Astronomy Unit

In general physics this time of year, I try to keep everyone’s attention by covering topics of particular “coolness,” including astronomy. Problem is, basic astronomy is harder for high school students than a physics teacher might think.

I cover the bare-bones basics of observational astronomy. This includes the motions of the earth and moon; apparent motion of the stars; and some “how do we know that” questions (like, the use of parallax to find the distance to nearby stars).

Why is astronomy so difficult? I don’t know. I know that elementary school teachers generally show the geometry behind eclipses and the phases of the moon. Yet, most of my class will say that the earth’s shadow is responsible for moon phases, and cannot reliably discuss the reason that we don’t have an eclipse every month. Similarly, I know that someone has taught my juniors and seniors why seasons occur… nonetheless, they invariably tell me that the earth is closer to the sun in the summertime.

What’s embarrassing and frustrating is that many of my students maintain these misconceptions EVEN AFTER we have discussed them repeatedly in class.

Anyway.

In class, I have a copy of the astronomical simulation program Starry Night Backyard, a globe, and a few scanned diagrams from a college introductory astronomy textbook. I have a general plan as to what I want to cover, but I also let the discussion follow student interest – I get more curiosity-inspired questions in this unit than in any other.

However, it is imperative that I keep students focused on the class discussion. If I’m not careful, I end up answering a good question for one student while the others fall asleep in the warm, dark, room as they dream of summer vacation and bikini-clad women. What do I do?

I assign a couple of questions for homework each night – each night’s assignment is designed to take about 30 minutes. Then, the next day, I give a 5-7 question multiple choice quiz. The quiz is partly based on the homework, and partly based on discussions from the previous day’s class. Students learn quickly that they are, in fact, responsible for everything that goes on in class.

As an extra reward, I give any student with a perfect score on a quiz a homework exemption, to use whenever he wants. (I discuss the use of exemptions in my April 24 post.) The combination of the quiz grade, the required homework, and the possibility of an exemption tends to hold student interest.

Below is a sample assignment and quiz. I can post more of these if people are interested – tell me what you’re looking for in a comment or an email.

GCJ

Assignment:
1. The radius of the earth is 6400 km; the radius of the sun is 700,000 km. Watch your significant figures carefully – note that we are looking for power of ten estimates only!

a. The diameter of the sun is how many times bigger than the diameter of the earth?
b. How many Earths could fit inside the sun? (Note that the answer to (b) is NOT the same as the answer to (a).)
c. Look up the mass of the sun and of the earth. How many times more massive is the sun?


2. Which is more dense, the earth or the sun?
a. First, answer based on what you already know or what you can look up online.
b. Next, answer based on your response to questions 1b and 1c above.


Follow-up quiz:

How much closer is the earth to the sun during our summertime than during our wintertime?
(A) About 3% closer
(B) About 30% closer
(C) About 3 times (300%) closer
(D) None of the above, the earth is actually farther away from the sun in summer.

On which of the following dates is the sun directly overhead at noon at the equator?
(A) June 22
(B) September 22
(C) December 22
(D) None of the above because the sun is never directly overhead at the equator
(E) None of the above because the sun is always directly overhead at the equator

On which of the following dates is the sun directly overhead at noon at Woodberry Forest?
(A) June 22
(B) September 22
(C) December 22
(D) None of the above because the sun is never directly overhead at Woodberry
(E) None of the above because the sun is always directly overhead at Woodberry

How many earths could fit inside the sun?
(A) A hundred
(B) A thousand
(C) A hundred thousand
(D) A million
(E) Ten million

How many times bigger than the earth’s diameter is the sun’s diameter?
(A) A hundred
(B) A thousand
(C) A hundred thousand
(D) A million
(E) Ten million

What do I do with seniors in the spring? Exemptions.

Ah, this time of year the faculty have the annual moan-fest about the lazy seniors. They’re into college, they don’t want to work, they are rude to the underclassmen, they caused the stock market crash, and so on. What’s to be done with them? Here’s an idea to keep them working: the exemption.

First, some background. I establish the homework routine in all my classes from day 1: we have homework every night, which usually consists of one or two problems whose solution must be communicated thoroughly. A student is allowed two extensions per five-week marking period, no excuses necessary. I collect homework during the beginning-of-class quiz, picking up papers from each student personally. If you don’t have homework right this instant, for whatever reason – don’t tell me about it, just take an extension. The extensions are due two days later for full credit.

What about the student who has already taken both extensions and doesn’t have homework? I can assign him to a special afternoon study hall. He has to leave his afternoon activity or practice early, and he reports to a proctor to work for 45 minutes. Problems completed in this special study hall can only earn about half credit maximum. And, all problems must be done eventually in order to earn a passing grade in the course.

By the spring, this routine is ingrained in my class. My seniors, like all seniors in the country, want to slide a bit. I want them to continue to work diligently on a nightly basis. Where do we compromise?

I give in a good bit by virtue of my yearly plan. In AP physics, I don’t present new material after April 1. It’s easier to convince seniors to practice problems on topics they’ve seen before than to learn something from scratch. In general physics, I cover optics, astronomy, and circuits in April and May. Optics is easy; astronomy is not, but it piques curiosity; circuits are easy and involve lots of hands-on lab work with a reasonably high wow-factor. I would not try to teach conservation of energy and momentum in the spring.

I still assign homework according to the standard routine. There’s no question in anyone’s mind that a failure to do homework will result in both a grade penalty and a loss of freedom due to the special study hall. So, work gets done. My seniors slide not by avoiding work, but by putting very little thought or attention into their work.

How do I fight this passive-aggressive approach to senior slide? I offer incentive for strong work in the form of the exemption. A student can use an exemption when he doesn’t have the previous night’s homework; unlike an extension, though, an exemption means that that night’s work never has to be done at all.

On a whiteboard on the side wall of my classroom, I’ve listed every student in my class along with two dashes representing their two allotted extensions per marking period. I put red checkmarks on the dashes each time an extension is used. When a student earns an exemption, I use a blue marker to make a large box by that student’s name. Everyone in every class sees the blue mark, and everyone without a blue mark is jealous. They all want exemptions.

Exemptions must be EARNED, and I make them reasonably difficult to obtain. In AP physics, a perfect fundamentals quiz earns an exemption; I award exemptions for perfect quizzes in general physics, too, when the quiz is based on the assigned homework. At the end of each week, I award an exemption to any student with an A homework average for the week.

I overheard some general physics students talking the other day. One gentleman had acquired his graded homework from Monday and Wednesday. He noted to his friend that he was off to a good start for the week… he and his friend actually calculated how well they had to do on the rest of the week’s homework in order to earn an exemption. I’m fine with that… they did five days worth of awesome, diligent homework in order to earn one night off. I’ll take that bargain with a senior in the spring.

Fundamentals quiz based on the 2008 AP Physics B exam

This time of year, many of us who teach AP Physics are giving last year's free response as a practice test. Great... but don't stop there. Make your students correct what they got wrong.

Below is a "fundamentals quiz" based on the 2008 free response exam. I can't post the original questions due to copyright issues, but you can find them here:

http://apcentral.collegeboard.com/apc/public/repository/ap08_physics_b_frq.pdf

After my class took this test, and after they did corrections, I designed this quiz. All of the quiz questions speak to raw recall issues -- no problem solving, just general facts and techniques that must be memorized. Try this!


(a) Two blocks collide and bounce off one another. What quantities are definitely conserved? Circle all that apply.

Kinetic energy momentum velocity force

(b) What does it mean for a quantity to be conserved?

(c) Define an elastic collision.


2.
(a) When a problem involves two interacting objects, how many free body diagrams must be drawn in order to use Fnet = ma?

(b) When a problem involves a changing net force, kinematics cannot be used. What do you use instead?

(c) Which of the following expressions represents the net force on the right-hand block on the flat surface above? Choose one and explain

o 4.0 N - Fspring
o 4.0 N
o Fspring
o Zero

(d) The blocks in the diagram above move with constant acceleration. Are they in equilibrium? Explain.

3. There are three right hand rules for magnetism. State the equation associated with each, and what quantity the right hand rule is used to find.

EQUATION This RHR finds the direction of what quantity?
RHR #1
RHR #2
RHR #3

4. (a) A ball is launched at a 30o angle with a 15 m/s horizontal velocity. What is the initial speed of the ball?

(b) What is the speed of the ball at the peak of the ball’s flight?


(c) When is the equation P = Po + ρgh valid?

(d) Where is the pressure in this fluid stream largest? Choose one.
0 at the peak of the flight
0 at the fountain’s opening
0 when the water hits the table
0 none of the above, the pressure is the same everywhere

5. Consider the first law of thermodynamics.
(a) What does the variable W mean? How do you find it from a PV diagram?
(b) What does the variable Q mean? How do you find it from a PV diagram?
(c) What does the variable ΔU mean? How do you find it from a PV diagram?

6. (a) What kind of mirror(s) can produce either a real OR virtual image?
(b) What kind of mirror(s) can produce a reduced image?
(c) What kind of mirror has a positive focal length?

7. Which equation below can be used to calculate the kinetic energy of an electron? Explain briefly why the choice you eliminated is incorrect.

E = ½mv²
E = pc

Random.org and randomizing lab partners

Want an easy way to assign random lab partners?

In a run-of-the-mill lab exercise, I have students work with a partner, but I collect analysis questions from every student individually. In these cases, I assign partners randomly. I don’t want them picking their friends, or competing for the “best” student in the class. If they picked a partner, they’re more likely to rely on that partner’s answers without thinking for themselves. Random partners build camaraderie in the class… not just for this week, but for the weeks to come. Folks had better be nice to one another, because who knows whether they’ll be stuck working together next week!

(On the other hand, if I have a longer, more involved lab in which I expect a combined report from a partnership, then I allow students to choose partners, or even to work alone. That way they don’t have an excuse if their partner slacks – they chose that partner!)

So anyway, how do you choose random lab partners? I used to use dice, or playing cards, or a calculator’s random number generator. These things took time. Wouldn’t it be great, I thought, if I could just type my class list into a program, and the program would spit back random partnerships?

Well, I found just such a program. Check out the list randomizer at www.random.org. The site itself is fascinating… you can read dissertations about the nature of randomness, the difference between a random number generator and a pseudo-random number generator, and all sorts of counterintuitive consequences of randomness. But the list randomizer is what’s made my labs run more quickly.

Try it out. All you have to do is copy your class list from, say, Microsoft excel. Then paste the list in to the website. Press go… and the class list is spit back in random order. Lab partners are read off the screen: the first and second name are partners, the third and fourth are partners, and so on.

The program is good for other purposes besides lab partners. I used it today to choose teams for a little review game in AP physics. I can choose random teams in my intramural league that I run in the wintertime. Other ideas? Post in the comments.

“Recurrent” labs: image distance for a convex lens

I’ve been reading The Physics Teacher journal for over a decade. Every issue contains at least one interesting idea that’s somewhat new to me. I encourage you not to be put off by the frequent buzzword-heavy piece by someone trying to show “scientifically” that his pet new teaching method works… mine each issue for the experiments, demonstrations, and new ways of thinking about old topics.

This month’s issue (May 2009) contains what, to me, is the most revolutionary article I’ve ever read in TPT. Mikhail Agrest, of the College of Charleston, writes about his approach to introductory physics labs, which he calls the “Recurrent” method. Agrest presents a fully developed method that includes pieces of things that I have done, but never completely in the way he suggests. I’m going to try a Recurrent lab tomorrow.

According to Agrest, a Recurrent lab consists of three separate stages. First, an essentially traditional lab is conducted in which a parameter (like the focal length of a lens) is measured. Next, students are asked to use that parameter to predict the results of a slightly different experiment – for example, use the measured focal length to predict the location of an image given an object distance. Finally, students must perform that very experiment in front of the teacher to verify their prediction. Students’ grades are based in part on the accuracy of the prediction.

I’ve done similar experiments in the past, in which students predict an unknown quantity for a grade. The major inspiration provided by Agrest is to let the students develop their experimental method first, before challenging them to make a high-stakes prediction. My own contribution is to make the final prediction into a sort of competitive game: the lower the uncertainty in the prediction, the more credit the lab group can earn.

Stage I: We conduct a standard laboratory exercise with a convex lens. Students project the image of a candle onto a screen, and measure image and object distances. I ask each partnership to set up a graph of 1/do vs. 1/di before they start collecting data – each data point is to be graphed immediately. This way the students better see the relationship between the physical measurements they make and the graph… if they just make a table and graph it later, the lab becomes an exercise in arithmetic manipulation. A substantial part of their grade will be earned for the quality of the graph’s presentation.

Stage II: Once a lab group and I agree that they have investigated a reasonable range of object and image distances, I give them a new object distance: 5 meters. They are asked to use their graph to predict an image distance, including an uncertainty. They will do some calculation, and discover that they’re really looking for the x-intercept of their graph. (Tomorrow, I’ll explain that they’ve found the focal length of their lens.)

I give guidance as to the format of the image distance prediction (i.e. “30 +/- 2 cm), but I let them estimate the uncertainty in any way they please. The rules for stage III will guide their determination of uncertainty.

Stage III: I will compare their measured focal length to the value stated on the box. Eight of twenty points for the lab will come from the accuracy of their measurement. I set up a system of rewards for these eight points:

0 points are earned if the box’s focal length does not fall within the stated uncertainty.
4 points are earned if the measurement matches the box’s focal length, no matter how large or crazy the uncertainty.
7 points are earned if the measurement matches the box’s focal length, and the uncertainty is 10% or less of the measured value.

Then, for all groups whose measurement matches the box’s focal length, bonus points are awarded: everyone gets one point for each group with a larger uncertainty.

I suggest the students imagine that I have hired them to predict the image distance… it is most important that they be RIGHT. After that, the more precise the prediction, the better. My own thought is that this kind of game teaches the deep meaning of experimental uncertainty better than any mathematical exercise. Much credit to Mr. Agrest for the inspiration to refine the experimental approach described here.

(And yes, folks, I'm aware that the picture at the top of the post is emphatically NOT a convex lens. Please feel free to explain how I know that in your comment.)

GCJ

The Physics Walk

I’m getting my class ready for the AAPT Physics Bowl, a national contest which consists of a 40-question multiple choice test. If you haven’t heard of this contest, I highly encourage you to check it out. It doesn’t cost much money; more importantly, it doesn’t cost much time, either. A single 45-minute period is sufficient for participation.

Even better, the physics bowl doesn’t really, truly require any “preparation.” The questions cover an extremely broad spectrum of physics topics, the scope of which is unpredictable from year to year. Therefore, the best way to prepare the class is merely to teach like you always do.

So, Greg, you say, why are you “getting your class ready” for the contest if there’s no preparation necessary? The secret is, what I’m really doing is reviewing for the AP exam using the Physics Bowl as a tool. Not every Physics Bowl problem would be an appropriate AP question, but physics concepts are the same no matter who’s asking the questions. The Physics Bowl provides me with an extra 40 question multiple choice bank every year. Woo-hoo!

I will administer the 2009 contest next Wednesday. This past week, we practiced by taking the 2007 test in class.

Another secret of my preparation is the manner in which I go over a multiple choice practice test. A long time ago, I would simply ask, “Who has questions?” This opening led to a most unproductive class, as only the student who asked the question would pay attention to my answer. My first solution to this dilemma involved the use of a scantron machine. The automatic grading machine provides me a report of how many students got each question wrong. Therefore, I knew which problems really needed discussion. *I* chose the problems to go over in class, and I informed everyone of how many students missed each one.

The next, and most important, step in going over a multiple choice exam is to require corrections. When we take the physics bowl, I award full credit for each question a student gets right; I also award full credit for each question he gets wrong initially, but gets right on a correction. (In a test correction, students write out an explanation for the correct solution to a multiple choice problem. See my previous post for details.)

Just knowing that they will have to correct their wrong answers inspires students to pay attention when I go over the test. Nevertheless, it’s springtime, my classroom has only one small window overlooking the vista of a dirty brick wall, and a young man’s thoughts naturally don’t want to concentrate on the ugly guy in the funny tie who’s droning on by the white board. Minds wander, no matter how energetic and interactive I try to make the class.

Can I prevent minds form wandering? Not figuratively, but I can literally insist on wandering minds… each year my classes take a Physics Walk to go over the practice AAPT Physics Bowl. I warn everyone to wear comfortable shoes and to be on time for class. We head out the door and down the wide, paved path to the Rapidan River. I only have about 15-18 people per class, and all are in decent physical shape – ah, the benefits of the boys’ boarding school, where a daily afternoon activity involving rigorous exercise is a requirement for all students. We can thus walk down and up the path at a good clip while staying together. I have a loud voice, so everyone in the class can hear me easily. We carry our Xeroxed copy of the test, and I go over each problem just the same way I would in class. I explain, ask specific students to give ideas, field questions from the audience, and so on. Since we’re on the move, though, I can see that my students are much, much more focused on the class discussion than they’d otherwise be. No one is doodling, staring out the window, or fantasizing about their date for the formal.

Try it… I don’t know (nor do I care) WHY the Physics Walk has proven to be so effective, I just know it is. If nothing else, I get to leave my dungeon I mean classroom on a 65 degree sunny day.

GCJ

Revealing test question topics

My AP class is ready to take the 2008 -- that is, last year's -- actual free response exam. We've been in real review mode for less than a week. That means that I've covered every possible topic on the exam, but the students are by no means confident yet. Everyone seems a bit overwhelmed by the sheer amount of material they need to know. That's okay, for now. In a month, after lots of targeted practice, they'll be fine.

Normally, when my students ask me what's on a test, I say "everything." Physics is a cumulative subject -- principles from earlier in the year, like force and energy, show up in every subtopic as overriding themes. But philosophically, I don't think I can say I've taught anyone physics if I give them license to forget anything that we covered more than a month ago.

A funny story that came out of my cumulative testing: one year a very bright student just wouldn't let this subject die. Chat kept asking me, "what exactly do we have to know?" He was concerned because a quiz had required the class to know that the period of the earth's rotation was 24 hours, a fact that -- gasp! -- I had not covered in class. "Do we have to know random stuff like that for the test?" He asked. I said yes. "How obscure is the information we have to know? You wouldn't ask us about, say, the gross national product of Tanzania, right?" I basically ignored that question. On the next day's quiz, everyone else got a set of straightforward multiple choice questions, while Chat's paper said, simply, "What is the gross national product of Tanzania?" He laughed with me, but I would have given him full credit had he answered the question correctly.)

A few years ago I took an idea from my history department colleagues. They occasionally distribute a list of possible essay questions before a test, and then use one of the possible questions verbatim on the actual test. The idea is, students will too often throw up their hands in despair if they are faced with studying for a broad spectrum test. But, if they have something concrete to prepare, they do much more work ahead of time, and that preparation is productive.

Now, I'm not going to give my test problems out ahead of time -- that would defeat the purpose of testing. Instead, in general physics I began announcing the general topic of each question. Even if all 7 questions covered every possible topic, the class felt better knowing exactly which question would cover which topic. They prepared in an organized manner. They entered the test with confidence, and performed well.

I state the topic of each question for every general physics test beginning with the first trimester exam. Of course, I have to be very careful not to fall into the trap of revealing too much. I do not not NOT want to be that teacher who says stuff like "I'd really suggest studying the coefficient of friction when a 20 kg sled comes to rest over a distance of 50 meters, hint hint hint. That might show up on the test." The test must be a fair evaluation of what the class knows and doesn't know. I don't believe I'm giving away anything by stating, for example, that they'll see a collision problem -- they should have been able to guess that themselves!

I've never given out the topics of AP problems, reasoning that the class doesn't get such a benefit on the May exam. But, for the first time this week, I tried announcing topics. The picture at the top of the post shows my whiteboard from this morning, when I foreshadowed the 2008 AP Physics B free response. I could feel some of the students' tension evaporating while I wrote -- "Ah, so I don't have to study circuits, they won't be there. Thank goodness." I was careful to point out that they will, in fact, be expected to understand topics that aren't covered this time; but we'll work on those things later. For now, my class is spending the evening watching basketball and reviewing just these seven topics. We'll see how they do tomorrow.

GCJ

Magnetic field due to a current carrying wire

Reader Scott Milczewski, who teaches at Brooklyn Technical High School, asked me about the deflection of a compass due to a current carrying wire. The question was, can I easily get enough current to see a visible deflection? Or do I need a special high-voltage setup?

The picture to the right shows my setup. The power supply is a standard Elenco Precision, and I'm using the variable voltage input. I don't use much voltage at all -- just a few volts gives me enough current in the wire to see a deflection.

The pictures below show the experiment itself. On the right you see the wire carrying no current... it's aligned (approximately) with the earth's magnetic field. The white end of the compass needle points north. In the left-hand picture, the wire is carrying a current from right to left. By the second right hand rule, this current produces a magnetic field beneath the wire pointing west. (Toward the bottom of the picture. Yeah, sorry, I should've aligned the compass markings with the earth's cardinal directions, but I didn't think of that.

So, why doesn't the compass needle point straight to the bottom of the picture, in the direction of the wire's magnetic field? Because the earth's field is still stronger. In fact, this setup could be used to calculate the earth's magnetic field. Use an ammeter to measure the current in the wire. Use the equation

to calculate the magnetic field due to the wire at the position of the compass needle -- that means the variable r will be equal to only a few millimeters, the distance from the wire nearly to the table. Then, use vector analysis -- the wire's field is perpendicular to the earth's field, and we know that the vector sum of the two magnetic fields points about 30 degrees down from the earth's field. That should be sufficient to get close to the 10^-5 T that is the typical magnitude of the earth's magnetic field.