The first first law assignment -- qualitative justifications of signs

The drawing shows a PV diagram in which a gas expands at constant pressure from A to B, and then goes from B to C at constant volume.  Determine the signs of ΔU, Q, and W for each of the two processes.  Justify your answers.

This is the first PV diagram question which I assign in my honors or AP course.  We have discussed the definitions of the variables in the first law, and how to determine the value of each variable from the PV diagram.*  

*Including the fact that the value of Q cannot be determined directly from the diagram without using the first law.

The solution, in the language and logical order that I prefer:

A-B:  

ΔU is positive, because the product of P and V is larger at point B than at point A.  

W is negative, because the volume increased.

Q must be positive by the first law, Q = ΔU - W, (+) = (+) - (-)

B-C:

ΔU is positive, because the product of P and V is larger at point C than at point B.

W is zero, because the volume did not change (or because there is no area under the curve from B to C)

Q must be positive by the first law, Q = ΔU - W, (+) = (+) - (0)

Note that I'm not yet asking for any quantitative answers.  That's too much for the first problem set.  I try to get my class totally comfortable identifying facts, assigning signs, and using the correct vocabulary for each term before I ask for numerical answers.  

Also, look how straightforward the answers.  ΔU is (3/2)PV; W is the area under the curve; and Q is determined from the first law.  It takes a lot of effort on my part to get students disciplined enough to used this approach.  They invariably want to, somehow, somewhere, talk about "molecules moving around:"  "Q is positive because when the pressure increases, the molecules have to move around a lot faster, leading to more heat."  Such a statement is worse than nonsense.  PV diagrams refer to macroscopic systems, and must be interpreted with reference to relevant equations and facts, only.  

This year, anticipating the difficulty of convincing students to use a disciplined, macroscopic approach to the first law of thermodynamics, I promised that the penalty for any reference to "molecules moving around" in a first law justification would earn double points off.  And sure enough, I had a student who lost double credit on this very problem.  But only one this year...

Summer 2012 with Jacobs Physics

Several folks have asked about my summer schedule.  As usual, I'll be running several AP summer institutes.

Do note -- you don't have to be teaching AP to come to an AP summer institute!  We discuss far, far more than simply "How do I teach my students to game the AP exam."  In fact, we don't discuss gaming the test at all.  Rather, we discuss physics teaching as professionals.  

I share what has worked for me, and for other teachers who have taught me; participants share their own ideas.  I do quantitative demonstrations on a variety of topics.  I share my tests and problem sets, for all levels that I teach.  You get to take home a CD containing not only some of my own handouts and ideas, but also the official College Board released exams -- with rubrics.  All of these materials can be used at every level of physics teaching.

Want to sign up?  Here's where I'll be:

June 25-29, Richmond, VA (through VASS, Virginia Advanced Study Strategies.  I don't know whether this one is open to the public or not -- send an email to the link at the VASS website, and ask!)

July 10-13, Kennesaw State University, Georgia (This one's four long days rather than five short days.)

July 16-20, North Carolina State University, Raleigh

July 30-Aug. 3, Manhattan College, New York City (Manhattan College is in The Bronx.)

Just the basics, not the sources, of electric, magnetic fields

Electric and magnetic fields frustrate me each year.  They're abstract, leading to few simple quantitative demonstrations.  They always seem to take their turn in the dark, cold, depressing months of January and February.*  And students are perennially confused between the source of an electric or magnetic field, and the victim of said field.

* Except that these were the most wonderful months of the year when I taught in Florida.

Ah, but this year I'm going to do something about that last point.

The AP Physics B redesign is said to be emphasizing "big ideas," physics themes which resonate beyond a particular topic.  For example, the idea of a conservation law permeates physics from mechanics, to rotation, to electronics, to nuclear physics... It takes a substantial level of real physics understanding to explain what quantities might be conserved in a specific situation, and why they are conserved, and just what exactly it means that a quantity is conserved.  Once the concept can be clearly and thoroughly articulared, the algebra involved in applying conservation of foo is generally trivial.  And so it goes with the concept of the field:  Once students get comfortable with the idea that a field of any sort is used to calculate the force on an object, using that force in a Newton's second law calculation becomes trivial.

Students become unintentionally familiar with the gravitational field g as the "conversion" between kilograms and newtons -- one kilogram on Earth weighs 10 N, but on Mars weighs only 4 N.  W = mg serves as what I call the "bible equation" for the gravitational field -- it relates the force on a massive particle to the gravitational field.  Once that gravitational force is known, this force can be drawn on free body diagrams and used in a newton's second law calculation just like tension, friction, or any other force.

Now, those of us who are experienced physicists know that the source of this gravitational field is the enormous mass of the Earth applying on all other massive objects, via Newton's law of gravitation  F = GMm / r².  But I ask you... who in his or her right mind teaches first-year physics students  F = GMm / r²  BEFORE W = mg?  No one.  Don't be silly. 

So why, why, why does every textbook in the universe teach F = kQq / r² before F = qE?!?

For many years, I've begun electrostatics with the definition of an electric field via F = qE, completely ignoring what might cause such a field.  A field simply exists in space.  If a charge is placed in the field, that charge experiences a force qE in the direction of or opposite to the field, depending on the sign of the charge. Only much later have I broached the confusing subject of fields produced by point charges or parallel plates.

Not only has this approach been effective in getting students to succeed on AP Physics B - style electrostatics problems... in their second year calculus-based AP Physics C course, my students have little trouble with electrostatics.  We can calculate an electric field using superposition, Gauss's law, calculus, whatever -- everyone understands that, once we have an electric field from any source, F = qE.

Currently I'm teaching Honors Physics I, which is intended to anticipate the AP Physics I redesign, rather than AP Physics B.  The "big idea" of a field permeates several different physics topics, and so is ripe for conceptual investigation.  In Honors Physics I, I will ignore sources of electric fields completely.  I want the class to be able to explain what a field does to a charged particle, not necessarily how the field came to be.  And I'll do the same thing with magnetic fields:  We'll discuss the bible equation F = qvB, and the right hand rule for the direction of the magnetic force on a charged particle.  That's it.  Magnetic fields due to current-carrying wires can wait for Physics C.

I encourage you to try ignoring the source of the electric or magnetic field.  If you're teaching to an exam (i.e. AP or Regents) that requires discussion of a field's source, throw that in as part of review at the end of the unit, or even at the end of the year.  Electricity and magnetism will never be easy for first-year students, but by simplifying the initial introduction to fields, you'll get better results long term.

How many soda bottles in Brian's raft?

The question from Dec. 14:

Mr. Jacobs’ friend Brian Jackson saved two-liter soda bottles throughout his senior year of college.  During “Haverfest," he duct taped the bottles together to form a raft.  He then successfully floated himself out onto the duck pond.

Estimate how many bottles Brian used.  Explain your reasoning thoroughly and show all calculations for full credit.

While the majority does not always rule in physics, in this case "they" were right on.  My reasoning:

Call Brian 80 kg or so.  His weight is then 800 N.  That weight must be supported by the buoyant force, which is equal to the density of water times the displaced volume times g.  If each bottle is fully submerged, it displaces 2 L, or 0.002 cubic meters.  The buoyant force created by one bottle is then (1000 kg/m^3)(0.002 m^3)(10 N/kg) = 20 N.  To get to 800 N at 20 N per bottle, you'd need about 40 bottles.

What if Brian's not 80 kg?  Well, as I have to point out to people, 80 kg is a reasonable estimate for Brian, but college guys who drink soda are often heavier; and, in a recent development of Haverlore, I have discovered that Brian supported a second person on the raft as well.  Furthermore, even if Brian were 75 kg, 40 bottles would have to be nearly fully submerged, leaving essentially no safety margin, and getting Brian's feet* wet.  This is an order of magnitude estimate... why not double the estimate to 80 bottles or so?  Then the bottles are in the neighborhood of halfway underwater.  Brian can sit dry, he can bring a friend, he can eat at the COOP** all he wants; 80 bottles will support him.

* Or more likely, his tuckus

** The yummy snack bar... it used to be too expensive for me, but now I find out that students can make their parents pay for the COOP as part of these newfangled meal plans.  Ach, and nowadays students can access email from their rooms, too.

What about the weight of the soda bottles themselves?  Some students will tell me "the soda bottles are of negligible weight."  Okay, but are they?  What's the evidence?  

Some students found that an empty bottle has mass about 40-50 g, for a weight of about half a newton or so. That means that each bottle will only support 19.5 N of Brian rather than the 20 N previously conjectured.  

Does that mean, as some say, that the proper answer is "41 bottles?"  No, certainly not.  As discussed in the previous paragraph, the uncertainty in Brian's mass, and in just how much of the raft is submerged, far outweighs this 3% change due to the weight of the bottle.  The answer is still somewhere around 80 bottles, or better yet, some dozens of bottles. 

Group work and in-class problem solving

How do you arrange for effective group work in class?

Last week, at the tail end of my class's study of static fluids, I had to miss a class for a debate tournament.  I decided to borrow a page from my colleague Curtis Phillips, who has been patiently teaching freshmen how to collaborate effectively in physics.  Occasionally, he puts his students in pre-assigned "pods" of three desks each, and assigns a problem for the class to work on.  He collects the assignment from everyone; however, he randomly chooses a single paper from each pod to grade.  All three members of the pod earn whatever score is earned by the random paper.

Now, I remember being furious at such arrangements in middle and high school.  Too often, I'd get an idiot in my group who didn't give a rip, and so was unwilling even to make an attempt; or occasionally I'd have a "partner" who enjoyed doing a poor job just to make me angry at him -- he didn't care about a silly score on a class assignment, but he thoroughly enjoyed watching me blow my top, then impotently appeal to the teacher for help.

And there lay the problem with such an approach.  The teachers who attempted this "group learning" method were not invested in the idea -- I found out that these teachers had been directed from above that they were to employ group learning methods, which of course would improve the performance of the lower-end students.  In practice, the teacher would assign the assignment and then sit at her desk grading papers.  My complaints about disinvested students fell on deaf ears... "I'm sorry, Greg," the teacher would say condescendingly.  "In the working world you will be forced to deal with different types of people.  You must learn to get along."*

* In the working world, of course, the analogous situation would result in either (a) the idiot being fired by a competent boss, or (b) me leaving for a different job where the employees and bosses do their respective jobs.  Interestingly, now that I've been in the "working world" for a quarter-century, I've been involved with both situations (a) and (b). 

Despite my own crapulent experiences with "group learning," the approach Curtis proposed can be sound.  The teacher simply must, must, must be personally invested in the students' work.  

I have seen Curtis perform his magic.  His groups of three are usually either hunched over, hard at work; or they are engaged in animated discussion.  And where's Curtis?  In the middle of the room, his wide eyes manically scanning the class as if he were at Helm's Deep watching for the approaching Orc army.  A student slumps in his desk; Curtis asks him a question about the problem.  A student starts talking about the upcoming semiformal; Curtis's adroit verbal manipulation lets him know, in so many words, to shut up and get back to work.

More importantly, he has no tolerance for the student who just doesn't care.  Now, you can propose what to do with such a student.  Give him an automatic F; remove him from the classroom; call his advisor or his parents; give him 50 lashes with a wet noodle.  I honestly don't know what Curtis would do with such a student, and neither does his class.  Everyone knows that Curtis has nuclear tools at his willing disposal, and so they try to avoid making Curtis resort to them.


But effectively moderating a problem solving session requires more than just a state trooper-style presence.  Especially since he teaches freshmen, Curtis is continually teaching the students how to collaborate effectively.  He's showing them skills we take for granted in our own or our seniors' academic lives.  For example, he'll say, "You look like you're stuck.  You haven't written anything down for ten minutes.  Why not ask your neighbor there for help?"  Or, "Okay, Joe, you've told John how to do the problem.  Now, John, you try it for a few minutes by yourself.  Don't ask Joe for help again until you are well and truly stuck."  Or even, "All three of you are working together.  So you should either all have the same final answer, or you should be arguing vehemently.  Which is it gonna be?"


What I did: In my own 11th and 12th grade college-level class, I gave them a fun problem (see the post about the soda bottle raft.)  I insisted that everyone work silently for 5 minutes until everyone had written down a reasonable approach.  After 5 minutes, collaboration was unlimited amongst the entire class.  They were told that I would collect a problem from everyone, but that I would grade only one, chosen randomly.  Everyone would earn the same score.


Afterward, I graded the randomly-chosen problem, cut off the student's name, and posted his work on the bulletin board with the grade.  Two of my sections earned essentially full credit.  One section earned just 1/10, though.  And interestingly, that student's work has been simply fabulous over the past week -- I think he took a bit of ribbing from his friends.

Soda Raft Question

And if any soda company would give me money, I'd use their
brand name in the problem statement. :-)

The following is a true story.  I use it as a problem in static fluids every year.  This year I assigned it when I was absent -- an upcoming post explains how I assigned the problem in class.  

For now, though, look at the poll at the left of the blog -- vote for your estimate!

1. Mr. Jacobs’ friend Brian Jackson saved two-liter soda bottles throughout his senior year of college.  During “Haverfest," he duct taped the bottles together to form a raft.  He then successfully floated himself out onto the duck pond.

Estimate how many bottles Brian used.  Explain your reasoning thoroughly and show all calculations for full credit.

A Tale of Proctored Study Hall, and Serious Written Attempts

Today's post: making our horses drink.

Part of my job as a boarding school "master" is to spend about one night a week on dorm duty.  This year, I've been assigned to supervise the Proctored Study Hall.  See, most of the school spends a couple hours nightly in quiet study time in their dorm rooms, in the library, or unsupervised in classrooms.  But, students are assigned to Proctored if they get a D, or if their advisor thinks they need a more structured nightly study environment.  Once a week, I have to be that structure.  Guh.

The nice aspect of Proctored is that I'm in regular contact with some students who truly need and want my academic help.  They appreciate that I show genuine interest in their assignments, even those outside of science.  It was established very early on in the year that proctored is a time for serious, diligent, but relaxed study.  The group knows by now that they are to get on with their work without distraction.

Thursday night, I was approached three separate times by three different 9th grade physics students for "help."  The first two came with a blank paper asking a specific question about a problem; the third had some work done, but not on the problem he was asking about.  

I gave the same response to all three: look, I'm happy to help, but (a) it's the middle of study hall, and a long discussion here would ruin the quiet atmosphere and distract your peers; and (b) I need to see your first, written effort before I help out.  So, please go back to your desk, make your best attempt, and then come back here at the break.  I'll talk you through the problem then.

Any guesses as to what happened next?  Go ahead, teachers who are reading this, write your guess in your notebook.  

(pause a beat while you guess)

When the bell rang for break, I individually reminded each of the three students that I'd be pleased to help them out now.  All three responded:  "No worries, I figured it out on my own, but thank you!"  

There's a lesson here.  Physics is a difficult subject, and physics teachers tend to work very hard to avoid gaining the reputation of  an unapproachable jerk.  Fair enough.  But in our zeal to be helpful, do we do our students a disservice?  I say, much of the time, yes.

A story from my first year of teaching:  I had been repeatedly berated by colleagues and parents for being mean and unapproachable.*  So when one of my honors seniors asked me for an individual appointment at the end of the next school day, I agreed -- even though that meant staying at the school three hours after the end of my last class, even though it meant going home in rush hour.  In came the student, right on time, with his book and problem set.  

* Interestingly, most of the folks calling me unapproachable were doing so without ever attempting to approach me.  But that's a different issue.

He said, "So, I'm having trouble with question number 1.  Can you help me?"  I dutifully pointed him toward the relevant equation, discussed with him how to approach the problem, and I waited patiently while he used his calculator to ensure that he was going to get the right answer.  Here I was, being approachable, helping a poor student learn physics!  People would stop complaining any day!  Right?

The boy filed question 1 away with a satisfied look.  He looked back at his problem set, and said, "Now, can you help me with question 2?"

This time, I was suspicious.  I asked, "Where did you start?"  He hemmed and hawed a minute, and then in response to my direct question, he admitted that he had not really done anything yet on any of the problems.

Well, that's simply unacceptable.  My job as a teacher is not to sit with my students, holding their individual hands until they get questions right.  My job in class is to give them the tools with which to approach problems.  Then, it's my job to set up an environment in which direction is available when people get stuck.  But they must first get legitimately stuck before they seek direction!  

A few years into my career I simply made the blanket statement that, while I love to help people with physics problems, I will not even entertain a question unless I first see a serious written attempt.  

Do you have a packed classroom during a morning or afternoon tutorial period?  Do you feel like you're overburdened because you have too many students who need your help, and not enough time or energy to help them?  Well, try implementing the serious written attempt rule.  I guarantee that the number of people who think they need your help will be cut in half; and, the time you need to spend to help each person will also be cut in half, because everyone asking for assistance is thoroughly familiar with the problem already.

Then the next step is to make anyone you help use their newfound knowledge to help the next student who asks:  "I'm glad you asked that, George.  Billy just asked me the same question... Billy, could you explain that issue to George while I help Mike on this other problem?  Thanks!"

Laboratory quiz question: pressure in a static column

A primary laboratory skill, one that is frequently tested on the AP exams, is determination of the physical meaning of the slope and intercept of a linear graph.  My own approach to such a question is to solve the relevant equation for the vertical axis of the graph, then to identify the variable representing the horizontal axis.  Anything multiplying this variable is the slope of the best-fit line; anything added to this term is the y-intercept.  We religiously go through this process of identifying the slope and intercept of a straight-line graph in every laboratory activity.

However, just doing laboratory work isn't enough to develop this skill.  In a 90 minute lab period or a lab report, a large subset of students will parrot their friends' answers or my suggestions without sufficient understanding.

So then, how do I check for "sufficient" understanding?  I give quiz and test questions that ask directly about the physical meaning of graphs that the class hasn't seen before.  For example, a recent "justify your answer" question showed a graph of weight on the vertical axis, and mass on the horizontal; what is the physical meaning of the slope of that graph?

It was instructive to read the justifications.  Most folks got that the slope is g, the gravitational field.  The stronger students recognized the relevant equation weight = mg; since weight is on the vertical and mass on the horizontal, whatever is multiplying m must be the slope.

The weaker students, though, got the correct answer reasoning from the units of the axes.  The vertical axis, they said, "was" newtons.  The horizontal axis "was" kilograms.  Since we've shown that g has units N/kg, the slope must be g.

I've got to force these weaker students to get away from the crutch of using units to determine a slope's meaning.  While such an approach is better than nothing, often the units of the slope won't obviously match any known quantity; or, a factor of 1/2 or 2π will be missed.  It's not like the method I'm proposing (of first writing the relevant equation) is too difficult for anyone.*

* The correct method does require remembering or looking up the correct equation, though, which is sometimes an obstacle; but that's a separate issue.

Below is a quiz that will help practice the skill of identifying the physical meaning of a slope.  Note that, by this point in the year, if we just graphed GAUGE pressure vs. depth, most of my class would have little trouble seeing that the slope is ρg.  The addition of the Po term in the equation for pressure in a static column causes difficulty.

1.    In the laboratory, you are given a tall graduated cylinder full of fluid, along with a pressure probe which reads absolute pressure.  You submerge the pressure probe in the fluid and record the reading in the probe P at various depths d below the surface.  The pressure at the surface is 1.01 x 10⁵ Pa.

A graph is made of P on the vertical axis and d on the horizontal axis.

(a)    Is the graph linear, or curved? 

o  Linear

o  Curved

(b)   If the graph is linear, explain how the density of the fluid r could be determined from the best-fit line.  If the graph is curved, explain what quantities could be graphed in order to produce a linear graph from which the fluid density r could be determined.

Want to referee a physics fight?

Okay, that title is overly dramatic.  Sorry.  But it's kinda technically accurate...

At the United States Invitational Young Physicist Tournament, teams present their solutions to four low-undergraduate research problems.  Then, the presenting team is evaluated and questioned by another team!  This process is called a "physics fight," a methodology developed by the International Young Physicist Tournament and adapted for the American version of the tournament.

The actual event resembles a combination of a thesis defense crossed with a scientific conference presentation crossed with a Lincoln-Douglas debate.  Teams are judged not only on their physics knowledge, but also on their ability to engage in questioning and discussion in a search for the truth of the problem.  

Want to be a juror?  See, I'm the president of this tournament's sponsoring organization.  We are in the process of recruiting jurors to referee these physics fights.  If you're a high school physics teacher or college physics professor, then we want YOU.  Everyone who has ever seen this USIYPT in action has fallen in love with the friendliness among participants, the outstanding physics, the poise of the contestants, and the professional  camaraderie amongst teachers, students, and jurors.  (Several invited jurors have liked it so much they've brought a team the next year.)

This year, the USIYPT will be at Oak Ridge Associated Universities in Oak Ridge, TN on February 3-4 2012.  The kicker is, the organization is supported only by student fees, for now.  We can't pay an honorarium, or even for a hotel room.*  But if you can get to Oak Ridge, we'll get you on the field for our intellectual Super Bowl.

*Not yet, anyway.  Anyone know a company or non profit that wants to grant us a budget for this thing? :-)

Go to usaypt.org for further details about the tournament; email me at greg.jacobs@woodberry.org if you'd like further information or a formal invitation as a juror.  (And I'd be happy to talk about physics fights at length on the phone as well if you'd like.)

GCJ