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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.  

GCJ


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'ĂȘtre 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.  

GCJ

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. 

29 December 2016

Start Teaching Newton's 2nd Law Without Numbers or Equations

You've gone through a unit on motion; your students know the difference between velocity and acceleration.  (Or, at least some of them do, some of the time.) Now you're ready to introduce F = ma.  What do you do first?

I think most physics teachers, and certainly most textbooks, recognize the necessity of diving into free body diagrams right away.  Somehow, you must show the difference between an individual force and the NET force.  I concentrate on getting students to write out the object applying and experiencing the force; this helps avoid including fictitious forces (like "force of motion"), and it makes a future discussion of the third law child's play.

But, what do you do with those free body diagrams, other than make them?  

(1) Some books and teachers jump to a mathamatical treatment of F = ma.  Practice problems in which the free body is used to determine the value of the net force, use the second law to determine acceleration, then use kinematics to get something like the initial or final speed of an object, or its time in motion.  Then you can do the reverse -- use motion information to calculate net force, and then the amount of an individual force.

(2) Others go from the free body diagram to a semi-quantitative treatment of F = ma.  That is, show mathematically and experimentally that at constant mass, a larger net force yields a larger acceleration; for constant acceleration, a larger mass demands a larger net force.  Linear graphs can be created to verify the second law relationship.  

While I get to both (1) and (2), I don't start there.  I start merely with free body diagrams and the direction of motion.

But Greg, you say.  Free body diagrams have nothing to do with the direction of motion.  

Yes.  That's the point.

Before I do any work with the relationship F = ma, I ask every possible question I can think of about how the object is moving.  Here we're considering motion in a line only; circular and projectile motion are for later on.  

For example: This cart experiences a 3 N force to the left, and a 2 N force to the right. 

* Which way is the net force on the cart?  (Left, because the greater forces act to the left.)

* Which way is the cart's acceleration? (Left, because net force is always in the direction of acceleration, and we just said net force acts left.)

* Which way is the cart moving? (No clue.  Acceleration and motion aren't simply related.  The cart could be moving left and speeding up, or moving right and slowing down.)

* Could the cart be moving to the right?  (Sure -- if the cart is slowing down.  Note that the most common answer which is utterly unacceptable is "Yes, if another object applied another 2 N force to the right.")

* Could the cart be moving left at 1 m/s?  (Sure, as long as its speed a moment later is greater than 1 m/s.  NOT "Yes, as long as its mass is 1 kg.")

* Could the cart be moving left at a constant speed of 1 m/s?  (No way.  The cart experiences a net force, so the cart has an acceleration, so the cart's speed must change.)

It's useful to let students play with the phet simulation "force and motion basics."  In class, I have students do a series of experiments in which they predict the force necessary to cause an object to speed up or slow down.  We don't worry about the actual value of acceleration, just the directions of motion and acceleration.  

Once my students are rolling their eyes at these sorts of questions, answering with the same voice that my son uses when I remind him to wear a jacket to school on a cold day... well, then you're ready to move on to lessons (1) and (2) above.









21 December 2016

Followup: Three years later, what do conceptual students remember about circuits?

In 9th grade conceptual physics, we teach circuits without calculators.  Rather than asking "determine the voltage across each of these series resistors", we ask "estimate the voltage across each" and "rank the resistors by the voltage across each."  We don't allow direct calculation to answer these questions.

Rather, we expect a semiquantitative use of ohm's law, combined with instincts developed in laboratory.  I describe my class's Zen methods in this post.  

Those students who learned circuits conceptually now make up half my AP Physics 1 class.  Can the former conceptual students handle circuits problems in which actual computation is necessary?  Can they deal with more complex circuits than straight-up parallel and series resistors?  Can they describe their conceptual understanding in language appropriate to a college-level examination?  Yes and yes and yes.

In the freshman class, I hand students a page with circuits facts written on it.  (Scroll down on the linkned page to see the facts appropriate to circuits.)  By the second day of the unit, students are using the facts to predict voltages and currents for series circuits.  We do no lecture, no "going over" the facts.  Why not?  Because freshmen wouldn't pay attention anyway.  The class gets in the habit of reasoning based on facts, not of mimicking a teacher's steps.

Freshmen do very well with open-ended "here are some new facts, now figure out how to make predictions with them."  However, I learned the hard way that seniors generally do not.  They expect you to show them what to do, and get pissy if you expect them to use information you didn't "go over" -- even if that information is the first bold line on a sheet you handed them. 

Nevertheless, since half of my seniors had seen circuits in 9th grade conceptual physics, I thought I'd try the open-ended approach.  I was taking a twofold leap of faith:  (1) I hoped that the conceptual veterans would have enough familiarity that they weren't flummoxed by more complex circuit problems, or circuit problems requiring calculation; and (2) I hoped that there was enough comfort with the concepts and with the equipment that the conceptual veterans could provide leadership and advice to those who were completely new to circuits.  

This time -- thank goodness -- my faith was rewarded.  

I handed out the AP version of my circuits exercises, the version that includes series-parallel combinations.    Everyone worked in a relaxed manner and at a similar pace.  Information passed smoothly throughout the class -- when I gave advice to one student, I found that I rarely had to give the same advice to others.  

The conceptual veterans recalled rather quickly the subtleties of straightforward series and parallel resistors.  They easily helped the others make their predictions and set up their circuits.  The team atmosphere we built in the freshman class paid its dividends, as the conceptual veterans assumed -- without suggestion from me -- the roles of tutors and facilitators.  Even the students who had never seen circuits at all moved along at the same pace as most of the class.  Even the student who was new to circuits and was absent the first class picked up the process quickly.

Did anyone struggle now that we included calculation, now that we included combination circuits?  Not at all.  Sure, I had to show two of twenty students how to deal with the combination circuit.  The rest either figured it out for themselves, or were taught by one of the folks I helped directly.  

I'm on my fourth attempt at teaching AP Physics 1-level circuits.  And this is by far the smoothest introduction I've had.  I'm ready now, after a week of class, to discuss the deeper language and tougher situations that AP Physics 1 requires.  Most everyone can already accurately fill out a VIR chart for a simple circuit.  I can focus on the whys and hows.

In other words, teach eighth, ninth, or tenth graders about circuits, but conceptually.  The very basic three-week unit we created has paid off tremendously in my AP Physics 1 class, even though the unit was three years ago, even though we never used a calculator. 

And I remind myself how important the work I do with freshmen is.  I'm planting seeds with them... seeds that I usually don't get to see germinate.  But germinate they do.

14 December 2016

Quizzes to follow up AP Physics 1 problem solving: Try composing tweets.

Old-tymie physics questions would simply ask, "Calculate the horizontal distance block B travels after it leaves the table."  Such a question will be vanishingly rare in AP Physics 1.

Case in point: consider 2010 AP Physics B problem 1 part (d).  You have a block pushed by a compressed spring.  The block collides with another block, then falls off a table.  No analysis, no articulation of principles necessary... just perform the calculation.

Don't get me wrong, 2010 AP Physics B problem 1 is a fantastic question.  It combines in one simple situation the three canonical approaches to classical mechanics: force/kinematics, momentum, and energy.  I assigned this problem verbatim to my AP class last week.

Of course, I encourage collaboration in and out of class, as do most of us.  Thus, a significant fraction of the class got the approach right because someone pointed it out to them.  No, that's not "cheating," that's working together.  Students engaged the problem individually, most got stuck somewhere, and then through conversation and direct advice, they figured out what to do.  Awesome.

I will certainly grade this problem.  Presenting the solution clearly is an important skill to develop.  And by grading the problem, I provide incentive to engage in the collaborative process.  I can tell the difference between Fred, who just kinda blindly followed a friend's work, and Jim, who himself showed each step clearly.  At this point I don't care that Jim showed each step clearly because George told Jim how to do each step.  Jim wrote out his work, and so made progress toward personal understanding.

Nevertheless, I need to evaluate my students' personal understanding of the process.  I need to help my students evaluate for themselves what they understand and what they don't.  After all, the AP exam is not a collaborative exercise.  Everyone, by May, needs to be able to independently figure out how to approach this type of complex problem.

More to the point, my AP Physics 1 students must be able to do more than just perform the calculational procedures that lead to a correct answer.  The exam might ask, "Explain how you would calculate the distance block B travels after it leaves the table."  And the response can't be "I multiply 1/2 times 250 times 0.15 m squared, then plug into p=mv."

So I give a quiz.  What kind of quiz can you give based on this problem, Greg?  I'm glad you asked.

Sure, you can give the same problem and change the numbers.  That's okay.  It doesn't put students on the track toward answering AP Physics 1 verbal response questions, but it's a start.

You could also change the situation slightly... have the block initially slide down a ramp rather than be pushed by a compressed spring.  Or eliminate the collision.  Or put the table on Mars.

I've discussed in this post how I ask for annotated calculations in order to check for understanding.  An interesting quiz might present a full solution in numbers and ask the student to annotate the calculation to explain each step.

Even then, students have a hard time recognizing what parts of a solution are important to annotate.  They want to describe the arithmetic: "I divided both sides by 0.15."  Or, they say "I used p=mv.".  Um, I know -- you just wrote "p=mv," you don't need to tell me again.

Ask: "Explain in two tweets how to solve the problem."  I propose that students have a friend at our rival high school who needs help, saying via twitter that they don't know what to do.  You have to help.  You get to communicate in only two tweets -- that's two sets of 140 characters each.

The secret to teaching students to write is to clearly define an authentic audience.  They know without me saying anything that an online friend doesn't want to hear the poor annotations I've described above.  They want to hear simple articulations of principles:

Spring energy becomes A's KE. That gives A's speed and momentum before collision. P conservation gives the blocks' speed after collision. 1/

Now, blocks are a projectile. Vertical kmatics gives time, d=vt gives distance since horizontal v doesn't change once blocks leave table. 2/

And this explanation is a strong response to the AP Physics 1 question, "Explain how you would calculate the distance block B travels after it leaves the table."