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13 June 2016

Write two equations, but DON'T SOLVE

Our students come into physics expecting a frustrating math course.  Then many get even more frustrated -- not only do they have to solve math problems, but they have to create their own problems to solve, to boot!  Guh.

In an honors or AP level course, it's important early in the year to make a big show of separating the physics from the math in problem solving.  Firstly, here are some facts, concepts, and a routine that will set you on the path to a solution; then, here's how you know that the problem is set up appropriately, that doing ninth-grade algebra will in fact lead to a solution.  I go so far as to write, in big capital letters, PHYSICS IS DONE.  Students do the same, initially to poke some fun at me, but then as a way of communicating their problem solving.

The canonical technique for recognizing mathematical solvability is to write a relevant equation, then to identify known and unknown variables.  Once we have a single equation with a single unknown, the problem is solvable; similarly, two equations and two unknowns is solvable.  But don't underestimate how intimidating the actual mathematical solution process to a two-equation system is to a high school student.  They may have passed algebra 1, but I trust my students to get accurate solutions even less than I trust the evil bastards of the TSA to get me to my gate in a timely, convenient, and comfortable manner.

Very early in the school year, I assign the hanging stoplight problem.  You know, an object is suspended by two strings, each at a different angle; determine the tension in each rope.  The solution requires algebraic manipulation of a full-scale two-variable-two-equation-system.  Those of you who have assigned this problem and observed your students can probably verify my report that many of those students spend 30-60 minutes doing math, often getting lost along the way.  A significant fraction get so frustrated that they simply give up, or follow a friend's solution blindly.*

* I know this because quite often that friend's solution is itself incorrect.  

Here's a great chance to make my point about the separation of physics and math.  By this point, in class we've emphasized over and over and over the three-step approach to equilibrium problems:

1. Draw a free body diagram
2. Break angled forces into components, if necessary
3. Write (up forces = down forces) and (left forces = right forces)

The majority of the students who spent the better part of an hour on this problem didn't follow these three physics steps carefully; they got too worried about the forthcoming mathematics.  

So, why not give a quiz in which students are given explicit instructions not to solve the two-variable system?

See the quiz below.  I find that it relieves much anxiety from those who got lost in the mathematics.  It sends an important message to those who didn't follow the process, because they see just how quickly they could have gotten to the answer by, well, listening to the teacher and following his advice.

Finally, note that the AP Physics 1 exam will not ask students to solve a true two-variable system of equations, ever; but "write two equations which could, together, be used to solve" is a legitimate form of AP question.  


Two ropes support a 33 kg stoplight, as shown above.  The goal of this problem is to find the tension in each rope, as on last night's homework problem.

I am NOT asking you to solve the problem completely in this quiz; rather, I want to see that you can quickly and accurately follow our four step procedure for solving equilibrium problems.

  1. Draw a complete free body diagram of the traffic light, including descriptions of each force. 
  1. Redraw the diagram, breaking force vectors into components where necessary.  Express components in terms of the given angles; i.e. do not simply write “Tx”, include the angle in your expression.
  1. Write two equations.  Circle the unknowns.  DON’T SOLVE.

07 June 2016

Report from the AP reading: Teach your class to write concise laboratory procedures. Please.

Howdy!  I've spent the last week grading, and training people to grade, the lab problem on the 2016 AP Physics 1 exam.  I'm a bit punchy, as you may expect.  Nevertheless, I encourage you to apply to be a reader -- I really, really love the people I meet here, even if I'm not always entirely enamored of grading papers for eight hours a day.

Part (a) of our question asks for a description of a laboratory procedure.  It could be answered in 20 words: "Use a meterstick to measure the height of a dropped ball before and after it bounces.  Repeat for multiple heights."

But oh, no... when America's physics students are asked to describe a procedure, they go all Better Homes and Gardens Cookery Manual on us.  Folks, it's not necessary to tell me to gather the materials, nor to remind me to first obtain a ball and a wall to throw it against.  Nor do you have to tell me that I'm going to record all data in a lab notebook, nor that I'm going to do anything carefully or exactly.  Just get to the point -- what should I measure, and how should I measure it.

Please don't underestimate the emotional impact on the exam reader of being confronted with a wall of text.  We have to grade over a hundred thousand exams.  When we turn the page and see dense writing through which we have to wade to find the important bits that earn points, we figuratively -- sometimes literally, especially near 5:00 PM -- hit ourselves in the forehead.  Now, we're professionals, and I know that we all take pride in grading each exam appropriately to the rubric.  Nevertheless, don't you think it's worth making things easy for us, when we be nearing brain fatigue?  Just as good businesspeople make it easy for customers to give them money, a good physics student makes it easy for the grader to award points.
Don't think I'm making fun of or whining about students here.  Writing a wall of text where a couple of sentences would suffice is a learned behaviour.   The students taking the AP exam are merely writing the same kinds of procedures that they've been writing in their own physics classes.  It is thus our collective responsibility as physics teachers to teach conciseness.  

"Okay, Greg, how do we do that?"  I hear you asking.  I have a two step plan.

(1) Give the students a word or sentence limit, and hold them to it.  For virtually any AP Physics 1 procedure, three sentences will do.  When your students list a twelvefold process, award no credit, and don't give in to the subsequent whining.

(2) Don't ever award credit for baloney.  When students have one nugget of valid description buried in a mountainside's worth of muck, just stop reading and award no credit.  The burden of proof is on the students to convince you they understand the methods they describe.  It's tempting to yield to after-the-fact whining and lawyering: "Well, if you really think about it, the meterstick could measure force if..." No and no.  

Fight the clarity and conciseness battles in October; then in May when your students take the AP exam, communicating experimental methods will be (a) easy and (b) quick.  

26 May 2016

Super-elastic popper toy for 2016 AP Physics 1 problem 2

Popper toy, obtained by my student Mark Wu
at the NASA store at the Smithsonian
Next week, I will be grading another experimental problem on the AP Physics exam.  Since 1996, at least one question on each AP exam has been posed in a laboratory setting, asking students to design and/or analyze an experiment.  This will be, I think, the twelfth experimental question I've graded over the years.

The 2016 AP Physics 1 exam problem 2 asks students to design an experiment to investigate whether a toy bounces perfectly elastically, at least for low impact speeds.  Then, the problem says, the experiment seems to violate a basic physics principle.  What the heck happened?  

The obvious explanation is that the toy stored some sort of energy internally, through a mechanism such as a wound rubber band or a rotating flywheel.  Then that internal energy was converted into mechanical energy in the collision.  But how could that happen in practice?

By an utter coincidence, when I was walking through our freshman dorm on duty Sunday night I discovered one of my AP students playing with the toy pictured above.  I've seen these popper toys before, but not like this one.  It has a small handle, sort of like the grip of a dreidel, that is accessible once the toy is turned inside out.  

Turning the toy inside out stores elastic energy.  Using the handle to give the toy spin as it falls stabilizes the orientation of the toy, so that when it hits the ground, the restoration of the toy to its original shape converts elastic to mechanical energy.  The toy bounces 2-3 times higher than its release height.  

My student found his toy in the NASA store at the Smithsonian Institute in Washington, DC -- that's probably why there's a picture of the space shuttle on it.  I found the identical toy on "", via a google search for "popper toy".  The intent of this site is for you to order hundreds of these toys with a customized logo for the purposes of distribution at a sales conference or a marketing event.  However, the site offers to sell you a couple of samples for $5 each.  I ordered the maximum of 3 for my class.  

So yet again, an AP question can be set up in the laboratory.  I'll give this problem on some test or quiz next year; immediately thereafter, I'll hand out the toys and ask the students to do the experiment they designed.

18 May 2016

Eight different approaches to laboratory work

In preparation for my AP Summer Institutes for 2016, I've redesigned how I present experimental work.

When I began teaching AP Physics B, I did lecture and problem solving four days a week, with lab work on the fifth day.  I integrated more and more experimental work into my daily classes, especially as I amassed equipment for each topic area.

Nowadays, experimental work is part of virtually every class all year.  My minimum goal is to get student hands on equipment three of five days each week; my students will tell you that the reality is more like four or five out of five.

Okay, many of you share this lofty goal.  But how to accomplish it?  Upperclassmen don't like routine; they will not be comfortable doing the same styles of activities every day all year, even if the topics change.

So, for Summer Institute and for reference purposes, I've categorized eight styles of lab work that I've been using for my classes.  All are applicable to teaching physics at any level, but are optimized for AP Physics 1 students.

The styles are listed roughly in the order I introduce them to my classes.  Remember, at the beginning of the year, students certainly aren't ready to do AP Physics 1 test problems in the lab with little guidance!  We can talk 'til we're blue about "open inquiry" and ideals of "student-centered learning", but it is incumbent upon us to teach fundamental skills before opening up the lab for the students to play.  That doesn't mean we TALK at students about lab skills; that means that each style of experiment builds skills in context that are taken for granted at the next style.

Read on... at my AP Summer Institutes (I'm doing four in 2016, listed in the sidebar -- please sign up!) I'll be doing experiments in each of these styles with all the participants.  And please bring your own ideas to share with us.

1. The Quantitative Demonstration

Instead of showing how to solve textbook problems in the abstract, try setting up the actual physical situation presented in the problem – do the problem, treat the answer as a prediction, and then verify the prediction experimentally.  Take a look at this post about my first day of AP Physics, or just search "quantitative demonstration" on this blog for more ideas.  

2. The whole class as a lab group for live data collection

For example… to get data for voltage vs. current to show the ohm’s law relationship:

·             *  I put a blank set of axes on the screen; I give everyone a hard copy of blank axes.
·             * I bring the class to the front of the room to see the setup – they see the voltmeter, ammeter, and how I vary the voltage by turning the dial on the power supply.
·             *  We discuss how to scale the axes such that the data will fill the page.
·             * Each student in turn is called to the front of the room to adjust the voltage, and to read and record current and voltage data.
·             * Before going back to his seat, the student writes his data in a chart on the board; and he graphs his data point on the screen.
·             * Meanwhile, each student is responsible for making his own personal graph.
·             * I move quickly – the next student is ready to go while the first student is still writing and graphing his data.
·             *  As the experiment goes on, students begin to suggest how to fill in such that the entire parameter space is explored.
·             * When we have plenty of data (usually meaning everyone in the class has had a turn), everyone draws a best-fit and calculates the slope.

·              * We estimate an average resistance with uncertainty from the class’s slopes – this always matches the resistance of the resistor nicely.

This is an excellent technique early in the year, when you’re introducing and modeling lab skills; whenever you need quick data – this takes maybe 1/4 of the time it would take for the students to do it independently;  and anytime you have only one set of equipment.

Here is a description of how I use this same technique on the first day of my conceptual physics class.

3. Quick data collection to verify prediction of a qualitative trend, or to determine the trend

Students must be able to describe the shape of a graph given the relevant equation; and students must be able to suggest the form of an equation given a graph of experimental data.

By scaling the axes ahead of time for the students (and being sure that the scale represents an appropriate range of values), you can save time in lab; more importantly, you focus the students on just this particular skill of translating equations to graphs and vice-versa.

4. Create a linear graph, use the slope to determine a physical quantity

I believe in putting data directly on a graph; I believe in hand graphing; I believe in taking slopes by hand.

If your students graph asthey go they understand intuitively what it means to “explore a parameter space.”  (And it’s easier to convince them to take more data if they haven’t put their stuff away and expected to be all finished.)

Your students are not skilled at graphing by hand; yet they are likely to have to graph data as part of an AP question.  You can teach them how to use excel to make a graph at year’s end.  And they’ll actually understand what excel is doing if they’ve been graphing by hand all year.

Similarly with taking slopes.  Make them write out (y2y1) / (x2x1).  Make them circle the points on the best-fit line (not data points) used to calculate slope.  Make them write the units of the slope.

Then make the students explain how to determine the physical meaning of a slope using equations, not just guessing based on the units of the vertical and horizontal axes.

5. Linearize a graph, use slope to determine a physical quantity

The AP physics exams expect students to be fluent in linearizing graphs.  See the 2009 Physics B problem 1 for the canonical example of an experiment requiring graph linearization.

This is one of the first linearization lab exercises I do.  We hold a cart on an inclined track with a string attached to a spring scale, varying the angle of the track.  Initially, we graph tension vs. angle – this graph is curved.  By writing out the relevant equation T = mgsinq, we recognize that a graph of tension vs. sin q will be linear with slope mg.

6. Open-ended determinations – are you hired?

Students aren’t usually aware of the intended audience for lab write-ups.  “Mr. Jacobs has done this experiment a million times, he knows how it works, and he saw us do it.  So answering these questions is just a formality.  He knows what I know and what I mean.”

So I make the audience someone OTHER than me, and put the writeup in a context they understand:

Imagine that you and your partner have been asked to make this determination for a Fortune 500 company as part of the competitive bidding process for an engineering contract. 

You will submit your marked pipes and an explanation of your methodology to the company.  From that writeup alone, they will decide which partnership to hire.

Therefore, I will have someone – not me – rank the submissions from strongest to weakest.  They’ll be placed in piles:

·        Hired (1 submission)
·        Not hired, but recommended to other companies
·        No action
·        Blacklist

7. Independent prediction exercises 

These are like quantitative demonstrations, but with the students doing all the work.  Other teachers do similar activities, calling them "stations".

I have students work independently, at their own pace.  They are welcome to collaborate; since everyone has something slightly different on their sheet, their collaboration is authentic.

I've posted about two of these:  One with energy, and one with the direction of force and motion.

8. Experiments taken (nearly) straight from the AP Physics exam

Virtually every AP Physics 1 problem can be set up in the laboratory.  I modify the problem so that it scales to the equipment in my lab; for example, using 500 g carts rather than 500 kg cars.  I often try to set up the experiments such that we can produce a graph, perhaps even a linear graph with a meaningful slope, even if that graph wasn’t part of the original AP problem.  I can't post these online, because they are based on College Board questions.  However, come to my AP Summer Institutes, and these exercises will be on the CD that you get.

13 May 2016

Mail Time: Why is there not a lot of rotation on AP Physics 1? (Or, is the seeming dearth of rotational questions a valid perception?)

Reader Sara Rutledge asked this question in the comment section of the post in which I linked to the solutions to the 2016 exam.  I think it deserves its own post, so as not to be lost in the depths down the page...
My students commented that the exam had very little rotational motion beyond the FRQ with rotational kinetic energy. Is there an effort by test writers to match up the percentage of objectives on a topic with the percentage of questions on the exam? We had spent a lot of our review time on torque and conservation of angular momentum, so students were surprised that the exam focused on linear concepts and didn't seem to have a balance. Do you have any insights/advice on this? 

Sara, my understanding is that what we think of as "topic areas" are virtually irrelevant to the distribution of questions on the exam. Questions are distributed by the combination of "Big Idea" and "Science Practice." 

For our purposes, that means a problem relating torque to angular acceleration is EXACTLY EQUIVALENT to a problem relating force to linear acceleration. Conservation of angular and linear momentum are equivalent in the development committee's eyes, as long as the questions use the same science practices. 

Now, I'm sure there are discussions among the committee about balancing linear and rotational concepts a wee bit. But I'm not privy to those conversations. In terms of the goals of test writing, an exam could in principle be entirely linear, or entirely rotational, and still be considered a valid exam. 

As always, I take the most inference from actual, authentic, released items. And in the first two years of the exam, those released items are more heavily linear than rotational. 

Now, we haven't seen the multiple choice. I'm personally skeptical that there weren't at least a couple of rotational problems on the multiple choice. I think students see what they want to see: they wanted a torque or angular momentum problem, didn't get it on the free response, so likely ignored or forgot that it showed up in the multiple choice. 

That said, unlike the old Physics B percentage distribution of topics, it's quite possible that torque and angular momentum were in fact a negligible portion of the AP 1 exam. 

This year. :-)


06 May 2016

2016 AP Physics 1 exam -- my solutions

I enjoyed writing my solutions to the 2016 AP Physics 1 free response questions.  You can find the questions linked via the official College Board exam site, here.

As always, I guarantee that I've earned a 5, but not that I get every detail right.

But more importantly, as we move farther in time from Physics B, remember that AP Physics 1 exam questions ask for explanations and creative descriptions.  Your answers may not be the same as my answers, yet may be fully correct.  Conversely, just because you cite the same general physics principles as I do doesn't mean you've earned full credit.  The quality of the explanation is the key.

My solutions can be found via this link, at PGP-secure.  This is a wiki for physics teachers only.  If you are a teacher but don't have access yet, follow the instructions at the linked page; you should be approved in a few days.  If you're not a teacher, get your teacher to join!


01 May 2016

The AP exam is tomorrow! What should I do tonight?


Shouldn't I do as many problems as I can before I fall asleep with my head hitting the 5 Steps Book on my desk?

Um, no.  Would you ask your football team to have an all-night weightlifting session the night before the state championship game?  Would you run 50 miles the day before the New York Marathon, just to be sure you're ready?

But I know there are things I'm not perfect at.  I could get better with some practice tonight.

No you couldn't.  Problem solving skills are just that -- skills.  They are built over time, over success and failure, over hard-won experience.  They're not going to improve overnight, no matter what you do.

But there is a chance that I could do a problem that shows up on tomorrow's exam!  Shouldn't I take that chance?

In one night of feverish cramming, sure, you might happen to do a problem similar to what's on the exam.  But every new think you put in your brain tonight will shove something else out.  Isn't it just as likely that the actual AP exam includes a problem that you worked on last week, but since you crammed so much on the eve of the exam that problem just blends together with everything else you've done?

More importantly, it's far more likely that when a recognizable problem shows up on tomorrow's exam, you're so worried and sleep deprived and anxious that you say "ah, I recognize that problem!  But I don't remember how to solve it... dang."

All my friends are cramming tonight, so my teacher and my parents expect that if I don't, I'm slacking.

Well, that's a different problem, one unrelated to physics.  I'm not a politician, I'm a physics teacher.  You may certainly point your teacher and your parents to this post.  Have them email me -- I'll tell 'em straight up that there is no benefit to studying the night before the AP exam.

That's easy to say, Greg Jacobs, but put your money where your mouth is.  Don't you expect your own students to study tonight?  Don't you at least wink wink at them suggesting some things to look over, perhaps in the 5 Steps book?

No.  I'm taking my students out to the school snack bar during the evening study time, for the express purpose of ensuring that they're NOT studying physics.

Look, folks.  At this point you're either ready for the exam or you're not.  There's nothing to be done except for focusing your mindset.  

Another analogy might be performers in a musical an hour before curtain on opening night.  All the practice is done.  Okay, it's a good idea to do a vocal warmup, as well as the mental warmup provided by some of those drama department games.  But should the director say, "hey, let's go through act 1 again, there's some bits we need to work on?"  No.  Just come onto stage brimming with confidence and energy.

You will make mistakes -- in the championship game, on opening night, on the AP exam.  That's to be expected.  If you go in with a positive attitude and a focused mind, then you'll be able to recover from a dropped pass, a flubbed line, or a paragraph response question that ties you up in knots.  

And if it turns out that you're dropping passes on every series, or you flub your lines in every scene, or you are flummoxed by all five free response questions... 

...then deconstruct how you should have approached the ENTIRE YEAR differently.  These aren't problems that practice the night before would have helped -- these are systemic issues of overall preparation.  Address those issues for next season.

For now, relax.  Go bowling.  Play cards with your friends.  Don't have an early night of it -- have a NORMAL night.  Go to bed the same time you always do.  Get up the same time you always do.  Take comfort in your regular daily routine.  

Show up to the exam knowing that you're as prepared as you're gonna be.  My parting words to my class on their way to the AP exam are simple.  



27 April 2016

Some practice quizzes to review before the AP Physics 1 exam

In the lead-up to the AP Physics 1 exam, I ask some short fundamentals-style questions on a quiz each day.  These questions are far less detailed than actual AP Physics 1 questions, but are deeper than my fundamentals questions leading up to the old Physics B exam.  The purpose of these quiz questions are to focus my students' review, and to focus their attention in class.  If I just said "listen while I tell you about gravitational mass again, even though I told you two months ago and you probably forgot," I'd get little useful knowledge imparted for the class time spent.  However, "let's answer the questions to this quiz you just took" keeps students invested -- if nothing else, they care whether they got a quiz question right five minutes ago.

How do I write these?  I put my fact sheets into's list randomizer.  Then I just riff on the facts in the order they come up.

Here's one quiz.  I gave them a strict 3 minutes to finish.  Feel free to use in your class.  I'll post another in the next day or two if people like them.

1.      What is the more common word for the “magnitude of the velocity vector”?

2.      One metal sphere has a charge of +3 mC.  A second metal sphere has a charge of -2 mC.  The spheres are touched together.  What is the charge residing on the two spheres while they are in contact?

3.      A planet’s orbit about a sun is elliptical.  Consider a system consisting of just the planet.  Is the planet’s angular momentum about the sun conserved?

4.      An object is hung from a spring scale, which reads 2.0 N.  Dividing by 10, it’s determined that the object’s mass is 0.2 kg.  Which kind of mass was determined?

5.      An object is pulled at constant speed to the right by a rope, which is angled 30o above horizontal.  The tension in the rope is 5.0 N.  Is the force of friction greater than, less than, or equal to 5.0 N.

6.    An object is attached to a horizontal spring, compressing the spring by 0.15 m.  A second object, twice as massive as the first, compresses the same spring by 0.15 m.  By how much has the potential energy of the spring-object system changed? 

26 April 2016

Just the facts: all of AP Physics 1

You may recall my post last year at this time, of a brief topic list for AP Physics 1.  That's been a useful document, as I've referred to it throughout the year each time we review for a major test or exam.

But with a week to go before the actual AP exam, I'm bombarded with more requests for a more detailed summary.  So here you go.  

I don't use a textbook in my classes.  Instead, I hand out fact sheets giving just the basics of each topic.  I expect my students to memorize the information on the fact sheets over the course of the year; importantly, my students know that they should NOT memorize anything else!  Success in physics, and on the AP exam, consists of applying these facts to new and interesting problems.

Anyone may use my fact sheet -- I'd love it if you'd cite the source, but that's not even that big a deal.  After all, these are simply facts of physics.  If facts of physics aren't public domain, I don't know what is.  :-)

Fact sheet link via google docs here:  AP PHYSICS 1 FACT SHEET

(Anyone, teacher or student, who can't open this for some reason: just email me, and I'll send a copy.)

If I've left something out, or if you'd like to argue about phraseology, please post in the comments.


24 April 2016

Rule 1 of teaching, and how it applies to AP exam review

This summer as you're preparing for your physics courses, I'd highly recommend reading the Teacher's Manual for 5 Steps to a 5: AP Physics 1.  It's a free download from McGraw-Hill.  The framing device for the manual is "5 Steps for You to Help Your Students Get 5s."  It discusses many of the specific approaches I take to my classes, all in the context of the AP Physics exam.  Of course, these approaches are equally applicable to teaching any level of physics.

Integrated throughout the text are what I'd consider the Three Commandments of teaching... not just teaching physics, but of teaching high school at all.  In the Teacher's Manual, I discuss these commandments with reference to beginning the course.  But they apply equally to the AP exam review that many of us are deeply engaged with this time of year.  

In case you're interested, Rule 2 is "Trust, but verify."  Rule 3 is "Your students don't listen to you.  (That's okay.  They don't listen to me, either.)"

Rule 1: Never condescend.

When setting the tone for your course in September, it's important that your students perceive that they are being treated like adults.  Yes, I understand that we are NOT officially teaching adults, and that some of our students will need intervention because their actions are not adult-like.  Nevertheless, the assumption of good faith on your part will go an enormous distance toward earning cooperation from your students throughout the year.  The majority of teenagers are, in fact, intellectually and emotionally ready to behave as adults.  But this majority can be hypersensitive to perceived disrespect or condescension.   

In the context of AP review:  It can be quite disheartening during review time to see our students making the same danged mistakes that we've worked on eliminating -- especially when such mistakes are made by the particular students who spent part of the year hostile, or lazy, or arrogantly overconfident.

Nevertheless... there's little point in reminding students about their personal shortcomings right now.  It's so tempting to say, "No wonder you're struggling.  Remember all those poor homework assignments?" or "Now, you would remember the definitions of wave properties if you had paid appropriate attention in class."  But do you really want to sound like a frustrated, nagging parent?  Your student will tune you out the same way he tunes out his mom when she complains about how he never helps out around the house.  

Just help the student, patiently.  Or don't help -- it's reasonable to politely and respectfully point to the correct fact sheet or old homework problem: "John, before  you try correcting this problem set, take a look at the wave definitions at the end of chapter 12.  I think that'll put you on the right track."  It's not your job to re-teach course material from scratch, but you should expect that even diligent students need reminders of things you studied earlier in the year.

It's not worth revisiting past failures in the runup to the AP exam.  Just be glad that your student is putting forth some kind of effort now.  Be respectful.  Lazy students know they're lazy without you rubbing it in their face.  And they're only going to change their future behaviour in response to a personal, internal decision to do so -- certainly not in response to a nagging physics teacher.