Quantitative acceleration exercise with video

When I run quantitative demonstrations for algebraic kinematics, I use the PASCO projectile launcher.  I know that it gives a consistent 4.8 m/s initial speed, I know free-fall acceleration, and I can easily measure distance to verify quantitative predictions.

Today I wanted to create a set of quantitative predictions that students can work on independently, with experimentally verifiable results.  I only have one projectile launcher, though -- they're $349 a pop.  But how else to produce an experiment with known initial speed or acceleration?

While I'd prefer to have students manipulating the equipment themselves, the next-best alternative might be video of me using the same carts, tracks, and motion detectors that my students are already accustomed to playing with.

So this morning I gang-pressed my ten-year-old (who is, obviously, much more tech-savvy than I) into taking a bunch of videos of me using a motion detector to make velocity-time graphs for twelve carts.  All twelve involve either motion at constant speed; speeding up from rest; or slowing down to rest.  I've put pictures of the velocity-time graphs into a single file at this link.  Or, you can look at the unaltered pictures of the full labquest result -- with both position-time AND velocity-time graphs -- that I posted on twitter.  Look up @gregcjacobs on 31 December 2013.*

*Yes, the pictures are rather dark... I couldn't get the labquest lit nicely for a picture without causing glare. If you can touch these pictures up and send me a new file, that would be awesome.

The twelve videos that go with the velocity-time graphs are available by searching "Jacobs Physics Accleration Video" at youtube, or clicking on this youtube link.  (Video credit for all twelve goes to Milo Jacobs.)

What exactly will I do with these graphs and accompanying videos?  Well, a lot is possible.  The simplest idea would be to ask a student to use the velocity-time graph to determine the distance the cart traveled in a video.  For example, v-t graph #10 -- picture above for convenience -- shows a cart speeding up from rest for 1.2 s to a max speed of 1.5 m/s.  Using kinematics, you can calculate an acceleration of 1.3 m/s per second, and a distance traveled of 90 cm.  

Then in video #10, you can pause the video and estimate the distance the cart traveled down the plane.  While the meter sticks below the track are not in enough focus (and are not aligned with the track's slope) to determine a distance to the nearest centimeter, I can see well enough to count about 10 decimeters -- i.e. 100 cm -- of motion from release until the cart hits the bottom of the incline.

If you want four-sig-fig precision, please use a java motion simulator.  And if you want professional videos in which the performer has the skill to notice that the blue cart doesn't contrast well with his shirt, well, please get in touch with a professional videographer.  This is the best that Milo and I can do... and I very much like the quality.  Part of laboratory work is discovering the limits of said lab work.  My hope is that by the end of the year my students understand that kinematics equations can make predictions within about 10-15% for most any situation in the physics classroom.  

Please feel free to use the graphs and accompanying videos, or to make better ones.  I will post someday once I flesh out the google doc with specific questions about the motion represented by each graph.

Next step:  adapting the graphs and/or videos to make a set of QUALITATIVE exercises for conceptual physics.

How do you tell the difference between AP and "regular" physics?

Josh Morckel writes in with the observation that the new AP Physics 1 curriculum pretty much covers the same state standards that his regular class covers.  That's not surprising, as (for better or for worse) the College Board was very careful in developing AP Physics 1 that it would meet the legislative criteria for a first-year physics course in as many states as possible.  Because state legislatures and political committees certainly have superior expertise in physics education than the professionals associated with the College board, I guess.  Phthph.

Disregarding my own impertinence, Josh's pertinent question is, if AP and regular high school physics are covering the same state standards, then what's the difference?  I think Josh is asking a twofold question here... (1) What is the difference in how I should teach these classes, and (2) How do I sell this difference to parents, administrators, and students who are ignorant of physics generally, and who see the same state standards listed in the course description?  Both of these questions should probably be answered similarly, so I'll start with:

If an AP and a Regular course cover the same "standards," how are the two classes different?

Don't use standards to define courses; use tests and exams, preferably as written by someone external to the course, to define courses.  Once you're clear on the level, topics, and depth of question that your students will be expected to answer, then you can make up a concordance with any state standards you need to.

What I do: My regular course for upperclassmen is based heavily on New York Regents exams.  You can see many, many previous years' exams here.  I teach my regular sections such that they can answer all the mechanics and waves questions, plus the lens/mirror questions from the pre-2002 exams, plus the circuits questions.  (I also added in a basic astronomy unit based on the Regents Earth Science Exam.)  Virtually all of my tests and exams are based on authentic Regents questions -- the only difference is that I include a "justify your answer" section in addition to multiple choice and open response.  If any physics teaching reader would like to see or use a sample test, please email and I'd be happy to share.

The AP Physics 1 exam covers much of the same material as regular/Regents.  The major difference is the depth of that coverage, as evidenced in the test questions.

A regular question can generally be categorized in a single topic area, and can be answered in one step, or two brief steps, or a one-two sentence explaination with reference to a single fact of physics.

An AP question generally requires cross-categorization across two or three topic areas.  Most require multi-step reasoning, or a two-three sentence explanation with reference to more than just one fact of physics.  AP questions, for the most part, require students to make connections across skills and topics.  You can take a look at a few of the kinds of questions the new exams will ask in the curriculum guide... but the Physics B questions you've been answering for years still give the right idea of multi-concept problems.

As an additional comparison, you might consider a conceptual class.  Conceptual Physics can cover many of the same topics as "regular" physics, but without using a calculator.  I make my conceptual test questions by rephrasing Regents questions, as described in this post.  Some teachers may find that their "regular" class is more like my conceptual class.  That's fine.  It all depends on your own feeling for what your students can do, and the style in which you prefer to teach.  A conceptual approach provides a greater contrast between AP and non-AP physics.  Feel free to email me if you'd like a sample conceptual test.

Okay, so how do I explain all this to parents and administrators who don't know anything about physics or physics teaching?

Me, I'd explain exactly what I described above, with a few hand-picked example questions on similar topics to illustrate the difference.  

  

Recognize that a truly bad administrator or an intransigently hostile parent an isn't going to be swayed by logical arguments, no matter how correct, no matter how well presented.  Forget them.  

I'm talking about how to approach an open discussion with competent, well-meaning, but physics-ignorant people.  Often, such folks's faces will quickly glaze over, just like my wife's face when I start talking about the differences between high school and professional football rules.  You're speaking a different language, but you're speaking it fluently and confidently.  The hope is that these folks will recognize your expertise and defer to it.  Even if you personally don't feel like a true physics teaching expert, you are far more expert than most; do what you think is right, and evaluate and acknowledge later if your suggestions need tweaking.  That's how you become an expert.

If you're lucky, your audience remains engaged, asks questions, and learns something new about physics and physics teaching.  Treasure such people.    

Take all that I write here as my personal opinion, which is informed, but not by the Almighty him- or her-self. Physics teaching is about teaching skills, not topics, and those skills can be taught using whatever topics and whatever standards you want.  Hopefully the approaches I've described, perhaps in combination with the College Board's materials and my own tests, can be useful to you in differentiating your courses.  Understand, though, that every school and every physics teacher is unique.  The world would NOT be a better place if only everyone would give the same tests, homework assignments, and quizzes each day as I do.*  Everyone reading needs to do what's right for your students, your school, and your personal style. 

I'm happy to talk directly with you or your administration if you need further help defining your courses.  Send an email.  Or attend a summer institute, or my summer "open lab," where you'll hear a multitude of ideas.   

GCJ

* That is, unless I were to get a seven-figure grant in the bargain.  Then we would live in a physics utopia.

If you sound like a lawyer, you're wrong

This regularly-uttered aphorism applies in so many physics teaching situations.  While my original use is lost in the mists of time, I suspect it involved me explaining why a student can't have more points on a test problem:

"Mr. Jacobs, the problem doesn't explicitly say that the car's acceleration is constant as it slows down.  So, in theory, it could have sped up first because it hit an ice patch on a downhill, then the velocity time graph could curve like so."  

No -- the problem says the car skidded to a stop, your graph makes no physical sense even given your crazy assumptions, this unit is all about making simple, reasonable assumptions about motion.  Still don't believe me?  You are making squirrelly arguments worthy of Antonin Scalia.  And if you ever sound like a lawyer in physics class, you're wrong.

But this phrase isn't just a pithy way of shutting up a student whining for grades.  

It also provides students guidance about the level of analysis necessary on a problem:

"The problem says the tabletop is 'smooth.'  But that doesn't necessarily mean no friction -- there's no such thing as exactly zero friction force.  The lack of explicity means that I must assume a friction value of reasonableness.*  So I'm going to assume mu is smaller than the smallest mu we've dealt with in class, even though that makes the problem very complicated algebraically."  

If you sound like a lawyer, you're wrong -- just interpret "smooth" to mean "friction is negligible."  Physics problems require reasonable assumptions, but they don't require tortured assumptions.

* Yes, for those readers who don't actually teach high school, students write like this.  No kidding.

This magic phrase can guide students to the depth of explanation necessary:

"Since the equation includes a squared term for the x-axis variable, the graph should look like a parabola.  But, a parabola can look like a line if the axes are zoomed in enough or on certain parts with less curvature than others (as we discuss on the first day of calculus).  Since the graph doesn't explicitly indicate the range of values for which we're graphing this data, I can't say for sure what the graph would look like.  It could be straight, it could be concave up -- assuming that mass can never be negative, which is a generally valid assumption except in some very special cases in extreme cosmology."  

Um, your first line was sufficient.  The rest sounds lawerly.  Once you start sounding like a lawyer, you're thinking way beyond introductory physics and the rough but accurate predictions we can make.

And finally, the phrase applies to teachers, too, as we grade papers -- if we have to make the lawyerly argument for the student, his answer is wrong:

"Hmm, I asked the student to draw and label forces acting on a block sitting still on an inclined plane.  This guy drew the weight, and a force labeled "Fn" straight upward.  Well, that up force could be the vector sum of the normal and friction forces; I know these are generally drawn separately, but if we were to add them together we'd get a resultant force of the incline straight upward.  And his Fn certainly could mean the "n"et force applied by the plane.  I'll give that credit."  

NOOOOO!  It's the student's responsibility to communicate correct physics.  Every time you worked on an inclined plane problem in class, and on every incline problem in your textbook, the normal force and (if applicable) the friction force are labeled separately.  And the conventional meaning of "Fn" in this context is the "normal" force.  Awarding credit requires you believing that your student (a) developed on his own the idea of labeling a single force to represent the vector sum of the friction and normal forces, (b) recognized the correct direction for that force, (c) redefined in his own mind (but not on the paper) the conventional meaning of Fn, and (d) communicated all these unlikely thought processes sufficiently.  Come now... isn't it far, far more likely that this student just automatically drew the normal force straight up rather than perpendicular to the incline?*  When you sound like a lawyer, you're reading way too much into a student's response.  Count it wrong and move on.  

* And in the one chance in a bobzillion that the student points out that he actually intended all of (a), (b), and (c), then you point out (d):  communication is part of physics.  If you have to explain your answer to me orally after the test is over, then the answer is wrong.  The time for communication is in writing, on the test.

Which thermodynamics variable is affected by an ice bath?

The problem:

A container of gas with a movable piston, initially at room temperature, is placed into an ice bath.  

Which variable in the first law of thermodynamics must be affected?

(A) Delta U

(B)  Q

(C)  W

(D) Delta U, Q, and W

(E)  None of them

A sample response from a reader:

If the volume of the container is kept constant then W = 0, so Q and Delta U must be affected.  If the temperature goes down then so must Delta U, but since W=0, then heat must be lost. I recognize the Delta U does not directly determine Q, that is hot does not equal heat added, but in this case I cant help but feel both are affected.

The correct answer, though, is (B):  Only Q, the heat added to the gas, must be affected by placing the gas into an ice bath.  So where is the mistake?

Look at the very first sentence, which contains a humongous "if":  IF the volume of the container is kept constant, then sure, I agree with the reasoning above.  But in the immortal words of Tia Carrere,* IF a frog had wings it wouldn't bump its arse when it hopped.

* What?  You don't recognize the reference?  Philistine, I sentence thee to watch Wayne's World, the 1992 film, 50 times.

Putting a gas in contact with an ice bath, hot plate, candle, or other means of heat transfer does just that -- transfers heat.  And heat transfer says nothing definite about temperature.

But, how can I remove heat from a gas without lowering the gas's temperature?  By doing work on the gas, of course... say the piston is compressed while the gas is in contact with the ice bath.  Say the ice bath removes 100 J of heat from the gas, but in compressing the piston I do 150 J of work on the gas.  Then, by the first law of thermodynamics, the internal energy of the gas INCREASES by 50 J.  Since internal energy alone relates to a gas's temperature, the gas temperature increases.

In this problem, the question is very clear that the container's volume can change.  The assumption of W=0 is unwarranted; W relates to the change in the container's volume, so is not necessarily zero here.  I love the way this problem stabs at the heart of the most common misconception in thermodynamics: the conflation of heat with temperature.

Zen: Don't make academic integrity about academic integrity.

One of last year's summer institute participants is having trouble with students copying homework solutions verbatim off of internet sources.  I have a sneaky feeling he's not the only reader with this problem, especially because I'm asked this sort of question frequently.  Here's the representative letter:

Dear Greg, 

I've been struggling with academic integrity the past few weeks, and I was wondering if I could get your perspective on it. I've noticed that many of my students (who are encouraged to collaborate and use outside resources) realized that there are complete solutions to really almost every single AP Physics problem out there. I've been using a combination of your problem sets and problems from my textbook (Cutnell 8th edition), and when I noticed that some students (especially sly but under-achieving students) have been providing solutions using formulas and approaches that we never talked about in class, I did a google search and discovered that these solutions are out there. Is this an issue that you've faced before? If so, how do you deal with it? If not, how have you avoided it?


I'm thinking of two solutions for how to deal with it; either 

1. I let them use these solutions and when they bomb their tests and quizzes, we can have a conversation like "But you've doing so great on your homeworks; why are you doing so bad on your quizzes?! Let's look at your homeworks and maybe find why there's a disconnect; oh you don't actually understand a lick about what you wrote, so where did you get these solutions from? etc"

or

2. Deduct massive points when students use a solution different from class. Obviously, the problem with that is Physics is all about having multiple solutions to solve the problem.

Beyond a shadow of a doubt, my students are using these online resources, but again, I'm not sure how best to deal with it. Any advice?

I guess I'd personally lean toward #2, but with a huge twist.

The important part is that you're not seen as playing "gotcha" with academic integrity.  Students sometimes think of integrity as a game of cops and robbers.  If you engage as cop, they play the role of robber and defense attourney.  Your role is more like that of coach... a player who cheats so as not to have to do all of the required sprints or pushups, or who is a dirty player, is letting himself and the team down.  It's less a matter of right and wrong, crime and punishment, as of respect for the game.

And there's why I'm not into approach #1.  Consider a football coach who let his players skimp on conditioning and weightlifting and then get crushed in the first game when they become winded after 10 minutes.  Is it legit for him to yell at the team, "See, you wimps didn't do the workouts, no wonder you lost."?  No, a good coach finds a way to make the team -- or at least the majority of the team -- take conditioning seriously so that they have the prerequisite physical stamina to perform in the game.  

You're positive the students are using online resources in a non-productive way.  So, start by giving parts of a problem as a quiz the next day:  "Explain what value you chose for the normal force on the cart, and why you chose it."  "Consider the problem from last night's homework, but with negative instead of positive charges."  Or even "Here's part (c) of last night's problem.  Do it, explaining each step."  The fact that they have to explain their solution means that they'd better understand what they did on the homework.  If they used an online solution reasonably, then awesome -- they can explain what they did and why, so who cares that they looked up the answer to start with.  More likely, they crash and burn, and they realize that their method was useless.

And there's the most important point, I think:  By giving this kind of quiz, you're not phrasing anything as an issue of academic integrity.  You're making the completely valid demand that students be able to explain homework, not just write answers by rote.  That's good physics teaching, and outside the realm of "cheating."  

So still grade the problems, but make the quizzes the bulk of the homework grade.  And you're right to give poor scores for students who use non-standard methods that you're pretty sure they made up.  If they complain -- which they probably won't, given their quiz performance -- then you simply ask them to use the methods you taught.  If they're smart enough to understand a new nonstandard method, then they're good enough to do it the easy way.  If someone tries to be a lawyer, point to the quiz, and say sorry, you don't understand this, you aren't getting credit for it -- period.  The evidence that you don't understand is in the quiz response.  

Remember, homework is about figuring out how to do the problems, not about how to get the right answer.  In English class, you might be given an essay prompt saying "Describe with textual evidence the meaning of Hamlet's 'to be or not to be' soliloquy."  If your answer is simply, "He's contemplating suicide," you earn an F-.... EVEN THOUGH YOUR ANSWER IS RIGHT.  If you "write" a treatise with big words that you obviously copied from the internet, but your in-class paragraph response shows that you think Hamlet lived happily ever after in the nunnery with Ophelia, then, well... you're probably not getting any credit for your homework essay.

Treat physics homework like English essays, where the presentation and communication matters; and follow up with pointed quizzes; and you'll likely find the integrity issues disappearing.  NOT because your students have come to any epiphany about being good little boys and girls, but because they'll see that cheating simply doesn't do any good.

These are my thoughts... not The One True Answer, but the way I'd approach things.  I'd love to hear other ideas in the comments.

Good luck!


GCJ

The first day of motion

On the first day of studying motion in conceptual physics, I start the class by having each student construct position-time graphs from motion diagrams.  The motion diagrams are made using spark timers and constant-speed carts, as shown in the picture.  

Spark timers are easy enough to use that I can just let them go at it with minimal instruction or supervision -- thread the paper through the machine, tape it to the cart, and voila.  Since the spark timer makes 10 dots per second, it's pretty straightforward to construct the position-time graph for the first 2 s of motion, because each dot simply represents 0.1 s.

(As an aside, if you have the older "ticker-tape machine" device that makes 60 impressions per second using honest-to-goodness carbon paper, you can just have students plot every sixth dot as 0.1 s.  It only took me eighteen years of teaching before I figured out that I didn't have to plot the time axis every 0.017 s.  And I didn't really figure it out, my colleague Curtis mentioned it to me, 'cuz I certainly never thought of that.  Guh.)

Once a group has a position-time graph constructed, I hand out just the first eight facts from my motion fact sheet and the problem set based on the first position-time graph.  (My original has a scaled grid for them to re-graph their data individually.  The scaled grid didn't come across on google docs... so feel free to email me for an original .doc copy.)  Everyone answers the questions with specific reference to the facts on the sheet.

Note that I do absolutely no lecture.  I've found that trying to tell students how to interpret motion diagrams and graphs is as useful as telling someone who's never played or watched football how a zone blitz works.  Nevertheless, it's amazing how quickly everyone figures out the meaning of various representations of motion when they are personally involved in creating those representations.  I eventually demand a nearly college-level understanding of motion graphs; but I get there by building from the ground up over many class periods.

The next day, or whenever a group is finished, we do the same exercise again, except this time with a PASCO cart sliding down an inclined track so that the cart is speeding up.  They answer similar questions about their graph.  Then we're off and running to use position-time graphs fluently to represent motion.

GCJ

Summer 2014 schedule -- AP Institutes, and perhaps a FREE seminar at Woodberry Forest

James Winterer asks:

Will you be presenting at any AP institutes this summer for the new AP Physics 1-2 courses?

  

I have three official AP Summer Institutes on the schedule right now:

* Walton High School in Marietta, Georgia June 23-26

* Mahopac High School in New York June 30-July 3

* Manhattan College, August 4-8

I might pick up one more if I get a good offer.  

For those who have attended my institutes in the past, know that my general approach to AP Physics will not change because of the new exams!  The same features of your course that I recommend and model -- quantitative demonstrations; regular, focused experimentation; quizzes, tests, and problem sets based on and graded in AP style -- will produce success on the new AP exams.  In fact, the new exams practically demand some of these features.  So expect much of the same material.  I will certainly bring in some rotation demonstrations, and I'll work with you to recognize how the new exams are different.  But at its heart, the new exams require that we teach thorough physics understanding, which is the same goal we've had for decades.

Would you be interested in an "Open Lab" at Woodberry Forest?  I've been considering offering a free two or three day seminar in my own classroom here at Woodberry.  We would discuss good physics teaching at ALL levels, from conceptual to general algebra-based to college-level to calculus-based.  We'll do some of the same kinds of things I do in my institutes, but with materials that I've developed independently over the years.  Now, I wouldn't be able to offer any official CEUs or whatever.*  But I think we'd have a good and useful time.

*Unless someone else is willing to figure out how to do the paperwork... Dammit, Jim, I'm a physics teacher, not a bureaucrat.

If you might want to attend an Open Lab, let me know in the comment section or by email; suggest a time in July that might work for you.  (Although I'm volunteering my time, you'd need to get yourself here on your own dime, and you'd need to put yourself up in the local hotel.)  If I get enough interest, I'll talk to my school to arrange the details here; I'd rely on crowdsourcing for advertising, so spread the word.

GCJ

Exam review: 9th grade conceptual physics optics, waves, and circuits exam

Trimester exam time here at Woodberry.  Yes, trimester -- we give exams before Thanksgiving, the first week of March, and the last week of May.  It's wonderful to have so many opportunities to give long exams, because students prepare diligently for these, and take them very seriously.  An exam is the best teaching tool I can think of.

A colleague in the history department this morning noted how the freshmen seemed low-key and not stressed.  Great!  That's exactly the attitude that Alex (the other 9th grade teacher) and I were consciously attempting to instill.  

I believe in predictable yet challenging exams.  The exam is not a place for cuteness, tricks, or extra-hard "let's see if anyone can get this" questions.  But then, I believe the same way about regularly scheduled class tests.  Conceptual physics test and exam questions always consist of questions adapted from New York State Regents Exams.  I don't throw in an AP question to challenge the top students; nor do I put a section of gimmee recall questions in.  Problem sets and regular quizzes use exam-style questions, too.  Thus, the students know exactly the style and level of difficulty to expect.

We have given three tests this year so far.  All were cumulative -- no, Johnny, you may not just forget everything about lenses and mirrors after the first test.  If you could, why should I bother teaching to begin with?  Two tests were heavy on the multiple choice; the third was just open-response.  Students were required to correct everything they missed on each of the first three tests.    So when I described the exam format -- two hours in which to complete 20 open-response and 40 multiple choice questions -- no one panicked.  They themselves commented, "it's just like a long test, then."

So how to "review" for the exam?  Freshmen especially can be crazy-anal about exam review, trying to cram way too much information from a textbook, or trying to game the test by memorizing the problems they think might appear.  That's unhelpful.  It's my job to guide them to doing the right sorts of things to review.

I start by posting all of the facts we've covered this trimester.  Click the link to see the file I posted.  I don't encourage anyone to read the textbook.  Instead, all year I've handed out fact sheets consisting of subsets of the posted file.  In the runup to the exam, I encourage students to work until they can recall every one of these facts with ease.  That's productive studying.

Then, I hand out a review sheet consisting of test-style problems.  I give enormous incentive* for students to not only complete the sheet, not only to correct their mistakes, but to get their corrections RIGHT.  It's one thing to memorize pages of facts... it's another to practice applying those facts to test questions.  The review sheet provides the same practice questions to everyone so that they all can discuss their answers with classmates.

* including substantial extra credit -- for perfect corrections only -- and the opportunity to attend a nacho party.  The nacho party is the more effective incentive.

Sending out the single-file fact sheet worked wonders.  This morning as I wandered the dorms, I found more than half my students using the fact sheet to study somehow.  They were quizzing each other orally.  They were creating their own written quizzes.  They were looking up facts to do practice problems.  They were making notations on the fact sheet so they could ask me questions when I came by.  No one ever, ever used a textbook like this in all the years I've taught.  But because I condensed the material to ten pages in which every single word is relevant, the fact sheet became not just useful but indispensable.  

Feel free to use the fact sheet for your class.  Every question on the exam is based on one or several of these facts. 

And if you'd like to see or use my exam, please email me.  I'd be happy to share.

GCJ

Who cares why you got it wrong before... just do it right.

Regular readers know I'm a True Believer in test corrections.  What better way to cement a student's understanding than to have him write out an explanation for each problem he personally missed on a test.

I discovered a new difficulty with test corrections in a general-level class today, one that I had never really noticed before.  My class spent an inordinate amount of time asking me and each other what was wrong with their original response; as a result, what should have been simple corrections took them for friggin' ever.

Interestingly, I have never had this issue on multiple choice corrections.  My students, whatever the level, just justify the answers quickly, without trouble.  See, on multiple choice questions, the scantron simply marks the answer right or wrong; there's no ambiguity about what part of the original response isn't right.

I've not had this issue with AP-level students on their free response corrections, either.  That's because I've always asked very detailed, targeted additional questions on the corrections.  They focus on answering my new question... and that question more often than not leads directly to the right approach.

But today was the first day I have done in-class corrections on a general-level all-open-response test.  The problems on this test are too simple to make my AP approach of targeted additional questions to be useful. As they faced an incorrect test and a blank page, I had a parade of students asking "did you mark off for just the wrong units, or was the answer wrong, too?"  "Is it my diagram that's incorrect, or the explanation?"  "Would this have counted had I said..."

AARRRGH!

Note that no one was arguing that they should have earned more points, or debating my ability to grade consistently.  We're well over that issue.  No, these were earnest questions, motivated by the desire to get the correction right, the desire not to make the same mistake twice.

Nevertheless, the interminable focus on "why did I get it wrong" kept too many students from focusing on what I wanted them to -- namely, just doing the problem right.  Even as I kept asking students not to try to figure out their mistakes, but to start each question from scratch, they couldn't let go:  "But, just tell me real quick so I know, was this part of the answer right or wrong?"  Several students spent 20 minutes trying uselessly to find the source of a mistake, but then finished in only 3 minutes when I forcibly removed their original problem from them.

And therein lies the solution.  Next time I want students to correct their open-response questions, I'm not returning the original test at first.  Instead, they'll get a blank test with the questions they need to redo circled.  Once they do their corrections, THEN they can have their original test back.  Not only does this new approach solve for the "why did I get it wrong?" issue, but it provides even more incentive to work steadily without distraction.  After all, they can't see their test grade until they get the corrections right.  :-)

I'll let you know how this goes when I try it next trimester some time.

GCJ

Graphs and circuits

John and Corey plot brightness of a mini light bulb with a vernier light sensor vs. voltage of a variable power supply.  They get a parabola, as they predicted.

James and Andrew plot voltage vs. current using a constant resistance.  The current was actually in microamps... With 9th graders, I'll work on this distinction soon by telling them that 1 amp is a LOT of current.  After they finished, I asked them to draw a new line representing what they'd get if they used a smaller constant resistor.

I'm trying to teach my freshmen to predict what a graph looks like.  We are well used to using equations like V=IR and P=V²/R, identifying the constant value, and drawing arrows to show which quantities increase or decrease.  Now I want them to be able to sketch graphs.

With these types of equations, we're only going to get one of about four general graph shapes.  Although I don't describe them in words to my class, for you I'd call them a sloped line, a parabola, a hyperbola, or possibly a flat line.  You can see these, with my very simplistic description of how to know which one we're looking for, here.  

The day after I hand these out, we do an in-class circuits graphing exercise in which students are asked to predict what four different graphs would look like:

* voltage vs. current for constant resistance

* current vs. resistance for constant voltage

* brightness of a bulb vs. resistance at constant voltage

* brightness of a bulb vs. voltage at constant resistance

The beauty is, each of these experiments can be set up very easily in our laboratory.  I have "decade boxes" which allow you to dial any resistance you want, from 1 ohm to 100 kilo-ohms.*  I have vernier light sensors, which measure brightness in lux.  

* careful... on the graphs that DON'T include the light bulb you have to use kilo-ohms rather than ohms so that the power dissipated by the resistance box doesn't exceed a quarter-watt.  Twice today a student accidentally turned the resistance box to zero, causing the resistor box to smell bad because it was starting to burn off the insulation.

In order to make this a relatively quick exercise, I provided a blank and scaled graph on the back page of each handout.  (Check the link above to see.  You may use these in your class.)  The key is, FIRST the students had to predict what the graph should look like; THEN, they had to do the experiment.  And sure enough, the graph looked like we expected.  

Can a normal force do work?

At the first-year physics level -- absolutely a normal force can do work.  If an object moves parallel (or antiparallel) to a normal force, then the normal force has done work.  

But how can that be?  A block slides to the left on a flat surface, say.  The normal force is upward, movement is left, so the motion is not parallel to the normal force.  No work is done by Fn.

That's correct.

Even for a block sliding up or down an incline, the normal force does no work.  The normal force by definition is perpendicular to the surface, and the block slides along the surface; no component of the normal force is parallel to the motion.

That's correct, too.

So how in the sam hill can a normal force possibly do any work?

What if the surface itself is moving?

Consider a person standing in an elevator.  The normal force is the force of the elevator floor on the person.  As the elevator moves upward, so does the person... so the normal force is parallel to the person's motion, doing work.  If the elevator moves downward, the normal force is antiparallel to the motion, and so does negative work.

Now I leave you with this... what if the elevator is slowing down as it moves upward, such that the normal force is less than the man's weight.  Does the normal force do positive work, negative work, or zero work?  I'll answer in a few days in the comment section.

Mail Time: Does electrostatics show up on AP Physics 1 or AP Physics 2?

Erika Sherger of New Jersey writes in with a question I've been asked before:

Is electrostatics in AP Physics 1 or 2?  The website lists it as a 2 topic but the two sample curricula for AP Physics 1 contain it.

Electrostatics in some form is on both exams.

In AP Physics 1, Coulomb's Law for the force between two electrical point charges will show up -- but that's it.  No mention of electric field, no electric potential, no vector addition for the force exerted by multiple point charges.

AP Physics 1 will also cover simple DC circuits.

In AP Physics 2, all of the algebra-based electrostatics you can think of will show up: fields and potentials due to multiple point charges, due to parallel plates, due to a dipole, electric field mapping (with vector fields, NOT with traditional field lines), capacitors, problems including electrostatics in combination with magnetic fields or other forces, more complicated DC circuits even sometimes including steady-state capacitor behavior...

I know it's a pain in the Dan Snyder to parse, but try searching the electronic copy of the curriculum framework for "point charges" or "Coulomb's Law."  The learning objectives are pretty clear as to what is expected in each course.

And, of course, buy McGraw-Hill's "5 Steps to a 5: AP Physics 1" when it comes out this summer!  :-)

greg

Grading AP Problems: Wrong, but Consistent

Joseph Rao, from Massachusetts, writes in:

I had a grading questions regarding the AP. I noticed on the scoring keys that usually a response is given full credit if it is using the correct approach, but with an answer that was calculated incorrectly.   I had a student on my recent exam who asked if she should receive points if she used the wrong approach on the first part, then calculated the second part of the question with another approach that was wrong, but made sense for the initial approach used.  When in doubt should I just following the scoring key for if they specify to use the answer from the previous question? I chose to not award points because neither approach helped get any closer to an answer. 

Joseph, you chose... wisely.

Now, before I even start answering this question, remember there's no such thing as a "typical" or general rubric.  You've gotta follow each one independently.  And the understanding among readers about how to deal with difficult responses will change on every problem, every year.  Teachers get themselves tied into all sorts of conundrums repeating memes like  "Oh, the AP awards points for substitution, but not for the answer."  That may have been true on one or two rubrics, but neither that nor anything else is a universal rule for AP rubrics.  Each rubric is designed independently.  You cannot game the test.

But to answer your question as best as I can:  If a calculation from part (a) must be used to answer part (b), usually credit is awarded just for the recognition that the answer from part (a) is used, whether that answer is right or wrong.  I call it "wrong but consistent" -- a calculation that leads to an incorrect answer, but which is consistent with previous work, I mark as "WBC."

Don't let students lawyer up, though.  Exceptions exist.  The most obvious exception is when a previous answer renders a future answer ridiculous (as in a car moving 1500 m/s, or the mass of a proton being 500 kg).  Or, if a previous answer renders future work trivial (i.e. calculating a force of zero newtons in part (a), meaning parts (b) and (c) would also answer zero somethings).

Sometimes, credit is awarded for a correct (not consistent, CORRECT) answer -- in this case, WBC work might earn partial credit, but not full credit.  

When in doubt, follow the rubric and use your physicist's spidey sense.  If you feel like you're awarding credit for bad physics, DON'T, regardless of how your student argues the rubric.  If you feel like you're not awarding credit for good physics, DO.  (And your student probably won't complain.)

In the case you describe, I can't imagine this student earning credit.  "Wrong but consistent" doesn't mean compounding error upon error.  It means, someone did everything right in one part of a problem, but not the other; we're going to credit the correct physics, and dock the incorrect physics.  If it's all incorrect, there's no room for credit.

And as a final note, one that I have to give every year to multiple students:  They are not allowed to go to Kansas City with the AP readers in order to serve as counsel for their test.  Grade the test, give it back, and don't accept any arguments about the rubric.  If you need me to serve as a final arbiter, you know where to reach me.

GCJ

Block on an incline -- trig identity or pythagorean?

Joel Houghton from Raleigh writes in about a problem I use in my AP class.  The block shown sits at rest on an incline.  The coefficient of static friction is 0.30.  What is the angle of the incline, and what is the normal force acting on the block?

(As an aside, usually this question is phrased with "maximums":  The MAXIMUM static friction coefficient is 0.30, so what is the BIGGEST angle at which the block can stay at rest?  I assign this problem in week 2 of my AP course, so I ignore the issue of maximums... as I stated it, the problem is still technically correct.)

Pythagorean Method:  Joel created a triangle out of force vectors. The 150 N weight acts straight down.  The normal force acts perpendicular to the incline.  The friction force (equal to 0.30 times the normal force) acts up the incline.  Thus, the weight is the hypotenuse of a triangle -- look at the diagram to the right, which Joel sent me.

Joel applied the pythagorean theorem to get an equation in a single variable:

(150 N)² = Fn² + (0.30 Fn)²

Joel solved for Fn to get 144 N.  Then he used the cosine function to get an angle of 16 degrees for the incline.

Vector Components and Trig Identity Method:  Joel's method is complete and correct.  I don't personally like to teach students to use a pythagorean approach here, though -- it is very difficult for first-year physics students to see, understand, and be able to create the triangle of force vectors.  Instead, I encourage an identical approach to every problem:  Break angled forces into components, then (for equilibrium) set up=down, left=right.

The weight breaks up into components down the plane (mgsinθ) and perpendicular to the plane (mgcosθ).  The two equilibrium equations become:

(0.30)Fn = mgsinθ
Fn = mgcosθ

Solving for Fn requires the trig identity that sin/cos = tan.  I tell my class that this is the ONLY trig identity they will be expected to use in AP physics... but this identity is in fact used relatively frequently.  Here, dividing the equations by each other yields tan θ = 0.30... which means, the angle of the plane is 16 degrees.

You solve this problem your way.  I merely pose two possible approaches.

The economics of late work

Teachers are often hung up on grading policies, especially those for late work.  We tend to model our approach after that of the English department: typically, an English teacher might subtract a letter grade for each day late.  So we do something similar, creating a sliding scale of credit, a scale whose complexity sometimes rivals that of the tax code, and adjusting the policy over the years in response to complaints and lawyerly arguments.

Stop.

What is the overriding goal, the most important purpose, of your homework "policy"?  You want your students to do their homework carefully, and to turn it in on time.  That's because well presented homework leads to learning physics well, which leads to success on tests, which leads to happy and smart students.

When you're structuring your homework "policy", then, don't think in terms of "what is a fair consequence for late work?"  Think instead about how to best accomplish the goal of receiving timely, well-done problems.

I don't think the English department is the best model for us as physics teachers.  English essays are -- usually -- assigned days or weeks in advance, and are due only occasionally.  If an essay is due every fourteen days, and won't be graded for another week after it's turned in, then one day doesn't really make so much of a difference.  In fact, I've had English teachers explain they'd much rather have a three-day-late but good essay than a poor essay turned in on time.

Physics is different.  I assign work every day at my boarding school.  At the day school, problems were due twice a week.  Problems are returned within a day or two in order to provide continual feedback, showing students where they do and don't understand new material.  Unlike the typical English teacher, I would prefer finished work to correct work.  The point of homework is to engage with the material, not to show mastery.  The goal of my homework "policy" is to produce that engagement.

A story... Can't cite it, but read it in (I think) the Wall Street Journal:  A daycare service in a large city was having trouble with clients picking up their kids well after the appointed pickup time.  Employees had no choice but to stay late, sometimes very late -- you can't just leave a 4-year-old on the doorstep and say "Mommy will be here soon, sit tight, bye now."

The service revised their policies to provide monetary penalties for late pickups.  That didn't help.  They made the fines for late pickup ever bigger... and yet, the rate of late pickups continued to increase.

Finally, the service tried something different -- they ELIMINATED MONETARY PENALTIES for late pickup.  Instead of a page in their handbook listing crimes and punishments (Late 5-20 minutes = $50, late 20-60 minutes = $200, etc.), they merely wrote that daycare employees expected to leave promptly in order to join their own families for the evening.  Repeated lateness was not considerate of the employees, and would not be tolerated.

Hah!  Late pickups were virtually eliminated.  The article I read speculated that by fining parents for late pickup, they had in the parents' minds created "late pickup" as an economic good which could be bought and sold.  The parents would do a cost-benefit analysis... is picking my kid up late worth the fine?  If so, I'll just pay the fine.  I can afford it.  And why are the employees so grouchy at me when I show up two hours late?  I'm paying them a bloody fortune for the late pickup, they should be happy for the money.

But without the fine, late pickup became not a saleable good, but a sin.  The frowning from the employees was no longer interpreted as ungratefulness for the opportunity to earn overtime pay; instead, the late parents were embarrassed and apologetic.  "I'm so sorry I took time away from your own family.  This won't happen again.  Please continue to watch my child and take care of him with love... I promise to respect your time in the future."

I think of homework the same way as late daycare pickup.  If I assign a sliding scale of grade penalties, I'm encouraging students to weigh the cost against the inconvenience of actually doing the work.  If a student is happy to settle for a C, he can decide to do just enough for that grade.

However, if I present missing homework as a sin, awarding no credit and requiring the homework to be done in any case, the rate of completed homework skyrockets.  Even half-arsed problem sets allow a student to engage with the material, and improves that student's understanding.  Since I've gone to some version* of "no credit for late work, period" I've had few complaints, and very few late assignments.

* In upper level classes, I allow two no-excuse-necessary extensions per marking period.

Anecdote from Burrito Girl:  Some physics teachers will say that they couldn't possibly give no credit for late work, because they'd have to deal with so many complaints from students, parents, colleagues, and administrators.  My wife and sidekick Burrito Girl used to teach English.  She took points off for late work according to a sliding scale.  She says that she got way more complaints about her policy than I ever get about mine.  Students, parents, and colleagues argued that the grade penalty shouldn't be as steep for a particular assignment, or that the policy should be adjusted, or that extenuating circumstances should apply...

In other words, you're going to have perpetual arguments whether you take off 10% or 100% for a late assignment.  Why not give a shot to the method that is most likely to convince students to engage with their physics problems on a regular basis?

Mail Time -- Why is my algebra-based textbook using calculus?!?

One of my summer institute participants wrote in the other day with a question that I've been asked in similar

from wyzant.com... this is NOT calculus!

form many, many times...

I discovered this morning that the textbook we have for the course, College Physics [by Serway and Vuille] has calculus-based content for 2D motion. I have resorted to using the textbook I have for general Physics, Physics: Principles and Problems by Glencoe, as an alternative for this section of material. Have any of you run into a similar issue or have any suggestions for other ways to communicate the necessary material at an AP level? I'm just wondering for this particular section, and if I run into a similar issue again down the road with content (since we're teaching algebra-based Physics).

Yeah, this is why I hate the standard-fare textbooks, written by Ph.D. physicists for Ph.D. physicists.  It's NOT calculus, even though it looks like it on first glance.  My correspondent pointed me to the section describing instantaneous velocity.  Serway uses a full page of equations, many of which look exactly alike to the untutored eye,* to make the simplest of conceptual points.

* My eye is tutored, but the 17 or 19 year old reading this text is not.  First rule of writing: know your audience.

The page in question uses mathematical notation that says the limit of a distance divided by a time as time goes to zero is the definition of instantaneous velocity.  Well, the eleventh grade student came to class angry: "We just started taking limits last week in my calculus class.  I've never seen this sort of thing before, and I don't understand it yet.  I thought you said we don't need calculus for this class!  How am I supposed to understand it?"

First, the general issue about algebra-based physics, calculus, and resources:  If students read texts or online information, they will often -- too often -- see mathematical explanations that resemble calculus.  See the picture above, which is using five rectangles to approximate the area under a curve.  "That's calculus, I know it!" says the novice.  Well, it's not.  The area of a rectangle is base times height -- that's 6th grade math, not calculus.  Even in algebra-based physics, we have to compare the slopes and areas of curved graphs... and you can expect someone to indignantly holler "Calculus!" when you draw the slope of a tangent line.  What "algebra-based" means is that we don't ever have to evaluate an integral or derivative of a function to make a numerical calculation or derivation -- it doesn't mean that we never look at curved graphs.

One of our tasks as a teacher of first-year physicists is to help them simplify tough ideas.  That means steering them away from poorly-written or misleading sources.  That means explaining in words, and minimizing mathematics.  A diligent but frustrated student must understand that yeah, the textbook is ridiculously confusing, but that doesn't mean you can get angry -- you simply have to find a different way to understand the topic.

Finally, the specific issue of Serway's presentation of instantaneous velocity:  All this math is just telling you that (1.) velocity is distance traveled per second, and (2.) "instantaneous" velocity means the velocity RIGHT NOW.  Distance divided by time is, generally, velocity.  If you use data over an hour, you get the average velocity for that hour.  But if you don't look at an hour, or a second, but at a fraction of a second, then you're looking at instantaneous velocity.  Serway is doing his highfalutin' physics professor best to say just that, but in mathematics.  I wish he'd speak English.

GCJ

Foucault Pendulum -- Latitude of a Google Doodle

On Wednesday, the Google Doodle showed a working Foucault Pendulum simulation.  As it happens, my research students are in the opening stages of a deep investigation of the Foucault in preparation for the US Invitational Young Physicists Tournament.    We are tasked with building a Foucault, using it to determine our latitude, and then conducting the error analysis to define the precision of the measurement.

What a useful coincidence... I added the question to my research students' quiz: "Determine the latitude portrayed by the Google Doodle."

The equation for the precession per day of a Foucault pendulum is 360 degrees times the sine of the latitude.  Solving, then, the latitude is the inverse sine of the precession per day divided by 360 degrees.*  We need to find the precession rate from the simulation.

*Explaining the geometry and conceptual physics behind this equation will be part of each research team's presentation at the tournament, of course.

One of my students sent a rather tetchy response, complaining that he'd have to sit there for most of an hour just to watch how long it takes for a peg to be knocked down.  Some cursory exploration finds a cheat:  look in the lower right corner at the clock face.  Click on the clock.  A slider appears, allowing you to fast-forward time.*

*A second slider allows you to adjust latitude.  I'm doing everything here for the default latitude when I just click on the doodle link.

I set the slider to 12:00, and fast-forwarded until all pegs were knocked down.  At 6:25 PM by the clock, the last peg was still standing; at 6:40 PM, the last peg had fallen.  This means that the pendulum rotates 180 degrees in somewhere between 18.42 hours and 18.67 hours.  Pro-rating this rotation rate, this works out to between 276 and 280 degrees per day.

Now plug into the relevant equation: the latitude of this pendulum is between 40.0 and 40.7 degrees.

Reader help, please:  I anticipated that the simulation either (a) used the geo-located latitude of the computer accessing the doodle, or (b) used a default latitude with some special meaning, such as Google's Mountain View, CA headquarters.  Oops.  I am located at Woodberry Forest, VA, 37 degrees north latitude; Mountain View is also 37 degrees north latitude.  Any clue where this Foucault is supposed to be?  (Or, alternately, any corrections to my calculations?)

And, if you'd like to participate in our tournament, solve three of these four problems and come to San Jose, CA on Jan. 31, 2014.  I'll be happy to help you out with both the physics and the attendance logistics.

Ray optics simulation

Screen shot is from the Phet site at the linked refraction demo.

Before I start talking about an awesome simulation, hear the standard disclaimer:  Online simulations are in no way a substitute for live quantitative demonstrations.  

That said, online simulations, if they're programmed correctly, can be extraordinarily useful: for making quick "measurements," for showing experiments and regimes within an experiment for which you don't have the equipment, for student use at home... As long as you are not trying to replace live equipment with a computer, simulations are wonderful resources.

The Phet interactive simulation site is one of the traditional favorites of physics teachers.  These have been maintained and developed over time by pros.  Note that they are free (with donations accepted), and that they require Java.

Today my conceptual class used a laser and a fish tank to make measurements of incident, reflected, and refracted angles.  Homework questions will ask qualitatively about which way light bends at various interfaces, about comparing angles, about how these angles change in different situations.  

My colleague Alex Tisch whipped out this phet simulation which runs exactly the same way as my in-class live demonstration.  It even comes with a protractor that you have to place properly to measure angles.  I particularly love the option of a "mystery material" for which you have to use the protractor to figure out the index of refraction.*

* In Regents or AP physics, I'd have students use Snell's law to determine the mystery index of refraction.  For conceptual, I could ask students to rank materials by their n, or to compare the material's index of refraction to that of water, say.

I'm not actually using this for any sort of official assignment, at least for now.  Rather, I just put a link on the class folder, and offered extra credit to anyone who actually downloads and plays with the simulation tonight.  If nothing else, I might use it myself in creating a problem -- a screen shot provides me a diagram from which I can ask virtually anything.  Alex did the live demonstration, then used the simulation to make many quick measurements without having to turn out the lights, click erasers to visualize the laser, draw the rays on the glass, etc.  

Thanks for the link, Alex!

GCJ

Take a picture of every demo and lab

Folks, I've been asked for years:  "Do you have a list of all of the quantitative demonstrations and lab setups that you do?"  I've never actually compiled such a list.  I just create on the fly, usually.  A quantitative demonstration is merely an end-of-chapter problem scaled such that the answer can be tested with available equipment during class.  Each year, I look in the equipment closet, set something up, and go with it.  I *like* the improvisational elements this approach brings to my classes.  Just as I don't want my students to think of laboratory as an object lesson in instruction-following, I don't want to fall into the trap of making physics teaching a strict note-following process, either.

That said, I often want to remember things year-to-year, and I often want to communicate to others what I'm doing.  I've never been organized enough to write down details of my demonstrations.  I've documented many demos on this blog with a photograph and description; but taking and uploading each photo, and then writing the description, has been a time consuming process.

Today, my colleague Curtis offered an elementary yet elegant observation about documenting his demonstrations.  He was frustrated because he didn't remember the experiment that we ran on the first day of conceptual physics last year, even though we had done it in detail last year, even though I described it to him again.  However, when I went into my classroom and actually set up the experiment for him, he instantly knew what to do.

This year, then, he took a picture of the setup with his phone; he emailed the picture to himself, and saved it in a file marked "lesson plans."  

See, I hate the term "lesson plan."  It implies that I should have pages of notes explaining what I'm doing in each portion of my class.  Well, I did have such notes the first couple of years I taught.  Now, though, I just set up a demo and improvise.  I don't need no stinkin' "lesson plan" -- The photo BY ITSELF is sufficient for reminding me what I did last year, for communicating to colleagues, and even perhaps for reminding students about setups.  Curtis even suggested using the photo as the basis for a lab quiz:  "Here's the setup from yesterday's demonstration.  Explain how to use the equipment present to measure angles of incidence and reflection."

My pledge for the next couple of years is to remember to take as many pictures of lab setups as I can.  This year I'll work on conceptual; next year will be AP Physics 1.  Hopefully I can compile a big file of picture after picture so that when other teachers ask for a list of demonstrations, I can forward these files.

And yes, I am aware that to folks who are more tech savvy and/or about a decade younger than I, this post must sound like "oh, it's good to have a collection of books, but they're especially useful if you take the books down occasionally and read them."  :-)

GCJ

Mail Time! Some quick questions about AP Physics

It's that crazy-arse time of the year, at which point I look at the calendar and say, "Oy, my next day without an obligation is the Wednesday before Thanksgiving."  So in honor of the start of school, here are a few quick questions from readers with quick answers.

From Joseph: 

Hi Greg. I was examining some of the grading done on the AP as well as how you graded some of your tests. I ... saw that you adjust the multiple choice scores slightly. The example I'm looking at says you multiplied the MC score by 1.304 after rounding then added that to the total FR points for the RAW AP score. Why did you adjust the MC? Does your strategy vary test to test? 

Hey, Joseph.  Both sections should be weighted to one minute per point.  Since on that test I gave 23 questions in 30 minutes, I multiplied the mc score by 30/23 to add to the free response.

From Youri, who has two questions:

1. I can't remember but on the AP do they go by significant figures or by given answer to 3 decimal places?? Can you clarify that for me.

Use 2 or 3 sig figs.  Not worth throwing a fit over with the students, though, compared to the other classic battles like using units or describing a solution thoroughly.

2. Do you have any cool demos I can do for kinematics, using a pasco track, carts, I have a fan for the cart, a labquest, a motion detector a force sensor...basically what you told me to get. I want to do a demo but I am not really sure what would be the most appropriate and useful to the kids???

Use the fan cart on the track with the motion detector and do qualitative and quantitative demos.  Like, what will the x-t or v-t graph of this motion look like?  Can someone make the cart create this graph?  What initial velocity will get the cart to stop at the top of this inclined track (given the cart's acceleration)?   Or, just what is the cart's acceleration given the v-t graph?  All sorts of fun stuff.  Choose an end-of-chapter problem, and scale it to a cart on a track.

From Jessica:

Random question. I have a student who is solving force problems with tangents instead of sines and cosines to break forces into components and determine magnitudes of force components. His math works. But I rarely see tangents show up on rubrics. Does it matter? As long as his math is sound? Or will it lose him points to not show force components in sines and cosines? 

Hey, Jessica!  His approach is fine, as long as the physics is correct.  Nonstandard but correct and clear approaches always earn full credit.  (As I sometimes say rather cheekily, that's why the College Board hires physicists to grade the exam rather than lawyers.  The rubrics are meant to be interpreted intelligently, not inflexibly.)

Good luck to all this year... please email questions as you have them.

GCJ

First AP Physics lab exercise -- cart on an incline

In my advanced / AP classes, the first week consists of demonstrations involving static equilibrium.  The homework includes equilibrium problems to solve.  After a week of demonstrations, problems, and quizzes, we do our first laboratory exercise.

I start by explaining* the general point of experimental physics -- we've solved lots of problems using the principles of equilibrium.  Now it's time to put these principles to a rigorous test, to provide experimental evidence that our problem solving methods are legitimate.  I do no further discussion of theory until we've collected loads of data.

* VERY BRIEFLY.  Students don't want to hear a lecture about the philosophy of experimental vs. theoretical science.  They will tune out instantly if I talk about this for more than about one minute; I want my class time spent collecting data, not listening to me drone on.

Next, I show the experiment:  At the front of the room, I stick a cart on an angled track.  I hold a string with attached spring scale parallel to the track, and read the scale; I put an angle indicator* on the ramp and read the angle.  I make a table on the board with a column for the tension in the string, and the angle of the incline.  I sketch a graph on the board next to the table, with axes labeled "Tension in the string (N)" and "Angle of the incline above the horizontal (degrees)".  I place a dot on the graph.  Then I make one more measurement... and we're just about ready to go.

* If you don't have the $20 PASCO angle indicator -- and you probably shouldn't -- use the "Clinometer" or "iHandy Level" app on the iPhone.  Android has similar and free apps.

The last thing I do before breaking everyone into groups is to briefly discuss the rules of laboratory, including that all data goes directly on the graph, and that you may not measure the same data point twice.  (Many students will nevertheless ignore these rules.  Don't get frustrated, just expect it and deal with it.  Even in my AP Summer institute, several teachers made a table of data without a graph, despite the fact that I said two or three times, very loudly, "You may NOT just make a data table now and graph later!")

Finally, I choose partners randomly with random.org, and we go at it.

"Go at what," you ask.  Where's lab sheet?

There is no "lab sheet."  The students have to listen and watch, then do the experiment.  If they didn't figure out what to do by watching, a lab sheet won't help.

So how do you set up all the stations before lab?

I don't.  I show everyone where the equipment is kept.  That's it.  They have to tie string themselves.  They have to find their own space to use, even if that space is in the hallway.  And, they have to clean up themselves.  This approach saves me time, sure; but it's also more authentic experimental physics.  Setting up themselves, with no lab sheet, makes the experiment less an exercise in following directions than in collecting data in which they have a personal connection.

How many data points do they collect?

They're not allowed to ask that silly question.  They keep collecting data until a first grader could clearly differentiate between the data points making a line or a curve.  When they think they have enough data, groups show me the graph, and I take a look.  More often than not on the first day I say, "what, you think five points provides a clear pattern?  Pah, back to the experiment before I send thee to the dungeons."  Then comes "Oh, this data is looking good, and does in fact look linear.  But the angles only go up to about 40 degrees.  Let's explore all the available angles... why not go up as steep as possible?  Then we'll be sure that the line continues."

Finally, groups will produce a graph that flattens out at larger angles.  At this point -- and NOT before -- do I show the free-body diagram and equations relating the tension in the string to the angle: T = mgsinθ.  No wonder the graph flattens... that's what a sine graph does for angles from 0-90 degrees!  This is a pretty awesome "ah-a!" moment for many students, one that wouldn't have happened if I had shown them the equation or analysis before we started.

All this data collection generally takes most of a 90 minute period.  Those who finish put away their equipment and begin the analysis, in which they make a new graph of tension vs. the sine of the angle... then they use the linear graph's slope to determine the cart's mass. 

I can discuss the analysis in a future post.  That's really of secondary consideration for now.  I'd like more physics teachers to separate data collection from data analysis.  I see so many students try to answer AP lab questions with equations and calculations... let's make sure that students can collect data, graph that data appropriately, and describe the appropriate use of equipment.  Then we can worry about linearizing graphs and taking slopes.