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24 February 2016

Projectile lab for conceptual physics

Astute readers may remember this post from 2010 about a projectile lab for general physics.  We used a set of photogates to measure the speed of a marble as it left a table.  When the marble hit the floor below the table, we measured the horizontal distance from the landing spot to the table with a meterstick.  A graph of horizontal distance as a function of horizontal speed is linear, and has a slope equal to the projectile's time of flight.  Some further kinematics calculations allow determination of the height of the table.

For my conceptual physics class, I changed the exercise a wee bit.  

I still had them collect data the same way.  If you're wondering, the two photogates are taped together, such that their apertures are 2.0 cm apart.  They are both plugged into a labquest.  The labquest is set to "pulse" mode, with 0.02 m programmed as the photogate separation distance.  The labquest spits out a speed each time the ball is sent through the gates.  

After each group produced a beautiful and linear graph with a bobzillion data points, I xeroxed their data table, handed a copy to each member of the group, and handed out this analysis sheet to each student.  We worked in class over a couple of days to answer the questions.  Each student had to answer individually, showing me as he finished each individual question.  Collaboration was allowed according to the five-foot rule; but straight-up copying not only wasn't allowed, it would have been ineffective.  Everyone had a slightly different best-fit line, and different table heights, to boot.

What was the difference between the 9th grade conceptual physics version, and the 11th grade general physics version?

Mainly, I didn't ask the 9th graders to calculate a slope.  I talked them through the analysis baby step by baby step, up to and including asking "what equation do we use for the horizontal motion, and why?" before allowing any calculation.  Then, instead of finding the slope and relating the slope directly to the time of flight, I asked them to use a point on the best-fit line (NOT a data point) to calculate the time the ball was in the air.

I helped these 9th graders carefully through the calculation, because this is more number crunching than we ever do.  But we are enough used to making a table and plugging into equations that most were very comfortable using a calculator to get the time in the air, and then the height of the table.  I just had to tell them that 80 cm is the same as 0.80 m.  

Aside -- Even though I didn't require or encourage any actual understanding of the unit conversion here, we did have some fascinating discussions of physical reasonability.  Those who plugged in distances in cm with speeds in m/s often calculated that the ball was in the air for 40 seconds.  A rare few said, "this doesn't make sense, what's wrong?"  Most just presented the calculation without comment.  So I asked them to count the 40 s the ball is in the air while I pushed a ball off a table... faces went red with embarrassment rather quickly.


Everyone eventually got a calculation of the height of the table.  I asked them to go measure the table height with a meterstick.  (Groups used different table heights, so this wasn't just a measurement for show.)  With the student watching, I calculated the percent difference between the prediction and measurement.  I stacked completed sheets in order from smallest percent difference to largest.  I will award a cheeseburger for the person whose prediction ends up closest to his measurement.

19 February 2016

Raise the stakes -- Get students to care deeply about their prediction

The scourge of the physics student is the tendency to get problems done merely for the sake of finishing the assignment, without really knowing or caring whether the approach is correct.  I'm asked all the time "Can I come to consultation period so you can give me more practice problems to do?"  I generally have to explain that it's not doing MORE practice problems that will help their understanding, it's paying careful attention to the practice problems that I already assign.

A couple of weeks ago I assigned this classic question about dragging a block at constant speed across a table: when I double the speed, what happens to the force I'm pulling with?  Most everyone generally gets this wrong on their first, individual attempt.  They revert to "logic" and "of course" in their justifications.  Even students who have carefully trained themselves to write facts of physics and connect those facts logically to the situation get the answer wrong -- they write a fact, yes, but then say "logically, of course, doubling the speed means doubling the force."  Or they write Newton's second law, TELL ME CLEARLY that acceleration is zero in both cases, then say "since the a doubled, the force must double as well."  

I'm not stating a new issue here -- all the physics teachers reading this are nodding their heads.  We will never get all of our students to answer this question the right way.   There's no magic, secret method that will turn all students into Newton's second law machines.   All we can do is use all of our tricks to maximize the number who do it right. 

Underlying all those tricks, though, is getting students to care very deeply about their prediction.  I often pose the thought experiment:  Will you bet $100 that your answer is right?  So often, the answer is, "sure, but let me change my answer real quick."  I then have the conversation about how they hadn't taken their initial answer seriously enough.

But that's a thought experiment.  Everyone knows I'm not REALLY going to bet them $100.  If nothing else, they know I'd always win.*  My point stands: there's no purpose in doing a physics problem if you don't really believe in your answer.  If students had to gamble money on the correctness of each answer, their problem sets would be vastly improved.

* I do get the occasional student willing to bet, reasoning that while I'd certainly win, they'd get their money back after I was sacked for gambling.

Given the prohibition against actually insisting our students bet money, can we instead set up a situation in which the students FEEL like there are high stakes to their prediction?

Some folks would put a grade on the line -- "this correct answer earns extra credit."  Sure.  But to me, that feels no different than grading their problem set.  If 4/5 of the students are already getting the answer wrong on a graded problem set, then clearly grades are an insufficient motivator.  The stakes have to be different.  Money isn't an option... but you have other "items" of value that you can use.

Last week I used gift certificates to the school snack bar.  Each certificate was for a single item -- a cheeseburger, order of fries, milkshake, whatever.  I've also used homework exemptions in the past; or, the ability to leave class early rather than work on a review packet.  These are all high-stakes items to my students.  They covet, ninth commandment be danged.  (Which is silly, when you think about it.  They're all paying some fraction of the astronomical school tuition to attend here, but they go nuts over a cheeseburger worth $1.65 at our subsidized snack bar.)

Now, here's the new bit -- I didn't just say "correct predictions earn a gift certificate."  No.  That wouldn't give the students any skin in the game.  There's not much given up if the prediction is wrong -- oh, well, no cheeseburger for me.

Instead I gave each student a gift certificate.  Everyone held, in his very hand, a piece of paper worth the coveted cheeseburger, with his name on it, even.  

Then, each student had to place his certificate on top of a card indicating one of the possible predictions: the force necessary to move the car will double, quadruple, or stay the same.  Only the certificates placed in the correct pile would be returned.

I've never seen such investment in the results.  You've heard the term "bear pit atmosphere?"  I've never been in a bear pit, but I've seen the reactions around a high-roller craps table.  Suddenly, my class was all nervous, excited, anticipatory... of the reading on a force probe.  The difference was, with the certificate in-hand, they were worried they might lose what they already felt like they had.  Why should there be a difference between "correct predictions earn a cheeseburger" and "here's a cheeseburger, now you can only keep it if you make a correct prediction?"  I know I've seen Nate Silver and his ilk discuss the psychological research.  I make no claims to know why this technique felt different, I only know that it worked. 

When, later that week, I had students write a correction on that problem, I got immediate, thorough, and correct justifications.  No more of this random wrong answer for the second and third time with a hangdog look telling me how hard physics is... this time, they remembered the answer and the justification -- because they "lost" a cheeseburger.  :-)

13 February 2016

Block sliding down a frictionless incline -- two different articulations of energy conversion.

A block of mass m is released from rest from the top of a frictionless incline a vertical distance h from the table underneath.  The incline is fixed to the tabletop.  Obviously the block speeds up as it moves to the bottom of the incline.  

In AP Physics 1, students will be asked carefully about energy conversion.  Depending on the system we consider, what are the "external" and "internal" forces?  How should we articulate the energy conversion that allows the block to speed up?

1. On one hand, consider the block alone.  It has zero kinetic energy to start, and some KE to end.   Thus, some force must have done work on the block.  (Since the we are considering the block alone, all forces acting on the block must be "external.")

The incline can't do work on the block -- the force of the incline on the block is perpendicular to the block's motion, so does no work.  The only work done on the block is from the force of the earth on the block -- gravity.  The amount of that work is the block's weight mg times the displacement parallel to the force's direction, i.e. the vertical displacement of the block h.  That work mgh is converted to the block's kinetic energy.  

2. Consider the block-earth system.  Now the earth cannot do work on the block-earth system because the earth is part of the system.  But the block-earth interaction produces a potential energy mgh at the beginning.  No work is done by external forces -- the only force external to the system is the force of the incline on the block, and that's perpendicular to the block's motion, and so can do no work.  The system loses mgh of potential energy, which is converted to kinetic energy of the block. 

09 February 2016

Rubric for a conceptual physics question for grading by peers

The table lists the coefficients of friction for four materials sliding over steel.  A 10 kg block of each of the materials in the table is pulled horizontally across a steel floor at constant speed.  Which block, if any, would require the smallest applied force to keep it moving at constant speed?

I asked this of my freshmen last week, as we come to a close in our Newton's second law unit.  We've done a large number of this type of problem, explaining the multi-step logic involved in justifying the answer.  This is not easy for a physics student of any level -- rather than simply applying a single fact or equation, this seemingly simple question requires students to make a number of connections.

An answer I'd expect:

Moving at constant speed means zero acceleration and net force, so the applied force is equal to the friction force.  The friction force is Ff = μFn.  The normal force on each block is the same, because with no vertical speed change Fn = weight, and all weigh 100 N.  So by the equation the smallest Ff takes the smallest μ -- that's copper.

I had students grade each others' work on this question to a five point rubric:

5 points:
¨  1 point for use of the equation Ff = mFn
¨  1 point for recognizing that the normal force is the same for each
¨  1 point for explaining why the normal force is the same for each (i.e. vertical net force or acceleration is zero)
¨  1 point for correct arrows OR several false calculations showing that we want the smallest m

¨  1 point for the correct answer

(That fourth point is phrased in language my freshmen understand and have seen before... for other physics teachers I'd say "1 point for showing how the equation supports finding the smallest μ.")

Now, you might come up with a bobzillion other valid rubrics.  I didn't give an explicit point for pointing out that the applied force must equal the friction force, for example; on another day I might have.  Five points for a single question on a problem set is a lot.  My students are expected to do four to seven problems of this type each night; I don't expect a thesis, just a few sentences using facts and equations which hit the important logical progression.  By the time I or classmates have looked at every problem most nights, plus all the similar in-class work, each student gets the feedback he needs to improve his understanding.

That is, each student gets that feedback if he looks at his graded work and gives a crap why it's right or wrong.  That's the holy grail of high school teaching, of course... leading our horses to water AND making them drink.  We need to deal positively and appropriately with the significant but frustrating population who keep making the same mistake over and over again, never listen to or care about feedback, but tell the universe with hangdog eyes how impossible physics is.

So that's why I have students grade each others' work.  Not only do they see the statements I'm looking for to award credit, but they have to read carefully for themselves to see whether someone else's paper meets the appropriate criteria.

I didn't "go over" this problem set -- because I would have helped just the one of the fifteen students in the class who was paying attention while I talked.

I didn't just post the solution -- because I would have helped the 0.3 of the fifteen students in the class who would take the time to look at the posted solution.  (And even then, I would have helped only five percent of the students who looked at the solution, because only that five percent looked more carefully than at the answer.)

I made the students grade each others' work, and I made them responsible for grading correctly.  The questions I answered in class were about how to apply the rubric.  Occasionally I would get a content question; my answer in those cases was carefully followed.  When I required corrections to the problem set, the students did excellent work, much better than if I had graded the set and passed it back.

Making students grade is one of the best ways to foster collaboration and a team atmosphere.  They realize quickly that correct answers aren't a matter of my opinion, that points aren't awarded randomly or arbitrarily.  The teacher is not the opponent -- rather,the class is working together to understand this mysterious natural world.  And I'll use every trick in my repertoire to foster such a positive and useful attitude toward physics class.

01 February 2016

US Invitational Young Physicists Tournament -- results from 2016

Shenzhen Middle School, USIYPT Champions 2016
The eighth annual US Invitational Young Physicists Tournament was held last Friday and Saturday, January 29-30, at Randolph College in Lynchburg, VA.  Eleven teams from around the world competed; results are listed below.

Phoenixville Area High School of Pennsylvania was atop the standings after the six preliminary rounds.  In the final rounds, Shenzhen Middle School, of Shenzhen, China, earned the championship trophy.

Champions: Shenzhen Middle School (pictured)
Second Place: Rye Country Day School, New York
Finalists: The Harker School, California; Phoenixville Area High School

Clifford Swartz Poster Session Champions: Nanjing Foreign Language School, Nanjing, China

Poster Session: 
Pioneer School of Ariana, Tunisia
Woodberry Forest School, Virginia
Phillips Exeter Academy, New Hampshire
High School Affiliated to Renmin University, China
Princeton International School of Mathematics and Science, New Jersey
Nanjing Foreign Language School, Nanjing, China
Cary Academy, North Carolina

I know that I and the USAYPT board thanks Randolph College, and physics department chair Peter Sheldon, for their extraordinary efforts in hosting and supporting the tournament.  

For 2017, the USIYPT will be held January 28-29 at the University of the Sciences in Philadelphia, hosted jointly by the university and by Phoenixville Area High School.  The problems for 2017 are listed below.

If you'd like information about participating -- either as a juror, or as the leader of a team -- please contact me.  A "Young Physicists Tournament" involves not just the presentation of research, but extensive discussion and conversation between teams about that research.  Teams are judged not only on the quality of their own research, but on their ability to communicate their understanding through asking and answering questions.  You will love it.

USIYPT Problems 2017

Granular materials
Build an apparatus that performs the following procedure: a rectangular container is placed on a vibrating base. The container is split into two equal parts by a vertical wall that is shorter than the outer walls of the container. An equal number of beads are placed in both containers at a level slightly less than half the height of the middle wall. As the base oscillates up and down at a constant frequency the beads jump above the middle wall from side to side; eventually they will all be in one side of the container. Explain this phenomenon and estimate how long the process takes for your apparatus.

Investigate the motion of a projectile inside a blowpipe.  Determine the conditions for maximum exit velocity when blown by the mouth.

Support a long, vertical tube containing water.  Heat the tube directly from the bottom and you will observe that the water erupts.  Arrange for the water to drain back into the tube to allow repeated eruptions.  Investigate the parameters that determine the eruption frequency.

Planck’s constant
Use LEDs to measure Planck’s constant, and explain the theoretical basis for your experiment. Measure the wavelength of the LED light directly, without relying on the manufacturer's data.  Describe the precision of your experiment and discuss if your margin of error covers the currently accepted value of the constant. You must build the experiment yourself from standard electronic parts, without relying on a commercially available Planck's constant apparatus.