30 January 2011

The "Big Three" Skills: What's the Point of an Introductory Physics Course?

No, I'm discussing a different "Big Three"
Most high schools teach two or three different levels of introductory physics.  There's the conceptual course, often offered at the ninth grade level; the "college prep" or "Regents" level; and then there's the AP, IB, or collegiate level.  In broad terms, the primary difference among the levels is twofold:  the depth of mathematics used, and the pace of the course.*

* People are often surprised to find that the algebra-based AP physics course uses no more mathematics than the Regents course; it's just that the pace is faster, and the depth of analysis of each topic is significantly greater, in AP.

In conversation with Curtis, our awesome conceptual physics teacher, the discussion turned to expected results:  What do we want our students to leave physics knowing? 

I am fully aware that this question is, to some extent, the physics teachers' equivalent of "So, what is the One True Religion?"  I am also cognizant that this question has provided fodder for Ph.D. theses, 100-page publications from the College Board, and even areas of public policy.  I nevertheless address the question.  If you're going to read this blog, you need to understand where I'm coming from.  And, I think the question has a far easier answer than do those who seek a degree for answering it.

Before answering, let me set the ground rules.  (Yes, I'm a debate coach.)  I will NOT make any agruments based on skills needed for future academic pursuits.  I expect each high school introductory physics course to stand on its own as either a salutatory OR a valedictory experience.  The high school introductory course should not be designed to create physicists, or to get students ready for medical school.  No, I think of high school physics the same way I think of high school American History -- it should provide a rigorous background because the subject is itself interesting, and because educated adults have some sort of knowedge of that subject.  If students are inspired to future study, if they are well prepared for further study, then that's a wonderful secondary outcome.

The next ground rule is that I refuse to address topic coverage.  Whether a course addresses fluid mechanics, or atomic physics, is more a matter of personal choice, available equipment, and administrative whim.  Good physics can be taught using any combination of textbook chapters. 

So, then, regardless of level, what do I want physics students to know how to do?  Here's my holy trinity, in no particular order:

1. Reason with respect to a relevant equation. No, not the ability to crunch numbers and come out with a correct answer... that's math. The physics skill is to say, without touching a calculator "If this doubles, what stays the same? What happens to the other variables?"

2.  Interpret Graphs.  There are only three things you can do with a graph:  find the slope, take the area under the curve, or read the axes.  I want students to develop the ability to know which of these things to do, and then to do them correctly.

3.  Understand the physical meaning of numerical quantities.  In the first month of class, a student might write down an answer as "29.43872743."  By the end, I expect that answer to be "29 m/s," and the student to be able to explain whether this is a car on the freeway, a cruising airplane, or a sprinter on the track team.

All three of these goals are attainable at any level of instruction.  Sure, AP physics B is going to teach a lot more relevant equations.  Sure, the more mathematically gifted students can get the hang of these skills more quickly than others.  So what?  All students in a physics class, even a 9th grade conceptual class, can develop these skills.

And you may have other goals as well:  maybe plugging correctly into a calculator IS important to you.  Maybe you want to develop writing ability, or an understanding of how physics relates to other disciplines.  Fine.  Go for it.  But I think even these other important skills -- all of which I do address somehow -- are subordinate to the big three.  Address the big three, and students have the foundation to approach anything else you want to throw at them.


27 January 2011

The USIYPT is next weekend (Feb. 4-5)

Next Friday-Saturday, February 4 and 5, I will be helping to run the 2011 US Invitational Young Physicist Tournament.  Six teams from across the nation will converge on Oak Ridge, Tennessee, to discuss four research problems in ritualized debates.

If you're near Oak Ridge, stop by -- these debates are quite entertaining, even to a lay audience.  But even if you're not able to attend, you might consider using some problems or ideas from the tournament.

All participating teams have been investigating three of four possible problems:

Dominos: "Numerous domino tiles are balanced on a table or floor with their long axis vertical with horizontal spaces that can be varied. When the first tile is knocked over a domino wave occurs. Predict and measure the speed of this wave and its dependence on various parameters.

Salt Water Oscillator: "Pour fresh water into tall container. Place a cup with a hole in its bottom surface on top of the fresh water. Prepare a solution of salt water and add some food coloring. Pour this solution into the cup on top of the fresh water and simultaneously push the cup down into the fresh water. Secure the cup so that the level of salt water is approximately the same as the level of fresh water. Observe the on-again and off-again flow of salt water into the fresh water. Predict the frequency of these oscillations from first principles, and compare to experiment. Investigate sizes of holes, salt concentrations, and other liquids."

Magic Motor: "Construct a DC motor without a commutator, using a single battery, a single permanent magnet, and a single loop of wire. Predict the frequency of rotation of this motor from first principles and compare to experiment."

Boiling Water: Some people say it is important to put a lid on the pot when you want to boil water for tea to save energy and time. Investigate this phenomenon.

What I love about these kinds of problems is that one could do a cursory experiment in a couple of lab periods.  However, a deep theoretical understanding, coupled with a thorough experimental investigation, takes much more time and effort.  And, there's enough issues to be investigated that different schools approaching the problems in different ways will have lots to talk about.  That's how real physics works -- competing research groups publishing and sharing their own understanding of interesting problems.
I think of my school's team as a graduate research group.  At the beginning of the year, I helped them figure out the correct experimental and theoretical approaches; I had to learn a lot about each problem, and then I had to *teach* what I had learned.
What was wonderful about today's final pre-tournament practice was that the students each said, "we don't need you right now."  I know I've done a good job when the research group is ready and eager to work independently.  They still had occasional questions, but the questions were of the style that professional physicists ask of one another -- not "you didn't tell me what to do, can I go to lunch?"  :-)
I can go on and on about the USIYPT.  In fact, several readers of this very blog are coming to the tournament next week, with the possible intent of forming their own team for 2012.  If you'd like to hear more about the tournament, take a look at usaypt.org, or give me an email.  After Feb. 6 I will post the tournament results here, and I'll mention NEXT year's problems.  I can't wait to get my juniors started on those.

25 January 2011

Personally Handwritten Notes

Dog from scienceblogs.com

It's the dog days of the school year here at boarding school.  My twelve wonderfully enthusiastic debate team members dragged themselves crossly through practice yesterday, missing that spark that had been propelling them the past two months.  I actually felt moved to cancel practice as a mental health day.  In class, I can read my students' faces -- they are present physically, but they're mentally beaten down.  This happens every January.  All will be better as the weather starts to warm and as the sun sets later.

Nevertheless, class moves on.  I ain't gonna just stop teaching.  I deliberately schedule a few non-traditional activities for January -- the student-written test, the four-day-long circuits lab -- but I've got to plow through some material somehow.  With our midwinter week off coming up, if I don't give a major quiz or test this week everyone will just tune completely out.

I tried something relatively new this week.  On Friday the AP class takes the "Big Butt Electricity Fundamentals Quiz;"  my general physics class has a major quiz on Saturday morning.  (Yes, we have Saturday morning classes.  No wonder everyone is beaten down, right?  :-)  )  But as an inducement to study, I announced today that everyone will be allowed to use any personally handwritten notes for these quizzes.

This is not an original idea -- I've seen many a physics teacher allow students to use a handwritten equation sheet.  In fact, I've generally avoided having the students write their own equation sheet, because they tend to write down every equation in the textbook, including intermediate steps in a derivation, and because they tend not to understand what they've written.  So I'm still giving the general class their equation sheet; the AP class knows what equations are on the official College Board equation sheet.  I'm expecting that the handwritten notes will not include merely equations. 

One student asked whether he could just bring his class notes -- I said, sure.  As long as they're not bringing in old tests, as long as they're not xeroxing their friends' notes or their textbook, then the process of preparing for the quiz will be as useful as the quiz itself.  And since we've already had numerous quizzes this year, everyone knows exactly the kind of questions that will be asked and the kind of notes that will be most useful. 

Will this work?  My hope is that I'll get better prepared students, even in the midst of the winter doldrums.  While I don't expect the personally handwritten notes to be a magic bullet to physics success, it just might work. 


17 January 2011

Poll result: direction of electric field due to point charges

This problem originated with an exercise in Serway, but I've made an important change.  I'll explain that change at the end of this post.  First, answer the question:

The blue charge at the top left produces an electric field that points to the left (toward the negative charge producing the field).  The blue charge at the bottom right produces an electric field that points down the page. 

So the vector sum of the electric fields produced by the BLUE charges is 45 degrees down and to the left. 

The red charge produces an electric field that points up and to the right (away from the positive charge). 

The total electric field now is the vector sum of the fields due to the blue charge, and that due to the red charge.  That total electric field must point in either direction (a) or direction (d) as indicated in the diagram.  Sure enough, the vast majority of poll respondents were split between these two directions.  Which is correct?

The answer hinges on which electric field is bigger:  the one due to the red charge, or the one due to the blue charges?

Each blue charge has the same size charge, and each is the same distance from the position where we're measuring the field.  So each blue charge produces a field with the same magnitude; by vector addition, the total field due to the blue charges will be (root 2) times the field produced by one of the blue charges.
The red charge has the same size charge as the blue charges, but is a larger distance from the relevant position.  So the red charge must produce a field that is SMALLER than that produced by either blue charge.

The field due to the blue charges is larger than the field due to the red charges, and pointing in the opposite direction.  So the vector sum of all these electric fields is pointing in the direction of the larger field, the one from the blue charges, the one in the direction of choice (d). 

Now for the teaching point.  Why did I change Serway's diagram?  The original problem had the red charge as +2Q.  Well, in that case you'd need to think carefully about the red electric field.  The charge producing the field is farther away than the blue charges, but the charge itself is bigger.  To get the answer right, you need to plug carefully into E=kQ/d2.  This problem is designed just to check my students' conceptual understanding of electric fields due to point charges -- I want to start simple.  Once everyone can merely find the correct direction of the electric field, once everyone can understand conceptually that a charge farther away from a field point produces a smaller electric field at that point, then we can start doing more complicated gemoetry and algebra.


14 January 2011

My unusual method of teaching thin film interference

I would NOT assign a soap bubble problem in the first
day or two of covering thin films -- why not?
Got a nice note the other day from William Haskell, a new physics teacher in New York.  He was reading my 5 steps book about thin films, and was initially confused.  I didn't mention phase changes at all! 

I said, in a thin film, the beam of light that passes through the film goes an extra distance 2t, where t is the thickness of the film.  So constructive interference occurs when that extra distance is a whole number m of wavelengths.  That's where the equation 2t = comes from.

When I teach thin films, I intially very deliberately fail to mention phase changes.  I'm just following the general principle of teaching physics:  start simple, add complexities later.  I want the students to become comfortable with the idea of interference in a thin film, with the relevant equation, with the meaning of m, with the types of problems that might be asked.  

So, everyone starts by solving thin film problems with no phase changes.  Then I introduce the idea of a phase change when light reflects off of a higher-index material.  We simply say, "if there is exactly one phase change, then switch the conditions for constructive and descructive interference."  

If I had made that statement on the first day of thin film study, I would have gotten blank looks.  By waiting until the class became comfortable with the no-phase-change approach, I ensure that they have the context for this complication.

Thanks for the note, William.  I will be giving an AP summer institute at Manhattan College this summer in the first week of August -- come on and join us!


09 January 2011

Multiple Choice poll: electric field due to point charges

The poll on the left is based on a picture from Serway.  I've changed it a bit, and not just so the Serway Lawyers don't come after me -- I've made the question more conceptual than mathematical.  Go ahead and vote.  I'll post results next weekend, along with a discussion of the change I made and why I made it.

FYI, my AP class has just begun studying electric fields due to point charges.  This is their first homework problem, with the request for a justification of the answer, of course.


08 January 2011

Mail Time: Bernoulli experiment troubles.

Michael Gray, of Georgia, writes: 

I have been preparing the Tennis Ball can experiment, but the water doesn't go quite as far as the math predicts. With a hole to top height of 18.5cm and a hole to floor height of 93.5cm I get a distance of 83cm. However, the stream is only reaching the high 70's of cm. Also, the water breaks up from a solid stream before it gets there making the exact landing point difficult to determine.

Any advice?

The stream breaking up is the problem, I think. In class, I've always hit the prediction dead on. But on Monday at a workshop in Alabama, I missed. See, I had quickly jury-rigged a gatorade bottle for this demo. I used my cheapo pocket knife to make a jagged hole. The stream was not particularly clean, but was breaking up. Sure enough, I missed -- I predicted 65 cm, but the stream only went 50 cm.

I suspect -- though I'll have to play around a bit to be sure -- that this demo depends on getting a "clean" stream out of the hole. After all, Bernoulli's equation explicitly is for "inviscid" flow, meaning no viscous drag.

Let me know if you try again, and I'll do the same.

06 January 2011

eMail Time: How much review time for AP physics?

From Vance Hurst, who teaches at Colquitt County High School in Georgia, and who attended my AP summer institute at Kennesaw State University last summer:

I am sitting here planning out my course pace for the spring semester. My question for you is this: When do you try to finish all of the material that is covered on the AP exam and do you do a cumulative review for the AP test. If you do a review, how many weeks before the the exam do you start it.

Hey, Vance... good to hear from you. My goal each year is to finish new material by the first week or April. After that, it's all review.

My fabulous department chairman at Woodberry, Jim Reid, suggested to me years ago that I not advertise on my syllabus that I'm doing a month of "review." Administrators, colleagues, parents, and students might look askance at the idea of so much review. After all, if it's "just" review, it must not be particularly important, so students should be okay to miss class, so students shouldn't have to do much work during that time... and so on.

But we as physics teachers know that "review" is precisely how physics is internalized. Ask anyone who's been through a physics program -- the first time they see a topic, it's confusing. The second and especially the THIRD time that a physics concept is presented, it usually sticks. I set up my AP class deliberately such that students see every topic presented two or three times -- once in the normal course of the course, once integrated into a subsequent topic if possible, and once again during the April review.

Jim and I agreed to call this four-week portion of AP physics by a special name. I chose "Putting it all together." I emphasize to colleagues and students that this time is NOT merely a review. Instead, it is a time when we focus on how all the disparate topics we have covered in isolation fit together. We are integrating and consolidating our knowledge and problem solving skills. In practice, I'm assigning old AP problems as homework, giving tests and doing corrections, doing loads of fundamentals quizzes, and running fun games and events, such as the physics walk and clicker contests.

A review by any other name would smell as sweet... right?


05 January 2011

The Roller Coaster Expert Speaks, by Justin Kreindel

picture courtesy of howstuffworks.com
In the 1998-99 and 99-2000 school years, Justin Kriendel attended my AP physics classes.  He was, even then, a roller coaster expert; by now, he says that he's ridden over 150 different roller coasters in the United States and abroad.  Justin was particularly interested in the physics of roller coasters.  In fact, for a reserach project he built a simple "linear synchrous motor," the same kind of motor that causes a roller coaster to shoot uphill out of its starting gate.

Since I just wrote two posts about roller coaster physics (look back a couple of days to see these), I sent Justin a link and asked for his input.  Below is his response.

Interesting question which, you probably guessed, I've put a lot of thought into over the years.  My brief thoughts at this late hour are these:

If you think of the center of mass as a point on the train (as opposed to where it really is, which is somewhere beneath the train when it is cresting an inverted U-shaped lift hill, I would think), the train always begins to accelerate when that center of mass is subject to a downward acceleration.  That is, the moment it reaches a downward sloping portion of the lift hill that is steep enough to overcome friction.  So that center of mass, I would think, accelerates to a speed of root 2gh, where h is the vertical distance of the drop, regardless of how the weight is distributed.

Another way I've though of it is in terms of work.  I would think that the chain lift does the same amount of work to lift a train of mass m to a height h regardless of how the weight is distributed.  Assuming a lift hill that starts on a flat section of track and then begins its ascent, I think you can look at it in terms of power necessary at various points of the train's ascent.  Compare two trains, one with weight in front, and one with the weight in the back, and think about what happens when each train first hits the lift hill.  More power is required initially on the front-loaded train, since that weight hits the ascent first.  The once the front begins to crest the lift hill, less power is needed to the push the rest of the train over the lift.  For the back-loaded train, I feel like the opposite happens.  Less power at first as most of the weight is in the back of the train, which takes some time to actually reach the ascending portion of the lift (remember, it starts flat).  But for whatever time in the beginning where less power was needed because the weight of the train was still on a flat portion of the track, you make up for it when the chain lift needs to keep chugging with more power until the very end of the train crests the summit.  I hope I'm making sense here.  Either way, the total amount power necessary (and in turn, the total amount of work done) seems like it would be the same regardless of the weight distribution.

As for Splash Mountain, it's not the best example to test your theory.  Disney greatly controls how wet you get.  A lot of the splash is from jets on the side of the bottoming out portion of the drop.  When it's cold, they just turn these jets off.  They can also control the depth of the water at the bottom of the drop.  Shallower water means less splash as well.  But, assuming all other things equal, I think it's difficult to test this either way.  Sure, when everyone's sitting up front, you're probably getting wetter.  But I feel like this is because the splash is produced by the front of the boat hitting the water, regardless of where the weight is distributed.  So with the splash being created by the front of the boat, it would make sense that those sitting at the front of the boat would get wetter, as that is where the splash "is".  With a full boat, this is very evident.  The people sitting up front often end up much wetter than those sitting in back, as they "block" the water from reaching those in the back.  Which is why it's fun on a log flume to try and duck down low when you hit the water, much to the dismay of those behind you, especially when you're know they've strategically chosen to sit toward the back to avoid getting as wet.  Or maybe just I enjoy doing that.

Regarding the post about "the back going faster," your analysis is exactly right.  When you're going over a drop, for instance, the radius of that drop stays fixed, but the speed of the train is changing as it traverses any given point of track. So if a point on the track is the beginning of a drop, then the front of the train is going much more slowly over that point than the back of the train.  Hence more negative G's (or "airtime") in the back of the train going over a drop.  The reverse happens of course when you crest a hill: the front of the train experiences more airtime at the crest than the back of the train.

-- Justin Kreindel

04 January 2011

Mail Time: Vernier pressure sensor and pressure in a static fluid column

Jeff Bourne, from Northfield High School in John's Creek, GA, writes in:

I took your AP Physics workshop at Oglethorpe U in the Atlanta area several years ago. I was looking over your unit on fluids, and I wondered how do you use the vernier gas pressure sensor to measure the water pressure at a specific depth in a graduated cylinder? I can't find a lab manual that outlines how to do that. I would appreciate any help you can give me.

Hey, Jeff... good to hear from you. I attach some hollow plastic tubing to the probe, and put a small rubber stopper on the other end of the tubing. The tubing is maybe 1.5-2 feet long -- the gas pressure sensor comes with some of this tubing and a stopper, as you can see in the picture.
First, I read the atmospheric pressure, which can range from 97 to 105 kPa depending on altitude, weather conditions, and the probe's internal calibration. Then I measure the depth of water in the graduated cylinder. I do the calculation with the class of what the pressure should be at the bottom using P = Po + rgh. For a typical graduated cylender I use, I get that the pressure at the bottom will be 2-3 kPa above atmospheric pressure, which is easily measurable by this probe.

Finally, I start the data collection (taking about 20 points per second). I feed the tubing into the cylinder until the stopper hits the bottom.  Voila, the pressure jumps from, say, 99 kPa to 102 kPa.


02 January 2011

More roller coasters -- do heavier riders go faster?

When I went to amusement parks as a middle- and high- schooler, my friends and I strategized carefully for the log flume.  We always put the heaviest people in the front.  Our reasoning:  we figured that way we'd go faster and get wetter.  Funnily enough, I don't remember ever performing a controlled experiment, or recording our results.  Perhaps I should return my Nerds of America membership card.

In retrospect, I think we had half of our conclusion right. 

I *think* that putting heavier people in the front does cause a bigger splash when the log flume hits the bottom, because the front end penetrates the water sufrace more easily -- fluid resistance generally depends on mass and surface area.  I have a wee bit of experimental evidence from last week's Disney trip. 

"Splash Mountain," pictured to the right, is essentially a sophisticated log flume.  As the temperature in Orlando had risen only to about 50 degrees farenheit, we wanted to minimize how wet we got.  And, as the temperature had risen only to about 50 degrees, we could ride pretty much as many times in a row as we pleased -- hardly anyone else was dumb enough to be in line.  We always sat in the last of the four rows.  It seemed as if there was a bigger splash when the front rows were occupied, though I cannot quantify the effect.  The only statement I can make for sure is that when people sat in the front row, they always got substantially wetter than we did.  So teenaged Greg was possibly correct about heavier people in front leading to wetter riders.

On the other hand, we were likely dead wrong on the issue of speed at the bottom of the ride.  The analysis will be different, I think, for a log flume and a roller coaster.  For a log flume, where the "log" is not particularly long compared to the length of the hill, one can probably consider the log as a point mass released from rest at the top.  The frictionless case is well studied in introductory physics -- the speed at the bottom will be root 2gh, where h is the vertical height of the hill, and so does NOT depend on the mass of the riders or the mass distribution.  (With air and water resistance the answer may change, but I'm not exactly sure how or how much.)

The roller coaster problem is more interesting.  Consider Big Thunder Mountain Railroad (covered in yesterday's post).  We do have to consider the mass distribution.  

On BTM, the train is hoisted up to the top of a hill, then released approximately from rest -- but not until most of the train has already gone well over the crest of the hill.  If the train is empty, or if the train has an approximately uniform distribution of riders from front to back, then its center of mass is somewhere near the center; the speed at the bottom will be root 2gh, with h measured from the center of mass's position at the top of the hill to the bottom of the hill.

Consider what happens, though, if we load up the heaviest riders in the front.  That moves the center of mass closer to the front.  When the train is released at the top, the center of mass will be lower than for a uniform rider distribution.  Thus, the h term is smaller, and the speed at the bottom is smaller.

If my analysis is correct, then the fastest speed should be obtained by putting heavy riders toward the back, so that they are right on top of the hill when the hoisting mechanism lets go of the train.  I don't have any experimental evidence, not even anecdotally.  (That's primarily because 37-year-old Greg can't ride even mild roller coasters more than once or twice without barfing.)

I know that amusement park physics is a popular endeavor.  A decade ago, I even took a few classes to the parks myself.  Now that we have wireless, portable, standalone probes like Labquest or the equpiment with Pasco's iphone app, it sure seems like hard data should be easy to acquire.  Has anyone done this?  I'd love to find out...


01 January 2011

Do you go "faster" if you ride in the back car of a roller coaster?

I just got back from a week of Disneyfication in Orlando.  See, I like Disney World.  From the time I left until I got back, I didn't once think about getting ready for the resumption of classes on Wednesday; and, I got to spend time with the seven year old Nachoboy without him complaining that I didn't play his game right.  The magic kingdom is special because it contains entertainment that he and I (and even Burrito Girl) all enjoy. 

In particular, the Nachoboy enjoyed Big Thunder Mountain Railroad (pictured to the right).  As roller coasters go, it's rather tame; no upside-downs, not an enormous drop.  Nevertheless, neither I nor Burrito Girl can ride more than about twice without feeling icky.  On a typical day last week, we would get up early to arrive precisely at the park's 7:00 opening so that we could take turns escorting the Nachoboy on Big Thunder Mountain over and over and over and over again.

At 7:00 in the morning, with only 20 people trying to ride, the operators were willing to give us our choice of seat, and were even willing to let us re-ride without getting off.  My first thought, to Burrito Girl's consternation, was to do a bit of physics...

Burrito Girl overheard an operator telling a rider that "you go faster if you ride in the back car."  Well, that's patent nonsense -- as you can see in the picture, the train of about six cars is attached together.  If the back car did go faster, then it would end up going through the cars in front of it.  That doesn't happen.  Q.E.D. 

Burrito Girl was unimpressed and unconvinced by this response.  "Look, I rode in the front and the back this morning.  When I was in the back, I felt myself thrown out of my seat when we went over the first big hill.  When I was in front, though, the ride was pretty tame."

And her observation makes perfect sense.  The whole train is always going the same speed at any given time, starting approximately from rest when the middle of the cart crests the first hill.  But by the time the back car crests the hill, the train has sped up significantly.

Consider a free body diagram of a rider when he crests the hill.  There's his weight pulling down, and the normal force pushing up.  The NET force, equal to his weight minus the normal force, must equal mv2/r, where r is the radius of the hill's curve, m is the person's mass, and v is the train car's speed.  Some brief algebra shows that the normal force is equal to the weight minus mv2/r.

So what is this "normal force?"  It's the force of the seat pushing up on the rider.  But it's also the "apparent weight" of the rider -- what a bathroom scale would read were the rider sitting on one.  The person's mass doesn't change regardless of the train's speed.  What does change is the v term.  Thus, the apparent weight of the rider gets SMALLER as the train's speed at the hill's crest gets bigger.

That's what Burrito Girl observed -- in the front, she crested the hill with minimal speed, and so her apparent weight was equal to just her regular weight.  Riding in the back, though, her train car had sped up by the time she crested the hill, so her apparent weight was smaller.  So, she felt lighter, like she was being thrown out of her seat.

Now, the front of the car is going just as fast as the back of the car all the time.  The difference is, roller coaster riders generally want to experience that feeling of a small apparent weight.  Riding in the back is thus the way to go -- not because you go faster than the front, but because you go faster AT THE TOP OF THE HILL.

Possibly another Disney-related roller coaster post soon.  Tomorrow I'll be in Birmingham, Alabama giving an AP physics workshop -- stop by if you're in town!