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20 May 2017

Conceptual Physics Tournament Sunday May 21 2017

[The following is a letter to my school's community describing our project-in-lieu-of-exam that will happen tomorrow.  If any blog reader is interested in creating something similar at her or his school, please let me know.  I'd love to help out!]

Folks, tomorrow is the first ever WFS Conceptual Physics Tournament.  

Instead of preparing for an exam, our students have been preparing to present and discuss the solutions to some rather deep problems, which are attached to this email.  Mentors from the AP Physics classes have helped the 3rd formers conduct experiments, to understand the underlying theory, and to deliver a two-minute talk.

Tomorrow, each student will be assigned to report in two "physics fights."  Think of the physics fight as a thesis defense.  The reporter presents his/her two-minute talk; and then the examiners engage in conversation with the reporter for five more minutes.  The examiners are probing how deeply the students truly understand the problem, and how clearly the students can articulate their understanding.

Physics fighting is a spectator sport.  We encourage all members of the community (including parents of 3rd formers!) to come out to watch a few physics fights.  These will take place in Manning and Kenan.  We will run approximately eight rounds, beginning at 1:00 and ending around 3:00.  The specific fight schedule will be posted in the dining hall and to the news folder around 12:30 Sunday.

Alex Tisch and Colin Manning have done tremendous work preparing their students, not just in the past couple of weeks, but all year.  The mentors have taken to their task with relish.  The 3rd formers have worked very hard, and are ready to demonstrate their knowledge.  Come see the fruits of their labor.  


11:30: Examiner arrival, lunch in Terry Dining Room
12:00: Examiner training in Terry Dining Room
12:30: Posting of fight card
12:50: Examiners and students move to fight rooms

1:00: Round 1
1:12: Round 2
1:24: Round 3
1:36: Round 4

1:48: Break; examiners switch partners

2:00: Round 5
2:12: Round 6
2:24: Round 7
2:36: Round 8

19 May 2017

AP Summer Institute: June 26-29, Mahopac, NY

Folks, a quick bit of advertising here... we're still looking for a few teachers to fill up my AP Summer Institute in Mahopac, NY from June 26-29.

At this and all of my summer institutes, I'll take you through all aspects of my AP Physics 1 classes.  We'll do some of the different kinds of experiments I've discussed on this blog.  We'll share ideas with each other - I leave every institute with new ideas to try out.  And I can discuss physics teaching beyond AP Physics 1, including conceptual physics as well as AP Physics 2 or C.

For those looking to meet various certification requirements, this particular institute allows you to earn graduate credit.

Please contact Mark Langella, the institute director and a pretty dang impressive AP chemistry teacher, for signup details.  You can contact him via the Putnam-Westchester Industry and Science Teacher Alliance.  

I hope to see you in New York...


04 May 2017

2017 AP Physics 1 solutions

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

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

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

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

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

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

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


01 May 2017

How long should my answers be on the AP Physics 1 exam?

Quick answer: probably shorter than you think.

Below are a variety of AP Physics 1 prompts, and how I would suggest structuring your answer.  Please note that, while I do grade the exams every year, I am writing here in the role of independent observer.  I am not a representative of the College Board.  These are my own simplified instructions to my own students, which may not be perfect in all situations.

Yet I think teaching is much better done by simple guidelines rather than legalisms.  If you want the legalisms, go to the College Board's course and exam description; and look at the AP Central page where they go in to great detail about the requirements for a paragraph response.  I don't think a student wants to see such detail.  I think, in fact, that we should actively discourage students from a rules-bound approach to any answers.  Encourage your students to simply answer each question, and move on.

On my last day of class before the exam, I will remind students of the types of prompts below, and my guidelines for the length of the response required.  And then I will let go, and wish them the best.

"Briefly Explain:" or "Briefly justify"  Answer in one sentence.

"Derive an expression:"  Use variables only, start with an equation from the equation sheet or a fundamental principle.  It will help to annotate your work with words, but complete sentences are not necessary.  Full credit can usually be earned without words at all as long as the mathematics is communicated clearly. 

"Describe a procedure:"  Two to three sentences, never more.  Say what you will measure, and what equipment you'll use to measure it.  And stop writing.

"Explain" or "Justify your answer:" About two sentences, or perhaps one sentence with reference to an equation.

"Answer in a clear, coherent, paragraph-length response:"  Five sentences, four is often enough.  Do not repeat the question in the answer. Get to the point.

For all responses except mathematical derivations:  Use sentences with subjects and verbs, but without fluff.  

What if I need more space than the question provides?  Then you are writing too much.  The amount of space provided is deliberate, and reflects the length of response expected.  Yes, I know you are allowed to use scratch paper and staple it into the book.  You're also allowed to publish your bank account information online.  Just don't.  

Don't fear for the lost point.  Students tend to write page-long essays because they fear that the grader will "take off" if they miss one small detail.  But those students miss the bigger picture.  Running out of time on question 5 could cost them seven points, while writing an extra page may in their imaginations earn one point.  And writing that extra page is far more likely to lose credit for an incorrect statement than to gain credit.  

Please don't be afraid.  Answer each question briefly and confidently.  If you have to guess, guess briefly.  Believe it or not, we readers know when you're just writing random crap because you have no idea how to approach a problem.  And rubrics are written such that they are unlikely to award credit for baloney.

Kick arse tomorrow.  Let me know how it goes.  I'll post my solutions when I can.


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.