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 satellite's mass changes its orbital speed as well become confused a bit when the simulation doesn't verify their answer.)

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.

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."

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

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 [that no longer exists] 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.

Update October 2023 - McGraw Hill has taken down the link.  HOWEVER!  The teacher's manual is now included in the 2023 and later versions of the 5 Steps Physics 1 books!  If you're having trouble finding this, please email me.

GCJ