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.

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."

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 2.1 N, within the 0.2 to 0.3 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.

Where do I get AP Physics 1 multiple choice test questions? The Big Amazing Resource. Update January 2019.

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.

Update January 2019: Okay, there's plenty of authentic AP Physics 1 and 2 questions available via your course audit - the College Board has released 40 of the 50 multiple choice from the international version of these exams each year since 2015.

But starting in 2019-20, audited AP teachers will have free access to a comprehensive online question bank that will include both released and unreleased items.  And more.  Stay tuned.  Still use the Big Amazing Resource, but it will be unnecessary shortly.

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.