AP Physics 1 2016 problem 3 - bumps on an incline

The question in question asked about a cart on a long, bumpy track.  Specifically, it demanded a sample velocity-time graph for the cart as it crossed several bumps; then it asked what should happen to the cart's speed in between bumps if the angle of the track or the distance between bumps changed.  

I heard from and about a number of teachers who complained.  What kind of crazy-arse experiment is this?  No one does this in their class.  Ridiculous.  The AP Physics 1 exam has jumped the shark already.

My reaction to this question was, "Cool, what a great experiment, I wonder if I could set this up in the laboratory?"  And this week, Zach Widbin did set it up.  

Zach's teaching in Phoenix, but he's from New York, so he attended my summer institute in Mahopac, NY.  On the last day of the institute, teachers spend a couple of hours playing in lab, setting up experiments that they can share and use in their own classes.  

He inclined a PASCO two-meter track by two degrees.  He wrapped rubber bands around the track at 40 cm intervals, providing the bumps -- see the picture at the top.  The cart was a PASCO smart cart, which sends velocity-time data to an ipad via bluetooth.  The velocity-time graph is to the right.  

The original question asked what the graph should look like... but also, what should happen with a steeper incline?  With a larger space between bumps?

Well, Zach checked those things out, too.  The steeper incline gave a faster max speed.  He did smaller bump spacing, and got a smaller max speed.

The AP question itself postulated a very long track, with 100 bumps.  Zach only had a few bumps.  But there's no reason we couldn't tie together several of these two-meter tracks and try this again.  In fact, PASCO makes modular 50-cm plastic track pieces which can fit together in as long or short a string as you'd like.  Someone who has access to a wood shop (or, for those who prefer sexy terminology, a "maker space") could get a long plank, and then drill bumps into the surface.  Zach's approach isn't the only way to go - it's the one-morning-at-an-institute version.  I'd love to see pictures of your own setup.

Making appropriate simplifying assumptions is a physics skill that we all must teach.

The comment section of my post about the 2017 AP Physics 1 exam is full of interesting discussions about the recent test.  One of the reasons I write this blog is to provide a venue for intelligent, professional teachers to share ideas and find advice.  I appreciate the good-faith questions, the reasoned comments.  I don't read posts in other venues about recent AP tests because they are too often full of us-vs.-them bile, full of ignorant complaints about the exam that really boil down to "I and my students were unprepared for this exam, and now I'm angry about my own failure."  Those who post to this blog display far more class than that, and I appreciate it.

The purpose of this post is to respond to and rebut some of the comments about the 2017 exam.  I'm going to say some of the posters are wrong; or at least that they hold some incorrect basic assumptions about AP physics.  I want to be clear -- I have total respect for those who have posted.  I mean no criticism of their motives.  It is entirely appropriate to discuss, or even criticize, AP exam questions.  The College Board does not and should not demand Trump-style loyalty; as much as I support those who create the AP Physics 1 exam, I will not fall into the role of Fox News.

Nevertheless, I see a continual theme in these comments, and in questions from teachers at my summer institutes, that betrays a fundamental misunderstanding about teaching first-year physics.

It is our job to teach students to make appropriate simplifying assumptions about physics problems.

A lot of discussion back in May concerned problem 4 on the 2017 exam.  A light disk collides with a heavy, pivoted rod.  The question asked, essentially, where should the disk hit the rod in order to induce the largest angular speed in the rod - close to the pivot, or far away from the pivot?  The straightforward solution required referencing either torque or angular momentum.  The best answer explains that the angular momentum of the disk mvr is larger when r, the distance from the pivot, is larger, giving the disk more angular momentum to transfer to the rod.

But wait, some folks said.  The problem never said the rod was uniform.  What is the rod weren't uniform?

As far as I can see, the answer still stands.  No matter the shape of the rod, the disk still transfers its angular momentum to the rod, and thus farther from the pivot means more angular momentum transferred.

Commenters made several arguments.  Let's start with:  (1) If we look at some possible mass distributions for the rod and disk using computer simulations, it's possible in some cases to get bigger speeds closer to the pivot.

I don't see it myself, but I'm not ruling out the possibility.  I know the problem stated that the rod was much more massive than the disk; I strongly suspect that the only way to get bigger speeds closer to the pivot is to make the disk itself big.  That said, I could easily be wrong here.

The big, friendly point, though, is that it doesn't matter.

The first step in solving any physics problem, at any level, is to make appropriate simplifying assumptions.  For example, when we calculate the normal force on me when I stand still, we ignore the buoyant force of the air on me, we ignore the force of Jupiter on me.  We just say the normal force in this case equals my weight.  It's not useful physics to say, "Well, what about the case when the wind is blowing 50 mph and your right foot has trouble staying planted?  And that buoyant force can in fact be calculated, it's nonzero.  Oh, and the force of Jupiter exists, it's just very small compared to your weight."

These statements are entirely correct... and they're entirely irrelevant to the problem as stated in an AP Physics 1 class.  We always make the simplifying assumptions that allow us to solve the problem.  THEN, if it turns out that our solution doesn't match a measurement, we can consider if other issues must be taken into account.  This is not just an introductory physics thing - this is how I was taught to do research.  Solve the basic problem first, then add complexity.

Once you have to concoct far-out situations to perhaps find a situation that could cause an argument, that argument is about semantics, not physics.  If you sound like a lawyer, you're wrong.

(2) But what if a student was confused, and dealt with a non-uniform rod?

Firstly and most importantly, no one did.  At all.  I was table leader for this problem.  I asked everyone I knew to watch for anyone who treated the rod as non-uniform, or for any student who indicated that she might be confused by the lack of specificity.  Not one of the 170,000 students that we looked at was, in fact, confused by the uniformity or non-uniformity of the rod.  Not one.  

I didn't ask development committee members, but I suspect they didn't consider the structure of the rod, either.  Set up the experiment in your classroom - who's going to use a non-uniform rod?  And if they do, either (a) the problem still works the same way, or (b) you have a problem way, way beyond the scope of AP physics 1.  

It is our job as physics teachers NOT to lawyer up in response to a question that might, maybe, in a professional physicist's mind have a deeper layer.  Rather, it is our job to show our students how even seemingly complex problems can have simple solutions which can be verified by experiment.  It's our job to teach students to answer the simple question rather than become paralyzed by the complex details.  We must show how "eh, the population of the US is something like 300 million people" rather than "we cannot make any statement about the US population because someone is born every 7 seconds, rendering any estimate immediately obselete.  

Excessive precision and detail is not to be lauded.  Excessive precision and detail is the enemy of understanding in introductory physics. 

Making students - not parents - self-select for an honors or AP course

An oft-repeated refrain: due to the ignorance of counselors and pressure from helicopter parents, too many students who aren't ready tend to be placed in advanced physics courses.

Understand that I believe in physics for all, not just for the best and brightest.  However, in order for a physics class to be successful, the participants have to be ready academically for the level of the course.  When students reach to take a level of physics that's beyond them, they generally have a miserable time... and they drag down the class such that everyone has a sub-optimal experience.  

Why reach?  When there's a general-level physics course available, the only people who should be placed in a higher course are those who would be bored by the simplicity of the general course.  Honors placement isn't a prize to be won, it's a match to be made.  Epidemic at the high school level is the student who is inappropriately pushed to take honors-level science and math courses, then successfully whines and argues for grades, just to be placed in an even higher-level course then next year... then crashes and burns in college, where the student-emperor is revealed to have no intellectual clothes.

I've talked to more than one high school teacher who adapted in ridiculous but practical fashion by cutting out unweighted, general-level courses altogether.  These folks label their basic course "honors physics," and their advanced course "AP physics."  They teach "honors physics" sort of the same way I teach my ninth grade conceptual physics.  Whatever works, I suppose.

I never want to shut a student out from ever taking an advanced physics course.  When physics teachers kvetch about unprepared students in their classes, the classic riposte is that "tracking" permenantly marginalizes those who don't have resources at home to push themselves academically.  This is a legitimate and important point.  Many not-so-great students could, in fact, handle advanced physics if they had been introduced to high-level quantitative skills early in their academic careers.  One of our goals as high school physics teachers should be to cast a wide net to catch everyone who can possibly learn our subject at some level.  

And right there is why I love teaching conceptual physics.  Any college-bound student - and probably a significant fraction of non-college bound students, too - can handle rigorous physics with no calculator use.  And a large fraction of conceptual students are then fully capable of success in AP Physics 1 as a second year course.

The trick, then, is to identify students ready for AP Physics 1 as a first-year course, while at the same time teaching an outstanding lower-level course to those who don't meet that bar.  How to do that in a political environment in which parents whose special children aren't selected for AP Physics feel personally slighted and storm your boss's office demanding retribution?

Your answer must depend on your particular school environment.  It likely begins with relationship building among the science faculty and administrative decision makers.  Make sure your counselors and principals and deans not only understand your placement procedures, but also the reasons behind your procedures.  Reassure them that you are serving all students, that those pitchfork-wielding parents' children will still be well-served by your program.

An elegant solution that has worked for us has removed placement decisions entirely from parents and administrators.  We place all 9th graders in a general-population conceptual physics course at year's beginning.  Three weeks in we resection, creating one AP Physics 1 section (labeled as "honors physics.")  Below is the procedure, as it's described to interested faculty and parents.

Students who are interested in honors placement have been asked to do two things.  We have been very clear with all sections, both orally and in writing, about the process.

(1) Honors practice problems.  We are posting one to two extra problems each week which are at the level expected of honors students.  Those who are considering honors are asked to solve these and turn them in.  We encourage the students to discuss their solutions with us before they are turned in if they have questions.  

(2) Honors quiz/test questions.  Each of our first three weekly assessments includes an honors-level question similar to the honors practice problems.  We ask the honors candidates to attempt these problems -- this gives us a gauge of how well they understood the practice questions.

After three weeks of class, the physics teachers will choose the honors section based on a holistic evaluation of all interested students.  We look at their performance and effort on the honors practice problems; at their performance on the honors assessment questions; at their effort and performance on the regularly assigned work, including laboratory work; and at whatever progress they do or do not make in the first three weeks.  We've found that the class is nearly self-selecting, in that those who attempt the honors problems figure out within a week or so whether they can -- or whether they want to --  handle that level of work. 

One important point about honors selection is that students must themselves want to take on this level of work.  We’ve had a number of students over the years who could possibly handle the material in honors, but they chose not to do the test questions, and thus to remain in regular conceptual.  That was a good choice universally for those students – they earned high grades, then had the opportunity to take the honors course in their senior year.  We are purposely trying to divorce the honors decision from the parents, advisors, and even physics faculty -- the students are the ones who are in large part deciding whether they can or want to do the work.

Deriving expressions in AP Physics 1

Reporting from the AP reading here in Kansas City, where I've discovered that Jack Stack barbecue is excellent, but still no match for Gates.  And, where I've been immersed for days now training people on the rubric for the 2017 AP Physics 1 exam problem 3.  

Based on my experience here, I think it's worth a reminder to teachers about the expectations for "deriving" an equation on an exam.

Introductory physics is all about communication of ideas, and not as much about getting the One True Answer to a problem.  Physics is not a math class.  

Students in my class may whine (early on, at least) about not getting full credit for a poorly presented problem that nonetheless includes the correct answer.  Okay, so your English teacher requests an essay with textual evidence analyzing Shakespeare's characterization of the Romeo/Juliet relationship.  Your entire essay: "He loves her."  You earn a failing grade, of course.  How effective or intellectually honest do you think it would be to whine that your essay deserves an A because the answer is right?  I mean, the answer is in fact right...

A derivation, like any physics problem, is an exercise in communication -- but a derivation requires communication primarily in mathematics.  Just because the answer is right, just because a student knows in her head what mathematical steps she intends to take, that doesn't mean the derivation has served its purpose.

So what SHOULD we expect from students on derivations?

1. Start from first principles, and explain what first principles you're using. That means something from a "facts of physics" list: Newton's laws, Kirchoff's laws, conservation principles, the definition of acceleration or impulse or power... most anything on the AP equation sheet or on my fact sheet will work.

2. Communicate the reasoning for each step.  I think words are best here -- an annotated derivation can hardly fail to earn credit where correct.  Try circling terms and explaining what they mean.  Try telling the reader why you've substituted various terms into the equation you began with.

3. Show enough detail that a strong physics student at another school can understand without asking for clarification.  The audience should NOT be the expert physicist.  I personally don't need to derive an expression for the acceleration of a three-body system connected over a pulley, because I've done so many of those problems that I can write the answer based on memory and instinct.  My students, though... they need to start with Newton's second law for the system, explaining what expression is used for each term and why that expression is relevant.  

4. Use algebra to communicate, not to solve.  I often see students take three steps merely to rearrange terms in an expression, using annotations like "commutative property" and "divide both sides by m."  Assume the audience knows how to do math.  Use the way the math is laid out to highlight reasoning.  For example, if you have energy terms before and after a collision, write all terms clearly in a single line, with before the collision left of the = sign.  Label each term with a circle and a couple of words.

I'm sure readers - both blog readers and AP Readers - may have some further thoughts.  Please post in the comments.