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