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

Static Fluids with Quantitative Demonstrations -- Detailed Class Notes

What's the buoyant force on a lionfish?  I ain't doing this
demo, but you can see the demonstrations I do do at  this link.

Regular readers are probably aware that my typical class period consists of one or more quantitative demonstrations -- I don't just solve an abstract example problem from a book, I physically set up the example problem as an in-class experiment.  Any calculation we make in class is verified by measurement. 

One of the questions I'm most asked is, "Do you have a list or writeup of all of your quantitative demonstrations?"  Unfortunately, I don't.  When a publisher (or the NSF) offers me a five figure advance, I'll consider writing a book.  

Until that glorious day, you ask, where do I look to find quantitative demonstration ideas?  Well, start by searching through this very blog, of course.  Sign up for one of my AP Summer Institutes (I'm doing four, I think, in 2012).  Every time you're choosing an example problem to use in your class lecture, think, "could I set this up in my classroom?"  Use a homework problem as the basis for a laboratory activity, and make your students create the setup.  Talk to other physics teachers, including those who are listed as followers of this very blog.  

Now, if you'd like an extraordinarily detailed description of what a class with quantitative demonstrations might look like, check out this piece I wrote for the College Board a few years ago.  They asked me to provide a "lesson plan" for AP-level static fluids.  I described each experiment, each check-your-neighbor question, each measurement that I make during class.  (If you've been to a summer institute, you'll recognize a few of these demonstrations.)

Do you have a quantitative demonstration that you use in class?  Tell me about it.  I'm open to guest posters on this blog...

Vernier Video Physics for the iPad 2: A Winner

For Thanksgiving, my family headed to a very nice cottage in West Virginia.  It had a number of wonderful amenities, not including internet, television, or cell phone service.  That was okay by me, because I spent several days grading exams and writing comments.  It’s amazing how much more focused I can be when I don’t have the option to check my email real quick, or to just see what the score of the game is.  It’s also amazing how much more boring it is to grade papers without any sort of electronic distraction.  Guh.

My eight year old occupied himself for hour after hour with a hand-held Pokemon video game.  In the rare moments when he tired briefly of having Waylord fight Trogdor (or whatever), he explored this loaner iPad 2 that I got from my school’s library.

For those who have followed Jacobs Physics for a while, you might remember that a year and a half ago my school provided me with an iPad, for use in physics class, while broadcasting football and baseball, and at debate tournaments.  My summaries of the iPad’s usefulness can be found here and here.  

Now, before you say “oh, my school could never afford that” or “what an extravagant place you teach at, Greg!”  think about the actual cost-benefit analysis.  I don’t use a smartboard – I tried it for a year, and found out that I never used any features that couldn’t be done with a dumbboard.*  I’ve found the iPad to be worth far more than the smartboard; yet, the iPad generally costs less than half a smartboard.   If your school can afford computers and smartboards, it can afford an iPad for the physics department.  The question becomes, is such a purchase worthwhile?

* A “dumbboard,” as I learned over the summer, refers to a computer projector shining directly onto a whiteboard.  Annotations to the screen can be done with dry-erase marker. 

Now that the iPad 2 includes a video and still camera, the answer is unequivocally “yes.”  Our department has had a high-quality digital camera for years.  When I want to take a picture of an experimental setup, I walk down the hall to get the camera.  I take the camera out of the bag, remove the lens cap, take the picture**, remove the USB cord, replace the USB cord and remove the correct USB cord, insert card into the card reader, click a mouse a few times, and voila – there’s the picture.  Finally.

**often the shutter won’t press without the magic incantation that goes, “Why the #$@@ won’t the dang picture take?  Is it on autofocus or something?”

With the iPad 2, the picture isn’t nearly as high resolution.  However, the picture taking process is reduced to (1) press button, (2) email picture.  That capability by itself might be worth the price of the iPad 2.  Think of all the measurements that can be made live, in class, with instant photography!***  And, portable skype is nothing to sneeze at.  I can show an equation during a live video chat; I can even show a live experiment to a remote viewer.  Not that I’ve done that yet, but if you would like to listen in to my honors or research class via skype, just let me know.

*** Of course, those of you who were smart enough to purchase smartphones have probably been doing this for years.  I still have a landline, and an office phone.  Sorry.

And with the Vernier video physics app, the revolution is complete.  Vernier’s logger pro software has always allowed easy frame-by-frame video analysis on the computer.  But the time to upload video and then to convert it to a usable format has always been an annoying barrier to using this feature except for research purposes.  On the iPad 2, the process is simple and quick.  The video collection can be done within the Vernier app itself – no saving and importing videos unless you want to.  The interface is easy to use and understand.  Within a few minutes, you can have position- and velocity- time graphs for any captured motion.

As a testament to this app’s ease of use, I produced a useful video and graph within minutes of first opening the app, without reading any sort of instruction manual.  Then, I showed my 8 year old how it worked.  He spent a couple hours taking and analyzing videos, proudly showing his grandmother that the dropped ball was going 600 cm/s, but the dog’s nose only went 150 cm/s.  I approve.

For $2.99, I can't imagine a more useful physics app.  Now, Vernier, your challenge is to make all your probes work wirelessly with an iPad version of logger pro.  Go for it.

Two Masses and a Pulley, and a New Misconception

The badly sketched picture to the right shows a classic mechanics problem.  Two equal masses are connected by a string over a pulley.  In this case, the table is frictionless.

Typically, a student is asked to determine the tension in the rope and the acceleration of the masses.  Great -- that's (mg)/2 and g/2.*  This problem is richer, though, than a mere calculation might suggest.  Take a look at a quiz I gave the other day:

* The quick way to get this is to consider both objects as a single system.  The net force on that system is the weight of the hanging mass, mg; the mass of the system is 2m.  By Newton's second law, a = g/2.

1.       A block of mass m is attached over a pulley to another hanging mass m, as shown above.   The surface is frictionless.  The system is released from rest.

     

(a)    What is the direction of the hanging mass’s acceleration?  Explain.

(b)   Is the acceleration of the hanging mass greater than, less than, or equal to g?  Explain.

(c)    Is the tension in the rope greater than, less than, or equal to mg?  Explain.

2.       A block of mass m is attached over a pulley to another hanging mass m, as shown above.   The surface is frictionless.  This time, the top block is given an initial velocity to the left and released. 

(a)    What is the direction of the hanging mass’s acceleration?  Explain.

(b)   Is the acceleration of the hanging mass greater than, less than, or equal to g?  Explain.

(c)    Is the tension in the rope greater than, less than, or equal to mg?  Explain.

Ideally, 1(a) is answered with a kinematic approach -- the hanging mass is speeding up and moving down, so acceleration is also down.  For 1(b), I've defined "free fall" as the situation in which no forces besides weight are acting.  Since a tension acts upward on the hanging mass, the mass is not in free fall and the acceleration is less than g.*  And in 1(c), acceleration is downward, so net force must also be down.  That means down forces greater than up forces, so the tension is less than the weight.

* Okay, sure, if the upward tension is twice the block's weight, the acceleration could be g, upward.  That's highly unlikely in hanging-block-and-pulley problems.  

Of course, question 2 is identical to question 1!  The hanging mass is moving up but slowing down, so acceleration must still be downward.  (Or, one could argue that the block on the table still experiences only one horizontal force, that of tension, so its acceleration must be to the right; the blocks must move as a unit, so the hanging block has downward acceleration.)  Once it's established that acceleration is still down, questions 2(b) and 2(c) follow as in 1(b) and 1(c).

By far the most common misconception here is that the net force must be in the direction of movement.  A student will commonly get question one reasonably correct, but then say "the block is moving upward, so up forces must be bigger than down forces."  This question is just one more salvo in my arsenal aimed at that piece of nonsense.  

Another typical misconception is that in question 1, since the hanging block is falling near earth, its acceleration must be g.  That's taken care of with a request to state the definition of free fall and a sheepish look from the student.

And, a common mistake is to justify (a) and (c) with circular reasoning:  The acceleration is downward because the weight is greater than the tension; the tension is less than the weight because the acceleration is downward.  This student doesn't earn full credit, but I'm not worried so much about his comprehension. 

I discovered a new misconception today, though.  One of my brighter students said acceleration was equal to g, and he stated the definition of free fall accurately.  He asked, "since the surface is frictionless, the block on the table doesn't require any force to move.  So why won't the rope will be slack, the tension zero, and gravity the only force on the hanging block?"

At first I was flummoxed.  I set up two carts on my track, and showed him that the string was in fact not slack.  But why on earth would he think that no friction leads to a slack rope?

In further conversation, I discovered that he was referring back to our class's multiple conversations about how no net force is necessary for motion at constant speed in a straight line.  A mass on a frictionless track, once moving, keeps moving, even without any tension to pull it.  My student wasn't processing that this block on this surface was accelerating, not moving at constant speed.  Once I pointed out how the blocks must move together, and therefore accelerate together, he got it.

How much is this post worth?

Woodberry Forest 21, EHS 12 in 2011.  But this picture
is from 2010.

Students, and too often parents and colleagues, usually approach a high school course as a point-earning game. While points and grades must exist -- they *do* motivate, and besides, you're not gettin' very far with your boss if you tell him "I'm not giving grades this marking period, okay?"* -- you can send a consistent message that you are an impartial arbiter in the game, not a teammate or an opponent.

* But, twelve years later I did just that.  See this series of posts. 

Consider the most commonly asked question in class at my school this time of year.  These are the High Holy Days at Woodberry Forest -- last Friday night was the bonfire*, and Saturday was The Game, a football match against our chief rival school.  This week marks review for exams, which start on Thursday. 

* Think the PAGAN ritual scene from the Dragnet movie, probably without the virgin sacrifice but with far more goat leggings

So, on the day before The Game, I passed out an exam information sheet containing basic form and content data.  In every section, without fail, someone asked, "How much will the exam be worth?"  To me, that's taking the point earning contest too far.  I'm not going to allow you to make a strategic decision about whether or not to study based on my answer.  

More to the point, what will the class response be to a dispassionate direct answer of "20% of the trimester, as stated in the syllabus?" 

(1) Half the class will instantly get out a calculator in order to determine the minimum exam score that will allow them to pass, or to maintain the grade that won't provoke parental ire.  Students who can't solve 3x = 5   for x will perform this calculation quickly and flawlessly.  

(2) The follow up question will be on the order of, "but, if we do well on the exam, will you weight that more heavily in our final grade?"  or, "Can we do extra credit?"

Why even engage in such gaming the system?  Considering the background of the big football game, I looked sadly at each student who asked that question.  I said, "Mr. Clark, when the football team gathers after practice today for one last conversation together before The Game, would you even consider asking 'Coach, how much is tomorrow's Game worth?'  And how would Coach react if he knew that the reason you were asking was so you could weigh just how much effort to give?"

Point made.  No follow-up questions about grades.  And we moved on to discussing physics.

Nacho, Nacho Day... and trimester exam review

This is just a repost that answers several frequently asked questions:

(1) How do you help your students review for a major cumulative exam?
(2) Why does your email say "Nacho Man?"

The point is, extra credit and food provide significant incentive to bring students into the classroom during what otherwise would be wasted independent study time.  Once students are in the classroom working diligently on physics questions, learning is happening even if music, conversation, and nachos are happening simultaneously.

Check out this post.

Peter Chen, a student who is well-versed in video production, intends to create a "cooking show" style clip about Nacho Day in our physics department.  I'll post the link in a month or so.

GCJ

No credit for ridiculous answers -- an impulse problem

I work very hard to differentiate my physics class from merely an applied mathematics class.  We do quantitative demonstrations nearly daily, in which a mathematical prediction is checked via direct measurement.  I frequently ask on homework problems, "Justify the physical reasonability of this answer."  My class is incessantly discussing how to figure out whether or not answers make physical sense, regardless of whether arithmetic is done correctly or not.

I amended a problem the other night from (I think) the Serway & Vuille text.  I gave them the graph to the right, and wrote:

1. A possible force vs. time curve for a ball struck by a bat is shown in the figure. 
(a) Calculate the impulse delivered to the ball.
(b) This 0.25 kg ball was initially moving toward the bat at a speed of 20 m/s.  Calculate the exit speed of the ball.

For part (a), most of the class figured out to take the area under the graph, which they better have -- that same day in class I had discussed how impulse can be found as the area under such a graph.  Some students estimated an average force, which would be around 4000 or 5000 N, and multiplied by 1.5 ms.  Fair enough.  

Understandable mistake #1:A few made the error of multiplying the MAXIMUM force of about 8,000 N by the 1.5 ms time interval.  I took off one point out of fifteen for that -- these students were at least approaching the problem with relevant physics.  This mistake makes the impulse wrong by a factor of 2.

Understandable mistake #2: A few also failed to read the horizontal axis, and multiplied by a time interval of 1.5 s, not 1.5 ms.  These students also were approaching the problem with correct physics, but made an arithmetic error.  Granted, the answer for impulse was off by a factor of 1000, giving them 7500 Ns instead of 7.5 Ns.  But I can't really expect anyone to have a serious physical understanding of orders of magnitude for impulse calculations, especially in the first two days of studying the topic.  So I took off just one point.

On to part (b).  

Understandable mistake #3:  The most common error was to fail to account for the direction change of the momentum vector.  The ball has a momentum of 5.0 Ns toward the bat before the collision.  The ball's momentum changes by 7.5 Ns.  But, that doesn't give the ball a final momentum of 12.5 Ns!  Since the ball changed directions, the momentum must have first DECREASED by 5.0 Ns to zero, and then increased in the direction away from the bat by 2.5 Ns.  

With the failure to account for the direction change of the ball, the exit speed works out to 50 m/s -- a lot, but still not unreasonable, as baseballs hit for home runs routinely exit the bat with speeds above 100 mph.  The correct answer is 10 m/s, or about 22 mph -- not a very hard hit, but also not unreasonable.  Anything related to a baseball in the tens of miles per hour is just dandy.  I took off just two points for failure to account for direction in a momentum calculation.

(Aside -- I'm an American, and I watch baseball.  However, if someone had assumed no direction change for the ball, given me the 50 m/s answer, and then discussed how the cricket batsman is allowed to propel the ball in the direction in which the ball was already moving, that student would have earned full credit and a piece of candy.)

What about the student who compounded error upon error?

Understandable mistake, combo platter:  The student who used the max force rather than the average force to calculate impulse, AND who didn't account for the ball's changing direction, got something like 68 m/s.  Well, that's about 150 mph, and still not horrid -- after all, that's only 40% above the typical 100-120 mph exit speeds in the majors.  (I'm recalling my Physics of Baseball by Robert Adair; I hope I have that value right.  Please correct me in the comments if I'm wrong.)  That answer loses only the two points for the direction change issue.

Terrible, Horrible, No Good, Very Bad Mistake: Oy.  I had several students who failed to see the units of ms, and found an impulse of 7500 Ns.  Then they carried through the mathematics in part (b) to find an exit speed of 30,000 m/s.  Oh, I say, whoa there.  Really?  30 km/s?  Mach 88?  Okay, Bugs Bunny threw faster than that in the Christopher Columbus episode (when he threw a ball around the world in about 2 or 3 s)... but other than in a cartoon world, NO.  These students lost an ADDITIONAL 5 points out of 15.  One sheepishly said, "well, the math said 30,000 m/s, but you didn't ask us to justify the reasonability."  I pointed out that in physics, physical reality always will trump mathematical manipulation.  It doesn't matter whether I *ask*, one should *always* be conscious of physical reasonability.

Epilogue:  One lone student made the Terrible Horrible No Good Very Bad Mistake, got 30,000 m/s... and pointed out "that is nonsense, a baseball can't ever go faster than 100 m/s or so, the answer is ridiculous but I don't know what I'm doing wrong."  He lost the one point for failure to read the graph properly, and one point for an incorrect answer... and that was all.  Reward those who demonstrate their commitment to physical reality.

"Group Quiz" on impulse-momentum

Happy and Sad Balls -- which one produces
more force when dropped onto a force plate?

I can't count the number of articles I read that sanctimoniously preach how physics teachers need to "actively engage learners," involve students in "peer instruction,", provide "inquiry-based interactions", or any other set of edu-buzzwords you can create.  These articles push a fundamentally correct point: that I'll have enormously less success if I merely talk at the white board than if I somehow get the class to involve themselves in the topic at hand.

But as with any other educational method, active engagement only works if it's done right.  The trick is to get students to care about the answer to the question you posed, and about the justification of that answer.  I don't want to read any other literature telling me that active engagement can be effective.  I want to know specifically how other successful physics teachers get their students to actively engage.

I incessantly ask "check your neighbor" questions, in which I give students time to write an answer; I give time for class discussion; and then I survey the class, or call on a random student to summarize his thoughts.  These are generally effective.  However, after a few weeks, the shine has gone off of this novel (to the students) activity.  I can see the beginnings of apathy cross my students' faces... "Oh, again with the neighbor arguing thing.  Gee whiz."

I've got to vary my approach if I'm going to keep class activities fresh and interesting.  I tend to ratchet up the reward for correctly justified answers to my check-your-neighbor questions.  One thought that I've detailed previously is to call on a random student after discussion... if that student can clearly and correctly answer my question, I'll cancel the next day's quiz. 

I generally give a daily quiz at the beginning of class.*  My colleague Paul Vickers modified my daily quiz to an occasional "group quiz," in which he assigned groups of 2-8 students to answer a check-your-neighbor-style question for a quiz grade.  The fact that it's called a "quiz," that the students perceive that their performance will directly affect their grade, keeps everyone focused and on-task.  Yesterday, I tried a new hybrid approach to a check-your-neighbor question.

* Why?  Because students *care* whether they get the answers right, so they pay attention when I go over the quiz better than they would pay attention to the same conversation without the context of a quiz.

The question:  I have a happy ball (one that bounces nearly to the height from which it was dropped) and a sad ball (one that hardly bounces at all).  I drop each ball from the same height onto a force plate.  Both balls have the same mass; both balls are in contact with the scale for approximately the same time.  

Question 1:  Which ball experiences a bigger momentum change?

Question 2:  Which ball causes a larger reading on the force plate?

The method:  I began like a standard check-your-neighbor question.  I wrote the questions on the board, and asked the students to write and justify an answer in their notebook.  After about a minute or two, I asked everyone to argue with his neighbor.  Nothing to see here, really; I did let the discussion go on a bit longer than usual, making sure that those who were still making physics points to each other had a chance to hash out any disagreements.  

Finally, I gave everyone a blank card.  I told them to write and justify the answer to each question as if it were a quiz.  I promised that I would choose a student's card at random to read to the class.  A correct answer with justification on the card would be worth an extra credit point for EVERYONE on that day's quiz.

Oh, boy, did I get careful justifications.  One class's random delegate explained the answer perfectly, earning the credit with no doubt.  The other class's delegate explained beautifully (but incorrectly) that since the balls have the same weight, the force plate must read the same value, and thus both balls will have the same momentum change.  Knowing that many class members had convinced themselves of this mistaken fact, we talked about why the force plate would NOT read the weight of the ball.  

Right or wrong, making the check-your-neighbor question into a quasi-quiz convinced all my students to write clear descriptions of their thoughts.  Even though I only looked at one answer per class, everyone took the writing seriously, and everyone could evaluate for himself the quality of his arguments.  

I may get away with this quasi-group-quiz once or twice more before it becomes just another day of class.  Then I'll have to provide a different sort of incentive for careful, invested participation.  I'm open to ideas -- email me, or post a comment.

GCJ

A cool thin lens script in honor of our 50th follower!

Wow... 50 followers now!  Thanks to Pal Fakete of Sydney for becoming the 50th.

Frequent contributor Michael Gray sent me a wolfram alpha script this morning on the thin lens equation.  Wolfram alpha, if you're not familiar, is a wonderful site that will suck you in with all the crazy things it can do.  You can use it as a calculator, equation solver, equation grapher, and more.  My students have occasionally used it to check their algebra or calculus on homework problems.  All I can say is, I wish this had existed in 1993 when I took my differential equations class.  I learned to use integral tables, that's for sure.

(What's an integral table, you ask?  Get off my lawn, whippersnapper.)

Anyway.  This particular script will solve the thin lens equation for any variable given any input.  Great -- so will your calculator.  What I love is that the script will include a ray diagram!  Your students can not only check their answers to lens questions, but they can see visually if their inputs make sense.

Why is the diagram so useful?  Well, any man jack can plug numbers into the thin lens equation.  What's tough is getting the signs of the input quantities right, and then interpreting the output.  The resulting ray diagram allows a student to interpret physically, not just numerically, whether an answer is reasonable.  A diverging lens gave me a real image?  Oh, I must have missed a sign.

Let's find another 50 readers, and I'll keep posting.  Send in your requests!

GCJ

"Gravity!" Fundamentals Quiz

The word "gravity" is, by itself, utterly ambiguous.  Nonetheless, our students will refer to a wide swatch of constants, principles, and equations by this single word.  While that's not necessarily a problem in the context of a conversation with friends, the lack of specificity can get students confused and blown up when trying to solve test problems.

To the right is part of a recent fundamentals quiz about "gravity."  (You can click on it to read it at full size.) I listed every possible equation or constant that has any tenuous connection to "gravity," and I asked students to identify these items in words.  Here's a summary of correct and (real) incorrect answers:

(a) Correct: Net force on an object in uniform circular motion, or just centripetal force.  

      Incorrect: centrifugal force, net force, centripetal acceleration, gravitational force

(b) Correct: Gravitational force exerted by any massive object on another, or just gravitational force.

      Incorrect: Newton's law, gravitational field, g

(c) Correct:  acceleration of an object in uniform circular motion, or just centripetal acceleration

      Incorrect: centrifugal acceleration, acceleration, centripetal force, net force, gravitational acceleration

(d) Correct: Weight, force of a planet on an object on the planet's surface.

      Incorrect:  free-fall acceleration, mass

(e) Correct:  Gravitational field produced by a planet, free-fall acceleration

      Incorrect:  Force of gravity, force of g, Newton's law, force of a planet, centripetal force

(f) Correct:  Gravitational field, or free-fall acceleration

      Incorrect:  Force of gravity, gravity, weight, free-fall force, gravitational constant

(g) Correct:  Universal gravitation constant

      Incorrect: Newton's law, force of gravity, free-fall acceleration, gravitational field, gravity