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28 April 2017

Mail Time: Last-minute questions before the AP Physics exams

The AP Physics 1 exam is next Tuesday.  Remember, no studying after Monday's class!  Lots of last-minute questions coming in.  Here are a few quick ones, with responses that sometimes are merely links to other posts.

From Nikki:  I'm confused on the AP Physics 1 Practice Exam Question 2. I understand the explanation in scoring guidelines, but it seems like they have ignored the PE due to the gravitational pull of the Earth and I don't understand why. Any chance you have some insight into this?

Nikki, the PE is for the earth-spring-object system, and is 1/2(k)(x^2) measured from the equilibrium position of the spring/object. This post gives further details.

From Paul:  If a student uses the language of calculus to justify or explain an idea on the AP exam, will that be accepted by the AP reader?  This came up because it is an algebra-based course.

Paul, please take a look at the second answer in this post.

From Matthew, four questions:

1) If you give practice exams ... What percentage on the multiple choice do your classes typically average? I am just curious as a gauge for myself and my classes moving forward.

Probably 60-65% on average with authentic physics 1 questions.

2) On the first FRQ part b is says a student would receive a point "for recognizing that the force causes a change in momentum or a change in velocity." Would the student have to state that? The question asks to calculate the magnitude of the external force on the system.

State or imply, mathematically or verbally.  Just writing "F=ma" doesn't cut it, but writing that and then trying to calculate a change in speed for a would probably earn the point.

3) If a student answer a part of the FRQ correctly and then adds something that is incorrect would they receive credit for the correct response?

No.  When there are multiple responses, we pick the one that earns the fewest points.  They can't game the test.  :-)

4) Is there any type of final reminder you cover with them before the exam?

Try this post here, about "BOUX" day.

From Michele: On the MC questions that are multi-select (two correct answers), how are they scored? Do students need to get both choices correct in order to receive credit?

They need both choices right to get credit.  No half points.

From Michael: For AP grading, are points taken of for not simplifying expressions?

Michael, as long as the solution is as required -- "solve for a in terms of given variables and fundamental constants" -- then any form of the solution is acceptable.

Got others?  Go ahead and post a comment or email me.  I'll see what I can do.

21 April 2017

Reviewing for the AP Physics 1 exam: No big practice exam, but Big Butt Fundamentals Quiz

I take an approach to exam review that's consciously different from what other teachers do.  I am doing no tests at all this month, no practice AP exams.  We're solving one authentic AP Physics 1 free response in each assignment; we're practicing a couple of multiple choice questions each day.  We're doing corrections on anything we miss.  I'm getting students to grade other students' work to an AP rubric wherever possible.

Why am I not doing practice exams?  Because every test we've taken all year has been in (or close to) AP format and style.  My students know how to pace themselves so as not to run out of time.  They know how to communicate enough to get credit, but not so much that they waste time and ink.  They know the level of difficulty they will face on multiple choice and free response problems... because we are doing some each day.

Importantly, while I'm giving some questions for homework, I'm doing others as brief in-class quizzes.  It is critical that students have practice working on AP level problems without a safety net, without the ability to ask friends or teachers clarifying questions.  But we do that all year, on every test and quiz!  Since I never allow students to ask questions on tests or quizzes, I feel no pressure now to give any further authentic AP practice.

One type of major assessment that I do use is the "Big Butt Fundamentals" quiz.  I give students 30 minutes to answer 30 questions that are, for the most part, straight off the fact sheet.  The first twenty questions are pure recall; the last ten require some processing, but are still testing misconceptions or ideas that are fundamental to students' knowledge of physics.  Feel free to use this quiz in your own class.  I create it by randomizing the fact sheet, and then just riffing off each fact.

The purpose of the Big Butt Fundamentals quiz isn't to play "gotcha".  It's to get students' noses into their fact sheet.  It's to show the students what they know well, building confidence; it's to show students what they might have forgotten, leading the students themselves to look up the correct answer or to discuss the question with friends.

I ask students to correct the Big Butt quiz by writing a complete sentence stating the reasoning or fact behind each answer.  Rather than just writing "kx", they'd write "the force of a spring is kx."  They are putting their answers in context.  

I don't ask for complete sentences as a punishment, or because my ed school training or my teacher's edition told me to... I'm making the students write so that they have a better chance of remembering a fact that they already got wrong once.  My students are generally cooperative with this rationale, because (a) I don't ask them to do much this time of year anyway, and (b) they see by now the connection between correcting what they get wrong the first time, and strong performance on future physics problems.   As we say, practice doesn't make perfect.  Perfect practice makes perfect.

20 April 2017

A large bug on the edge of a DVD

A large bug of mass 5.0 g lands on the outside edge of a DVD*.  The DVD has mass 9.0 g and radius 6.0 cm.

*DVDs are still a thing, right?  Or, at least I expect that most of my 15-18 year old students know what a DVD is without further explanation.  Or, I'm an old man.

I use this setup to introduce newton's second law for rotation, and the additive nature of rotational inertia... and then to discuss conservation of angular momentum.

(a) Does the bug's presence significantly affect the rotational inertia of the DVD?

By itself, the DVD is a disk, with rotational inertia (1/2)MR2.  That gives 160 g*cm2 as the disk's inertia.

The bug adds its rotational inertia algebraically.  The bug should be treated as a point object, whose rotational inertia is MR2.  That gives 180 g*cm2 as the bug's inertia.

The rotational inertia of the bug-DVD system is then 340 g*cm2. The addition of the bug nearly doubles the DVD's rotational inertia; thus the presence of the bug is significant.

(b) Initially the bug and DVD are rotating at a constant angular speed.  Then, the bug moves to a new position 3.0 cm from the DVD's center.  Explain why and how the DVD's rotational speed changes.

No external torques about the center are exerted on the bug-DVD system ('cause no net force at all acts).  Thus, angular momentum is conserved.

Angular momentum is When the bug approaches the center of the disk, the bug's (and thus the system's) rotational inertia decreases because the R term in the inertia formula decreases.  To keep angular momentum from changing, then, the ω term must increase.  The DVD will speed up its angular velocity.

(c) Does the bug exert a torque about the DVD's center as it moves toward the new position?

Tricky.  There's no EXTERNAL torque on the bug-DVD system.  But angular momentum can still be conserved when internal torques act.  The torque of the bug on the DVD would be internal to the bug-DVD system.

Consider the DVD by itself.  It changes its angular speed.  So by Newton's second law of rotation, it must experience a net torque.

What can possibly provide that net torque?  The weight of the DVD and the normal force of the spindle on the DVD both act through the center of the DVD; they provide no lever arm, and thus no torque.

The only other possible provider of torque is the bug.  But how, in terms of torque equaling force times lever arm, can the bug do that?

Since the bug rotates with the DVD, a static friction force must act between the DVD and the bug.  That friction force acts tangent to the rotation of the disk, and thus has a lever arm with respect to the disk's center.

17 April 2017

Mail Time: Why do released AP Physics 1 exams include only 40 multiple choice?

Reader Aaron Shoolroy asks, in the comment section of a separate post:

The Physics 1 exam description says 50 MC questions, but it seems like all of the secure exams available through the course audit page have 40 questions. Does anyone know how many MC questions will be on the actual exam this year? 

Aaron, I'm sure you're not the only person wondering.  The AP Physics 1 and 2 exams will, as stated in the course description, include 50 multiple choice questions.  The last five of these will be "multiple correct", requiring the student to select both of the correct answers for credit.

So then, why do the released exams only give us 40 multiple choice?  Long answer coming.

During the Physics B dynasty, multiple choice exams were only released every five or so years.  See, a subset of the questions on each test are re-used on future tests in order to provide concordance from one exam to another.  For example, if the student population taking the test does better on these re-used questions, then the overall exam scores should go up -- even if performance on the rest of the test doesn't likewise improve.  That repeated subset of questions serves as an experimental control.

In order to keep a statistically significant bank of these re-usable questions, the College Board carefully hoarded them.  By only releasing exams every five years, it was easily possible to keep a secure set of questions in circulation.

During the development of the AP Physics 1 and 2 courses, one of the major points of pointed feedback to the committees said, please stop with the learning objectives, and give us practice questions.  I know I delivered that message more than once, and I wasn't the only one.  

See, people listened.  The College Board pledged to release the international version of the test nearly in its entirety every year, for the purpose of providing materials for use in class.  That's an enormous wealth of material for teachers, to the extent that we're only three years into the course yet I haven't been able to assign all available questions this year.  

(By the way, most of those released exam items are only available to those with an active AP course audit account.  That's to ensure that these items remain secure enough that it's unlikely students can simply google the solutions to them.)

I know the development committee and the ETS physics people have had to work extra hard the past few years in order to meet the demand for all these test items.  I have told them in person, I'll continue to tell them in person, and I'll say it here -- THANK YOU.  By releasing so much authentic exam material, they've allowed teachers and students to get a real sense of the form, content, and degree of difficulty of the exams.  They've allowed me to assign authentic practice in the lead-up to the exam.  They've provided me with practically unlimited laboratory ideas - virtually every question can be investigated experimentally.

Oh, but you asked me a question, and I rambled.  Why are there only 40 questions on the released exams?  Because the College Board removed the 10 questions that will be re-used in future years for statistical purposes.  Losing those ten questions is more than a fair trade for 40 multiple choice and five free response items, which are more valuable than gold to an AP teacher this time of year.

08 April 2017

For April AP Physics 1 classes: Here's a list of experiments, go do them.

At this point in my senior-level AP Physics 1 class, we have learned all necessary fundamental skills.  We have practiced solving problems with forces, motion, energy, momentum, rotation, circuits, and waves.  We have learned the critical laboratory skills, including how various equipment works, how to present data graphically, and how to use the slope of a graph to analyze data.

In the last month of the course, I'm using class time to put all these skills together in practice.

I have two 90 minute classes each week.  In these, I've been starting with 20 minutes or so of preliminaries: a TIPERS-style quiz, discussing the quiz, taking questions on homework.  Then I release the class to play.

What do they play with?

I've given the class a list of seven experiments; I can come up with more as necessary.  The list is below.

A student picks one and begins work.  I am happy to help with equipment questions, but not with "how am I supposed to do this?" questions.  (For those, I ask them to collaborate with a classmate.  That works at this stage of the year.)

How do they report their results?

Very informally.

I ask for a few sentences describing what they measured, and what equipment they used to make the measurements.  I ask for a few sentences describing how the data was analyzed, and how the data answers the question posed.  That's it.  No "formal lab report", no "purpose / procedure / results / conclusion."

Sure, occasionally I get a student who tries to give me a page with a bunch of messy numbers on it.  I simply send him back to his desk to do it right.  But this removal of formality in lab work has worked wonders for years.  It mimics what students will be asked to do on the AP exam -- in just a few minutes, writing by hand, describe an experiment including procedure and analysis.

What if I don't have enough equipment for everyone for these setups?

Part of the beauty of this approach is that I never have more than a couple of folks at a time working on each experiment.  Students are directed to work in any order they desire.  Often they will choose based on which experiment's equipment is available.

If several labquests are on the fritz - as they often are - it doesn't matter.  Because (a) students will have incentive to choose an experiment that doesn't involve the labquest, and (b) students will have incentive to figure out new and interesting methods for measuring what the labquest can measure.  For example, rather than plug in motion detectors to the labquest, they might learn to use video analysis on their phones.

Here's my list.  Each one can take anywhere from 20 minutes to an hour.  You'll recognize some 'cause they're inspired by old AP problems.  One (number 7) was created by a veteran of my class when he needed a project in another class.  I'll probably post some other time with specific notes about each... but for now, these have been a good start to independent lab work in the spring.

1. A transverse wave is traveling on a string.  If the frequency on the wave machine is doubled, what is the new average speed of the point?  Use a high speed camera on slow motion to directly measure the average speed.

2. Use a pipe, a meter stick, and a frequency generator to determine the speed of sound at room temperature.  Find somewhere with a temperature below 50 degrees F, redo your measurement, and see if the speed of sound has changed.

3. A 1 kg object traveling on a frictionless horizontal surface collides head-on with and bounces off of a 0.5 kg object initially at rest.  Give experimental evidence for (a) the percent of total linear momentum that was conserved, and (b) the percent of total mechanical energy that was conserved.

4.  In the circuit shown above, the sum of the resistances of resistors R1 and R2 is 80 kΩ.  Resistor R1 and the 80 kΩ. resistor are now swapped.  A student claims that the current must always increase in the right-hand branch of the circuit, because the total resistance of that branch must decrease.  Test this claim experimentally.

5. Create two pendulums: one with 50 g of hanging mass, one with 100 g.  Release both from the same angle.  Predict and give experimental evidence to show how each of the following differ for the two pendulums:
Maximum kinetic energy
Maximum acceleration

6. We’ve learned that the period of a pendulum is independent of the amplitude.  Provide experimental evidence for this claim; present your results graphically.

7. You are given two objects to be placed on either side of a pivot, as shown above.  The total mass of the two objects is known.  You may vary the distances from the pivot at which you place the objects.  Use the slope or intercept of a linear graph to determine the mass of each object experimentally.

27 March 2017

That "hole through the center of the Earth" question

I'm always asked these sorts of things.  Go figure.  I suppose it comes with the job, like the Air Force general based in New Mexico who continually deals with Area 51 speculation.

If you dug a hole through the center of the Earth, and jumped in, would you stay at the center because of gravity?

This experimentalist's answer:

No, because (a) the engineering barriers to digging said hole are insurmountable, and (b) if you weren't crushed, you'd be asphyxiated or, more likely, burnt.  Look up the temperature of Earth's core.

The theorist's answer:

Assume the hole is wide enough that there are no forces other than the gravitational interaction between you and the Earth.  The gravitational field INSIDE the Earth is zero at earth's center, always points toward Earth's center, and gets bigger as a linear function of distance from the center.  (The mathematics here are the same as when using Gauss's Law to determine the electric field inside a sphere of uniform charge density.  The 1/r2 dependence only occurs outside the sphere.)

By definition, when an object experiences a linear restoring force, its motion is simple harmonic. Thus, you'd oscillate about the center of the Earth like an object attached to a spring.  If you jump in from Earth's surface, then, you'd speed up until you passed earth's center, after which you'd slow down, reaching the surface on the other side of the earth before you repeated the process ad infinitim.

13 March 2017

"Does that make sense?" Don't take 'yes' for an answer.

I am at heart the most straightforward, literal person in the universe.  I mean what I say, and I say what I mean.  And I hear the words that people say, too often without considering the body language and social cues behind the words.

Consider the friendly sophomore from Norte Dame Academy, at the, I dunno, 1988 or so Kentucky State Latin Competition.  We met there and had been talking throughout day.  Her team's bus was leaving before the award ceremony.  She gave me her number, and said, "please call me tomorrow to tell me the results." So, the next day I dutifully called.  I gave her the results.  I congratulated her.  I said goodbye.  I never saw her again.  Sorry, Lisa.

Or, the wonderful woman in grad school who, after we had hung out together several afternoons, said "Can you come over to my apartment tonight?  My roommate will be out.  I'll cook you dinner." I accepted.  I thanked her for the yummy meal, and left.  Sorry, Michelle.

Or, and more pertinent to this blog, the diligent junior in the weekly problem solving sessions that my college paid me six bucks an hour to run.  I showed her how to solve a problem involving the work-energy theorem.  I asked her if the approach I suggested made sense.  She said, "yes."  I took her at her word.  Sorry, Alex.

I suspect that most readers are shaking their heads at the first two stories, wondering how I could be so clueless.  Had I recognized Lisa's or Michelle's body language and tone of voice, events would have turned out less dull, or at least differently.  And decades after the fact, I now have the perspective to recognize what I missed.  Most people wouldn't have misunderstood these cues in the first place, of course; I had to work consciously on interpreting social subtext, even though such interpretation comes naturally to others.

Over twenty-plus years of teaching, I've similarly had to continually analyze and re-evaluate my students' body language and tone of voice.  In 1994 I believed Alex when she told me she understood my explanation.  Why would she have said "yes" if the real answer was "no"?  In retrospect, there could be any number of reasons.  Among others:

(a) I'm a proud, diligent student, and I cannot admit to myself or (especially) to a peer that I don't get something; 

(b) I don't quite understand this right now, but I have irrational confidence that if I stare at the problem for another 20 minutes I'll magically see the light; or 

(c) I really wish Greg would shut up and stop explaining, and the only way I can tell him that without seeming rude is to pretend I understand.

Nowadays, when I explain something one-on-one to a student, I still ask, "does that make sense?"  But I'm ignoring the verbal content of the response.  I'm watching for and listening to body language and tone of voice.  Students often use words they don't mean.  Their tone usually gives their true thoughts away; it's practically impossible for a high school student to send false messages with body language.  

What am I looking for in response to "does that make sense?"

When I explain how to approach a physics problem, I always make the student go back to his seat and write up the solution in his own words.  So I'm watching how he leaves the vicinity of my desk.

The student who truly understands my explanation can hardly wait to get back to his seat to put his newfound knowledge into practice.  He usually moves with confident purpose.  Sometimes he'll have a bit of sheepishness about him, because he realizes he should have figured this out earlier.  

The student who's still confused walks much slower, with his eyes turned upward or downward.  He's in no rush, because either he's still thinking about what I said, or perhaps he's frustrated that I won't just tell him the right answer and he's throwing a wee tantrum.  

So, when the confident student comes back a moment later, I can move him along without thinking about it -- he's got it.  

But even if the less confident student comes back with a correct answer, I still push a bit.  I ask a few more questions to test for understanding.  I make him write each step of reasoning explicitly, even though I might have let the confident student slide by with some things implied.  I don't harass or embarrass, of course... I simply recognize that this student has shown me through his body language that I have to do more to help him.

02 March 2017

Woodberry Forest Conceptual Physics Tournament -- want to be an "examiner"?

My school has for years given three sets of exams, one each trimester.  This year, though, we're limited to two written exams.  For the last trimester, we're encouraged to create a cumulative project of some sort in lieu of an exam.  Yay.

Thus, we are creating the Woodberry Forest Conceptual Physics Tournament.  This competition for our 9th graders, to be held at 1:00 on Sunday May 21 2017, replaces their final exam.*

*No, to be clear to all, we're not giving an A to the winner and an F to the person in last place.  That's silly.  We're just having a fun, competitive tournament, to determine a winner.  Judges aren't awarding grades.

How does this tournament work?

On May 2, I will reveal a slate of three problems to the 73 participants.  These problems will be old AP Physics 1 "paragraph response" questions.  Except, rather than just answer in a paragraph, the students will spend the month of May setting up experiments to provide evidence for their answers.  By tournament time, each student will be expected to be prepared to discuss the solution to two of the three problems, with both theoretical and experimental support.

At the tournament, each student will participate in two "physics fights."  Think of these physics fights like a miniature version of a graduate thesis defense.  Students will have a strict limit of three minutes to present their solution to the examiner.  An examiner then will engage each student in conversation about the problem for five minutes.  The students are judged by the examiner not only on the quality of their solution, but also on their ability to discuss the solution, to confidently hold a conversation with the examiner.

How do the students prepare?

Starting on May 2, all conceptual physics classes the rest of the year will be devoted to tournament preparation.  They'll set up experiments in class, they'll be assigned to write up their solution as homework, they'll practice presenting.  

Most importantly, my AP physics classes will spend their final weeks of the school year serving as mentors to the conceptual students.  I will assign each AP student to lead groups of three or four 9th graders.  The AP student will dive into the problems with the freshmen, helping to create and analyze experiments, helping the freshmen to understand the details of their presentations, and serving as mock-examiners in practice sessions.  This mentoring serves as the final project in lieu of the exam in the AP classes.

We need examiners.

The key, I think, to any class project is external assessment.  I and the other conceptual physics teachers will play the role of coach and advocate, always encouraging and helping the students to deepen their understanding of the problems and to improve their presentations.  Our relationship will be purely supportive, enthusiastic, positive.  

We can't then turn around and grill these same students as examiners!  That'd be like our football team's coaching staff refereeing the state finals.  Even -- especially -- if their officiating were fair, the coach-student relationship, both in practice and after the game, would be irrevocably compromised.

So we need examiners.  We can pay.

Would you like to come to Woodberry on May 21 to be an examiner?  My guess is we'd ask you to arrive at lunch time, like 12:00.  We would have a meeting of all examiners in our beautiful dining hall over lunch.  

Then we'd ask you to be the examiner for a couple of hours' worth of physics fights -- depending on how many examiners we get, you'd probably be asked to run 8-12 rounds.  Then, we will gather everyone into our auditorium for the top two participants to engage in a final physics fight for the championship.

In any case, my goal is to be done by 3:30, or possibly (it's our first time running this) 4:00 if there are logistical issues.  No later -- our students will be attending the final seated meal with their advisors that night followed by study hall, so we can't run late.

We will pay you $100 plus lunch (and even dinner, if you'd like to stick around) for your time.  (If you're coming from more than a few hours away, we can put you up on campus on Saturday or Sunday night.) I think you'd find that the camaraderie among the examiners and the engagement with the students will make the trip worthwhile.

Who's eligible as an examiner?

Certainly any physics teacher, or anyone with a physics / math / engineering background.  I'm inviting alumni whom I've taught in an AP or AP-equivalent course to come back to judge.  I'd also welcome any alumni of your advanced physics class, even if they're still seniors in high school.  As long as you can engage in conversation about physics at the AP level, as long as you can recognize good and bad physics, we'd love to have you.  When I run the USIYPT, I find the mixture of undergraduate / graduate / professor / high school teacher / industrial physicist / retired physicist on the juror panel allows some amazing relationships to develop.  I'd love to create a similar vibe here.

How can I sign up?

Send me an email, or contact me via Twitter, or call me -- my contact information is on the Woodberry Forest School faculty page.  I'll send you more information, including the three problems, and our current draft of the judging rubric.

22 February 2017

Rank the voltages: experimental evidence

 The question: 

The three circuits above are all connected to the same battery. Each resistor represents an identical light bulb.  Rank the circuits from greatest to least by the potential difference across bulb A. If more than one circuit has the same potential difference across bulb A, indicate so in your ranking.

The (very much in-depth paragraph-style) answer: Since all bulbs are identical, they have the same resistance.  By Ohm's law with the same R for each, whichever bulb takes the largest current also has the largest voltage (i.e. potential difference) across it.  

The equivalent resistance of the parallel combinations gets smaller the more parallel resistors are added.  So circuit 1 has the largest equivalent resistance, with circuit 3 the smallest -- consider each resistor to be 100 ohms, and you get 200 ohms in circuit 1, 150 ohms in circuit 2, and 130 ohms in circuit 3.  

Bulb A takes the total current in each circuit, so consider Ohm's law for the circuits as a whole.  In that case, the voltage of the battery is the same for each; the circuit with the smallest equivalent resistance takes the largest total current.  So rank the circuits 3 > 2 > 1.

The common misconceptions: I gave this to my class as a quiz, and most got it wrong.  I saw four typical categories of wrong answers:

* Since the batteries are the same, each bulb in each circuit takes the same voltage.  (No, just each circuit as a whole takes the same voltage.)

** Since the batteries are the same, they each provide the same current.  (No, batteries provide voltage, not current.)

*** Since bulb A is closest to the battery, it must take the greatest voltage.  (No, "closeness" to the battery has no bearing on a circuit problem.)

So far, this is standard fare misconception-bustin' physics teaching.  Because I posed this problem as a quiz, the class waited expectantly for me to reveal The Answer.  Ho hum... those who got it right reflexively pumped their fists, those who got it wrong either made sad eyes, or used some sour-grapes reasoning to convince themselves why they could have gotten it right.  And then they forgot the whole thing.

Or did they?

"Okay, there are the light bulbs.  You know where the wires and power supplies are kept.  Go set up the three circuits and show me which bulb A has the largest current.  Take a picture of your circuits to show me."

Ah, sh*t just got real.  

The photos are by my student Clay Tydings.  He conveniently labeled bulb A in each picture.  Now we can all see that bulb A is brightest in circuit 3.  

To address the misconceptions above, you can have the students measure voltage across the battery, and across each bulb, with the voltmeter.  If you're brave, you can even have them measure current from the battery.  They'll see The Answer, that bulb A carries the largest current in circuit 3.

But they also see that (*) the bulbs take different voltages, (**) the battery takes the same voltage every time but different currents, and (***) the voltages across each bulb don't change even when we place bulb A "last" rather than "first" by switching the leads from the battery.  

I find myself asking the class to set up the experiment proposed by a quiz problem all the time in AP Physics 1.  We've established the class's lab skills; we have introduced and practiced all topics at a basic level; we have 90 minute class periods with which to work.  So why not make the students verify an answer experimentally?  The AP exam will certainly ask them how to design experiments!

16 February 2017

Mail Time: I can't find the other force acting on this block!

Reader Josh writes in:

The system shown is traveling at a constant speed.  There is friction between block B and the ground, and there is friction between block B and block A.  We've been arguing where the second force is in the horizontal direction on block A is, if it even exists.  The forward force on A would be the static friction but I'm lost on where the other one is.  This is driving me bonkers...

Have we written a bogus question? If not, can you tell us where we're going wrong?

Ooh, what a great question.  Constant speed, eh?  In a straight line, so equilibrium? 

I think we all agree on the BOTTOM block's free body:  normal force of ground on B upward, weight downward, contact force of A on B downward, force of rope on B forward, and friction force of surface on B backward.

There's no horizontal forces acting on block A.  If there were, it'd be speeding up or slowing down, which it's not.  

You say "the forward force on A is static friction."  Well, static friction takes on any value up to the maximum.  I agree that static friction must act WHILE THE BLOCKS SPEED UP.  Once they attain constant speed, though, the static friction force drops to zero.  If the block slows down again, then the static friction force on A will be backward. 

What a great AP Physics 1 question.  More complicated than you thought, I suspect.  :-)

06 February 2017

USIYPT results 2017 from University of the Sciences, Philadelphia

The 2017 United States Invitational Young Physicists Tournament was held last weekend, January 28-29, at the University of the Sciences in Philadelphia.  I can't thank the hosts enough -- Elia Eschenazi, Michele Albert, and the rest of the folks from USciences who helped out were most hospitable and supportive.

Congratulations to all, but in particular, to Rye Country Day School (pictured) and coach Mary Krasovec.  They won their second title behind a particularly strong presentation of their experimental measurement of Planck's constant.  

The final round scores and places, noting that by tradition the finalist teams share first through fourth place:

Rye Country Day School , NY         77 points, champions
RDFZ of Beijing*                             72, 2nd place
Phillips Exeter Academy, NH          71, 3rd place
The Harker School, CA                    70, 3rd place
Qingdao No. 2 High School**          68, 3rd place
Woodberry Forest School, VA          56, 4th place

* Officially The High School Affiliated with Renmin University, China; known also as RDFZ.
** First-time participants from northern China

The Clifford Swartz Trophy is awarded annually to the winner of the USIYPT poster session.  First-time participant Vanke Meisha Academy won this prize.

And this year, the US Association for Young Physicists Tournaments for the first time presented the Bibilashvili Medals for excellence in physics.  These are awarded not based on ranking among the schools, but on overall score regardless of place.  This year, in addition to the trophy winners and final round participants, Pioneer School of Ariana, Tunisia earned a Bibilashvili medal.

This was the largest tournament in the ten year history of the event, with thirteen schools participating, including:

Shenzhen Middle School, China
Phoenixville Area High School, PA
Cary Academy, NC
Princeton International School of Mathematics and Science, NJ
Nanjing Foreign Language School, China

What about 2018?

The 2018 USIYPT will be held on January 27-28 at Randolph College in Lynchburg, VA.  The four problems involve measurements of the moon's orbit, coupled mechanical oscillators, projectiles in air, and radiation from incandescent light bulbs.  Full problem descriptions are shown at the USAYPT problem master's blog. 

If you'd like to know more about the USIYPT -- a physics research/debate tournament for high schools all over America and the world -- please contact me via email.  We're particularly interested in recruiting physics teachers, professors, graduate students, and industry physicists as jurors.  


Physical versions of energy bar charts

Like many of us, I use energy bar charts extensively.  Though my students don't all understand every detail of them all the time, the charts are the best way I know of to get them to stop plugging numbers into equations and think for a moment about how energy is transferred.  Just as "why don't you draw a free body diagram" generally gets students un-stuck on a force problem, "why don't you draw an energy bar chart" usually sets everyone on a path to success when energy is involved.

My personal touch on the energy bar chart is to insist that each bar be annotated.  Even just a couple of words help, like "it's moving" under the KE bar, or "at its lowest position" when the PE bar is zero.
Still, I don't have the sense that my class internalizes the deeper meaning of the bar chart: that the total energy on the left side, plus the "work done by external forces" column, must equal the total energy on the right side.  They know only because I tell them repeatedly; it seems an afterthought for my students, rather than the entire raison d'être for the chart.

How can I help my students understand intuitively that bars in the chart must be transferred among columns rather than just drawn randomly?  How can I help them see that the "work done by external forces" column is the only place where it's okay to add or remove bars?

Kelly O'Shea and Chris Becke -- and I'm sure others, but these are the ones I've seen recently -- have made physical versions of the bar chart.  I'll show you both...

Physical energy bar charts from Kelly O'Shea, @kellyoshea
Kelly tweeted this picture.  Her setup seems so simple: just a bunch of wooden blocks, pegs, and post-it labels.  Simple, maybe, but elegant.  Each setup is just the right size to put on a lab table for each small group to use in their problem solving.  I can imagine asking each group to take two pictures of the blocks: one representing the initial energy configuration, and one representing the final energy configuration.  Then I could ask something like "why are there two more blocks in the second picture than the first?  Where did they come from?"  And I'd expect an answer referencing work done by external forces.

Water-based energy bar charts from Chris Becke, @beckephysics
Chris uses water in labeled beakers to represent energy.  By setting up in the front of the classroom by the sink, he can explicitly show how work done by external forces affects a system's energy status.  Look at his labels; the faucet is "+work" and the drain is "–work."  My students when they draw bar charts can just magically sketch a few more lines in the "Wext" column to add energy to a system.  Kelly's students have to at least physically grab or throw away extra blocks.  But Chris's setup requires turning on the faucet, or dumping water down the drain, in order to include work done by external forces.  The meaning of "external" just got real.

I don't mean to suggest that either Kelly's or Chris's physical bar chart approach is the superior one.  I'd personally use Kelly's blocks in my bog-standard style of class in which students and small groups work on predictions and experiments; I'd use Chris's faucet-based chart on occasions when I want to present demonstrations from the front of the room.  

I *do* mean to suggest that if you're going to use energy bar charts as a teaching tool, I think it's worth setting up some form of physical bar chart rather than just drawing on paper.  I'm gonna have to try these.

30 January 2017

The Physics Community - remarks from the USAYPT President.

We just finished the 2017 US Invitational Young Physicists Tournament at the University of the Sciences, Philadelphia.  Please congratulate Rye Country Day School of Rye, New York for their victory.  I'll post full tournament results in a few days.

Below is my brief, slightly edited, address to the assembled throngs tournament's closing ceremonies.  The audience consisted primarily of high school student participants.  

I need to make sure you all know where I stand, though it's not like you probably don't know already. 

I believe in physics fights.  I believe in this tournament.  I believe in having us all together every year, where we compete with each other; but where we are also colleagues. Where we award a trophy, but where we also talk to one another as physicists.  Where we have people from seven different American states, and two different other countries. (Five of our schools are from the same country - China - but they are from all over China, just like the American schools are from all over the USA.)  Folks, we have people from all over the world, of diverse backgrounds, all speaking the common language of physics.  That, above all, is what the USIYPT is about.

I cannot countermand executive orders.  I can not make laws in the United States.  I have no influence there.  And it's just as well that I have no influence there.  I am not a politician.

Where I do have influence, though: I can help all these folks get together to speak the common language of physics to each other in person, to build relationships... such that in ten or twenty years, when YOUR generation is in charge of this country or your respective countries, you will know good people in America.  You will know good people in China.  You will know good people in Tunisia.  You will have the relationships and the background -- both a scientific background and a cultural background -- such that you can make different decisions. 

And I hope that by then the world will be a better place, due in very small part to our efforts.  


16 January 2017

Mail Time: Rigorous definitions of circuit properties in AP Physics 1

Buckeye native Matthew writes in with a question about circuits in AP Physics 1.  He’s referring to my summary post of the topics on the exam

Greg - Happy New Year!. As I am outlining the second semester of the year I am having difficulty finding information about

Non-rigorous definitions of voltage, current, resistance
Rigorous definitions of voltage, current, resistance

Any information you could provide me about finding the differences between non-rigorous or rigorous would be appreciated. 

I am thinking (hoping) that I already address this and just have not been exposed to the terms non-rigorous and rigorous when it comes to the definitions?!?!

Matthew, great timing -- I just worked on this difference with my AP class last week.  

"Rigorous" and "non-rigorous" definitions are my own personal terms, not anything to do with materials published by the College Board.

I start circuits on the very first day with the non-rigorous definitions:

Non-rigorous definitions of voltage, current, resistance
Voltage is provided by a battery.  Voltage is measured in units of volts.
Resistance is provided by a resistor, a lamp, or any electronic device.  The units of resistance are ohms (W).
Current relates to the amount of charge flowing through a resistor.  The units of current are amps.
Ohm’s law states that voltage is equal to current multiplied by resistance:  V = IR.

With just these facts, I can have students graph current and voltage to verify or discover the relationships in ohm's law; I can have students measure brightness of a bulb as a function of voltage and resistance to discover the power equation. And then we can do basic semi-quantitative questions with single resistor circuits, like "I replace a 10 ohm resistor with a 20 ohm resistor, by what factor has the current in the circuit changed?"  

Then we move on to circuits with series and parallel resistors, then to combinations of resistors, then to light bulbs, then to circuits with switches, using ammeters and voltmeters. I like to give circuit TIPERs, but make the students set up the situations experimentally to verify their prediction.

During these first couple of weeks, I never mention Kirchoff's laws -- rather, we have rules about current and voltage for parallel and series resistors which are a poor person's statement of Kirchoff.  (“Voltage across series resistors is different for each, but adds to the total.”)

Finally, once we've done all of this... everyone has a personal, intuitive understanding of what current and voltage are.  That understanding has been built on experience through problem solving, lab work, right and wrong answers.*  In eduspeak, this personal, intuitive understanding is referred to as an "operational definition."

*Never through analogy, though.  If students create their own analogies, great.  But direct experience without analogy has proven far more effective at building knowledge and avoiding misconceptions than any analogy I've ever tried.  Voltage and current aren't truly LIKE anything else.  

So, with that personal understanding built, it's time to introduce the rigorous definitions:

Rigorous definitions of voltage, current, resistance
Voltage is energy per charge.
Current is charge per time.
Power is energy per time.
Potential difference is a synonym for voltage.

Remember, your students aren't likely to come into the course with an operational definition of charge; and gaining the experience necessary to develop what charge truly means requires, I think, a full-on AP Physics 2/C treatment.  And "energy" is still a bit fuzzy in students' minds.  (These rigorous definitions can actually help students develop their operational definition of energy and charge, since they're so solid on voltage and current.)

I therefore tell the students to translate from rigorous language into our non-rigorous definitions.  When they see a problem like "rank these bulbs based on how much energy is gained by an electron passing through" they recognize that as asking about energy per charge; that just means "rank by voltage," which my class is well trained to do.

The last bit about circuits we do is to use Kirchoff's laws, and to make voltage vs. position-in-circuit graphs.  Here I use the terms "electric potential" and "electric potential difference" with impunity.  But by this time voltage is such an ingrained concept that the class has little difficulty anymore.

08 January 2017

What advice can I give a student with a C right now?

This showed up in the comment section from my August 2016 post in which I write a letter to my upcoming AP class.  It deserves a response in a full post, because I suspect that many physics teachers are confronting just this kind of problem this time of year.

A very concerned mother here. My very strong student pulled her first C in her life in the first semester of physics. We have tutors, spoken multiple times to the teacher and everyone says that she understands the materials, and almost always does badly on the test. When asked, she says that the test is so different she does not know what to do. As an engineer who had taken high levels of physics, I am really at a lost to help her. As an experienced teacher what advice can you give her. We need to make the next upcoming semester rock! Appreciate your kind assistance.

Now, remember that I have no direct contact with this specific student, so I can't give anything more than general advice. That said, I've seen this pattern many times -- historically outstanding student who gets As in history and biology, diligent, willing to work hard with support at home from subject matter experts... yet does not perform on physics tests.

The general advice starts with recognizing that there is no magic bullet. Neither this student's parents, her tutors, her teacher, or I can instantly create success. Physics skills are learned gradually, over time. They come quicker for some than for others.

That said: It's very, very hard for me to train even good physics teachers to back off and make students struggle without giving away answers. Students (and parents!) with good intentions often treat homework as a "just get the answer" exercise without engaging in the process.  Thus, in so many cases as you describe, the student's extensive support network is HURTING rather than helping. When tutors and expert parents get involved, students tend to ignore the part about "here's how to approach the problem" and think instead "thank goodness, I got the answer" -- no matter how good the tutoring might be.

So my fundamental advice is to let your daughter struggle. Give her loving emotional support, just as you would if she were on a softball team and kept striking out. When she asks questions, don't solve problems with her, don't help her figure out mistakes.  It's her homework, let her do it. Instead, advise her to think all the time about the process of getting answers, the general approach to different kinds of problems, even if she doesn't get the exact right answers. Help her keep focus on the big picture of all the things she's done well -- both in and out of physics class -- and don't engage with Chicken Little talk.

It's very likely that, by year's end, she'll start making connections and improve dramatically. I've had a number of students making Cs this time of year who ended up with 4s and 5s on the AP exam. Things often click after long-term exposure to physics.

It's also possible that she pulls a C for the year. That's okay, too. I have struck out every at-bat for four games in a row; I've earned Cs on tests and in classes. Those strikeouts and Cs no more define me than they should define your daughter.