey send a one-tile-amplitude pulse to me AT THE SAME TIME that I send a pulse to him, the wave pulses interfere in the middle – knocking down just a couple of cups. You see, this is a manifestation of constructive interference. In the middle, the amplitudes of the wave pulses add to form, briefly, a pulse of amplitude two tiles, knocking down the cups.

There’s more you can do with the snakey – move the cups closer and demonstrate DESTRUCTIVE interference, show what a longitudinal wave looks like, show harmonics of standing waves on the snakey, and more. Play with the setup, see what else you and your students are interested in.

GCJ

What do YOU want me to post about?

Christmas/Chanukkah/Saturnalia break means I can procrastinate my grading for weeks.  I have some other writing to do (I'm working on the next edition of the Everything Kids Football Book, buy yours now!), but I certainly would like to update this blog in between gulps of Cheese Nog.

What do you want to hear about?  Do you have questions about how I teach a particular topic?  Questions about an assignment that you give, or that I give?  Have an idea you want to share with me?  Send it in!  Post in the comments section, or send an email to me at greg_jacobs@woodberry.org. 

One-off assignments, and avoiding politics

The underlying point of the article "Read Any Good Science Lately?" (in The Physics Teacher, March 2009) is that (a) assigning reading beyond the textbook can be beneficial and inspirational, and (b) such reading assignments must be carefully constructed lest students treat them with a "read because teacher told me to" attitude which serves as an obstacle to comprehension and enjoyment. Patricia Blanton is right-on here. I tend to refer to such assignments outside the traditional realm of physics problem solving as "one-off" tasks, in the spirit of Scott Adams' Dilbert.*  I'm concerned that Ms. Blanton subverts the usefulness of her idea with educational and political baggage.

In a general (non-AP) class especially, reading or research assignments can provide a welcome break from the routine of problem solving. From the students' perspective, they might be pleased to earn a grade using skills with which they might be more comfortable -- reading and writing have been part of their lives for years, while physics problem solving is often a new and intimidating skill. From the teacher's perspective, the "one-off" assignment allows us to show our students aspects of physics beyond equations and experiments.

Now, let's be brutally honest about that last sentence. As soon as we get beyond problem solving and laboratory work, most of what we do will be colored politically in some way. Ms. Blanton unveils her pet causes in her article through the assignments she suggests: women in science, environmental effects of nuclear power, and global economic inequity. Your own political issues may be less obvious, but still present: for example, my bugaboos about pseudoscience and belief-without-evidence are apparent to all as soon as I assign reading or writing on these topics. I don't care how purely academic you make such an assignment, your personal opinion is on raw display.

That's not necessarily a bad thing. But it must be handled carefully.

It doesn't matter how much your students like or respect you, they are still teenagers who question everything, and who have an innate anti-authority streak. And they don't like to be told what to think. If it's obvious from the start where the teacher stands on an issue, the typical teenager has one of two reactions: (1) My writing better support what the teacher thinks so I can get a good grade; or, (2) I'll find a way to show that teacher how wrong he is. Either way, you don't get the effect you want out of the assignment.

What's the solution? I don’t know that there is one. I’d say, keep your cards close to your chest at first, and you’re likely to avoid the two major obnoxious teenager reactions.

If you come out, guns a’blazin’ about how nuclear waste will lead to the death of all mankind, or about how nuclear power is the only possible savior of industrial society, your class is done listening. Their research is virtually guaranteed to be inauthentic.

But if, instead, you make a conscious effort to conceal your own position… well, then you might provoke some serious thought. Provide a counterargument to anyone in the class who makes a statement of opinion – and do so WITHOUT SMIRKING, even if you have to say something you consider personally outrageous or offensive. You are making it clear to your students that the only route to success on this assignment is reasoned logic.

Then, if your own position is truly supported by sound evidence, students will find and quote that evidence. You can subsequently argue with your students about the quality of evidence rather than about your (or their) pet opinions.

Now, don’t get me wrong here – I DON’T think that physics class is an appropriate place to be doing social studies research, or addressing highly charged political issues. I do think you can do successful reading and writing projects that involve physics, as long as you stick to the science and avoid the politics.  If you choose to attempt these one-off tasks for whatever reason, tread carefully on highly charged opinions, or risk sabotaging the entire point to the exercise.

* Scott Adams, author of the "Dilbert" comic strip, theorizes that a successful corporate manager minimizes the "one-off" tasks required of employees in order to keep up production and morale. A "one-off" task is anything not directly related to the enterprise at hand. For example, an engineer sketching a machine component is on-task; the engineer filling out a timesheet allocating his efforts among different departmental accounts is "one-off." For physics teachers, grading papers or setting up demonstrations is on-task; discussing minutia about dress code enforcement is one-off. Adams cautions that "one-off" tasks are often useful, or even important. He does not suggest that such tasks be eliminated altogether; rather, he suggests they be severely limited, so that most of an employee's time is on-task, and so that any one-off task receives the employee's full attention.

Jacobs Physics: Upcoming Public Appearance!

Folks, I will be running the "experienced teachers" section of the one-day AP Physics workshop on Monday, January 4, at Georgia Perimeter College in Dunwoody, GA.  (That's essentially in Atlanta.)  I'm flying into Atlanta on January 3, running the workshop from 8-3 on Jan. 4, and then flying home. 

Sign up for the workshop via the College Board website.  Or, if you're in the area on Sunday afternoon, let me know, and we'll find a place to watch the NFL playoffs and talk physics.

Other public appearances in the far future include at least three AP Summer Institutes this year:

* Morehead State University, Kentucky, July 12-16;
* North Carolina State University, July 19-23;
* Manhattan College, July 26-30

Tell your friends!  Get your tickets now, while they last!  No shoving in line, please.

First contact with E&M

In AP physics B, it's time to start electricity. The portion of the course dealing with electricity and magnetism is a non-negligible 25% of the exam.  This is also the most difficult section of the course, because it deals with such abstract concepts as "charge" and "field".  I still do as many quantitative demonstrations as I can, especially with magnetic forces and electric circuits.  But when it comes down to it, it's not straightforward to give my students an easy mental picture of, say, a +0.2 μC charge at rest in a 200 N/C electric field.

On the first day that I broach the subject of electricity, therefore, I try to make the explicit connection between electricity, magnetism, and MECHANICS.  I point out that the whole point of the E&M unit is to apply the mechanics we've learned to a new and strange regime, that of charges.  It requires a considerable leap of faith and reasoning to deal with a problem as simple as, "a proton at rest experiences a force of 10^-17 N to the right.  What is its speed after 10^-15 s?"  Because it's a proton, and because the numbers are "so small," suddenly the concepts of Fnet=ma and kinematics become impossible.

So my very first quantitative demonstration is done with the PASCO e/m device, pictured above.  This is an expensive but worthwhile item.  I put in a capital request a few years ago, and the money came through.  Purchasing one of these would be good use of grant money.  Or, if you can't find the money to buy one of your own, check with the local college's physics department -- most colleges have large numbers of these lying around for use in the freshman lab, and you may be able to borrow one for a week.

Now, this device can do many awesome things.  You can deflect electrons electrically with charged plates; or, you can use a magnetic field to bend electrons in a circle.  The relevant voltages and magnetic fields are either printed right on the device, or are read clearly off of the power supplies.  Certainly this would be a good demonstration in the magnetism section, to show that you can in fact predict the magnetic field given the radius of electrons' circular motion, or to predict the speed of electrons in a circle, or to verify the equation for electrical potential energy, qV.  But at the begninning of the unit, all these concepts are completely foreign.  I do something much, much simpler.

All I tell the class is that I have electrons that have been given a kinetic energy of 4 x 10^-17 J.  (Sure, I figured that out using qV... but I say NOTHING about that to the class.)  Then, I tell the class that these electrons experience a magnetic force that acts as a centripetal force, and that is equal to qvB.  I tell them the value of this magnetic field thing labeled as B, which equals 7.8 x 10,^-4 T. 

The question:  what is the radius of the electrons' circular motion?

We follow a Newton's Second Law approach, drawing a free body diagram, setting the net force equal to ma, where acceleration is v²/r.  We solve in variables first to get r=mv/qB. We use the definition of kinetic energy (and the looked-up mass of the electron) to calculate the speed of the electrons.  We look up the charge of the electron.  Plugging in, we find that the radius of the circular motion should be in the neighborhood of 6 or 7 cm. 

Then I turn on the device and hit the lights.  We see a dim greenish circle inside the big globe, a circle of diameter that we measure to be... between 12 and 14 cm. 

Follow-up questions that I ask right there:  1. If I increase the magnetic field thingy, what should happen to the circle of electrons?  Well, since B is in the denominator, the radius should get smaller.  (Then I increase the current to the Helmholz coils, increasing the magnetic field, and the circle gets tighter.)  2. If instead I give the electrons more kinetic energy, what should happen to the circle of electrons?  Well, increasing the kinetic energy increases the electrons' speed.  Since v is in the numerator, the circle's radius should get bigger.  (Then I increase the voltage on the electron gun, increasing the electrons' speed, and expanding the circle.)

This demonstration provides a nice "gee, wow" effect, while hammering the point:  once an electricity or magnetism problem can be phrased in terms of forces or energies, then it becomes a mechanics problem -- and we already know how to deal with those.

Department of the Obvious: Test Corrections Work

Don't know whether you saw the December 2009 edition of The Physics Teacher. This generally excellent magazine has given me untold helpful hints, lab ideas, and physics concepts to think about in the context of teaching high school (and low undergraduate) physics. In fact, I have a co-written article being published in next month's edition, about the USAYPT, the organization that made the mistake of appointing me President. (Check us out at http://www.usaypt.org/!)

This month, TPT explains how they use "Assessment Corrections" as a teaching tool. Great idea, obviously. What bugs me about this article is certainly not that I think anyone "stole" the idea of corrections from me! Of course they didn't. In fact, I "stole" the idea from Haverford professor Lyle Roelofs -- pictured above --  who inflicted test corrections on us in Advanced Quantum Physics in 1994.  He offered half credit back on the test if we corrected out mistakes.  A classmate astutely commented, "Lyle, you know we're going to do the corrections, because without them our grades are lousy, but with them the grades are good.  So even though corrections aren't required, you're insidiously getting us to do them."  Lyle just smiled.

Anyway.  What bugged me about this article was the conceit that it was determining, through the use of a scientifically valid theory, that assessment corrections are useful, and that corrections help students learn.  The article is full of phrases like "formative assessment"  and "metacognition."  AARRGH! 

Okay, okay, okay.  I know that college professors, especially those the education departments, need data to take new ideas seriously.  And that makes some sense - even I ask other teachers “so does it work?  How can you tell?” When other teachers tell me about their pet new idea, whether I think it awesome or terrible on the surface. The authors are communicating clearly and well, with their intended audience in mind.

But look, readers, I don't care what your "theoretical basis for assessment corrections" is, or whether you even have one.  Does anyone ever ask Roger Federer for the "theoretical basis" for his forehand?  Does anyone ask Albert Pujols for the "theoretical basis" of his swing?  No, these folks just do what works.  They're probably happy to share what they know about what works for them, but what works for them may or may not work for another professional. 

Physics may be a peer reviewed science, but physics teaching is far, far closer to art than science.   Good artists may do things in a similar manner, but they don't need peer-reviewed evidence to know they're doing something right.  All anyone -- INCLUDING ME -- can tell you about a physics teaching method is, "it worked for me, it worked for lots of other people, here's how I do it, now try it if you'd like."

Test corrections work for me.  Test corrections apparently work for a lot of people who write PER articles, too -- you can read the TPT article for useful examples of how other teachers have made the corrections assignment.  Corrections worked for Lyle Roelofs.  They have worked for a number of attendees at my summer institutes.  They will probably work for you.

Thermal expansion – quantitative demonstration

It’s easy to discuss thermal expansion in terms of students’ experience. They see expansion slats in sidewalks all the time. They may have noticed highway bridge expansion joints (and if they haven’t, they will probably be able to see one within 24 hours if they’re observant). Evidence for the existence of thermal expansion abounds.

However, creating measurable expansion in the classroom is a challenge. The coefficient of linear expansion for virtually all materials is on the order of 10^-5 K^-1. So even with a temperature increase of 100 K, an object will expand by about 0.1% of its length.

I can think of three experimental ways to create a reasonable thermal expansion demonstration:

1. Create an enormous temperature increase. Not practical, though, because even a 1000 K temperature change only causes a 1% length expansion.

2. Use a very, very long object, so that the 0.1% increase is big enough to see. Well, if you heat a 10 m long rod by 100 K, it will expand by about a centimeter. I don’t know about you, but I don’t have a 10 m rod handy, nor do I have room for it in my classroom, nor do I have a way of heating it relatively uniformly.  Ugh.

3. Get a measuring device that can measure itty bitty length changes.

I’ve gotten method number 3 to work in my classroom. Yesterday I used one of those metal rings with a wooden handle that come with commercial thermal expansion kits. I used a micrometer (pictured), which has can measure plus or minus 5 thousandths of a millimeter, to measure the WIDTH of the ring. You see, linear expansion happens in all directions. The width of, say, a rod will expand by the same percentage as will the length. I choose to measure the width of the ring because my micrometer can measure that easily.

The width at room temperature was 4.30 mm. I heated the ring for a minute or two in a Bunsen burner. I used an infrared non-contact thermometer – pictured to the right, available for no more than $30 – to find that the ring’s temperature rose to about 220 degrees Celsius, an increase of about 200 degrees over room temperature. Thus, an order of magnitude estimate of the ring’s expansion is that ΔL/L = (10^-5)(200) = 0.2%. Since I don’t know what my ring is made of, I can merely guess that the expansion should be in the neighborhood of a few tenths of a percent. I measured a new length of 4.33 mm, an increase of about 0.7%, which works for me.