Setting up AP Physics 1 problems in lab: "Student on a Raft"

On the last day of my AP Summer Institutes I ask participants to spend time just playing in lab.  In particular, I ask everyone to set up something related to a published AP Physics 1 problem.  As a result of this activity - at and beyond my institute - you can see

* Which battery drains first? (Frank Prost, Tom Mellin) (2017)

* Energy vs. time for a cart on rough surface (Nadia Lara, Joey Konieczny) (2015)

* Bumpy Track (Zach Widbin) (2016)

* Waves on a vertical string (Walter Keeley) (2016)

A few weeks ago at TCU, Stephen McAliley wanted to set up the multiple choice problem about a student on a raft in a pool, from the official 2014 practice exam.  Summary: A student starts on the right end of a raft, and walks to the left end.  Which of several pictures correctly represents the location of the student and raft relative to the bottom of the pool?*

*I can't post the problem itself for lawyerly reasons.  But this is easily enough detail to understand the elegance of Stephen's experiment that you'll see below.

I think of this and similar problems as not about relative motion, but about center of mass behavior.  The center of mass obeys Newton's laws.  Since no net force acted on the student-raft system, its center of mass did not change speed from rest.  Then the answer to the original multiple choice question is obvious by inspection.  

This seems like an easy enough problem to set up experimentally - fetch me a raft, a student, a pool, and a video camera.  Not so fast, my friend.  The raft's mass needs to be significant compared to the student's.  And while we have a swimming pool on campus, it's not anywhere close to my classroom.  Peter Bohacek has set it up*: if you have a subscription to Pivot Videos, take a look at "Boy on a surfboard".  

*Of course he has.  My niche is setting up classic physics problems scaled to equipment and space in my high school laboratory.  Peter's superpower is setting up classic physics problems at any scale he wants, with whatever equipment he can get his hands on, with high quality video that includes measuring tools.  Imagine I were writing high quality short stories; then Peter is creating the billion-dollar film, complete with epic action sequences and a score by John Williams.

In the video below, you'll see Stephen's elegant in-class tabletop setup.  The "student" is represented by the PASCO constant speed bulldozer.  The "raft" is a bin, underneath which are two PASCO carts on a track.  Friction between the track and the "raft" is minimal; the weights on top of the bulldozer ensure that the bulldozer doesn't slip on the bin.  To get the student to walk across the raft, Stephen turns on the bulldozer.  Watch:

In the original problem, the raft and student were of equal mass, so that the center of mass was located halfway between the student and the raft's center.  In Stephen's classroom version, the bulldozer and the bin/carts are certainly not of equal mass; and I don't know where the center of mass of the bulldozer is.  

The question I'd ask using this video or live setup, then, is "where's the center of mass of the carts-bin-bulldozer system?"  

Preventing the slacker culture from taking hold in your class

Last fall I “shadowed” a senior through his class day. I wrote numerous pages about the experience for our school’s prefessional development app. (What really, Greg writing long-winded commentatry about teaching? Imagine that.)

Among other things, I reflected on how my school - like *every* school I’ve taught at or visited - has two distinct levels of student engagement. The difference between an honors class and a general class isn’t always just the rigor, or even the brainpower of the students; it’s also the intellectual engagement of students, their willingness to wrestle seriously with ideas to the best of their ability. 

A number of students over the years have hinted that the main reason they are happy taking solely honors classes is that they can avoid the less-serious students.  For example, one bright and engaged student was quite frustrated in our un-tracked 9th grade English and history, and not because his classmates were “dumb”, not at all.  He was frustrated because so many of them approached schoolwork as an exercise in minimization of effort, and thus poisoned all interactions among classmates.  I observed the same issue when I taught a required junior-senior physics class one year. And it happens on the athletic fields, too – every season we have teams or programs that are dumping grounds for those who not only don’t give a crap, but are actively perverse in their lack of crap-giving.  It is practically impossible for a serious student or athlete to have a positive experience once the slacker culture begins to prevail.

This is where toxic teachers complain regularly and publicly - in the faculty lounge, on twitter, in front of parents, even - about how kids these days don’t care, won’t listen, are bad down to their very soul. Well, that doesn’t help.  You talk about a teenager or group of teenagers behind their back, and they *will* find out - and then they will live down (or up!) to your prejudiced notion of them. It’s one thing to occasionally vent because you’re frustrated. It’s another entirely to make repeated sweeping generalizations or accusations about the quality of students’ personal character.

And yet... the slacker culture exists, and will persist if teachers don’t actively fight it. Yes, I know you don’t have the administrative support to dismiss every student who causes you a problem; I also know that even the best teachers with the best administrators usually don’t have all the support they’d like from above. But fight we must.

How have I fought the poisonous slacker students over the years? 

·        Attrition.  I make it more time consuming to disengage than to engage.  Once students give up the fight, once they see that *I’m* not giving up, once they see that neither their advisor nor their parents nor the academic dean is going to tell me to back off, they recalibrate their minimum effort.  Sometimes just enough, but they recalibrate.

·        Reputation.  Where students have taken my class by choice, they’ve generally known what to expect from me, and so they’ve pretty much cooperated from the get-go.  Once I successfully build a positive physics culture in one class, that culture became contagious over long time frames. Exceptions includes my first year at each school, and the year I returned to the upperclass AP section after a long absence. Those years were quite difficult and frustrating for me.

·         Avoidance.  I teach primarily 9th grade now, and 9th graders are poor rebels.  Honors students of any age, once I’ve establish my reputation, are usually pleased to focus and learn in a positive atmosphere.  Research students that I’ve hand picked are thrilled to work with me and my expertise – they very much appreciate my “trust but verify” approach.  

But the upperclass, required general physics class? Our department puts teachers where they can best succeed. The other physics teachers do better than I do with that class because they are more in tune with the non-serious student, and they all have better relationships with those folks, especially given their extracurricular work.  One teacher simply wasn’t particularly demanding of such students, and thus won cooperation with those few things he did demand. The other two have better instincts about how to be successfully demanding of typical general-level upperformers, just as I have better instincts in other situations. That’s more than okay, that’s awesome - different people with different talents make for a well-functioning department.

·         And finally, reasonable expectations. I'm careful never to assign work outside of class that could possibly be construed as busywork. I am respectful of students’ time - I don’t assign summer work, or work over breaks. I taper my class so that seniors have much less to do in the spring than in the fall. Students need to see that I’m never asking them to do something for the purpose of, in their perception, asserting my authority.
Does it all work? Never perfectly.  When a cadre of slackers persists, my job is to ignore them, to instead pay attention to the vast majority of students who appreciate my dedication and expertise.  Eventually, perhaps one of the slackers sees the light and joins the positive culture - in which case I welcome him, never ever shaming him with reminders of his previous intransigence.  Some never adapt; but they can’t spread their poison effectively, because their classmates don’t allow it to spread. Hopefully.  I have to fight this battle every year.  I have to have faith every August that the positive culture will prevail.  I’m usually rewarded.

Inserting equations into google docs - Equatio

Holy moly!  I have spent ridiculous amounts of time over the years trying to write professional-looking equations in my physics assignments.  Or often, I've spent enormous amounts of time simply scanning bad-looking handwritten equations.  Participants in my Purchase College AP Summer Institute last week showed me a wonderful computer and tablet app that seems to be a boon directly out of the star that I wished upon.

Take a look at Equatio.  It says it's free for teachers - I had to sign in with my google account, then it downloaded quickly and without trouble.  (My google account is through my school - no clue whether this will work with an unaffiliated personal account.)  

Then I went into google docs, where this toolbar sat at the bottom of the screen.  The toolbar gave me a couple of helpful hints, but was otherwise unobtrusive.  I tried typing the equation for the period of a pendulum.  "T =" was typeset in italics without fuss.  Then I wrote "2pi", at which point a menu came up asking if I wanted a capital or lowercase pi.  But I didn't even have to click!  The top choice was the more common lowercase pi, so I just hit enter to insert the  and move on.  

(Of course, I'm not using google docs right now - I'm in Blogger's "compose" window, where I don't have access to Equatio.  Nevertheless... I can copy and past the Equatio picture from docs into this window here.  As you can tell, the pi that I pasted is larger than I want.  But it's there!)

To get the square root symbol, I typed "root."  But I also typed "sqrt" to get the same thing!  And "sq" gives me a menu of options!  In other words, I don't have to remember arcane code, I don't have to click slowly through an enormous tableau of options... I just have to hint at the symbol I want, and lo, the symbol shows up.  Wow.

Typesetting the fraction was automatic - I typed "L/g" and I got a vertically set fraction with a horizontal fraction bar, all centered under the square root symbol.  Here's the final result:

I suppose I could nitpick and complain that the L is too high, too close to the top of the square root symbol.  So what.  I inserted this equation in barely more time than it takes to type a standard English word.  And the copy-paste function worked into MS Word, into this post, wherever.

I've been told (though I haven't yet tried) that on a tablet it can do handwriting recognition - that is, write the equation above, and the typeset version will magically appear.  

Your tests, at least, should look professional.  I don't mind sending out an in-class or homework assignment with handwritten items, with fifth generation bad xeroxing, with unaligned graphics that I literally copied and pasted to a page by hand.  I won't do that for a test, though.  A professional looking test is taken more seriously by your students.  So I've gone to great lengths to get professional looking equations.  Equatio has shortened those lengths.  Yay.