Coulomb's Law problem for AP Physics 1

When you're looking for AP Physics 1 problem ideas, start with old AP Physics B exams, especially the B exams between 1996 and 2014.  These are a treasure of interesting situations, many of which can provoke more AP Physics 1 style questions than you can possibly ask in one school year.

In AP Physics 1, Coulomb's Law problems are restricted to the force exerted between two isolated charges.  Usually Coulomb's Law questions will appear on the multiple choice.  You'll see semi-quantitative questions, like "double the mass and halve the charge of one object, what happens to the electrical force?"  You'll also see questions about the "relationship" between Coulomb's law and Newton's Law of Gravitation.  

What about the free response? Interesting problems like 2010 AP B #3 are only appropriate for AP Physics 2 - that problem includes three charges, and asks about the vector sum of several forces.

Take a look, though, at 2009 AP B #2.  There, two equal-length strings support objects of known mass and charge.  The strings each hang an a known angle from the vertical.  Ooh... just two charges, but the situation is ripe for questions that go beyond straight-up plugging into Coulomb's Law.

This problem isn't suited as-is for Physics 1, of course.  It asks about electric field lines, which are not part of P1 (and are deprecated in P2 in favor of vector field notation).  It asks about electric potential produced by several point charges.  Skip those parts.

To rewrite for Physics 1, start with parts (c) and (d) of the original.  Part (c) asked for a free body diagram of one of the two hanging objects.  Part (d) brilliantly asked students to write two equations that could be solved simultaneously for the tension in and angle of the string.  Explicitly, students were instructed NOT to solve the equations!  Since AP Physics is not a math class, we don't care whether students can carry through the algorithmic solution to such a problem.*  We do in fact care whether students can set up a system of equations, and then recognize whether the system is solvable.

* More precisely, we already know that our class of 20 students can create 20 different solutions.

So I assigned parts (c) and (d) only, and added a third part: 

While the charge on object 1 remains positive Q, the amount of positive charge on object 2 is increased to 2Q.  Describe any changes in the arrangement, and explain the physical reason for those changes. 

I don't need the precise location of the new equilibrium position - that's way, way beyond the scope of AP Physics 1.  All I'm looking to see here is indication that the separation between charges will increase, because the force of object 2 on object 1 (and vice-versa) is now larger.  At the original locations, the horizontal component of the string's tension would no longer balance the electric force, and so there'd be an acceleration outward.

Another possible question based on this situation might be to ask whether, with charges Q and 2Q, the angles of the two strings would be the same as each other, or different from each other.  

You got another question based on this situation?  Add it in the comments!

Thoughts about mentoring new teachers

I was asked, "what does your department do to mentor new teachers?"

We haven't done anything formal, nor do we really want to.  The veterans have generally taken it on themselves to keep in touch with the new people, answering questions and being available as we can.  My philosophy is, there's no point in talking at new teachers before school starts more than we already do (and we already talk at them way too much).  Teaching – for the first time, or at a new school – must be experienced.  "Mentoring" consists of showing through our actions the type of teacher we hope that the new folks will become.  The best way for new young teachers to learn is to watch the pros, and then to talk shop.  

I think veteran teachers underestimate the fear of failure and the desperate, beaten-down mindset of the new teacher.  (Possibly because we have consigned those dark years to the deepest inaccessible recesses of our brains.)  I remember being so, so worried about doing things wrong, knowing that I was not as comfortable and in charge as my colleagues, knowing that there were complaints everywhere from students testing my resolve, feeling the disapproval of my colleagues.  I beat myself up so much -- and colleagues and bosses beat me up so much -- that I never really realized what a damned good job I did in my first couple of years.  I felt like I was expected to be perfect, and then to get better; I felt like, even though I recognized and tried to learn from my mistakes, that nevertheless I was always in danger of being sacked for my lack of perfection.  (And in fact my contract was not renewed.  At two separate schools.*)  It wasn't until I had been teaching for nearly a decade that I stopped feeling like I had to prove myself every day.

* How’d you like your physics programs now, schools that booted me out the door?  

My wife taught English as a 22 year old who was the youngest person on faculty, and one of only four women.  She similarly felt the constant disapproval from colleagues, the *perceived* disapproval from the older men in her department even when it wasn't there, and the disapproval from herself for not being practically perfect in every way.  She never noticed just how badly she was being treated by the school; she just assumed anything that wasn't perfect was all her fault.  Her colleagues, her students, and the administration drove her out of teaching.  And that is too bad, because she was really, really friggin' good for a new teacher.  She would be bloody amazing now had she stuck with it.  

Those same effects were *this* close to driving me out of teaching, but for one kind offhand comment from a veteran.  I'm glad I stayed, but I still sometimes wonder why I did.   

I suppose I think of mentoring new teachers much like sabermetrics thinks of evaluating baseball managers -- it's not possible for a manager to significantly improve his team's chances of winning by making "good" strategic choices.  The best managers statistically are the ones who back off and don't make actively stupid strategic decisions.  In that vein, formal observations and formal, scheduled discussions are often more intimidating / loaded with perceived disapproval than effective.  But those veterans who take care to develop personal and professional relationships with new teachers will place themselves in a position to serve as a sounding board, and then to gently offer advice where asked.

I can tell you what sort of "mentoring" did NOT work well.  It was NOT effective when I was told to use the calculus teacher down the hall as a resource -- he was actively unfriendly, unhelpful in a practical sense, and unenthusiastic about helping; he threw in some piss poor advice to boot.  I needed someone to tell me when I did things well, to talk through my ideas without dismissing them immediately out of hand, to allow me to try new things without prejudging the results.  I needed someone to vigorously shut down ridiculous complaints, to smite loser arseholes (like those who were caught but not held accountable for hollering "BITCH!" outside my wife's classroom her first year), to quelch the malicious gossip from students and less-than-friendly colleagues before it could snowball.  Then, only then, did I need someone to give me advice.  What I actually got was a bunch of old folks who freely dispensed advice, but who also sent messages in body language that I wasn't part of their club, and that it was largely my fault that the students whined about me -- blame the victim.  Know that this isn't just a me and my first school issue -- my wife had the EXACT SAME experience.  And I'll bet you know of someone else with this experience, too.

Just telling a new teacher to work with veterans who aren't invested in mentoring does not work.  One cannot be mentored when every event, every question is loaded with judgmental baggage.  It takes a special, special veteran teacher to build enough trust with a new young teacher such that the new teacher is willing to open up, to ask tough questions, to ask for advice, and to take advice without feeling sandbagged.  The number of veteran teachers capable of building that trust is, sadly, negligible. 

We should, wherever possible, put new faculty in close physical proximity with veterans who are easy to talk to.  A while back we got three physics teachers new to my school, two of whom were new to teaching as well.  Having the three of them share an office was priceless.  I was just down the hall, and was always in the coffee room.  Just that proximity let us develop a camaraderie.  We want new folks nearby to those who will be both helpful and nonjudgmental; folks who will not butt in unless asked (or unless it's blindingly obvious that butting needs to be done).  Even if no actual advice is dispensed, just watching the professionalism of our veterans builds a positive corporate culture in which we have to convince faculty to STOP working rather than to start.

Point is, there can be no formula for mentoring new or young teachers.  So much is driven by personalities and relationships.   I'd say that former football coach Clint Alexander has been a better academic mentor to me, and to a large number of our faculty, than pretty much anyone else I've met professionally - when I had trouble with a student or a colleague, I asked Clint for advice, even though he wasn't a fellow teacher in my department.  Our head track coach has mentored his assistants in a way that goes well beyond track.   We can't know ahead of time whose spouses or families will get along with those of a new teacher.  We can't predict who will get along well within a department, or who will become more friendly with teachers on a coaching staff.  

All we can do is continue to hire and develop veteran teachers who remember what it was like to be new, and who consider it their job to support new folk in an atmosphere of authentic, non-judgmental caring.  Keep the control freaks, those who judge, those who give too much credence to silly kid complaints, far away from the newbies.  Keep those who work hard and professionally visible and prominent; make it clear to the new teachers through our actions what phenotypes of teachers are valued by the school.  That's all we can do.  After that, teachers will have to sink or swim on their own abilities.

Handing back work

It seems like such a small thing... but the manner in which you hand back routine student work makes a difference, especially in the tone of the class.

Firstly, let me kindly point out the underlying principle that, speaking in generalities, students don't care about a routine assignment once they've handed it in. 

Don't believe me?  Try an experiment.  Don't place students' work directly on their desks.  Rather, place the work easily accessible in the back of the room, or on top of a table down the hall, somewhere that requires a student to exert extra but minimal effort to get the assignment.  Do this for at least three routine assignments. By the third, I'll bet that only a couple of students bother to go get their papers, even if "going" to get the papers requires merely a walk to the back of the classroom while people are filing into the room.

For years now I've handed back student work in a slotted cabinet in the back of the room.  Each student has a numbered slot into which his papers are placed.  Only one or two students go back there on any given day, unless I make them. 

It's important that students know you're somehow looking at and evaluating their work; otherwise they won't take it seriously.  In the long term, your students really do appreciate your care in crafting, reading, and handing back routine assignments, because they will eventually recognize that your care for their assignments is an expression of your care for them personally.  Right now, though, yesterday's problem set might as well be as ancient and relevant as the OJ Simpson trial.

So why don't I force students to look at their previous work by placing it on their desks?  

In that case, I'm practically begging students to argue about points, to wonder why they only got two out of three when their friend got three out of three "and he said the same thing!"  I'm encouraging questions on the order of "well, if you really think about it, this answer could be right, can I have some points back?"  Faced with a graded paper, my students look straight at the final score, then at their classmates' final scores; then they start rationalizations that go so far beyond sour grapes as to become aged wine.

By returning papers in the back of the room, you have a grace period to tell the class briefly "hey, on last night's problem, you can't set the tension in the rope equal to mg, because the object is speeding up.  You have to write Newton's second law for both objects and combine the equations."  Everyone paid attention to that 20 second statement; everyone is now constructively considering whether they made that error or not.  Had their papers been in front of them, 3/4 of the class would have been leafing through the pages trying to mine for points, and won't have heard your statement anyway; half of the rest are considering whether the number of points they lost for that error was commensurate with their sense of justice, or whether they should summon Batman to fight for their points back.

Usually, a student who makes a couple of errors on a problem set doesn't need to have those rubbed in his face; it's far better just to mention common errors in general, but then move along.  They've been brought up in a system where 93% is an A, where anything less is on par morally with trigamy.  They get way too upset about their lack of perfection.  If they don't see their paper, even if they're purposely ignoring their paper in order to avoid confronting their imperfection, then that's a positive result.

Of course, there are times when you need a student to take a look at a routine assignment, particularly when that student's responses were nowhere close to on target.  In that case, require an extra help session of that student, and make him go get his work to show you.  This is the time to make the student redo the problem the right way... when there's no social value to the performance art inherent in "but teacher, can't I have pity points for writing F=ma?"  Redoing the problems from scratch can build confidence and bust misconceptions.

And, handing back the rare major test can be done without recourse to the back-of-the-room method.  I suggest either handing back a blank test with an indication of which problems require correction; or, discussing common issues briefly while holding on to the tests in the front of the class.

For regular assignments, though, you avoid a lot of headaches by making students take a bit of an extra effort to fetch their work.  You can focus on physics, rather than lawyerly discussions about grading.