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30 April 2018

The Jacobs Physics Podcast: AP Physics 1 2017 problem 3.

I recorded a 30 minute episode in which I discuss - with digressions, of course - the third problem on the 2017 AP Physics 1 exam.

You can see the problem via this link to the official College Board website.

Then, click here to listen to the podcast!

I'd love to hear your feedback; in particular, I'd love for you to tell me what you'd like me to discuss on a weekly podcast if I continue it.  You can find my email through the Woodberry Forest School website.


23 April 2018

Do I need to know about pressure/displacement nodes in AP Physics 1?

I was asked about standing waves in pipes on the AP Physics 1 exam.  Specifically, is it important for students to understand the difference between a variation in air pressure, and a variation in the amplitude of particle displacement?

On one hand, it is certainly important to understand nodes and antinodes in closed and open pipes.  When the boundary conditions are the same (closed at both ends, open at both ends) the fundamental frequency is v/2L and all multiples of the fundamental frequency can be played; when the boundary conditions are different (open at one end and closed at the other), the fundamental frequency is v/4L with only odd multiples available.  

Then, we have to understand the WHY behind these facts.  Students must be able to draw pictures of standing waves, must be able to identify the wavelength as it relates to a picture of standing waves and as it relates to a pipe length, understand why the speed of waves is constant, how the wave speed relates to the speed of particles in the material, how the particles actually move in a transverse wave and how that relates to the pictures and to the wave's amplitude.  (Whew.)

But, when drawing standing waves, are we drawing a representation of the air pressure or the particle displacement?  And, does it matter?

Any time you're wondering about what will be tested on an AP exam, be as a biblical fundamentalist: ignore peoples' pronouncements and go straight to the source text.

I've just been through four released AP Physics 1 exams.  Not a single question addressed the difference between air pressure and particle displacement.  Now, that doesn't mean a question next year or the year after couldn't do so, because the AP Physics 1 exam is only a few years old.  

Nevertheless, I'm taking a Bayesian approach.  The difference between particle displacement- and air pressure- representation is extraordinarily abstract, and difficult to understand for a student who hasn't studied fluids, anyway.  The mathematics and representations of standing waves work fine even if students don't know what exactly they're representing.  Therefore, I don't address this issue of pressure vs. particle displacement.  

If that means my students have to guess on one multiple choice question every half-decade, that's a price I'm definitely willing to pay for simplifying their understanding of standing waves in a pipe.

22 April 2018

Why is the net force on a car greater than on the driver?

A reader of my 5 Steps to a 5: AP Physics 1 book sends some kind words about the book, and then asks:

Number 2 in the Forces and Newton's Laws review chapter is about the net force on a driver vs. a drag racer.  To calculate the net force on the drag racer you omit the mass of the driver.  I was wondering about the logistics of that.  How can you only use the mass of the car and not include the driver?  I do understand why the force on the driver only includes the mass of the driver.  The seat exerts the force on the driver's mass.  But that seat force would also be backward on the car, and so to accelerate the car at the acceleration determined would require the additional force on the driver, correct?

The net force on the car is its mass times its acceleration. Sure, the driver may be pushing backward on the car; the road is also pushing forward on the car.  That's all true, but all the question asks for is the net force on the car, which does mean the force of the road minus the force of the driver.  I don't know the value of either of those forces.  I just know about the car's mass and its acceleration.

Similarly, you're right that the only horizontal force on the driver is the force of the car.  That's the net force on the driver.  Yet, that net force is still equal to the driver's mass times her acceleration.

Since the car and driver move together - when one speeds up, the other does too, by the same amount - they have the same acceleration.  Thus ma must be bigger for the more massive car.

16 April 2018

Students: you don't need more AP practice problems.

This is the time of year when physics teachers tend to be approached by hyperconcerned AP students worried about the upcoming exam.  "Can you find me more practice problems?  I want to do as many as possible so I'm prepared." 

The teacher's answer should almost always be "no." 

Huh?  Um, Greg, why not provide more practice problems?  Why shouldn't students be encouraged to study more, especially when it's they who are taking the initiative? 

I'll give you two reasons.

For one: It's the quality of preparation that is useful, not the quantity.  I've assigned an enormous number of AP practice problems as homework, tests, quizzes, and in-class exercises.  For each of these, I've helped students understand what they've done right and wrong, and how to do better on the next exercise.  We don't just do a problem and forget about it. I check homework and make students redo problems that they substantially didn't understand.  We grade each others' quizzes in class.  We do test corrections.  In-class exercises lead to discussion, or sometimes experimental verification.  

In contrast, handing students a thick pack of review problems encourages the mindset of just getting the answer right, without the deep engagement required when working in conjunction with a formal class.

And a thick pack of review problems can't possibly be useful unless the problems are themselves high quality.  I just got an email from a prominent supplier of inferior physics lab equipment saying something like "With the AP exam approaching, try these practice questions for $99!"  Stupid, stupid, stupid.

Authentic old AP free response questions with authentic rubrics are available to students through the College Board's official site.  The five steps book has an enormous number of questions, each with a thorough solution, not just an answer.  These are publicly available to students - and the 5 Steps book costs a fraction of $99.

I've seen some of the material that's peddled by others as AP exam preparation.  It's uniformly terrible.  Pick up a random other prep book and look at the content and style of questions.  The GOOD ones are repackaged AP Physics B material, heavy on the calculation, nowhere near the style and depth of the true AP Physics 1 exam.  Folks, there aren't that many people in the country qualified to write AP Physics 1 questions.  The vast majority of those are already in the employ of ETS and the College Board.

For two: I refuse to feed the test anxiety beast.

At this point in the school year, with three weeks to go before the AP exam, I'm tapering my AP class.  We are winding down, not up, in our preparation.  I have a lot of reasons for relaxing my demands in April, but a primary one is to emphasize with my actions that "test anxiety" can be limited by building a positive culture.

We've done the necessary deep practice all throughout the year.  I've ensured every day that students have not just done the homework, but they've paid careful attention to it; if they don't, they come in for consultation.  For each incorrect answer on a test, my students write a clear correction.  We've built the habit that practice doesn't make perfect; perfect practice makes perfect.  

By year's end, all of my students know what they can and can't do.  They understand their strengths and weaknesses, and how to play to those strengths on the AP exam (because they've done so on eight AP-style practice tests already).  They know how to handle the adversity that is sure to come on an exam on which 70% is a top score.  They've already done their practice problems on tests and quizzes and homework - that's how they know all of the above.

What message would I be sending, then, if I kept handing ever-larger sets of practice questions in the lead-up to the exam?  I'd be destroying the confidence I've struggled so hard to build.  There's no need to scare students into studying more.

Top students tend to work themselves into a state right before an exam.  Or, they do more and more practice problems as a way to show off to their peers... it's the secular equivalent of the holier-than-thou churchgoer.  But we're talking about top students!  They don't need to study more.  What are they going to do, turn their 5 into a 6?  Make them relax, both for their own mental well-being and for the sake of their classmates.

But what about students who will struggle to get a 3?  They will do better with a low-key approach, too.  Rather than shame them for not knowing everything - which is what we do, like it or not, when we shove a stack of practice problems at them - focus these folks on just a few topics that they can improve upon.  They're not going to get a 5 because they studied for days.  But, a few judicious hours here and there might well secure that 3.  

So, don't encourage more practice.  Encourage good, targeted practice in the weeks before the exam.  Encourage a relaxed, confident attitude in the days before the exam.  When students recognize intellectually and emotionally that AP exam day is just another day at the office, then your class is ready to rock.  No extra practice questions required.

02 April 2018

Targeted quiz to check for homework understanding

In the previous post, I discussed an AP Physics 1-style problem about Coulomb's law. That was my students' homework assignment due Monday.

On homework, students are allowed and encouraged to collaborate while obeying the five-foot rule. This means they may talk to one another, even look at each others' work, as long as they separate themselves whenever they're writing something to be turned in.

Yes, I do suggest you ask for obedience to the five-foot rule, even if you're at a school where copying answers is an unfortunate part of the culture.  It's difficult politically to enforce a "no copying" rule, partly because of the feigned innocence and ruthless mother-bear-defending-her-cub response you'll get by even suggesting that students might have engaged in cheating.  It's not difficult at all, though, to show that the five-foot rule has been violated, and to demand adherence: since you're not framing any requirements in terms of integrity or honesty, you tend to get compliance from students and support from parents and administrators.

Nevertheless.  I hear from teachers all the time that their students simply copy the best student's answer on homework problems, rendering meaningless the whole activity of doing homework.  Even at my current school where the students are impeccably honest and careful about the five-foot rule, I still have a minority of the class who write down a solution without thoroughly understanding it.  That's not useful to anyone. How is it possible to make students engage with the assignments?

One approach that's been successful for me is the targeted quiz.  I collect the homework... then I assign a five minute quiz asking questions similar to what was on the homework.  The idea is, students who understood the problem solving process on the homework will do well on the quiz; those who merely mimicked a friend will not do well, and thus the quiz will provide the context they need to figure out what they didn't get.

Below are the questions I asked based on Monday's Coulomb's law problem.  Take a look... see how a student who understood the homework, even with assistance from a friend, will answer quickly and confidently.  See how a student who copied a friend's answers will be clueless, especially on 1 and 3a.

That's what makes a good targeted quiz - it sends the message that answers don't matter, comprehension of solution methods does matter.  And I don't have to lecture or nag at all.  I just go over the quiz.

1. Show how to find the distance between charge 1 and charge 2 in terms of X and θ.

2. Draw and label vectors to represent the forces on object 1.

In part (c), you were asked: Using the conditions of equilibrium, write—but do not solve—two equations that could, together, be solved for θ.

3a. Explain in one sentence how we are going to get the two equations.  

3b. If we are writing two equations, how many unknowns may there be in the equations?

3c. What is incomplete about these two equations as the solution:  

Tcosθ  = mg
Tsinθ  = Fe