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04 May 2017

2017 AP Physics 1 solutions

I enjoyed writing my solutions to the 2017 AP Physics 1 free response questions.  You can find the questions linked via the official College Board exam site, here.

I very much like the direction the "quantitative-qualitative translation" question has gone.  Twice, students were given an equation, and asked why it does or does not make physical sense.  That's such a great skill to develop, and to test.  And I loved the experimental question... the experiment itself was quite straightforward.  But the "based on this data, how do you feel about this conclusion?" question was amazing.  It gets at the heart of evaluating quantitative evidence, at basic numeracy.  If every journalist and politician in America could answer this question accurately, the world would be a better place.

Okay, now I'm going to link the solutions.  But, please note that due to College Board copyright rules, only teachers can access them.  The PGP-secure website requires verification that you are a teacher in order to sign up.  

One of my favorite people, Gardner Friedlander, runs this teachers-only wiki.  He became quite frustrated last year because so many students asked for access -- many pretended to be teachers. Folks, Gardner isn't stupid.  He verifies that you're a teacher.  Please don't make him come after you for impersonating a teacher -- he will take away your birthday.

So, students, do you want access?  Ask your teacher to join PGP-secure.  Your teacher may share the solutions "for face-to-face teaching purposes."  

As always, I guarantee that I've earned a 5, but not that I get every detail right.  Please note my mistakes in the comment section.

My solutions can be found via this link, at PGP-secure.  This is a wiki for physics teachers only.  If you are a teacher but don't have access yet, follow the instructions at the linked page; you should be approved in a few days. 

GCJ

27 comments:

  1. Was it just me, or did this year's free response questions seem markedly easier than the previous two years? Also, I think the best thing to come out of this test was the series of twitter memes about Lab Group 5.

    Anyway, a question about the student's wrong equation in FRQ #4 this year: so, I can spot a few problems with this equation. Nowhere in the prompt does it say how many problems you have to find in order to get full credit, though. For example: the units don't work out, and that could be criticized, but so too could the specific decision to put I in the numerator. Or someone could go after the "4" exponent specifically. What's the policy on open-ended questions like this, where more than one reasonable answer exists? Is any one answer enough to get full credit? I could easily see a kid overthinking this and writing way too much because they keep seeing one problem after another, even when they should generally stop at a shorter answer (as you pointed out in your previous post).

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    1. I don't know about policy... Notice that I only identified one issue. While I could see a student overthinking this, it is our job to teach our students NOT to overthink such a problem. You're not supposed to write an essay... answer the question, and stop. Don't risk saying something wrong. And if you "lose" one point because of an oversight, well, who cares - you'll do better by moving along, focusing on the rest of the test, and not stressing.

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    2. I'm pretty sure the units work out--the equation was Ivx/md^4... replacing I proportional to MR^2 and canceling m's and x's or d's you end up with a v/x which is the correct units for an angular speed.

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    3. I'm a bit late commenting, but I was reading this all from the beginning. I'll first say that I came to appreciate "easy" questions after being told that some were used on the graduate comprehensive exam we took because they tested clarity of mind over mindless use of the coolest technique available. They are also easy to grade. Fewer arguments over what partial credit to assign in the rubric.

      What I liked about 3 (c) was that the units DO work out, so a student might waste time on checking that rather than looking at how it fits with the qualitative reasoning in 3 (a). Why worry about whether the exponent on d should be 4, which requires using equations that you were specifically told not to use, rather than question whether particular exponents should be positive or negative? Direct and reciprocal dependences are the first thing that someone should look at when considering if an expression is physical or not.

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  2. I totally agree that these FRQ seem much easier this year - lots of comments on the difficulty of the MC this year.

    Question: This is the first time I have noticed "low-friction" rather than prompting the student to either include or ignore friction. Do you think they actually want them to consider the different normal forces and frictional forces that result in the different slides?

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    1. "Low-friction" should be read as "ignore friction" or "work done by friction is negligible." That's the case in the laboratory, when we use PASCO carts and tracks and ignore friction, still mostly getting accurate results.

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    2. I struggle with why would they introduce this new term "low-friction" and not use the other terms which have been used before? Most of my students said they assumed they were supposed to account for friction when they read this problem. It just seems like a reason to cause confusion where it isn't needed. Do you think if students accounted for friction in their answers it would still be accepted?

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    3. Anonymous, please see my reply to Jason below. It's the same issue: AP Physics 1 teaches the physics skill of figuring out how and when to make simplifying assumptions. I can't speculate about the rubric... I'll be at the reading, though, and I'll see what happens there. The rubric is by no means set yet.

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  4. I believe that there is an issue with Problem 3, part (a). While it is true that maximizing the value of x for the disk will maximize the angular momentum of the system (which, of course, must be conserved during the collision), this will also maximize the value of the total moment of inertia of the system which could, depending on the mass distribution of the rod, end up giving a smaller value for omega_final. The question makes it clear that the mass of the rod is much greater than that of the disk, but there is nothing in the question about the rod being uniform, and there is no statement or implication that point C, being the midpoint of the rod, is supposed to mark the center of mass.

    Given how tricky the wording has occasionally been on some questions in the past, and how important it has sometimes been for students to pay close attention to assumptions they might naturally make that aren't necessarily valid given the exact wording of the problem, I really do believe it would be incorrect to jump from maximizing angular momentum of the system by maximizing x to the conclusion that this will maximize omega-final. At the very least, I would hope that students would make a clear statement of any assumptions they are making as part of their answer.

    Incidentally, a correct derivation (which students were specifically told not to do!) of the value for omega_final must use the parallel-axis theorem because the disk will begin to rotate after it collides and sticks with the rod, and then calculus. A result of this is that the answer for maximizing omega_final (by taking the derivative of this equation for omega-final with respect to x and setting to zero), and whether this means that x should be on the left side or the right side of point C, depends not only on the mass distribution of the rod (which, if close to the pivot, would result in x needing to be to the LEFT of C, even with m_rod >> m_disk), but also on the radius of the disk (the larger the radius, the larger the value of x).

    Overall, I think that Problem 3 part (a), which was presumably meant to be a simple conceptual question, would actually make a great entire problem for AP Physics C Mechanics if some of the points that I've included are used as follow-up items.

    Is there something that I'm missing with this question? In my opinion, if what I'm saying is valid, this would seem like something that should have been easy to spot during the vetting process.

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    1. Jason, you're right that the full version of this question, including derivations, makes for a great physics C question. But that's not the point here... in AP Physics 1 we are supposed to answer basic conceptual questions with straightforward language with reference to relevant physics principles. Is the rod uniform? It doesn't matter. Is point C the precise center of mass? It doesn't matter. (The answer is the same either way.) All this question wants to know is, given that the rod is very massive compared to the disk, where do you aim the disk so the rod rotates fastest? And what basic physics principle supports that statement?

      Now, I recognize that you're worried about a student who makes the problem more complicated than it is. But my huge point is that AP Physics 1 demands that students be able to make appropriate simplifying assumptions. That's a physics skill, one I teach to freshmen and to high-undergraduate-level research students.

      If you start making lawlerly arguments, starting sentences with "well, actually," or finding the one case in a hundred when the problem seems to be ill-posed... well, then, you're probably on the wrong track. I teach students the "if you sound like a lawyer, you're wrong" rule as a guide to the simplicity we're looking for. See my Dec. 14 2013 post for a deeper discussion.

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    2. Thanks for the response, Greg. I agree that if a student was to bring this to me, raise the points that I brought up and the fact that the space only allows for one or two sentences, I would say to assume that the rod is approximately uniform and move on.

      I also realize, though, that isn't fostering creative problem solving one of the skills that AP Physics 1 is trying to bring about? With that in mind, my impression with some of the questions in previous years has been to specifically highlight areas in which it might be natural to assume such unstated things as rod uniformity, COM being near midpoint, etc., but where the student must shed these sorts of mental anchors in order to come to a full understanding of the physics.

      Regarding the idea that the answer is the same whether or not the rod is uniform or C is the COM, I must disagree. A full derivation (including using the parallel axis theorem) yields that the best value of x is x = sqrt((I_rod/m_disk)+0.5(R_disk)^2). If we assume that the disk is small compared with the rod, the second term goes away. However, if the mass is concentrated sufficiently near the pivot, an idea which I must insist is not at all far-fetched, we get that x < C, even with I_rod>>m_disk.

      While I agree with the lawyer analogy, I think it works best if the lawyerly arguments wouldn't change the overall analysis. But is mass being concentrated near the pivot really a lawyerly argument? One can imagine a number of reasons why someone might want to set up such a situation, so I really don't believe that this is a pathological situation. The great majority of problems like this that I have seen before in textbooks and other problems have qualifiers such as "uniform mass" or "constant density", so the lack of such qualifiers would, in the minds of many, be a cue not to assume such things.

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    3. I'm pretty sure you are neglecting that x is confined to be less than or equal to the length of the rod. When you add in this constraint--the only relevant portion of the function you mention is from x = 0 to x = L. If you graph the function you can see the maximum of the graph (where omega starts to decrease) is far beyond the length of the rod.

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    4. I considered that possibility when I was exploring the problem at the beginning, and whether or not the maximum is beyond the length of the rod depends on the dimensionless moment of inertia (which I'll just call K): the question is what is K*m_rod/m_disk. While m_rod >> m_disk, it is still possible for K to approach zero. As K-->0, x-->0. It's fun to check this out on desmos.com/calculator using the various sliders--one for I_rod, another for m_disk. The equation for omega is omega = vx/(I_rod/m_disk + x^2) in the limit where we assume the disk radius is small. (The value of v doesn't affect the location of the peak.) (If not, this adds another term that is also variable and can approach zero.) When playing around with these sliders, it's important to note that m_rod >> m_disk does not necessarily imply that I_rod >> I_disk for a non-uniform rod. (However, it *would* imply this if they called point C the center of mass--this would have saved a lot of discussion!)

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    5. I actually also explored this and pondered it for a bit when my students asked about this problem. In the end, I think it's obvious to us teachers that we should the assume the mass to be evenly distributed--whereas a student likely would not have seen mass unevenly distributed and would not think of this anyways.

      What does trouble me is that some students may derive the equation for omega and see the x^2 term in the denominator somehow rationalize this to be an inverse relationship (naively). However, the problem asks the students not manipulate equations, so in a way they are guided toward a more torque-related response.

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    6. To me, I would think that the possibility of an uneven mass distribution is exactly the type of logic that we would expect the students who get 5's to employ, but not the students who get 4's. (Note that I'm not saying that I'd expect them to assume an uneven mass distribution--just that they would consider this possibility.) I'm thinking specifically back to that ridiculous (IMHO) problem last year where students were supposed to somehow realize that they were dealing with a superelastic collision. I had one student last year who assumed a superelastic collision on that problem, and he was one of my 5's; everyone else I spoke with assumed that there was some breakdown in the ball becoming less elastic with increasing impact velocity, i.e. the change in slope going the other way. Similarly, while I haven't asked him, I bet that my aforementioned student from last year would not assume an even mass distribution here--that's just his thinking style. As for me, it was quite easy and early to assume an uneven mass distribution for a very simple reason: I noticed the part about the rod mass being much greater than the disk mass after I had already spent a bit of time on the problem. :-) Thus, I already had it in my mind that the answer would definitely depend on the parameters of the bar.

      That's a good note on the equation for omega. As you say, the problem asks for students not to manipulate equations, but if they start to become troubled by the logical possibilities regarding the bar, they might derive an equation on separate paper "just to be sure", and then come to incorrect conclusions.

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    7. Regarding the last observation that you didn't notice the statement about the rod mass until after you had worked on the problem for awhile, you just explained why it is important to read the entire problem before answering it. Tell your students about your experience so they can learn from it! The sentence before the first question is as important as the question itself, as is the instruction "without manipulating equations" that follows the possible answers.

      When you ask at the start "Is there something that I'm missing with this question?", I would say you missed that they never said the disk was uniform! Your formula should have I_disk in it. You can't assume more, although you might be allowed to assume that the disk's radius of gyration is << d based on the picture.

      Finally, I think it is fair to assume (and perhaps state the assumption) that the statement about the masses is tantamount to a statement about their respective moments of inertia about the axis. Changing the radius of gyration of the rod merely shifts the threshold for what "much more" means quantitatively. If they had merely said "more", your concerns would be valid BUT you couldn't answer the problem without resorting to equations. And if you have to use equations, you are reading it wrong.

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  5. BTW, I should probably clarify that I really haven't been approaching this in the context of, "How might I find something wrong with this problem?" (I promise!) I approached it from a student perspective: "The best choice looks like x = L, i.e. x > C, but I'm worried about the possibility of a non-uniform mass distribution--let's see whether my answer is supported by an actual mathematical derivation"--something along the lines of parts (b) and (c), which I think are awesome questions for AP1. Then, when I found that my fears seemed to be justified, I started squawking about it to my colleagues and then, to get increased clarification, here. While it might seem otherwise, I'm really not trying to cause trouble. :-)

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  6. Do you have any idea when the international version (E) will be available in the secure documents? August? Most of my typical top students had that version and want me to go over it with them at some point.

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  7. I don't know for sure, Greg. The last couple of years it has been available around October or November.

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  8. Do we know for sure that the international version will even be released? I know they've done it the past few years because it's a new course, but I imagine eventually they'll stop, or only release it once every five years like they did with Physics B.

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  9. Any thoughts on how short a question number 5 is? I can't figure out how 7 points could come from those two graphs/drawings. Seems like maybe it needed one more part to make 7 points to me.

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    1. Two thoughts.

      It is just as short as question number 1. The suggested time implies to me that the students should be as careful with details in the sketch as they are with the paragraph. Good writers get more time on the drawing, and good graphers get more time on the paragraph.

      What is the velocity AT t = 1? (I've never bothered to get access to the secure answer sets to see if Greg cares about this detail, but why not worry about that instead of worrying about the inertia of the disk?)

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  10. Do you plan to upload the ap physics 2 2017 free response solutions too?
    It would really help if you do coz I'm gving the exam in late testing
    Thank you

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  11. Sorry, I'm not teaching AP2 this year, so I'm not writing out my solutions. They'll be published on the College Board site in September.

    But, any teacher is welcome to write up solutions and post them to PGP-secure. If you need help with that process, please email me.

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  12. Greg,
    I noticed the phrasing "briefly explain reasoning without manipulating the equation" showed up a few times on the AP 1 FR. I have interpreted this phrasing to mean "do not fabricate values and solve for an unknown" (which is many of my student's favorite end around moves for conceptual/algebraic problems). Was this added to keep solutions more in line with analyzing and applying the concepts instead of a plug and chug approach?

    Thank you for your time

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  13. Jason, you pretty much nailed it. "The first resistor's voltage increases because I calculated 4 V the first time and 8 V the second time" is at least in the right direction. But "The first resistor's voltage increases because it always takes the same fraction of the battery's voltage, and the battery's voltage increased" is excellent physics reasoning. Then, when the student can show in variables the calculation showing that the first resistor the same fraction of the battery's voltage, his training is complete.

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