Super-elastic popper toy for 2016 AP Physics 1 problem 2

Popper toy, obtained by my student Mark Wu
at the NASA store at the Smithsonian

Next week, I will be grading another experimental problem on the AP Physics exam.  Since 1996, at least one question on each AP exam has been posed in a laboratory setting, asking students to design and/or analyze an experiment.  This will be, I think, the twelfth experimental question I've graded over the years.

The 2016 AP Physics 1 exam problem 2 asks students to design an experiment to investigate whether a toy bounces perfectly elastically, at least for low impact speeds.  Then, the problem says, the experiment seems to violate a basic physics principle.  What the heck happened?  

The obvious explanation is that the toy stored some sort of energy internally, through a mechanism such as a wound rubber band or a rotating flywheel.  Then that internal energy was converted into mechanical energy in the collision.  But how could that happen in practice?

By an utter coincidence, when I was walking through our freshman dorm on duty Sunday night I discovered one of my AP students playing with the toy pictured above.  I've seen these popper toys before, but not like this one.  It has a small handle, sort of like the grip of a dreidel, that is accessible once the toy is turned inside out.  

Turning the toy inside out stores elastic energy.  Using the handle to give the toy spin as it falls stabilizes the orientation of the toy, so that when it hits the ground, the restoration of the toy to its original shape converts elastic to mechanical energy.  The toy bounces 2-3 times higher than its release height.  

My student found his toy in the NASA store at the Smithsonian Institute in Washington, DC -- that's probably why there's a picture of the space shuttle on it.  I found the identical toy on "branders.com", via a google search for "popper toy".  The intent of this site is for you to order hundreds of these toys with a customized logo for the purposes of distribution at a sales conference or a marketing event.  However, the site offers to sell you a couple of samples for $5 each.  I ordered the maximum of 3 for my class.  

So yet again, an AP question can be set up in the laboratory.  I'll give this problem on some test or quiz next year; immediately thereafter, I'll hand out the toys and ask the students to do the experiment they designed.

Eight different approaches to laboratory work

In preparation for my AP Summer Institutes for 2016, I've redesigned how I present experimental work.

When I began teaching AP Physics B, I did lecture and problem solving four days a week, with lab work on the fifth day.  I integrated more and more experimental work into my daily classes, especially as I amassed equipment for each topic area.

Nowadays, experimental work is part of virtually every class all year.  My minimum goal is to get student hands on equipment three of five days each week; my students will tell you that the reality is more like four or five out of five.

Okay, many of you share this lofty goal.  But how to accomplish it?  Upperclassmen don't like routine; they will not be comfortable doing the same styles of activities every day all year, even if the topics change.

So, for Summer Institute and for reference purposes, I've categorized eight styles of lab work that I've been using for my classes.  All are applicable to teaching physics at any level, but are optimized for AP Physics 1 students.

The styles are listed roughly in the order I introduce them to my classes.  Remember, at the beginning of the year, students certainly aren't ready to do AP Physics 1 test problems in the lab with little guidance!  We can talk 'til we're blue about "open inquiry" and ideals of "student-centered learning", but it is incumbent upon us to teach fundamental skills before opening up the lab for the students to play.  That doesn't mean we TALK at students about lab skills; that means that each style of experiment builds skills in context that are taken for granted at the next style.

Read on... at my AP Summer Institutes (I'm doing four in 2016, listed in the sidebar -- please sign up!) I'll be doing experiments in each of these styles with all the participants.  And please bring your own ideas to share with us.

1. The Quantitative Demonstration

Instead of showing how to solve textbook problems in the abstract, try setting up the actual physical situation presented in the problem – do the problem, treat the answer as a prediction, and then verify the prediction experimentally.  Take a look at this post about my first day of AP Physics, or just search "quantitative demonstration" on this blog for more ideas.  

2. The whole class as a lab group for live data collection

For example… to get data for voltage vs. current to show the ohm’s law relationship:

·             *  I put a blank set of axes on the screen; I give everyone a hard copy of blank axes.

·             * I bring the class to the front of the room to see the setup – they see the voltmeter, ammeter, and how I vary the voltage by turning the dial on the power supply.

·             *  We discuss how to scale the axes such that the data will fill the page.

·             * Each student in turn is called to the front of the room to adjust the voltage, and to read and record current and voltage data.

·             * Before going back to his seat, the student writes his data in a chart on the board; and he graphs his data point on the screen.

·             * Meanwhile, each student is responsible for making his own personal graph.

·             * I move quickly – the next student is ready to go while the first student is still writing and graphing his data.

·             *  As the experiment goes on, students begin to suggest how to fill in such that the entire parameter space is explored.

·             * When we have plenty of data (usually meaning everyone in the class has had a turn), everyone draws a best-fit and calculates the slope.

·              * We estimate an average resistance with uncertainty from the class’s slopes – this always matches the resistance of the resistor nicely.

This is an excellent technique early in the year, when you’re introducing and modeling lab skills; whenever you need quick data – this takes maybe 1/4 of the time it would take for the students to do it independently;  and anytime you have only one set of equipment.

Here is a description of how I use this same technique on the first day of my conceptual physics class.

3. Quick data collection to verify prediction of a qualitative trend, or to determine the trend

Students must be able to describe the shape of a graph given the relevant equation; and students must be able to suggest the form of an equation given a graph of experimental data.

By scaling the axes ahead of time for the students (and being sure that the scale represents an appropriate range of values), you can save time in lab; more importantly, you focus the students on just this particular skill of translating equations to graphs and vice-versa.

See this post for a specific idea about circuits.

4. Create a linear graph, use the slope to determine a physical quantity

I believe in putting data directly on a graph; I believe in hand graphing; I believe in taking slopes by hand.

If your students graph asthey go they understand intuitively what it means to “explore a parameter space.”  (And it’s easier to convince them to take more data if they haven’t put their stuff away and expected to be all finished.)

Your students are not skilled at graphing by hand; yet they are likely to have to graph data as part of an AP question.  You can teach them how to use excel to make a graph at year’s end.  And they’ll actually understand what excel is doing if they’ve been graphing by hand all year.

Similarly with taking slopes.  Make them write out (y₂ – y₁) / (x₂ – x₁).  Make them circle the points on the best-fit line (not data points) used to calculate slope.  Make them write the units of the slope.

Then make the students explain how to determine the physical meaning of a slope using equations, not just guessing based on the units of the vertical and horizontal axes.

5. Linearize a graph, use slope to determine a physical quantity

The AP physics exams expect students to be fluent in linearizing graphs.  See the 2009 Physics B problem 1 for the canonical example of an experiment requiring graph linearization.

This is one of the first linearization lab exercises I do.  We hold a cart on an inclined track with a string attached to a spring scale, varying the angle of the track.  Initially, we graph tension vs. angle – this graph is curved.  By writing out the relevant equation T = mgsinq, we recognize that a graph of tension vs. sin q will be linear with slope mg.

6. Open-ended determinations – are you hired?

Students aren’t usually aware of the intended audience for lab write-ups.  “Mr. Jacobs has done this experiment a million times, he knows how it works, and he saw us do it.  So answering these questions is just a formality.  He knows what I know and what I mean.”

So I make the audience someone OTHER than me, and put the writeup in a context they understand:

Imagine that you and your partner have been asked to make this determination for a Fortune 500 company as part of the competitive bidding process for an engineering contract. 

You will submit your marked pipes and an explanation of your methodology to the company.  From that writeup alone, they will decide which partnership to hire.

Therefore, I will have someone – not me – rank the submissions from strongest to weakest.  They’ll be placed in piles:

·        Hired (1 submission)

·        Not hired, but recommended to other companies

·        No action

·        Blacklist

7. Independent prediction exercises 

These are like quantitative demonstrations, but with the students doing all the work.  Other teachers do similar activities, calling them "stations".

I have students work independently, at their own pace.  They are welcome to collaborate; since everyone has something slightly different on their sheet, their collaboration is authentic.

I've posted about two of these:  One with energy, and one with the direction of force and motion.

8. Experiments taken (nearly) straight from the AP Physics exam

Virtually every AP Physics 1 problem can be set up in the laboratory.  I modify the problem so that it scales to the equipment in my lab; for example, using 500 g carts rather than 500 kg cars.  I often try to set up the experiments such that we can produce a graph, perhaps even a linear graph with a meaningful slope, even if that graph wasn’t part of the original AP problem.  I can't post these online, because they are based on College Board questions.  However, come to my AP Summer Institutes, and these exercises will be on the CD that you get.

Mail Time: Why is there not a lot of rotation on AP Physics 1? (Or, is the seeming dearth of rotational questions a valid perception?)

Reader Sara Rutledge asked this question in the comment section of the post in which I linked to the solutions to the 2016 exam.  I think it deserves its own post, so as not to be lost in the depths down the page...

  

My students commented that the exam had very little rotational motion beyond the FRQ with rotational kinetic energy. Is there an effort by test writers to match up the percentage of objectives on a topic with the percentage of questions on the exam? We had spent a lot of our review time on torque and conservation of angular momentum, so students were surprised that the exam focused on linear concepts and didn't seem to have a balance. Do you have any insights/advice on this? 

Sara, my understanding is that what we think of as "topic areas" are virtually irrelevant to the distribution of questions on the exam. Questions are distributed by the combination of "Big Idea" and "Science Practice." 

For our purposes, that means a problem relating torque to angular acceleration is EXACTLY EQUIVALENT to a problem relating force to linear acceleration. Conservation of angular and linear momentum are equivalent in the development committee's eyes, as long as the questions use the same science practices. 

Now, I'm sure there are discussions among the committee about balancing linear and rotational concepts a wee bit. But I'm not privy to those conversations. In terms of the goals of test writing, an exam could in principle be entirely linear, or entirely rotational, and still be considered a valid exam. 

As always, I take the most inference from actual, authentic, released items. And in the first two years of the exam, those released items are more heavily linear than rotational. 

Now, we haven't seen the multiple choice. I'm personally skeptical that there weren't at least a couple of rotational problems on the multiple choice. I think students see what they want to see: they wanted a torque or angular momentum problem, didn't get it on the free response, so likely ignored or forgot that it showed up in the multiple choice. 

That said, unlike the old Physics B percentage distribution of topics, it's quite possible that torque and angular momentum were in fact a negligible portion of the AP 1 exam. 

This year. :-)

GCJ

2016 AP Physics 1 exam -- my solutions

I enjoyed writing my solutions to the 2016 AP Physics 1 free response questions.  You can find the questions linked via the official College Board exam site, here.

As always, I guarantee that I've earned a 5, but not that I get every detail right.

But more importantly, as we move farther in time from Physics B, remember that AP Physics 1 exam questions ask for explanations and creative descriptions.  Your answers may not be the same as my answers, yet may be fully correct.  Conversely, just because you cite the same general physics principles as I do doesn't mean you've earned full credit.  The quality of the explanation is the key.

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

GCJ

The AP exam is tomorrow! What should I do tonight?

Nothing.

Shouldn't I do as many problems as I can before I fall asleep with my head hitting the 5 Steps Book on my desk?

Um, no.  Would you ask your football team to have an all-night weightlifting session the night before the state championship game?  Would you run 50 miles the day before the New York Marathon, just to be sure you're ready?

But I know there are things I'm not perfect at.  I could get better with some practice tonight.

No you couldn't.  Problem solving skills are just that -- skills.  They are built over time, over success and failure, over hard-won experience.  They're not going to improve overnight, no matter what you do.

But there is a chance that I could do a problem that shows up on tomorrow's exam!  Shouldn't I take that chance?

In one night of feverish cramming, sure, you might happen to do a problem similar to what's on the exam.  But every new think you put in your brain tonight will shove something else out.  Isn't it just as likely that the actual AP exam includes a problem that you worked on last week, but since you crammed so much on the eve of the exam that problem just blends together with everything else you've done?

More importantly, it's far more likely that when a recognizable problem shows up on tomorrow's exam, you're so worried and sleep deprived and anxious that you say "ah, I recognize that problem!  But I don't remember how to solve it... dang."

All my friends are cramming tonight, so my teacher and my parents expect that if I don't, I'm slacking.

Well, that's a different problem, one unrelated to physics.  I'm not a politician, I'm a physics teacher.  You may certainly point your teacher and your parents to this post.  Have them email me -- I'll tell 'em straight up that there is no benefit to studying the night before the AP exam.

That's easy to say, Greg Jacobs, but put your money where your mouth is.  Don't you expect your own students to study tonight?  Don't you at least wink wink at them suggesting some things to look over, perhaps in the 5 Steps book?

No.  I'm taking my students out to the school snack bar during the evening study time, for the express purpose of ensuring that they're NOT studying physics.

Look, folks.  At this point you're either ready for the exam or you're not.  There's nothing to be done except for focusing your mindset.  

Another analogy might be performers in a musical an hour before curtain on opening night.  All the practice is done.  Okay, it's a good idea to do a vocal warmup, as well as the mental warmup provided by some of those drama department games.  But should the director say, "hey, let's go through act 1 again, there's some bits we need to work on?"  No.  Just come onto stage brimming with confidence and energy.

You will make mistakes -- in the championship game, on opening night, on the AP exam.  That's to be expected.  If you go in with a positive attitude and a focused mind, then you'll be able to recover from a dropped pass, a flubbed line, or a paragraph response question that ties you up in knots.  

And if it turns out that you're dropping passes on every series, or you flub your lines in every scene, or you are flummoxed by all five free response questions... 

...then deconstruct how you should have approached the ENTIRE YEAR differently.  These aren't problems that practice the night before would have helped -- these are systemic issues of overall preparation.  Address those issues for next season.

For now, relax.  Go bowling.  Play cards with your friends.  Don't have an early night of it -- have a NORMAL night.  Go to bed the same time you always do.  Get up the same time you always do.  Take comfort in your regular daily routine.  

Show up to the exam knowing that you're as prepared as you're gonna be.  My parting words to my class on their way to the AP exam are simple.  

KICK BUTT TOMORROW.

-GCJ