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## 29 June 2017

### AP Physics 1 2016 problem 2 - 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.

1. Not going to lie, I didn't much care for that particular problem. When I've run this by my students who took that exam and then took my AP Physics 2 class the next year, the results basically read like an IQ test more than a physics test, because it's written as a thought experiment and not a real experiment. What I mean by that is, students fell squarely into two camps: those who guessed wrong and then tried to justify their guess with physics reasoning that was doomed from the start, and those who guessed correctly and whose answer probably looked reasonable pretty much no matter what reasoning they followed it up with. Furthermore, every student who got it wrong came away with the conclusion, "Oh well, I guessed wrong [about the graph shape]," rather than learning anything from it.

I'd have liked this problem better if they had done what they did with the Lab Groups Finding Coefficients of Friction problem from this year's exam, and collected class data and asked the students to analyze it rather than predict the shape of a graph. That way, students could show their analytic skills in a more step-by-step manner that more accurately reflects their level of scientific knowledge.

Lastly, a more general point: "Predict what will happen," or, "Predict what the data will look like," is always going to be a tricky format of question in a course where hypotheses can and will be wrong all the time, and that's supposed to be okay, as long as one knows how to test it and determine from data the reason why the hypothesis turned out to be incorrect. So I guess what I'm saying is that Bumps was a theorist's question in what I thought was supposed to be primarily an experimentalist's course and exam.

2. I must not have been following you closely when last year's exam was released. I have to say that I rather like the bumpy track question because there shouldn't be any guessing at all! They tell you what happens, and the rest starts with basic physics based on just a few obvious forces. Sort of the same point you made about this year's exam. But that isn't why I posted a comment. I have a question about those Pasco Smart Carts.

The data show the same kind of drop outs that we get with a Pasco motion detector and a cart with a reflector. Annoying, which might be a good enough reason to spend money (money we don't have right now) to get some. How does it happen in this case? Is it because they get distance from a wheel encoder, which fails when the cart bounces off the track momentarily in this experiment? If so, the data should be "perfect" otherwise, but I see odd defects for smooth sections of the track. Are those just the usual minor effect of increased uncertainties resulting from subtraction when the program calculates the velocity estimate, like we also get with a motion detector? Are they worth the money?

3. Oh, and kudos to Zach! That is the way to think like a teacher who is also a physicist.

4. CCPhysicist, I completely agree with you - I love the bumpy track problem. It's exactly what we are looking for in a quantitative-qualitative translation question: connect mathematics to a thought experiment about a situation that the student is unlikely to have seen specifically in her or his own laboratory experience.

As for the PASCO carts... you're right that the data is hardly different from what.you'd get with a motion detector. My instinct is that your point about taking numerical derivatives is dead-on. However, I still haven't figured out exactly how these new toys work.

If you already have motion detectors that are easy to use, then there's no reason to break the bank to buy smart carts. But if you need to replace a dead motion detector or labquest, a smart cart might be a good alternative.

1. Thanks for the info!

My guess is that it works much like the rotation detector we also have, sensing fractions of a revolution and turning the accumulated displacement into distance by knowing the radius of the wheel. I've always assumed that the rotation detector uses a toothed wheel encoder with what looks like 0.5 deg resolution, but there isn't room for that in the Smart cart.

What I like is that the Smart cart also has a load cell. We only have a few of those, for demonstrations rather than lab or active learning experiments.

5. I may not know much, as some character once said ... but I was taught that the best thing to do is assume everything is a point, a line, a sphere, or a cube. Why? Because it simplifies things enough so that we can think about ... and model them. If you follow this path, then all the questions ... what if it isn't uniform? what if it ... ? simply disappear. It's what I constantly tell my students, what I constantly model for them. I tell them SIMPLIFY. ASSUME symmetry. "Much less than" means "IGNORE it. Think "a mosquito hits a speeding freight train" and think "what effect does it REALLY have?" If we try and account for all the "lumps" we will never arrive at a reasonable approximation. I also teach them that we are approximating reality and that as we use increasingly more sophisticated math ... in later courses ... we get "closer" approximations. The idea here is that we need to keep the moving parts to a minimum.