31 October 2014

Are Kepler's Laws part of AP Physics 1? No and Yes.

Debby Heyes, who attended my open lab this summer,has a quick AP physics 1 question:

Are Kepler's Laws included in the course?  

Fast answer: no.  A search in the curriculum guide for "Kepler" gives no results.

Deeper answer: Yes AND No.  Kepler's laws by name are not part of the curriculum, but some of the behavior of planetary orbits described by Kepler's laws is part of AP Physics 1.

The "equal areas / equal times" law can be stated as a consequence of angular momentum conservation.  An orbiting planet experiences no torque relative to the central star (because the gravitational force always points back to the center of rotation, meaning the distance term in "torque = force * distance" is zero).  Therefore, the planet's angular momentum about the central star is conserved.  Treating the planet as a point object, its angular momentum is given by mvr, where r is the distance to the central star.  When r goes down -- i.e. when the planet is closer to the sun -- v goes up, meaning the planet moves faster in its orbit.  That's essentially Kepler's law.

The "period proportional to the 3/2 power of the radius" law is merely a consequence of Newton's second law and circular motion, at least if we consider circular orbits only (which we emphatically do in AP Physics 1).  Set the gravitataional force equal to ma, where the acceleration in circular motion is v2/r.  Then the speed of an object in circular motion is the circumference divided by the orbital period.  Solving for period gives the Kepler's law relationship -- and we should be able to do that and understand it in AP Physics 1.

The law that says "all orbits are ellipses with the sun at one focus" is not in any way on the AP Physics 1 exam that I can tell.

An exercise I'm running...  I'm asking students what happens to the speed necessary to maintain a circular orbit if (a) the central star's mass is doubled, (b) the planet's mass is doubled, or (c) the planet's distance from the central star is doubled.  I hand everyone a different half-page of paper with one of these three questions asked; for more variety, some of the papers say "tripled" or "quadrupled" rather than doubled.  Students are guided to solve in variables for the speed, then to use semi-quantitative reasoning to see what happens to the speed.

Then, I pull up "my solar system", a phet simulation.  Using the "sun and planet" preset, students are asked to change the simulation as described on their paper to see if they get a circular orbit.  (Those who told me that changing the planet's mass changes its orbital speed as well become confused a bit when the simulation doesn't verify their answer.)


28 October 2014

When do you give your first test?

Barry Panas, the John Oliver of AP Physics consultants, writes in with a question:

How long does it take you to reach your first full physics test in your "first" course of physics with any group of students? I'm specifically thinking of the course that introduces student to kinematics (etc.). How long do you spend in that very first unit to the point of a test?

Complex answer.  Start with this year in AP Physics 1: I've been giving a 10 question multiple choice test once a week, then every third week I instead give a 40 minute free response test.   So the very first test happened after three weeks.  That was enough to get through graphical and algebraic kinematics, plus Newton's second law in one dimension. 

Since I only have 40 minutes to test, I decided to go with two AP-style 7 point problems plus three "short answer" questions.  All my tests this year will be in this format.  My trimester exams -- one to be given in November, one in March -- will be 30 minutes for 17 multiple choice questions, followed by a full-on 90 minute, 5 question AP Physics 1 style free response exam (three 7-pointers, and two 12-pointers).

Historically in my upper-level intro classes:  I've given tests every four weeks.  These tests have been 80 minutes or so long, including free response, short answer, and multiple choice.  In the regular-level sections, this has gotten me through virtually all of kinematics.

The advantage of shorter but more frequent tests is obvious -- they get more frequent feedback, and tests aren't as big a deal.  However, the advantage of longer tests is that students usually do better the longer the test.  More questions mean more likelihood to find something easy to knock out, leaving time to play with a tougher question.  

Either way, I've always stuck to a few guiding principles:  

All tests are of identical format.  Just as students are taught not to read the directions on an SAT or AP test (if you don't know the directions ahead of time, you're sunk), they shouldn't be asked to read directions to any types of questions they haven't seen before.  I publish the instruction sheet and the test structure before test day.

The time per problem is identical on all tests.  In AP, I use the AP time ratio of about two minutes per point free response, and just about two minutes per multiple choice item.  In lower level classes, I make sure to keep the same time-per-item-type ratio on all tests throughout the year.

All my tests are cumulative, meaning there's no need to schedule unit tests:  wherever we are in the course, the test covers everything to that point.  The test DATES are set from year's beginning.

21 October 2014

Friction coefficient on an object of unknown mass -- lab, homework simulation, or test question


I've been a fan of Phet's "Force and Motion: Basics" simulation for several years now.  It includes several tabs: the "tug of war" which inspired a daily quiz that I'll likely post soon; a "motion" tab that allows you to apply forces and see the speed change, but in animation and in a speedometer; and an "acceleration lab" tab that allows for all sorts of investigations connecting net force, acceleration, mass, and speed.  I'd suggest downloading the java version and playing with it for a while.  In fact, I give extra credit to my students merely for noodling around with this simulation for at least ten minutes one night.


A few weeks ago, I discovered the "friction" tab.  You can see a screen shot above.  By clicking on the "applied force" slider, you cause the stick figure to push on the box in either direction with any amount of force.  The checkboxes in the yellow area allow you to display the net force, the individual forces, the masses of the objects, and a speedometer.  Students can see that pushing the box doesn't cause the box to move immediately in the direction of the push; rather, the box slows down or speeds up based on the direction of the net force.  That analog speedometer does more to bust the misconception of net force being in the direction of velocity than anything I can do or say in class.  

But wait -- there's more.  I clicked the checkbox that says "masses."  As you might expect, the mass of each object is displayed.  You can make the girl sit on the box, and she'll even hold the 200 kg refrigerator without complaint if you make her.  Great.  Students can see how the speed changes more or less rapidly when different masses and forces are involved.

Take a careful look at that wrapped present in the bottom right corner.  Its mass is displayed as a question mark.  Ooh... that seems like an invitation to an open-ended investigation.

My question: determine the coefficient of friction between that present and the surface (with the default setting for the friction slider).  That's not a simple plug-and-chug problem because the mass of the present isn't known -- okay, the simulation displays the value of the friction force, but it doesn't tell you the value of speed or acceleration.  So neither "Fnet = ma" nor "Ff = μFn" gives enough information to solve with a single trial and single equation.

Students are asked to write up their solution in a single page, as if this question were a job audition for their engineering firm.  I have a different teacher or an advanced student rank all the submissions, placing each in one of four categories:

"Hired" (one submission only)
"Recommended to other companies"
"No recommendation"
"Blacklisted"

Hints about using this idea:  For one thing, be sure to open the simulation in java.  I unfortunately had one class open using html5, which is simpler to use and which works on ipads.  But on that version of the simulation, the mass of the present is displayed for all to see.  Oops.

Secondly, there's no reason to stick with this as a pure simulation.  Use wooden blocks, or the PASCO friction apparatus (which is just an open plastic box with a rough bottom surface and a place to attach a string).  Don't allow anyone to measure the mass of the wooden block, but ask them to determine that and the coefficient of kinetic friction using force probes or spring scales only.  The only reason I did this with the simulation rather than as a live, hands-on laboratory exercise is that we had done enough already with that friction apparatus this year.

And finally, this would make a great AP Physics 1 essay-style short answer question:  "In a clear, coherent, paragraph-length response, describe how you would determine the coefficient of kinetic friction between the block and the surface using a spring scale and other known masses."

09 October 2014

Fan cart on an incline, and the beginnings of an AP Physics 1-style problem

I started my presentation on inclined planes the way I've always started it -- with a quantitative demonstration.  I placed my venerable rechargeable 310-g PASCO fan cart, whose fan produces a force of 0.26 N, on a PASCO track.  To what angle should I incline the track so that the cart remains on the track in equilibrium?

I demonstrate the solution using the standard three-step Newton's Law problem solving procedure -- draw a free body, break the weight into components, and write Fnet = ma in both directions.  In this case, because acceleration is zero, the weight component down the incline mg sin θ equals the 0.26 N force of the fan.  Solving for θ gives an angle of about 5 degrees.  That's easy (and impressive) to verify with an angle indicator.

The next problem I pose posits the same cart released from the top of a 10 degree incline; what will be the cart's acceleration?  This time, instead of solving myself in front of the class, I have each student work through the problem himself.  When someone gets an answer, I hand him one of the fan carts, a motion detector, and a labquest -- it's his job to verify the answer.  Usually we predict an acceleration of 0.87 m/s/s, and we measure something in the neighborhood of 0.77 to 0.86 m/s/s.  I'm happy with that -- at most 11% off from the prediction.

However:  Yesterday a group kept getting between 0.56 and 0.60 m/s/s for the acceleration of the cart.  Now, rather than 11% off, this group was 31%-35% off.  That didn't seem right.  What was going on?

The first words everyone spewed were "because of friction."  Stop it.  It's rare that the true cause of a laboratory discrepancy can be attributed solely to neglecting or miscalculating friction.  And in that rare case that friction is indeed the issue, "because of friction" is never an appropriate answer.  Explain how the force of friction, or the work done by friction, would change the relevant equation; and then convince me that the measurement is different from the prediction in a way that would be accounted for by that force of or work done by friction.

This group measured an acceleration that was smaller than predicted; but the other groups were pretty much right on.  That implied that the carts might have been different in some way.

These PASCO fan carts operate on a rechargeable battery.  "Could our cart's battery be dying?" the group asked.  Let's see... the weight component down the incline of mgsinθ = 0.54 N is independent of the fan.  It's the force of the fan up the incline that would change depending on the battery, and that  fan force is subtracted from 0.54 N to calculate the net force.  A smaller fan force due to a dying battery would mean that the net force down the plane would be greater, not smaller, giving more than the predicted acceleration.

So the cart's battery wasn't dying.  We realized that two of my three carts were newly purchased over the summer.  I used a force probe to measure the force of the fan on the new carts -- I got 0.32 N, more than the 0.26 N from the old fan.  Aha!

What a wonderful AP Physics 1 problem you've discovered.  You could describe the situation... then ask some of the questions below:

* How would you experimentally measure the cart's acceleration after it's released from the top of the 10 degree incline?
* Predict the cart's acceleration after it's released from the top of the 10 degree incline.
* How would the cart's acceleration change if rather than being released from rest it were instead given a brief shove to cause it to move up the 10 degree incline?
* The cart's acceleration is measured to be substantially less than the prediction.  Does that mean that the force of the fan was greater or less than the assumed 0.26 N?
* How could you experimentally measure the force provided by the fan?

I know when I write any sort of physics problem -- whether for the College Board, for my book, or for my class -- I often begin with an actual situation I've encountered in my laboratory.  Do you have an experiment that lends itself to a good AP Physics 1-style verbal response sort of question?  Post it in the comments, or email me; maybe I'll use that as the basis for a "Mail Time!" post.

GCJ




08 October 2014

5 Steps to a 5: AP Physics 1 Teacher's Manual now available

As part of the 5 Steps to a 5: AP Physics 1 book, I wrote a Teacher's Manual.  It's finally available... you can go to this page here to get it.  (You need to give McGraw-Hill your name and school address... uncheck the box about upcoming promotions, and I don't believe they will spam you about anything.)

I've listed many of my quantitative demonstrations in this manual, along with some general pieces of teaching advice which reprise things I've posted on this blog.  I've approached the manual under the conceit of "5 steps for you to help your students get 5s."  Hope you like it... Please send comments.

GCJ



26 September 2014

Mail time: velocity-time graph that crosses the horizontal axis

A correspondent asks:

Hi Greg. I was doing some questions and I'm unsure about a certain response. I'm looking at a velocity vs time graph where the graph is linear and cuts right through the x-axis going in the neg. direction. At EXACTLY the point of intersection do we state that the acceleration is negative because the slope is negative or zero because at that instant the object has zero velocity?

My instincts want me to say negative, but last year I went with zero, sooooooo I'm not really sure.

I've made a graph of what I think you're looking at... see the picture.  You want to know, "What is the direction of the acceleration at point A?"  This is a classic question, with a corresponding classic point of student confusion.  This graph could represent, among other things, a ball thrown upward in free-fall -- it moves upward, slows, stops briefly, and speeds back up toward earth.  

Two ways I'd phrase my answer:

(1) Just because velocity is zero does not mean that acceleration is zero.  Otherwise, gravity would have to turn off just because a ball reaches the peak of its flight.

(2) Acceleration is the slope of a v-t graph.  The horizontal axis isn't special -- the slope of that line doesn't change anywhere, so the acceleration is negative everywhere, both for positive and negative and zero velocities.





24 September 2014

Can an Electric Field Be Negative?

A correspondent writes in:

I've been telling my class that the electric field cannot be negative.  1. Its direction is set and then 2. the value is set.  And since the value corresponds to the predetermined direction, it is always positive.

One of my international students from China used the vector argument.  Since electric field is a vector quantity, can't we 1. choose our direction first - independent of the field and then 2. determine the direction of the electric field and how it meshes with our predetermined direction?  Was I terribly wrong to say that E-field cannot be negative?

My response:  I say an electric field can never "be negative."  Electric field is a vector -- it has magnitude and direction.

Sometimes in a 1-dimensional problem, by convention physicists choose one direction to be positive, one negative.  For example, if south is the negative direction, then a car slowing down moving north might have a "positive" velocity and "negative" acceleration.  And the kinematics equations require algebraic use of the negative signs.  Nevertheless, the magnitude of the acceleration vector would still be 4 m/s/s*, and the direction would be south; the magnitude of the acceleration can never be - 4 m/s/s.

*  not even positive 4 m/s/s, just plain ol' 4 m/s/s

It's legitimate, though crude, to apply the same reasoning to the electric field.  Define up as positive.  Then a 200 N/C electric field that points down could be called "-200 N/C."

But there is NO REASON EVER TO DO THIS IN INTRODUCTORY PHYSICS.  EVER. 

(You can see some of my reasoning in this post: Never trust a student with a negative sign.)

Students get into trouble if they try to use F=qE, and plug in negative signs for q and E to get negative forces.  Negative forces?  What are they?  Forces also have magnitude and direction.  You can't have a -300 N force, just a 300 N force in the downward direction.*

* Again, pedants can argue that such notation can be made self-consistent.  I'm teaching introductory physics, with students who still struggle with the idea that "-300 N" doesn't mean "bad 300".  It's far more important to use notation that addresses the physical meaning of a quantity than notation that maybe, perhaps, with expertise, can be made mathematically reasonable.

So don't ever use negative signs with electric fields -- they're too easy to confuse with negative charges, which mean something completely different, and negative potentials, which are again different.  Have students state a magnitude and direction of an electric field without negative or positive signs:  "200 N/C, to the left."

15 September 2014

Giancoli's stoplight problem -- scale it down and set it up in the lab

A classic problem -- I think I first found it in the Giancoli text, but some variant is in all comprehensive problem sources -- asks for the tension in two angled ropes supporting a hanging object, given the mass of the object and the angles of the ropes.  The version I assign includes a 33 kg stoplight, a 37 degree angle, and a 53 degree angle.

Firstly, adapt the problem for AP Physics 1 rather than the traditional AP B course.  To do that, I begin the question by asking "Is it possible to calculate the tension in the left-hand rope?   If so, explain with words and without numbers how the tension could be calculated.  You need not actually do the calculations, but provide complete instructions so that another student could use them to calculate the tension."  It's okay if students choose to do the calculation first, then tell me how it's possible.  Of course, the obvious approach is to explain that we can set up two equilibrium equations (one vertical, one horizontal) with two unknowns, so the problem is solvable.

Next, I ask for the solution for the tension in the left rope.  They calculate something like 220 N.  

In class, I remind everyone that any numerical solution to a physics problem is not really an "answer," but more accurately a "prediction" of the result of an experiment.  I should always be able to verify a prediction by setting up the suggested experiment.  Thing is, I don't have a 33 kg object to string up from ropes.  Why not?  Because, 33 kg is like 70 pounds.  The mass sets in my classroom don't go above about 1 kg.

And there lies the way to verify the prediction -- scale everything down by a factor of 100.  I do have 330 g to put on a hanger.  Then, I should get a tension in the left rope not of 220 N, but of 2.2 N.  

In the above picture, I've arranged the lengths of the ropes such that the angles are in the right neighborhood.  Sure enough, the left rope read a tension of 200 N, within the 0.2 to 0.3 N N tolerance I expect on a typical classroom spring scale.

Not only does this experiment reinforce the physical meaning of the problem's solution, not only do we see whether the answer is "right" or not, this experiment can help emphasize why the answer "221.43 N" is utterly ridiculous.  The scale can't read better than about 2.2 N or 2.1 N -- it can't read 2.145 N.  Only two digits mean anything (not two decimal places, two DIGITS).  Seeing a "scale reading" rather than an "answer" is the first step toward internalizing that physics is about experiments, not numbers.

08 September 2014

Where do I get AP Physics 1 multiple choice test questions? The Big Amazing Resource.

Testing isn't as simple as it used to be.  Over AP Physics B's 40+ years of existence, enough authentic multiple choice questions had been released to satisfy even the most prolific tester.  However, now that we've moved into the AP Physics 1 era, a lot of those questions are useless; even those that are in the spirit of the new exam need to be rephrased, especially to bring them down to four rather than five choices, and to minimize but not eliminate the questions that require calculation.

Of course, you can go to the College Board's official AP Physics 1 page via AP Central.  There you'll find some sample questions in a file conveniently marked "sample questions."  You can get more in the official "course and exam description.  Finally, if you've ever completed a course audit for AP Physics B or AP Physics 1, you'll be able to download the released practice exam.  Go to your account, go to "add a course," add AP Physics 1, and download the exam.

The 5 Steps to a 5: AP Physics 1 book includes a full practice exam, as well as some good questions at the end of the content chapters.  Or, try looking at the supplements to the Serway textbook's 10th edition; they've hired some seriously connected people to write sample questions for them.  And those of you who have attended my summer institutes or this past summer's open lab have a CD of materials.  Look in the "honors physics" folder, and then look at the quizzes.  Many of those daily quiz questions can be used either verbatim or with minimal revision.  

But the Big Amazing Resource for AP Physics 1 and 2 is the newest version of Matt Sckalor's AP Physics workbooks. About half a decade ago, Matt compiled every released AP Physics B multiple choice question into a single workbook, organized by topic.  Over the summer, a number of AP Physics consultants -- that is, people with intimate knowledge of the new courses -- rewrote these questions so that they meet the spirit of the new Physics 1 and 2 exams.  Now, this new and improved workbook is still not vetted by the committee.  It ain't perfect.  But it is a treasure trove for those who need to make some close-to-authentic tests.

How do I access this Amazing Resource?  The only way is to go through "Pretty Good Physics -- Secure."  Most of this blog's readers already have an account there.  If you don't, you should -- follow the link, and follow the instructions to sign up.  The process is simple but may take a few days, because it is critical that the site administrators verify that all members are honest-to-Bob physics teachers.  

Then, get into the site and search for "workbook."  Out will pop the new workbooks, all ready for you to copy and paste into your tests.

Do you know of another good resource?  Let us know in the comments.

04 September 2014

My students are only averaging 80% on the daily quizzes. What do I do?

A frequent concern this time of year for both teachers and students is grades.  The optimism of the first few days of school has faded... the students have probably gotten back a bunch of quiz and test scores, jolting them into the reality that they're gonna fail this course, and then they won't make the honor society, nor get into college, or at least the right college that would allow their parents to brag at cocktail parties.  Holy #$&*, they'd better go drop this course RIGHT NOW.


I'm sure virtually everyone reading this blog has confronted the described mentality.  One way to deal with it is reasoned logic. Explain rationally and calmly that...


Oh, yeah.  Reason and logic don't seem to be the strong points of students who get carried away with the dramahz.  So maybe we need a different approach that doesn't necessarily include a rational basis.

The first and most important step in damping out this particular fire is to develop a relationship with the college counselor and the director of academics -- that is, the person ultimately responsible for college placement, and the person ultimately responsible for course changes.  These folks generally do have a rationalist approach to their job, and they are used to dealing with artificial drama; what they often don't understand is the nature of a physics course.  Meet with them.  Talk to them informally as well as formally.  Bring them cases of beer.  

Explain how your course works, that it's not about memorizing facts as much as using facts in new situations.  Assure these folks that you don't intend to fail the majority of your students.  I explain that any student who diligently completes all assigned work will earn a minimum of a B- for the year, but that there may be pitfalls along the way.  John Burk likes to compare his class to a theatre production: after a week of rehearsal, the scenes are quite rough, the actors don't know their lines, and the chemistry among characters hasn't yet jelled.  So should we just give up 'cause it ain't perfect yet?  Certainly not... think of physics as year-long preparation to perform on a year-end exam.  Things are expected to be rough at the beginning.

Then work on the students.  There's vast literature -- including on this and other physics teaching blogs -- about how to develop a "growth mindset" among the class.  It's critical at the course's beginning that you NOT discuss points or grades or college plans with any student or parent.  Nevertheless, it's a reasonable expectation that students be put at ease that their 75% quiz score doesn't mean they're getting Cs and having their lives ruined.

My approach is to tell them once -- only once -- how I calculate grades.  For me, 80% is an A, 70% is a B, 60% is a C, and 50% is barely passing.  I've in the past used a "square root curve -- that works fine as well.  When we approach the first test, I show up front the AP scale, in which about 65% is a 5, 50% is a 4, and 35% is a 3.  Then I allow test corrections to earn half credit back for any points they miss.

The final, critical point to the physics teacher is: don't try too hard to make students "feel better" about being in a hard course.  

When my own offspring is upset that we -- GASP! -- ask him to mop the floor, I find that it doesn't help his mood when we sympathetically and pleasantly try to acknowledge his annoyance and assuage his irrational anger.  "Don't worry, it won't take very long" or "Hey, it's not that big a job today, the floor isn't particularly messy" provoke more tantrums from the boy than if we just go away and leave him to the task.  Similarly with your students.  The more you sympathize, the more you try to talk them through and acknowledge their irrational dramah, the more they play up said dramah and talk themselves into a negative spiral of emotion.

Just keep going with the course.  As more and more of your students start to experience success, those shrill, distraught voices will become as whispers in the wind, drowned out by the veritable thunderstorm of positive confidence.