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29 March 2016

Teaching with physics fights: conservation laws in a direct measurement video

Perhaps my favorite of Peter Bohacek's "Direct Measurement Videos" shows a collision between a marble and a wooden block.  The marble rebounds; the block both translates and rotates after the collision.  

In my classes (and in my AP summer institutes) I pose three questions:

(1) Is linear momentum in the horizontal direction conserved?
(2) Is angular momentum about the origin [marked in the video] conserved?
(3) Is mechanical energy conserved?

Each of these questions is quite deep, requiring evidence from the video, calculation, and clear explanation.  It's one thing to say "yes, the linear momentum is always 0.19 Ns," supported by two pages worth of chicken scratch.  But can a student coherently present his calculation so another physics student can follow it?  Can he explain not just the equations used to produced the 0.19 Ns value, but why those equations are valid, the meaning of the values used in the equations, and how those values were obtained from the video? 

We want students to explain "The marble is moving at constant speed, so d = vt is valid.  The marble goes 23 cm in 5 frames; using the 960 fps frame rate gives a speed of 44 m/s."

We don't want "I used the ruler to get 23 cm, divided by 5, multiplied by 960 because there are 960 frames in one second, and that's 4.6 times 960 which equals 4416, but with sig figs and dividing by 100 to convert from cm/s to m/s I get 44 m/s."

Describing a calculation is a difficult skill.  Students tend to want to show haw they did some algebra; and they don't understand me when I tell them that the algebra isn't important.  I'm still struggling to teach this skill.  I'm no expert, but I can offer a few hints.

A time or space limit provides necessary structure.  When I ask for a written discussion of one of the questions above, I give a strict one side of one page limit.  Then there's no room for digressions.  In an oral presentation, I give three minutes max.  Students have to decide for themselves what information is important enough to spend precious time on.  And with practice, they learn to state results rather than to belabor arithmetic.

Questions and evaluation from outsiders can focus students quite well.  This is the universal trick to teaching writing or presentation skills: creating a clear and authentic audience.  When students know they will be questioned -- or "examined" -- by a classmate, alumnus of the course, or even by another teacher, they work differently.  To me, students think they merely have to convince me that they know the answer.  To outsiders, students recognize that they have to explain their methods as well; and they intuitively meet a higher bar for convincing those outsiders of their own competence.

A ritualized physics fight combines a time limit with external evaluation.  I'm training my 9th grade honors class to give three minute oral "reports" in answer to each of these questions.  Eventually, I'll have an "examiner" from outside the class -- a senior in our research course -- ask questions of the reporter.  I'll even plant a "challenge question" with the examiner, so that each student can expect to get questions at both a basic and advanced level.  

Here's the rubric to which the examiner will evaluate the reporter.  Note that I've indicated to the examiner some features of the reporter's explanation that I expect to see -- for example, if the reporter doesn't indicate somehow that the marble's linear momentum after collision subtracts from the rod's momentum to get the total, then there's some missing physics.  But most of the rubric is non-specific to the problem at hand.  The examiner is asked to evaluate the reporter's competence at explaining the video evidence and how the evidence leads to an answer.

What guidance do I give the students as they prepare?  At first, very little, just a demand for practice.  I show everyone the rubric (with the problem-specific elements and the challenge question redacted).  I give time in class to practice; the evening's assignment is to practice twice in front of other students.  Then I serve as examiner for some practice fights against randomly chosen students.  After a few of these, I demonstrate how I might present a similar problem in just three minutes.  I require more practice.  It's the upcoming physics fight against an external examiner which keeps everyone motivated to improve.

Want to have a physics fight with me?  Physics fights are the basis for the US Invitational Young Physicists Tournament, where each team serves as reporter and examiner for three rounds each.  But the USIYPT problems (the link goes to the problems for the 2017 tournament) could each result in an undergraduate thesis.  The USIYPT is designed for the top high school physics students in the world.  What about your AP Physics 1 students in their first year of study?  What about your really talented honors freshmen?  Shouldn't they be able to try physics fights too?

While there's not a formal, national-level tournament (yet) pitting teams in physics fights over high school level problems, I see no reason we can't arrange "friendlies".  I've posed three problems above, each appropriate for a three minute presentation and five minute examination.  Do you want to challenge me and my students to a physics fight?  We could do this by skype or the equivalent.  Your student gives a report, my student does the examination.  Then one of my students reports with one of yours examining.  For now, I am inviting people for "friendlies" only, where we can fill out the rubric and make comments, but without true competition.  Eventually I'll figure out a way to have scoring, a miniature competition, and a "winner."  But really, we're all winners if we're getting our students to communicate about physics, right?

24 March 2016

Feedback Inertia -- finding the right amount of effort necessary to check an answer

It was Matt Greenwolfe of Cary Academy who first articulated this concept to me while I was visiting last week.  He formerly used an online simulation to help his students practice translating physical motion into position-time graphs.  But he found that the instantaneous feedback of the simulation led to pure guesses about what the graph should look like.  Not enough feedback inertia.  

Then he created a programmable robot: students draw a position-time graph on the computer, plug a cord into the robot, press the download button, wait a moment, disconnect the cord, and press start.  The robot performs the motion represented by the graph.  Matt found that because there were a few minutes of effort involved in connecting and disconnecting the robot, students were more likely to think carefully about their original graph.  Just the right amount of feedback inertia.

I'll start with the obvious: Physics frustrates many good students, because it does not yield to memorization.  Other subject require learning of facts; physics additionally requires learning the processes that, in combination with those facts, produce correct answers.

Yet the answers to physics problems seem deceptively simple.  Increase, decrease, or remain the same; up, down, left, or right; speed up, slow down, or steady speed.  Even quantitative problems can be* reduced to picking the right equation out of only a few reasonable options, and then assigning one of just a couple of possible values to variables.

*Shouldn't be, but can be

Much of physics teaching, then, consists not just of helping students to find the right answers, or even of explaining the correct process.  We have go farther -- we have to put students in situations where they internalize for themselves the methods of getting answers that work.  Such internalization takes the right kind of practice, and just the right style of feedback.

Students love instantaneous feedback: when answers are available in the back of the book, by clicking on an online simulation, through webassign or its clones.  But does checking an answer instantly (and correcting it if wrong) really lead to understanding?  Sometimes... but because the negative feedback comes so quickly, the process can quickly devolve into horse games.  Students will make another educated guess, and be given a false sense of security if the next guess is right.  Even if you award a declining scale of class credit, it's still a higher priority for most students to be done than to maximize credit.  Not enough feedback inertia.

The other extreme is the extended laboratory activity.  We might have students make a high-stakes prediction, then collect abundant data to verify or de-verify the prediction.  Fabulous... but the longer it takes to collect and analyze that data, the farther divorced the students are from their original prediction.  Furthermore, their mindset becomes less about dispassionate understanding than about proving themselves right.

It's unlikely that a teenager says, after an hour of data collection, "oh, I predicted a line here, but I got a curve.  Oh!  That's because this is a sine function, which looks linear at first.  So next time I should look carefully at the relevant equation rather than assume that all increasing functions are straight lines."

More likely, the thought process is, "Come on, it sorta looks straight, can't you count this right?  Oh.  I guess I predicted wrong.  Shit."  Too much feedback inertia.

The trick is to strike a balance between these two extremes.  Students need feedback quickly enough that they have the opportunity try a new prediction before they lose mental contact with their prediction method.  But they need enough of a barrier to feedback that they don't guess, but rather pay careful attention to their prediction method.  Being wrong has to hurt, but only a wee bit.  And that's what I mean by feedback inertia: the inherent difficulty of checking an answer.

Feedback inertia can come in many forms.  Matt uses his robot.  I use my line of students at the front of the room -- because they have to wait in line to check their answers, students think a bit more carefully about what they're writing.  Or, I use simple experiments which require a few minutes of walking to the back of the room, or picking up a labquest to plug in.  

Now, longer experiments have an important place in physics courses, as do sets of multiple choice practice with instant feedback.  I'm not saying that everything that I or you do must include an ideal amount of feedback inertia.  I'm suggesting that the concept exists; and its application is most important when students are introduced to a new topic in which they have to build mental models to understand how to predict simple physical behavior.

Got another way of optimizing feedback inertia?  I'd love to hear it in the comments.


11 March 2016

Mail Time: Why don't all the versions of the power equation work for the 2015 AP Physics 2 circuits question?

Kasey from Texas emails in with a puzzling issue from AP Physics 2.  Paraphrasing:

In the circuits question from the 2015 AP Physics 2 exam [that's problem 2, available at this link], I get the solution to part ii using P=I2R, but I don't get the same answer using P=V2/R.  Does this equation not work?  Shouldn't all versions of the power equation give the same answer?  What am I missing?

Your instincts are correct that any form of the power equation should give the same answer.  However, you have to be vigilant about using the values of voltage, current, and resistance that are relevant to the circuit element being considered.

Problem 2 on the 2015 AP Physics 2 exam shows a circuit diagram.  Before the switch is closed, two identical resistors are in series with a battery.  Closing the switch puts another identical resistor in parallel with one of the series resistors.  The original AP question labels the important values with variables.  For the purposes of this discussion, I'll use a 10 V battery with identical 10 Ω resistors.

The question asks a comparison of the power dissipated in that first resistor -- the one that remains in series with the battery -- before and after the switch is closed.  I'll go through the calculation two ways: once with P=I2R, and once with P=V2/R.

With P=I2R:  The first bulb takes the entire current in the circuit.  Before the switch is closed, that's the voltage of the battery (10 V) divided by the equivalent resistance of the circuit (20 Ω), 0.50 A.  So the power dissipated by the first resistor before the switch is closed is (0.50 A)2 * (10 Ω) = 2.5 W.

After the switch is closed, the circuit's equivalent resistance is now 10 Ω + the 5 Ω equivalent resistance of the parallel combination, for a total of 15 Ω.  The total current is now (10 V) / (15 Ω) = 0.67 A; since the first resistor is still in series with the battery, it takes this current.  So the power dissipated by the first resistor is (0.67 A)2 * (10 Ω) = 4.5 W.  To answer the originally posed question, the power in the first resistor is multiplied by 1.8 when the switch is closed.

With P=V2/R: The voltage across the first bulb is not the entire voltage of the battery.  Before the switch is closed, the two series resistors split the 10 V of the battery equally.  (You could also see this by doing the complete Ohm's law analysis -- the total current in the circuit is 0.50 A as shown above; multiply V = IR for each resistor to get 5 V across each.)  So the power dissipated by the first bulb initially is (5 V)2 / (10 Ω) = 2.5 W.  Same as I calculated before.

After the switch is closed, the voltage across the first bulb changes.  Now, the first bulb is in series with the parallel combination.  Thus the voltage doesn't split evenly; more goes to the series resistor 'cause it has a larger resistance than the parallel combination.  The equivalent resistance of the circuit drops, increasing the total current in the circuit to 0.67 A as shown above.  To find the voltage across the first resistor (which takes all 0.67 A 'cause it's in series with the battery), use V = (0.67 A) * (10 Ω) = 6.7 V.  Now we can use the power equation with the voltage and resistance corresponding just to the first resistor: (6.7 V)2 / (10 Ω) = 4.5 W, again the same as before.  The power in the first resistor is still multiplied by 1.8 when the switch is closed.

Why would my students get different answers with different forms of the power equation?  Most likely, someone used the voltage of the battery  rather than just the voltage across the single resistor in P=V2/R.  Less likely but still possible* is  that the student calculated the current in the first resistor using just the 10 Ω resistance rather than the equivalent resistance of the circuit.

*Possible?  Having graded AP exams for 15 years, I'll tell you, every mistake in the universe is *possible*, just like any location of an electron in a hydrogen atom is *possible*.  An individual student's answer merely resolves a wavefunction that maps probabilities of making each possible mistake. 

09 March 2016

The Story of Byron and the Tunisian Physics Team

Fall 2013: In the midst of preparation for the upcoming US Invitational Young Physicists Tournament, we heard from students -- Ahlem, Chada, and Mohamed -- at a school in Tunisia: Pioneer School of Manzeh 8.  They were excited about coming to that year's tournament in San Jose, California.

I was impressed with the efforts these students made in order to get all the crazy logistics taken care of so that they could attend.  They had to raise money to travel and to pay the hotel costs; Chada even went on Tunisian television with a plea for financial help.  They made travel reservations themselves, including arrangements for a few days extra in San Francisco after the tournament.  They slogged through the immigration issues and visa processes.  I don't know how much time they even had to work on the physics problems.  But, it looked like everything was all set for their attendance.

A few days before the team was to depart, Ahlem sent word that their teacher's visa had been denied.  D'oh!  But Perry, an American engineer who had helped with their financing and logistics, agreed to serve as their team leader at the tournament.  He'd meet them there.  No worries.

And thus, this team of three 17 or 18 year old students who had never been out of their country left Tunisia for San Jose.  Those of you who watch television serials recognize this part of the story as when everything goes wrong for the protagonists.

Remember the 2014 Atlanta Snow Jam?  That was just two days before teams were to arrive in San Jose.  The Atlanta airport was still recovering from being nearly shut down.  Ahlem, Chada, and Mohamed got through Paris, arrived in Atlanta on time, and looked for their flight to San Jose.  Which, of course, was delayed by an hour.  And then was canceled.  Our Tunisians were rebooked on the later flight, the one that was to depart at 11:00 p.m. eastern time.  Still no worries, other than a very late-night arrival on the eve of the tournament.


I first met Byron at an AP summer institute that I taught.  He was relatively new at teaching AP Physics, but he was clearly an outstanding physicist and physics teacher.  When the USIYPT was held in Oak Ridge, Tennessee, he came to judge -- it wasn't that far of a drive for him from Chattanooga.  

We were hoping that perhaps Byron could get together a team to participate in the 2014 tournament.  That didn't work out, but Byron managed to get approval to head to San Jose as a judge.  Fantastic!  The USIYPT is great professional development, a place where really strong high school physics teachers and education-minded college professors gather and talk shop.  Those of us running the tournament were thrilled to have Byron back with us, not just because he's one of those really strong high school teachers, but because we like him.  And we appreciated that he was willing to travel cross-country in order to participate.

Byron contacted us on the big travel day.  It turned out that all flights from Chattanooga to Atlanta were canceled, due to recovery from the Snow Jam.  I expected him to shrug his shoulders and apologize for not being able to make it.

Instead, he informed us that he'd brave the drive into and across Atlanta to catch his connecting flight to San Jose.  He had checked, and the roads had cleared up.  Wow, thank you, Byron, we said... that's going the extra mile.  Or, more literally, the extra 117 miles along I-75.  


As astute readers will have noticed, the initial flight from ATL to SJC was canceled.  Byron rebooked on the late flight, and settled down to wait.  

I'm still not sure how Byron and the Tunisian students recognized each other.  Somehow, though, the weary travelers began talking.  They discovered they were headed to the same place.  Ahlem, Chada, and Mohamed told Byron about all they had done to arrange their trip, and why their teacher couldn't come along; Byron told them a bit about what to expect at the tournament.  They talked about their respective schools, the similarities and differences.  The conversation was intercultural, but with substantial common ground -- Tunisia and Tennessee may be worlds apart, but a physics teacher and physics students always will be able to entertain each other.


As was nearly inevitable, the late flight to San Jose was canceled.

Everyone together -- Byron, Ahlem, Chada, Mohamed -- went to the reservations counter together to figure out how to get to San Jose.  The best option was the late flight to San Francisco, which was still running on time, departing in just 20 minutes from a nearby gate.  Then the drive down to San Jose would be only an hour.

But there was only space for Byron, the single flyer, on the San Francisco flight.  The party of three could not be accommodated.  They'd have to fly the next afternoon. 

Well, that wasn't going to work for Byron.  "Put me on tomorrow's flight as well, please," he said.  They made themselves a party of four.

Byron found a hotel with three available rooms and shuttled everyone to the hotel.  He took everyone to breakfast the next morning, and then back to ATL to see how many flight cancellations they'd have to endure: none.  The afternoon flight to San Jose in fact arrived on time.  I finally met Ahlem, Chada, and Mohamed when they arrived with Byron at the hotel restaurant at 8:00 p.m. pacific time, 11:00 p.m. eastern time, 5:00 a.m. in Tunisia.  The four of them weren't even grouchy from all the travel -- they were tired and hungry, sure, but primarily they were excited to have finally, together, found a way to San Jose.


Of course I, the Tunisians, the Tunisians' parents, and everyone involved with the tournament thanked Byron profusely for his help.  Byron could have, possibly should have, just gone home that night from Atlanta.  He was a volunteer, after all.  He could have slept in his own bed with his wife, and then either stayed home for the weekend, or tried to rebook from Chattanooga the next day.  Or he could have just jumped on that San Francisco flight.  But he didn't; he wasn't going to abandon these students to sleep in an airport five thousand miles from home, not when he had the means to take care of them.  

As everyone in turn expressed his or her thanks, Byron graciously pointed out, "you would have done the same."  And, you know, he's probably right.  I, and everyone I know involved in the USIYPT, routinely go well beyond the call of duty in order to serve the participating students.  (One might suggest that, since we are all volunteers, even taking on any duty is beyond the call of duty.)

But there's a long way between "I probably would have done the same" and "Byron did go through two days of travel heck because three Tunisian students -- whom he'd never met -- needed him."  He stepped up when called.  

And I hope I'll be all the more sure to step up when I'm called.

Thank you, Byron.

04 March 2016

Calculating work -- what force, what distance... or just use the work-energy theorem

Athenian* Christina Curtis writes in with a frequently asked question about calculating work.

She's from Athens, Georgia, not the one with the Apocalypse Acropolis.

Consider a box of mass m being pushed up a frictionless incline at constant speed by a person.  We know the angle of the incline θ, the distance along the incline d, and the vertical height of the incline h.  What force and what distance do we use to calculate the work done by the person?

It is valid here to use the definition of work as force times distance, because all of the forces involved are unchanging.  If the forces were varying, as on a curved track or for something in simple harmonic motion, you'd have to use the area under a force vs. distance graph, or go straight to the work-energy theorem.

When using work = force x distance, the distance you use must be parallel to the force involved.  (Or, equivalently, the component of force you use must be parallel to the direction of displacement.)

One approach, then, is to use the vertical displacement multiplied by the vertical component of the force applied by the person.  We know the vertical displacement is h, and the vertical component of the person's force is simply mg.  The work done by the person is mgh.

A second approach is to use the distance along the incline multiplied by the force of the person on the block.  To get equilibrium in the direction parallel to the incline, the person pushes with a force mgsinθ.  So the work done by the person is (mgsinθ)(d).

Wait a second!  How do we get two different answers using two different approaches?

We don't.  In this geometry, the sine of the angle θ is h / d.  Using that relationship, you can see that the two expressions we've derived above for work are equivalent.  Either approach -- using the force component that's parallel to displacement, or using the displacement component that's parallel to force -- works.

But it might be easiest to use the work-energy theorem.

Students tend to default to work = force x distance.  But the work-energy theorem is more generally valid, and is often less confusing.

The work-energy theorem says that work done by an external force is equal to the change in kinetic energy plus change in potential energy plus the change in internal energy.  Here, consider the block-earth system.  The block has no change in kinetic energy 'cause it moves at constant speed.  It has no change in internal energy 'cause it doesn't change its temperature, and doesn't have anything inside it storing energy through rotation or something.  So the work done by an external force -- that is, the work done by the person -- is just equal to the change in the block's potential energy.  That's mgh.

Ideally, we'd get our students to default to using the work-energy theorem to calculate work done, then only use force x distance if they have to.