First AP Physics lab exercise -- cart on an incline

In my advanced / AP classes, the first week consists of demonstrations involving static equilibrium.  The homework includes equilibrium problems to solve.  After a week of demonstrations, problems, and quizzes, we do our first laboratory exercise.

I start by explaining* the general point of experimental physics -- we've solved lots of problems using the principles of equilibrium.  Now it's time to put these principles to a rigorous test, to provide experimental evidence that our problem solving methods are legitimate.  I do no further discussion of theory until we've collected loads of data.

* VERY BRIEFLY.  Students don't want to hear a lecture about the philosophy of experimental vs. theoretical science.  They will tune out instantly if I talk about this for more than about one minute; I want my class time spent collecting data, not listening to me drone on.

Next, I show the experiment:  At the front of the room, I stick a cart on an angled track.  I hold a string with attached spring scale parallel to the track, and read the scale; I put an angle indicator* on the ramp and read the angle.  I make a table on the board with a column for the tension in the string, and the angle of the incline.  I sketch a graph on the board next to the table, with axes labeled "Tension in the string (N)" and "Angle of the incline above the horizontal (degrees)".  I place a dot on the graph.  Then I make one more measurement... and we're just about ready to go.

* If you don't have the $20 PASCO angle indicator -- and you probably shouldn't -- use the "Clinometer" or "iHandy Level" app on the iPhone.  Android has similar and free apps.

The last thing I do before breaking everyone into groups is to briefly discuss the rules of laboratory, including that all data goes directly on the graph, and that you may not measure the same data point twice.  (Many students will nevertheless ignore these rules.  Don't get frustrated, just expect it and deal with it.  Even in my AP Summer institute, several teachers made a table of data without a graph, despite the fact that I said two or three times, very loudly, "You may NOT just make a data table now and graph later!")

Finally, I choose partners randomly with random.org, and we go at it.

"Go at what," you ask.  Where's lab sheet?

There is no "lab sheet."  The students have to listen and watch, then do the experiment.  If they didn't figure out what to do by watching, a lab sheet won't help.

So how do you set up all the stations before lab?

I don't.  I show everyone where the equipment is kept.  That's it.  They have to tie string themselves.  They have to find their own space to use, even if that space is in the hallway.  And, they have to clean up themselves.  This approach saves me time, sure; but it's also more authentic experimental physics.  Setting up themselves, with no lab sheet, makes the experiment less an exercise in following directions than in collecting data in which they have a personal connection.

How many data points do they collect?

They're not allowed to ask that silly question.  They keep collecting data until a first grader could clearly differentiate between the data points making a line or a curve.  When they think they have enough data, groups show me the graph, and I take a look.  More often than not on the first day I say, "what, you think five points provides a clear pattern?  Pah, back to the experiment before I send thee to the dungeons."  Then comes "Oh, this data is looking good, and does in fact look linear.  But the angles only go up to about 40 degrees.  Let's explore all the available angles... why not go up as steep as possible?  Then we'll be sure that the line continues."

Finally, groups will produce a graph that flattens out at larger angles.  At this point -- and NOT before -- do I show the free-body diagram and equations relating the tension in the string to the angle: T = mgsinθ.  No wonder the graph flattens... that's what a sine graph does for angles from 0-90 degrees!  This is a pretty awesome "ah-a!" moment for many students, one that wouldn't have happened if I had shown them the equation or analysis before we started.

All this data collection generally takes most of a 90 minute period.  Those who finish put away their equipment and begin the analysis, in which they make a new graph of tension vs. the sine of the angle... then they use the linear graph's slope to determine the cart's mass. 

I can discuss the analysis in a future post.  That's really of secondary consideration for now.  I'd like more physics teachers to separate data collection from data analysis.  I see so many students try to answer AP lab questions with equations and calculations... let's make sure that students can collect data, graph that data appropriately, and describe the appropriate use of equipment.  Then we can worry about linearizing graphs and taking slopes.

Mail Time: What if I have to start a physics lab from absolute scratch?

A participant at my summer institute writes in...

I hope this email finds you well. 

It does, except that I am in no way ready for my fantasy football drafts, and Arsenal is negotiating with Satan Himself Luis Suarez.  In other words, my non-fantasy life is going quite well, thanks.  :-)

The note continues:

So, here is the thing... I went into a Science Department meeting and found out quite to my dismay that the school has absolutely no equipment for Physics demo or labs, which I knew going into it that they didn't have much, I just didn't think they wouldn't have anything at all.

I was told that if I made a list I could order some equipment using the curriculum budget, which I am still unclear what that means on a financial point of view, my assumption is that it won't be anything extravagant...

So here is my problem, this is slightly overwhelming, having never taught physics before, I am not entirely sure what are the essentials when it comes to equipment and it's basically going to come down to what demos do I absolutely need and how can I do them with a minimum of resources?

Do you have any suggestions or advice on what I should put on this equipment list of things to order? Anything will help. It more or less dawned on me today that I am basically on my own when it comes to physics at the school.

Aah, you're stuck building from scratch.  That sucks, but at least you're being offered something.  Just AP Physics 1 for now, right?  As we discussed, the course audit provides you some leverage -- it requires a laboratory experience that is in some way comparable to a college physics lab.  You can certainly wait to sign off on the audit until you have some minimum equipment.  (Or you can offer to teach just "Physics" rather than "AP Physics" for now.)

If I'm you*, I get a Vernier Labquest 2 with a motion sensor, force sensor, it comes with a voltage probe, and maybe a force plate.  Then I get a Pasco 2 meter track with a set of cars.  That'll run you in the neighborhood of $1000 as a start-up.

*  Ed. note: grammar correct.  Sportscaster subjunctive mood.

For this year, I'd scrounge other stuff (basics like rods and clamps, spring scales, etc) from other departments, local colleges, hardware stores, and parents.  As the year goes on, make a wish list of the equipment you'd like to have.  When the opportunity comes up to buy something, have a list so you know exactly what you want right away.  

Good luck... hope this helps.  

Picture -- Manhattan College AP Summer Institute

Eighteen folks attended the institute in the Bronx this week.  They asked for a group photo; they asked me to upload the picture to the blog.  Here it is.  We had a great time.  Thus ends this summer's professional development.

As for the next year, anyone reading this is welcome to visit me at Woodberry.  I won't be running any workshops during the school year, but I expect to run a couple of summer institutes in 2014.  Stay tuned for the schedule.

My only major travels this year -- at least as currently planned -- include Northwest Indiana the week before Christmas, and San Jose, California for the USIYPT  on Jan. 31-Feb. 1.  If you're close, plan on saying hello.

Don't worry, the blog will continue.  If you have questions or ideas for a post, please send them along.

GCJ

Don't Mess with my Story

One of the Great Skills of the physicist is to make appropriate simplifications to a situation.  Experienced physicists don't think it's entirely a joke to "assume a spherical cow" -- it's a reasonable and necessary assumption if you're trying to approximate the terminal speed of a cow in air.

* That's part of a "discussion question" in the humor masterpiece that is Dave Barry's History of the United States: he claims that the fastest animal on Earth is a cow dropped from an airplane, which (he says) can go 120 miles per hour.  I started a calculation to check that.  But what model should I use for the force of air resistance here?  As long as the flow is laminar, Stokes Flow is appropriate, giving the force on an approximately spherical particle in a material with known density and viscosity.  So I assumed a spherical cow.  Really.

But the skill of making broad and reasonable assumptions must be taught to aspiring physicists.  The highest end of this teaching for me occurs with my research students.  They are presented with a difficult but penetrable research problem such as "magnet stack" -- develop a theory to predict the spacing between circular magnets as shown in the picture, and compare to experiment.  Ooh ooh ooh, the excited first-time researchers say.  We need to model the magnetic field due to cylindrical ferromagnets, and the force of each magnetic dipole on each of the others.  The middle magnet experiences at least four forces, some upward, some downward... what about the torque that causes the top magnet to twist?

STOP!  I say.  Don't get ahead of yourself -- build your understanding in small, straightforward steps.  Today I want you to start with just two magnets and a force probe -- measure the force on the top magnet as a function of its distance from the bottom magnet.  Measure the distance between them.  Take a magnet apart to see what the actual structure of the ferromagnetic stuff is.  Look up the theory for the force between two bar magnets.  Eventually we'll get to the complicated stuff, but for now, you need to assume a spherical cow.

In the first year course, it's just as important to start teaching appropriate simplification.  I see two major mistakes made by novices:

(1) Obsessing over irrelevant detail

A ball is dropped from the table.  How long does it take to hit the ground?  "But what about air resistance?" someone asks.  I show that a wadded-up paper and a 500 g mass hit the ground at the same time when dropped from the table.  "But there's still air resistance, your equations are bogus."  Yes, and what about the force of Jupiter?  It's there!  Oh, whoops, a bus in China just headed out of Beijing, changing the Earth's mass distribution and thus its gravitational field here.  Better include that, too... or, I can make the calculation using g = 10 m/s per second and get an answer that's going to match any measurement I can make to within 10% or so, which is quite useful.

(2) Focusing beyond the problem at hand

A cart on the track slows down while moving left: draw a free-body diagram.  "What force is acting left?"  Nothing.  Without a gravitational or electric field pulling left, and without a contact force pushing left, no forces act that way.  "Then how can the cart be moving that way?"  It just is.  "Baloney, I know things don't get moving by themselves, something had to apply a force to push the cart!"

It's obvious to me that any forces that might have accelerated the cart from rest happened before the action described by the problem, and so have nothing to do with the solution.  But that's a major obstacle to understanding for the novice.  Many physics teachers have a regular method to diffuse this sort of misconception.  I make a Hitchhiker's Guide reference by answering "how did the cart get moving?" with "The Almighty Bob came down from On High and spake, 'There Shalt Be A Cart Moving To The Left."  By the end of the year, that reference can be used to explain all sorts of things, like What caused the 300 N/C electric field?  and How did the electron get into the higher state to begin with?

In this week's Manhattan College summer institute, Paul threw out his own running gag -- "Don't mess with my story."  In his mind, each problem is telling a descriptive story, and the student who asks physically irrelevant questions beyond the boundaries of the story are like hecklers at a Shakespeare performance*.  Deal with the situation as presented here.  Don't read more into it than there is; don't add in effects that don't really affect the object in question.  If you're uncomfortable, think of the problem as a story, and suspend your disbelief... 

* "Hey!  Don't kill yourself, Romeo!  Really, she's alive... Gawd, I want a happy ending for once."