Static Fluids with Quantitative Demonstrations -- Detailed Class Notes

What's the buoyant force on a lionfish?  I ain't doing this
demo, but you can see the demonstrations I do do at  this link.

Regular readers are probably aware that my typical class period consists of one or more quantitative demonstrations -- I don't just solve an abstract example problem from a book, I physically set up the example problem as an in-class experiment.  Any calculation we make in class is verified by measurement. 

One of the questions I'm most asked is, "Do you have a list or writeup of all of your quantitative demonstrations?"  Unfortunately, I don't.  When a publisher (or the NSF) offers me a five figure advance, I'll consider writing a book.  

Until that glorious day, you ask, where do I look to find quantitative demonstration ideas?  Well, start by searching through this very blog, of course.  Sign up for one of my AP Summer Institutes (I'm doing four, I think, in 2012).  Every time you're choosing an example problem to use in your class lecture, think, "could I set this up in my classroom?"  Use a homework problem as the basis for a laboratory activity, and make your students create the setup.  Talk to other physics teachers, including those who are listed as followers of this very blog.  

Now, if you'd like an extraordinarily detailed description of what a class with quantitative demonstrations might look like, check out this piece I wrote for the College Board a few years ago.  They asked me to provide a "lesson plan" for AP-level static fluids.  I described each experiment, each check-your-neighbor question, each measurement that I make during class.  (If you've been to a summer institute, you'll recognize a few of these demonstrations.)

Do you have a quantitative demonstration that you use in class?  Tell me about it.  I'm open to guest posters on this blog...

Vernier Video Physics for the iPad 2: A Winner

For Thanksgiving, my family headed to a very nice cottage in West Virginia.  It had a number of wonderful amenities, not including internet, television, or cell phone service.  That was okay by me, because I spent several days grading exams and writing comments.  It’s amazing how much more focused I can be when I don’t have the option to check my email real quick, or to just see what the score of the game is.  It’s also amazing how much more boring it is to grade papers without any sort of electronic distraction.  Guh.

My eight year old occupied himself for hour after hour with a hand-held Pokemon video game.  In the rare moments when he tired briefly of having Waylord fight Trogdor (or whatever), he explored this loaner iPad 2 that I got from my school’s library.

For those who have followed Jacobs Physics for a while, you might remember that a year and a half ago my school provided me with an iPad, for use in physics class, while broadcasting football and baseball, and at debate tournaments.  My summaries of the iPad’s usefulness can be found here and here.  

Now, before you say “oh, my school could never afford that” or “what an extravagant place you teach at, Greg!”  think about the actual cost-benefit analysis.  I don’t use a smartboard – I tried it for a year, and found out that I never used any features that couldn’t be done with a dumbboard.*  I’ve found the iPad to be worth far more than the smartboard; yet, the iPad generally costs less than half a smartboard.   If your school can afford computers and smartboards, it can afford an iPad for the physics department.  The question becomes, is such a purchase worthwhile?

* A “dumbboard,” as I learned over the summer, refers to a computer projector shining directly onto a whiteboard.  Annotations to the screen can be done with dry-erase marker. 

Now that the iPad 2 includes a video and still camera, the answer is unequivocally “yes.”  Our department has had a high-quality digital camera for years.  When I want to take a picture of an experimental setup, I walk down the hall to get the camera.  I take the camera out of the bag, remove the lens cap, take the picture**, remove the USB cord, replace the USB cord and remove the correct USB cord, insert card into the card reader, click a mouse a few times, and voila – there’s the picture.  Finally.

**often the shutter won’t press without the magic incantation that goes, “Why the #$@@ won’t the dang picture take?  Is it on autofocus or something?”

With the iPad 2, the picture isn’t nearly as high resolution.  However, the picture taking process is reduced to (1) press button, (2) email picture.  That capability by itself might be worth the price of the iPad 2.  Think of all the measurements that can be made live, in class, with instant photography!***  And, portable skype is nothing to sneeze at.  I can show an equation during a live video chat; I can even show a live experiment to a remote viewer.  Not that I’ve done that yet, but if you would like to listen in to my honors or research class via skype, just let me know.

*** Of course, those of you who were smart enough to purchase smartphones have probably been doing this for years.  I still have a landline, and an office phone.  Sorry.

And with the Vernier video physics app, the revolution is complete.  Vernier’s logger pro software has always allowed easy frame-by-frame video analysis on the computer.  But the time to upload video and then to convert it to a usable format has always been an annoying barrier to using this feature except for research purposes.  On the iPad 2, the process is simple and quick.  The video collection can be done within the Vernier app itself – no saving and importing videos unless you want to.  The interface is easy to use and understand.  Within a few minutes, you can have position- and velocity- time graphs for any captured motion.

As a testament to this app’s ease of use, I produced a useful video and graph within minutes of first opening the app, without reading any sort of instruction manual.  Then, I showed my 8 year old how it worked.  He spent a couple hours taking and analyzing videos, proudly showing his grandmother that the dropped ball was going 600 cm/s, but the dog’s nose only went 150 cm/s.  I approve.

For $2.99, I can't imagine a more useful physics app.  Now, Vernier, your challenge is to make all your probes work wirelessly with an iPad version of logger pro.  Go for it.

Two Masses and a Pulley, and a New Misconception

The badly sketched picture to the right shows a classic mechanics problem.  Two equal masses are connected by a string over a pulley.  In this case, the table is frictionless.

Typically, a student is asked to determine the tension in the rope and the acceleration of the masses.  Great -- that's (mg)/2 and g/2.*  This problem is richer, though, than a mere calculation might suggest.  Take a look at a quiz I gave the other day:

* The quick way to get this is to consider both objects as a single system.  The net force on that system is the weight of the hanging mass, mg; the mass of the system is 2m.  By Newton's second law, a = g/2.

1.       A block of mass m is attached over a pulley to another hanging mass m, as shown above.   The surface is frictionless.  The system is released from rest.

     

(a)    What is the direction of the hanging mass’s acceleration?  Explain.

(b)   Is the acceleration of the hanging mass greater than, less than, or equal to g?  Explain.

(c)    Is the tension in the rope greater than, less than, or equal to mg?  Explain.

2.       A block of mass m is attached over a pulley to another hanging mass m, as shown above.   The surface is frictionless.  This time, the top block is given an initial velocity to the left and released. 

(a)    What is the direction of the hanging mass’s acceleration?  Explain.

(b)   Is the acceleration of the hanging mass greater than, less than, or equal to g?  Explain.

(c)    Is the tension in the rope greater than, less than, or equal to mg?  Explain.

Ideally, 1(a) is answered with a kinematic approach -- the hanging mass is speeding up and moving down, so acceleration is also down.  For 1(b), I've defined "free fall" as the situation in which no forces besides weight are acting.  Since a tension acts upward on the hanging mass, the mass is not in free fall and the acceleration is less than g.*  And in 1(c), acceleration is downward, so net force must also be down.  That means down forces greater than up forces, so the tension is less than the weight.

* Okay, sure, if the upward tension is twice the block's weight, the acceleration could be g, upward.  That's highly unlikely in hanging-block-and-pulley problems.  

Of course, question 2 is identical to question 1!  The hanging mass is moving up but slowing down, so acceleration must still be downward.  (Or, one could argue that the block on the table still experiences only one horizontal force, that of tension, so its acceleration must be to the right; the blocks must move as a unit, so the hanging block has downward acceleration.)  Once it's established that acceleration is still down, questions 2(b) and 2(c) follow as in 1(b) and 1(c).

By far the most common misconception here is that the net force must be in the direction of movement.  A student will commonly get question one reasonably correct, but then say "the block is moving upward, so up forces must be bigger than down forces."  This question is just one more salvo in my arsenal aimed at that piece of nonsense.  

Another typical misconception is that in question 1, since the hanging block is falling near earth, its acceleration must be g.  That's taken care of with a request to state the definition of free fall and a sheepish look from the student.

And, a common mistake is to justify (a) and (c) with circular reasoning:  The acceleration is downward because the weight is greater than the tension; the tension is less than the weight because the acceleration is downward.  This student doesn't earn full credit, but I'm not worried so much about his comprehension. 

I discovered a new misconception today, though.  One of my brighter students said acceleration was equal to g, and he stated the definition of free fall accurately.  He asked, "since the surface is frictionless, the block on the table doesn't require any force to move.  So why won't the rope will be slack, the tension zero, and gravity the only force on the hanging block?"

At first I was flummoxed.  I set up two carts on my track, and showed him that the string was in fact not slack.  But why on earth would he think that no friction leads to a slack rope?

In further conversation, I discovered that he was referring back to our class's multiple conversations about how no net force is necessary for motion at constant speed in a straight line.  A mass on a frictionless track, once moving, keeps moving, even without any tension to pull it.  My student wasn't processing that this block on this surface was accelerating, not moving at constant speed.  Once I pointed out how the blocks must move together, and therefore accelerate together, he got it.

How much is this post worth?

Woodberry Forest 21, EHS 12 in 2011.  But this picture
is from 2010.

Students, and too often parents and colleagues, usually approach a high school course as a point-earning game. While points and grades must exist -- they *do* motivate, and besides, you're not gettin' very far with your boss if you tell him "I'm not giving grades this marking period, okay?"* -- you can send a consistent message that you are an impartial arbiter in the game, not a teammate or an opponent.

* But, twelve years later I did just that.  See this series of posts. 

Consider the most commonly asked question in class at my school this time of year.  These are the High Holy Days at Woodberry Forest -- last Friday night was the bonfire*, and Saturday was The Game, a football match against our chief rival school.  This week marks review for exams, which start on Thursday. 

* Think the PAGAN ritual scene from the Dragnet movie, probably without the virgin sacrifice but with far more goat leggings

So, on the day before The Game, I passed out an exam information sheet containing basic form and content data.  In every section, without fail, someone asked, "How much will the exam be worth?"  To me, that's taking the point earning contest too far.  I'm not going to allow you to make a strategic decision about whether or not to study based on my answer.  

More to the point, what will the class response be to a dispassionate direct answer of "20% of the trimester, as stated in the syllabus?" 

(1) Half the class will instantly get out a calculator in order to determine the minimum exam score that will allow them to pass, or to maintain the grade that won't provoke parental ire.  Students who can't solve 3x = 5   for x will perform this calculation quickly and flawlessly.  

(2) The follow up question will be on the order of, "but, if we do well on the exam, will you weight that more heavily in our final grade?"  or, "Can we do extra credit?"

Why even engage in such gaming the system?  Considering the background of the big football game, I looked sadly at each student who asked that question.  I said, "Mr. Clark, when the football team gathers after practice today for one last conversation together before The Game, would you even consider asking 'Coach, how much is tomorrow's Game worth?'  And how would Coach react if he knew that the reason you were asking was so you could weigh just how much effort to give?"

Point made.  No follow-up questions about grades.  And we moved on to discussing physics.

Nacho, Nacho Day... and trimester exam review

This is just a repost that answers several frequently asked questions:

(1) How do you help your students review for a major cumulative exam?
(2) Why does your email say "Nacho Man?"

The point is, extra credit and food provide significant incentive to bring students into the classroom during what otherwise would be wasted independent study time.  Once students are in the classroom working diligently on physics questions, learning is happening even if music, conversation, and nachos are happening simultaneously.

Check out this post.

Peter Chen, a student who is well-versed in video production, intends to create a "cooking show" style clip about Nacho Day in our physics department.  I'll post the link in a month or so.

GCJ

No credit for ridiculous answers -- an impulse problem

I work very hard to differentiate my physics class from merely an applied mathematics class.  We do quantitative demonstrations nearly daily, in which a mathematical prediction is checked via direct measurement.  I frequently ask on homework problems, "Justify the physical reasonability of this answer."  My class is incessantly discussing how to figure out whether or not answers make physical sense, regardless of whether arithmetic is done correctly or not.

I amended a problem the other night from (I think) the Serway & Vuille text.  I gave them the graph to the right, and wrote:

1. A possible force vs. time curve for a ball struck by a bat is shown in the figure. 
(a) Calculate the impulse delivered to the ball.
(b) This 0.25 kg ball was initially moving toward the bat at a speed of 20 m/s.  Calculate the exit speed of the ball.

For part (a), most of the class figured out to take the area under the graph, which they better have -- that same day in class I had discussed how impulse can be found as the area under such a graph.  Some students estimated an average force, which would be around 4000 or 5000 N, and multiplied by 1.5 ms.  Fair enough.  

Understandable mistake #1:A few made the error of multiplying the MAXIMUM force of about 8,000 N by the 1.5 ms time interval.  I took off one point out of fifteen for that -- these students were at least approaching the problem with relevant physics.  This mistake makes the impulse wrong by a factor of 2.

Understandable mistake #2: A few also failed to read the horizontal axis, and multiplied by a time interval of 1.5 s, not 1.5 ms.  These students also were approaching the problem with correct physics, but made an arithmetic error.  Granted, the answer for impulse was off by a factor of 1000, giving them 7500 Ns instead of 7.5 Ns.  But I can't really expect anyone to have a serious physical understanding of orders of magnitude for impulse calculations, especially in the first two days of studying the topic.  So I took off just one point.

On to part (b).  

Understandable mistake #3:  The most common error was to fail to account for the direction change of the momentum vector.  The ball has a momentum of 5.0 Ns toward the bat before the collision.  The ball's momentum changes by 7.5 Ns.  But, that doesn't give the ball a final momentum of 12.5 Ns!  Since the ball changed directions, the momentum must have first DECREASED by 5.0 Ns to zero, and then increased in the direction away from the bat by 2.5 Ns.  

With the failure to account for the direction change of the ball, the exit speed works out to 50 m/s -- a lot, but still not unreasonable, as baseballs hit for home runs routinely exit the bat with speeds above 100 mph.  The correct answer is 10 m/s, or about 22 mph -- not a very hard hit, but also not unreasonable.  Anything related to a baseball in the tens of miles per hour is just dandy.  I took off just two points for failure to account for direction in a momentum calculation.

(Aside -- I'm an American, and I watch baseball.  However, if someone had assumed no direction change for the ball, given me the 50 m/s answer, and then discussed how the cricket batsman is allowed to propel the ball in the direction in which the ball was already moving, that student would have earned full credit and a piece of candy.)

What about the student who compounded error upon error?

Understandable mistake, combo platter:  The student who used the max force rather than the average force to calculate impulse, AND who didn't account for the ball's changing direction, got something like 68 m/s.  Well, that's about 150 mph, and still not horrid -- after all, that's only 40% above the typical 100-120 mph exit speeds in the majors.  (I'm recalling my Physics of Baseball by Robert Adair; I hope I have that value right.  Please correct me in the comments if I'm wrong.)  That answer loses only the two points for the direction change issue.

Terrible, Horrible, No Good, Very Bad Mistake: Oy.  I had several students who failed to see the units of ms, and found an impulse of 7500 Ns.  Then they carried through the mathematics in part (b) to find an exit speed of 30,000 m/s.  Oh, I say, whoa there.  Really?  30 km/s?  Mach 88?  Okay, Bugs Bunny threw faster than that in the Christopher Columbus episode (when he threw a ball around the world in about 2 or 3 s)... but other than in a cartoon world, NO.  These students lost an ADDITIONAL 5 points out of 15.  One sheepishly said, "well, the math said 30,000 m/s, but you didn't ask us to justify the reasonability."  I pointed out that in physics, physical reality always will trump mathematical manipulation.  It doesn't matter whether I *ask*, one should *always* be conscious of physical reasonability.

Epilogue:  One lone student made the Terrible Horrible No Good Very Bad Mistake, got 30,000 m/s... and pointed out "that is nonsense, a baseball can't ever go faster than 100 m/s or so, the answer is ridiculous but I don't know what I'm doing wrong."  He lost the one point for failure to read the graph properly, and one point for an incorrect answer... and that was all.  Reward those who demonstrate their commitment to physical reality.

"Group Quiz" on impulse-momentum

Happy and Sad Balls -- which one produces
more force when dropped onto a force plate?

I can't count the number of articles I read that sanctimoniously preach how physics teachers need to "actively engage learners," involve students in "peer instruction,", provide "inquiry-based interactions", or any other set of edu-buzzwords you can create.  These articles push a fundamentally correct point: that I'll have enormously less success if I merely talk at the white board than if I somehow get the class to involve themselves in the topic at hand.

But as with any other educational method, active engagement only works if it's done right.  The trick is to get students to care about the answer to the question you posed, and about the justification of that answer.  I don't want to read any other literature telling me that active engagement can be effective.  I want to know specifically how other successful physics teachers get their students to actively engage.

I incessantly ask "check your neighbor" questions, in which I give students time to write an answer; I give time for class discussion; and then I survey the class, or call on a random student to summarize his thoughts.  These are generally effective.  However, after a few weeks, the shine has gone off of this novel (to the students) activity.  I can see the beginnings of apathy cross my students' faces... "Oh, again with the neighbor arguing thing.  Gee whiz."

I've got to vary my approach if I'm going to keep class activities fresh and interesting.  I tend to ratchet up the reward for correctly justified answers to my check-your-neighbor questions.  One thought that I've detailed previously is to call on a random student after discussion... if that student can clearly and correctly answer my question, I'll cancel the next day's quiz. 

I generally give a daily quiz at the beginning of class.*  My colleague Paul Vickers modified my daily quiz to an occasional "group quiz," in which he assigned groups of 2-8 students to answer a check-your-neighbor-style question for a quiz grade.  The fact that it's called a "quiz," that the students perceive that their performance will directly affect their grade, keeps everyone focused and on-task.  Yesterday, I tried a new hybrid approach to a check-your-neighbor question.

* Why?  Because students *care* whether they get the answers right, so they pay attention when I go over the quiz better than they would pay attention to the same conversation without the context of a quiz.

The question:  I have a happy ball (one that bounces nearly to the height from which it was dropped) and a sad ball (one that hardly bounces at all).  I drop each ball from the same height onto a force plate.  Both balls have the same mass; both balls are in contact with the scale for approximately the same time.  

Question 1:  Which ball experiences a bigger momentum change?

Question 2:  Which ball causes a larger reading on the force plate?

The method:  I began like a standard check-your-neighbor question.  I wrote the questions on the board, and asked the students to write and justify an answer in their notebook.  After about a minute or two, I asked everyone to argue with his neighbor.  Nothing to see here, really; I did let the discussion go on a bit longer than usual, making sure that those who were still making physics points to each other had a chance to hash out any disagreements.  

Finally, I gave everyone a blank card.  I told them to write and justify the answer to each question as if it were a quiz.  I promised that I would choose a student's card at random to read to the class.  A correct answer with justification on the card would be worth an extra credit point for EVERYONE on that day's quiz.

Oh, boy, did I get careful justifications.  One class's random delegate explained the answer perfectly, earning the credit with no doubt.  The other class's delegate explained beautifully (but incorrectly) that since the balls have the same weight, the force plate must read the same value, and thus both balls will have the same momentum change.  Knowing that many class members had convinced themselves of this mistaken fact, we talked about why the force plate would NOT read the weight of the ball.  

Right or wrong, making the check-your-neighbor question into a quasi-quiz convinced all my students to write clear descriptions of their thoughts.  Even though I only looked at one answer per class, everyone took the writing seriously, and everyone could evaluate for himself the quality of his arguments.  

I may get away with this quasi-group-quiz once or twice more before it becomes just another day of class.  Then I'll have to provide a different sort of incentive for careful, invested participation.  I'm open to ideas -- email me, or post a comment.

GCJ