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25 May 2009

The Wall of 5s: Inspire your students with local history

Sports teams are nearly obsessed with their history. Who was the best catcher in Cincinnati Reds history? Johnny Bench’s jersey is prominently displayed above the outfield fence. In what years did the Boston Celtics win the NBA title? Look at their banners. Even at the high school level, one is likely to see championship banners hanging from the rafters in the gym. For those with competitive swim teams, it’s impossible to avoid the large board with pool records, team records, league records, state meet records, national records, world records, solar system records, and so on.

Why do sports teams advertise their individual and team successes so blatantly? For one, public displays help build a community of fans and team alumni. History is a huge part of sport. People want to point to an artifact, turn to the person next to them and say, “I was there.”

(Baseball is my favorite professional sport. I watch games with thirty seasons of context, even more than that if you count how much I’ve read and the stories passed down from older generations. Yet, I’m cognizant that without history, baseball seems like merely a lot of random throwing, occasional running, and men scratching themselves in polyester suits.)

Furthermore, public reverence for history inspires a new generation of players and aspiring players. Little catchers in Cincinnati pretended to be Johnny Bench. It’s humbling for a 21 year old first-time major leaguer to enter Yankee Stadium, knowing he’s playing on the same grounds* as the holy trinity of Ruth, Gehrig, and DiMaggio. Rookies are not only awed by history, though, they are inspired by it. Someone who sees the pool record in the 400 individual medley displayed prominently on the wall might, consciously or not, make it her goal to get her own name up there someday.
*Or, as of 2009, next door to the same grounds, anyway

So why do I mention all this in the context of a physics teaching blog? I encourage you to build your own community of physics students through recognition of your own class history.

In my classroom, I hang banners from the walls. A poster with a giant “5” on it hangs for each year I have taught AP physics; on that poster are written the names of each person from that class who scored a 5 on the exam. We sometimes come in first or second in or region in the AAPT Physics Bowl; when that happens, we hang a poster. We’ve had success in the US Invitational Young Physicist Tournament; that means a banner for each year of coming in first or second.

Now, I faced some criticism for my “Wall of 5s” in my early days of teaching. Administrators and parents fretted that I didn’t care about my students who were going to earn less than a 5. Well, that was a ridiculous and offensive suggestion, I thought. The track team proudly displays their team records, but does anyone ever suggest that the track coach doesn’t care about his runners who aren’t record holders? Lower Marion High School in suburban Philadelphia retired Kobe Bryant’s jersey; does that mean that their basketball coach cares any less about his current team than his NBA all-star alumnus? Of course not. So I didn’t appreciate the suggestion that I was incapable of teaching ALL my students in the presence of a board honoring the best.

(That said, I do make a point to repeatedly remind the class that, during the school year, I care less about their scores than about their progress, and that I do love and support every one of my students regardless of what score they end up with. I concede that students need to see that love and care in my words as well as in my actions.)

The other objection I heard regularly was that honoring my students with 5s so prominently might cause hopelessness or intimidation in the next year’s class. However, I’ve found precisely the opposite effect: the Wall of 5s is INSPIRING to the next year. Why? In the fall, my current students see the names on the Wall, they know these Jacobs Physics alumni who are just one year older than they. Current students see that not only the very top “genius” level folks are getting 5s, but also some of the folks who come off as ordinary get their names up there. They see viscerally that it doesn’t take an 800 SAT math in order to ace the AP physics exam, because they know people who had only 600 SATs but who nevertheless made it onto the Wall. The Wall of 5s buys me a lot of credibility: “If THAT guy can get a 5, then so can I.”

In the end, these objections quieted, and my class just made the blank template for my 12th poster in the Wall of 5s. It is not at all uncommon for an alumnus to make a special trip down to my classroom for the express purpose of showing his sibling / parent / girlfriend his name up on the Wall of 5s. Occasionally they take pictures.

I’ve a couple times had parents offer to revise my crudely hand-drawn posters into framed, professional-looking wall hangings. I don’t want that. I love the fact that the design for the “5” posters initiated with a student (I think it was Katie Toews, class of 1998 at my previous school); I love the fact that since Katie made the first few, each class has colored in their own poster. It's all about building community.

21 May 2009

Conceptual physics exam review – momentum

A few weeks ago I described a review exercise for the AP exam involving a classroom response system, aka “clickers.” I divide the class randomly into teams of two, and ask a series of multiple choice questions. Teams are given plenty of time to discuss the answer, we go over the answer, and points are awarded – one point for the correct answer, and one bonus point for any group that got the answer WRONG. (Why this scoring? It encourages discussion within the group, but discourages bright students from giving away the answer to the class.)

This morning I covered a colleague’s 9th grade conceptual physics class. John asked me to run a review on the concepts of impulse, momentum, and conservation of momentum. He warned me that the students were likely rusty… it’s been months since they covered these ideas, and the students weren’t necessarily nailing everything to begin with.

In such a case, I like to ask a variety of multiple choice questions about the same physical situation. Many of the questions are simple recall, intended to remind everyone about a fundamental fact that must be used with a following question. (In the exercise, I reveal and discuss each question one at a time.) Because I don’t change the problem setup, students don’t have to read and refocus for each question – they can focus directly on the relevant concepts. The problems below are inspired by an AP free response problem. I distributed JUST the figure and the three-sentence description in hard copy to each group.

Beware of your time constraints. I tend to allow 1.0-1.5 minutes for each question, followed by several minutes of discussion. These take a long time! I got through seven in 30 minutes.

A 70 kg woman and her 35 kg son are standing at rest on an ice rink as shown above. They push against each other for a time of 0.60 s, causing them to glide apart. The speed of the woman immediately after they separate is 0.55 m/s.

1. What is the equation for momentum?
(A) mv
(B) ½mv2
(C) Fv
(D) mg
(E) ma

2. What are the units of momentum?
(A) newtons
(B) m/s2
(C) joules
(D) watts
(E) kg·m/s

3. What is the magnitude of the total momentum of the two people before they push?
(A) 39 kg·m/s
(B) 19 kg·m/s
(C) 58 kg·m/s
(D) 20 kg·m/s
(E) 0 kg·m/s

What is the magnitude of the total momentum of the two people AFTER they push?
(A) 39 kg·m/s
(B) 19 kg·m/s
(C) 58 kg·m/s
(D) 20 kg·m/s
(E) 0 kg·m/s

5. What is the woman’s momentum after the push?
(A) 39 kg·m/s to the left
(B) 19 kg·m/s to the left
(C) 58 kg·m/s to the left
(D) 20 kg·m/s to the left
(E) 0 kg·m/s to the left

6. Who has more momentum after the push?
(A) The woman
(B) Her son
(C) Both have the same momentum

7. What is her son’s momentum after the push?
(A) 39 kg·m/s to the right
(B) 19 kg·m/s to the right
(C) 58 kg·m/s to the right
(D) 20 kg·m/s to the right
(E) 0 kg·m/s to the right

8. Who moves faster after the push?
(A) The woman
(B) Her son
(C) Both move the same speed

9. What is her son’s speed after the push?
(A) 70 m/s
(B) 0.23 m/s
(C) 0.90 m/s
(D) 0.55 m/s
(E) 1.1 m/s

10. Whose momentum changes more during the push?
(A) The woman
(B) Her son
(C) Both have the same momentum change

11. What is the term that means “change in momentum?”
(A) Kinetic energy
(B) force
(C) impulse
(D) potential energy
(E) power

12. Impulse is change in momentum. What is another equation for impulse?
(A) Mass time acceleration
(B) Mass times velocity
(C) Force times velocity
(D) Force times time
(E) Mass times gravitational field

13. Who experiences more force during the push?
(A) The woman
(B) Her son
(C) Both experience the same force

14. Who experiences more acceleration during the push?
(A) The woman
(B) Her son
(C) Both experience the same acceleration

15. By how much does the woman’s momentum change during the push?
(A) 39 kg·m/s
(B) 19 kg·m/s
(C) 58 kg·m/s
(D) 20 kg·m/s
(E) 0 kg·m/s

16. What are the units of force?
(A) newtons
(B) m/s2
(C) joules
(D) watts
(E) kg·m/s

17. How much force did the woman experience during the push?
(A) 21 N
(B) 71 N
(C) 23 N
(D) 700 N
(E) 65 N

18 May 2009

Last test in general physics

The school year is winding down now.

(So why haven’t you posted in a week, then?)

Well, because it was busy last week: AP exam and such. I’ll have lots more to say about the AP, especially as I plan to grade problem B2. Until then, though, I’ll talk about finishing the year in my general physics course.

I’ve always done circuitry as the last unit in general physics. It’s not necessarily easy, but it’s different and fun, with lots of hands-on lab work. When I am convinced that students can solve for current and voltage for each resistor in a simple circuit, we move on to building an AM radio. I buy an Elenco AM radio kit for each student. (You can get these through Fischer Scientific… or you can get them even more cheaply online if you search hard enough.) I show them briefly how to solder, then I have them follow the instructions to assemble the radio. It takes about five class days, and about 70% of the radios end up working.

Nowadays, I’m not allowed to give a final exam to my seniors – and all but three of my class are seniors. So I give a last test about a week before the end of school. This isn’t a cumulative final exam, but rather includes topics from the last trimester: optics, circuits, and astronomy.

For optics, I give question 6 from the 2007 AP physics B exam. This is an experimental question in which students graph 1/di and 1/do for a lens. My class did this very experiment a few weeks ago. Thus, I can expect my general class to perform well even on a somewhat difficult AP problem.

For circuits, I give question 3 from the 2007 physics B exam. This question begins with a ranking task about a simple circuit, and then asks for some calculations. Once again… this is EXACTLY what we have been doing in class.

For astronomy, I ask a series of seemingly simple questions about the sun, earth, and moon. Careful… my students consider these kinds of questions quite difficult. This year I spent more time than ever on just basic solar system astronomy, and it’s paid off – but still, very few people got these problems completely correct.

If you ever decide to run a 1-2 week astronomy unit, these questions, among others, can help you set the goals for your topic coverage. Take a look at the problems below.

But first, why did I post the Corona ad in which the moon serves as a lime? Something is astronomically wrong with the advertisement. Post a comment or send an email to suggest what that is.

1. (15 points) The tilt of the earth’s axis is 23o. Consider the view of the sky from the vantage point of the north pole. Justify each answer briefly.

(a) On June 21, what will be the highest altitude of the sun above the horizon?
(b) On the equinoxes, what will be the highest altitude of the sun above the horizon?
(c) On December 21, what will be the highest altitude of the sun above the horizon?
(d) Describe the path that the sun takes through the sky over the course of one day in June. Explain your reasoning, of course.
(e) Now consider a time of day and year that you can see the stars from the north pole. Where in the sky will you see the north star?
(f) Describe any circumpolar stars you would see. Explain your answer.

2. (15 points)
(a) During what phase of the moon can a lunar eclipse occur?
(b) Show with a sketch the relative orientation of the earth, moon, and sun during a lunar eclipse.
(c) Explain why we don’t see a lunar eclipse EVERY month.
(d) At what times during the day and/or night is a full moon visible? Explain.
(e) Explain why we see phases of the moon, i.e. why we sometimes see crescent or half moons.

08 May 2009

Mail Time! -- adiabatic vs. isothermal process

Reader Elizabeth Walker writes:

"I have trouble telling the difference between an isothermal process and an adiabatic process on the graph. What am I missing?"

The Nachoman responds:

In an isothermal process the product of PV will be the same everywhere. An adiabatic process will drop below the isothermal process (assuming expansion). Why? Because ΔU = Q + W. An adiabatic process MEANS no heat added or removed, thus Q = 0.

The gas expands, so work is done BY the gas. That means the variable W is negative. By the first law, then, ΔU must also be negative... meaning the temperature of the gas must decrease. The product of PV will be smaller as the gas expands, meaning that the adiabatic process drops below the isothermal process on the PV diagram.


BOUX day

Every baseball announcer has a catch phrase; similarly, every physics teacher has some personal or instructional quirk that identifies and (hopefully) endears him or her to the class.

My own catch phrase is “BOUX!” This comes from an old Dave Barry column, in which he describes the difference between New York Mets fans (who say “Boo! You stupid bum!”) and Montreal Expos fans (who say “Boux! Voux dumme bumme!”) Or something like that.

Throughout the year, I write “Boux!” on papers that demonstrate major fundamental errors. For example, saying that a box must move to the right because it experiences a net force to the right – Boux! Saying that the acceleration of a ball is zero at the peak of its flight because its velocity is zero – Boux!

On the last day of class, I open a blank page in Microsoft word with the word “Boux!” at the top. The class is encouraged to shout out mistakes they might make that would earn a “Boux!”. This exercise serves several purposes. It is cathartic, in that the class sees that EVERYONE, even the smartest student, has at one time or another earned a boux. Furthermore, as students begin to think about the three hour exam coming up on Monday, they remind themselves of mistakes that they can easily avoid. My hope is that if someone begins, say, to use conservation of kinetic energy in a collision problem, that person might stop himself, saying “oh, wait, Mr. Jacobs would sure say “Boux!” to that, ha ha.”

The whole exercise is generally lighthearted and fun… and it produces an interesting study guide. Here’s a list of the class’s “Boux!” list from last year. Enjoy! And good luck on Monday.

1. Adding electric fields without considering direction

2. Putting centripetal force on a FBD

3. Mg always points down, not at an angle

4. Acceleration does not equal zero at the top of a ball’s flight

5. Units (or numerical values) on variable problems; no units on a numerical problem.

6. Adding voltages with directions

7. Putting a sign on the charge when calculating electric field

8. Using a point charge equation when a field was produced by the Almighty Bob

9. Putting anything other than a force on a FBD

10. One rope = one tension (Jacobs Law of tensions)

11. Object distances are never negative

12. Assuming equilibrium for an Fnet problem when a is not zero

13. Mixing up sin and cos when breaking vectors into components

14. Putting both components and a force itself on a FBD

15. Leaving a free response problem completely blank

16. Saying F=ma when only FNET = ma

17. Setting a random voltage = IR

18. Assuming that if heat is added, temperature goes up

19. Assuming KE is conserved in a collision

20. Using left hand for a right hand rule

21. Drawing rays that refract through a mirror or that reflect off of a lens

22. Using kinematics when acceleration is not constant.

23. Fishing for equations

24. Putting acceleration anywhere but toward the center in circular motion

25. A normal force does NOT necessarily equal mg!

26. Putting Fn not perpendicular to the surface

27. Measuring an optics angle not from the normal

06 May 2009

AP exam review: 2004 B1, Roller Coaster

It's time for that final AP exam review. Today's post gives a multiple choice review exercise based on an old AP exam question; tomorrow I'll describe my final classday activity.

As I've discussed before, just doing an AP practice problem does not provide sufficient review. Practice problems must be followed up somehow. Usually I have students do corrections on what they missed. But for a fun change of pace in the spring, I get out my classroom response system (my "clickers") and run a little contest for extra credit.

Before I go on, please note that (a) this contest works just fine without "clickers" -- just have the groups write their answer really big on a piece of paper and hold it over their heads. And, (b) this type of review is not confined to AP physics. AP questions can be carefully selected, or edited, for use with your general high school physics class. You can use this as final exam review.

How the contest works
This contest is based on problem 1 from the 2004 AP physics exam. For lawyerly reasons I can't post the actual question here, but you can get it via this link:

First, I have the students do this problem to the best of their ability on their own. This usually means as a quiz.

Next, I use to divide the class into teams of two. Each team gets one clicker

Now, I ask the multilpe choice questions that you see below. I ask them one at a time, giving at least 60 seconds for the teams to discuss the correct answers. After the 60 seconds, I collect responses, and then go over the correct answer

Scoring: Each team gets one point for the correct answer, and one more point for each group who doesn't get it right. There are a bazillion ways to score a contest like this... I've found that this particular scoring makes students less willing just to listen to the smartest students without thinking for themselves. I get good arguments amongst the class, which is what I'm after.

Here are the questions I ask:

1. At which labeled point does the car attain its maximum speed?
(A) I
(B) II
(D) IV
(E) V

2. To calculate the value of the car’s maximum speed, do we use kinematic equations (vf = vo + at and so on) or conservation of energy?
(A) Kinematics must be used
(B) Conservation of energy must be used
(C) Either kinematics or energy conservation may be used
(D) Neither kinematics nor energy conservation will produce a solution

3. What general formula for potential energy do we use here?
(A) mgh
(B) ½mv2
(C) ½kx2
(D) qV
(E) (3/2)nRT

4. What general formula for kinetic energy do we use here?
(A) mgh
(B) ½mv2
(C) ½kx2
(D) qV
(E) (3/2)nRT

5. To calculate the speed at point B, which of the following formulas is correct?
(A) mg(90 m) + 0 = 0 + ½mvB2
(B) mg(50 m) + 0 = 0 + ½mvB2
(C) mg(40 m) + 0 = 0 + ½mvB2
(D) mg(30 m) + 0 = 0 + ½mvB2
(E) mg(20 m) + 0 = 0 + ½mvB2

Which of the following free body diagrams correctly represents the forces acting on the car when it is upside down at point P?
(A) A
(B) B
(C) C
(D) D
(E) E

What is the weight of the car?
(A) 700 N
(B) 7000 N
(C) 700 kg
(D) 7000 kg

What is the magnitude of the NET force on the car?
(A) mg
(B) Fn
(C) Fn – mg
(D) Fn + mg

What is the magnitude of the car’s acceleration?
(A) 0 m/s2
(B) 28 m/s2
(C)[(28 m/s)2 / (20 m)]
(D) 10 m/s2

What is the direction of the car’s acceleration?
(A) Down
(B) Up
(C) Left
(D) Right

Imagine changing the (still frictionless) track such that point B is still 50 m off of the ground at the top of a circular loop, but the circular loop has only a 15 m radius. What happens to the speed of the car at point B?
(A) It is smaller than before
(B) It is larger than before
(C) It is the same as before

Consider the same track with NON-negligible friction. What is true about the speed at point B now?
(A) It is smaller than 28 m/s.
(B) It is larger than 28 m/s.
(C) It is still 28 m/s.

How could we adjust the track with NON-negligible friction so that its speed at point B is the same as we calculated previously?
(A) Make the radius of the circle smaller
(B) Make the radius of the circle bigger
(C) Make point B closer to the ground
(D) Make point B higher off the ground

05 May 2009

Upcoming public appearances

As the school year winds down, it's time to make summer plans. I will be running several AP summer institutes, and I will be doing a good deal of travel.

If you'd like to attend a week-long Jacobs Physics seminar (also known as an AP Summer Institute), you have two opportunities. I will be at Morehead State University in Morehead, KY from July 13-17; I will be at Manhattan College (which is NOT in Manhattan, but is in the Bronx) from July 27-31. To sign up for these College-Board sponsored sessions, go to either university's website.

I encourage you to attend the summer institutes even if you don't teach AP physics, or if you have seen someone else's AP institute. Over the week-long course, I emphasize quantitative use of demonstrations by SHOWING you how I do and use these demos. I discuss the "Less is More" approach to physics teaching. You will get my library of assignments -- quizzes, tests, and homework -- on disc, along with the opportunity to discuss their use.

I will be traveling a bit during the rest of the summer, including to the AP reading in June. Although I am only giving two formal summer institutes, I offer my services at other times. If you would like me to talk physics teaching with you and/or your colleagues, I'll be happy to. If you want a formal seminar, I can negotiate fees with the sponsoring organization.

However, if you want just an informal discussion for an hour or two, I will do that in exchange for all the pizza I can eat at the most lowbrow pizza joint near you. (Pictured is Big Ed's Pizza in Oak Ridge, Tennessee, which is up with Langel's of Highland, Indiana on my favorites list.) Please let me know if you're interested!


June 8-18, Fort Collins, CO

June 20-22 or so, Pittsburgh, PA, and perhaps southern Ohio

July 13-18, Morehead, KY

July 27-31, New York, NY

August 10-24, San Francisco, CA (with a stop in Yosemite)

All the rest of the time I'm in Woodberry Forest, VA, which is between Charlottesville and Washington.