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22 February 2017

Rank the voltages: experimental evidence

 The question: 

The three circuits above are all connected to the same battery. Each resistor represents an identical light bulb.  Rank the circuits from greatest to least by the potential difference across bulb A. If more than one circuit has the same potential difference across bulb A, indicate so in your ranking.

The (very much in-depth paragraph-style) answer: Since all bulbs are identical, they have the same resistance.  By Ohm's law with the same R for each, whichever bulb takes the largest current also has the largest voltage (i.e. potential difference) across it.  

The equivalent resistance of the parallel combinations gets smaller the more parallel resistors are added.  So circuit 1 has the largest equivalent resistance, with circuit 3 the smallest -- consider each resistor to be 100 ohms, and you get 200 ohms in circuit 1, 150 ohms in circuit 2, and 130 ohms in circuit 3.  

Bulb A takes the total current in each circuit, so consider Ohm's law for the circuits as a whole.  In that case, the voltage of the battery is the same for each; the circuit with the smallest equivalent resistance takes the largest total current.  So rank the circuits 3 > 2 > 1.

The common misconceptions: I gave this to my class as a quiz, and most got it wrong.  I saw four typical categories of wrong answers:

* Since the batteries are the same, each bulb in each circuit takes the same voltage.  (No, just each circuit as a whole takes the same voltage.)

** Since the batteries are the same, they each provide the same current.  (No, batteries provide voltage, not current.)

*** Since bulb A is closest to the battery, it must take the greatest voltage.  (No, "closeness" to the battery has no bearing on a circuit problem.)

So far, this is standard fare misconception-bustin' physics teaching.  Because I posed this problem as a quiz, the class waited expectantly for me to reveal The Answer.  Ho hum... those who got it right reflexively pumped their fists, those who got it wrong either made sad eyes, or used some sour-grapes reasoning to convince themselves why they could have gotten it right.  And then they forgot the whole thing.

Or did they?

"Okay, there are the light bulbs.  You know where the wires and power supplies are kept.  Go set up the three circuits and show me which bulb A has the largest current.  Take a picture of your circuits to show me."

Ah, sh*t just got real.  

The photos are by my student Clay Tydings.  He conveniently labeled bulb A in each picture.  Now we can all see that bulb A is brightest in circuit 3.  

To address the misconceptions above, you can have the students measure voltage across the battery, and across each bulb, with the voltmeter.  If you're brave, you can even have them measure current from the battery.  They'll see The Answer, that bulb A carries the largest current in circuit 3.

But they also see that (*) the bulbs take different voltages, (**) the battery takes the same voltage every time but different currents, and (***) the voltages across each bulb don't change even when we place bulb A "last" rather than "first" by switching the leads from the battery.  

I find myself asking the class to set up the experiment proposed by a quiz problem all the time in AP Physics 1.  We've established the class's lab skills; we have introduced and practiced all topics at a basic level; we have 90 minute class periods with which to work.  So why not make the students verify an answer experimentally?  The AP exam will certainly ask them how to design experiments!

16 February 2017

Mail Time: I can't find the other force acting on this block!

Reader Josh writes in:

The system shown is traveling at a constant speed.  There is friction between block B and the ground, and there is friction between block B and block A.  We've been arguing where the second force is in the horizontal direction on block A is, if it even exists.  The forward force on A would be the static friction but I'm lost on where the other one is.  This is driving me bonkers...

Have we written a bogus question? If not, can you tell us where we're going wrong?

Ooh, what a great question.  Constant speed, eh?  In a straight line, so equilibrium? 

I think we all agree on the BOTTOM block's free body:  normal force of ground on B upward, weight downward, contact force of A on B downward, force of rope on B forward, and friction force of surface on B backward.

There's no horizontal forces acting on block A.  If there were, it'd be speeding up or slowing down, which it's not.  

You say "the forward force on A is static friction."  Well, static friction takes on any value up to the maximum.  I agree that static friction must act WHILE THE BLOCKS SPEED UP.  Once they attain constant speed, though, the static friction force drops to zero.  If the block slows down again, then the static friction force on A will be backward. 

What a great AP Physics 1 question.  More complicated than you thought, I suspect.  :-)

06 February 2017

USIYPT results 2017 from University of the Sciences, Philadelphia

The 2017 United States Invitational Young Physicists Tournament was held last weekend, January 28-29, at the University of the Sciences in Philadelphia.  I can't thank the hosts enough -- Elia Eschenazi, Michele Albert, and the rest of the folks from USciences who helped out were most hospitable and supportive.

Congratulations to all, but in particular, to Rye Country Day School (pictured) and coach Mary Krasovec.  They won their second title behind a particularly strong presentation of their experimental measurement of Planck's constant.  

The final round scores and places, noting that by tradition the finalist teams share first through fourth place:

Rye Country Day School , NY         77 points, champions
RDFZ of Beijing*                             72, 2nd place
Phillips Exeter Academy, NH          71, 3rd place
The Harker School, CA                    70, 3rd place
Qingdao No. 2 High School**          68, 3rd place
Woodberry Forest School, VA          56, 4th place

* Officially The High School Affiliated with Renmin University, China; known also as RDFZ.
** First-time participants from northern China

The Clifford Swartz Trophy is awarded annually to the winner of the USIYPT poster session.  First-time participant Vanke Meisha Academy won this prize.

And this year, the US Association for Young Physicists Tournaments for the first time presented the Bibilashvili Medals for excellence in physics.  These are awarded not based on ranking among the schools, but on overall score regardless of place.  This year, in addition to the trophy winners and final round participants, Pioneer School of Ariana, Tunisia earned a Bibilashvili medal.

This was the largest tournament in the ten year history of the event, with thirteen schools participating, including:

Shenzhen Middle School, China
Phoenixville Area High School, PA
Cary Academy, NC
Princeton International School of Mathematics and Science, NJ
Nanjing Foreign Language School, China

What about 2018?

The 2018 USIYPT will be held on January 27-28 at Randolph College in Lynchburg, VA.  The four problems involve measurements of the moon's orbit, coupled mechanical oscillators, projectiles in air, and radiation from incandescent light bulbs.  Full problem descriptions are shown at the USAYPT problem master's blog. 

If you'd like to know more about the USIYPT -- a physics research/debate tournament for high schools all over America and the world -- please contact me via email.  We're particularly interested in recruiting physics teachers, professors, graduate students, and industry physicists as jurors.  


Physical versions of energy bar charts

Like many of us, I use energy bar charts extensively.  Though my students don't all understand every detail of them all the time, the charts are the best way I know of to get them to stop plugging numbers into equations and think for a moment about how energy is transferred.  Just as "why don't you draw a free body diagram" generally gets students un-stuck on a force problem, "why don't you draw an energy bar chart" usually sets everyone on a path to success when energy is involved.

My personal touch on the energy bar chart is to insist that each bar be annotated.  Even just a couple of words help, like "it's moving" under the KE bar, or "at its lowest position" when the PE bar is zero.
Still, I don't have the sense that my class internalizes the deeper meaning of the bar chart: that the total energy on the left side, plus the "work done by external forces" column, must equal the total energy on the right side.  They know only because I tell them repeatedly; it seems an afterthought for my students, rather than the entire raison d'ĂȘtre for the chart.

How can I help my students understand intuitively that bars in the chart must be transferred among columns rather than just drawn randomly?  How can I help them see that the "work done by external forces" column is the only place where it's okay to add or remove bars?

Kelly O'Shea and Chris Becke -- and I'm sure others, but these are the ones I've seen recently -- have made physical versions of the bar chart.  I'll show you both...

Physical energy bar charts from Kelly O'Shea, @kellyoshea
Kelly tweeted this picture.  Her setup seems so simple: just a bunch of wooden blocks, pegs, and post-it labels.  Simple, maybe, but elegant.  Each setup is just the right size to put on a lab table for each small group to use in their problem solving.  I can imagine asking each group to take two pictures of the blocks: one representing the initial energy configuration, and one representing the final energy configuration.  Then I could ask something like "why are there two more blocks in the second picture than the first?  Where did they come from?"  And I'd expect an answer referencing work done by external forces.

Water-based energy bar charts from Chris Becke, @beckephysics
Chris uses water in labeled beakers to represent energy.  By setting up in the front of the classroom by the sink, he can explicitly show how work done by external forces affects a system's energy status.  Look at his labels; the faucet is "+work" and the drain is "–work."  My students when they draw bar charts can just magically sketch a few more lines in the "Wext" column to add energy to a system.  Kelly's students have to at least physically grab or throw away extra blocks.  But Chris's setup requires turning on the faucet, or dumping water down the drain, in order to include work done by external forces.  The meaning of "external" just got real.

I don't mean to suggest that either Kelly's or Chris's physical bar chart approach is the superior one.  I'd personally use Kelly's blocks in my bog-standard style of class in which students and small groups work on predictions and experiments; I'd use Chris's faucet-based chart on occasions when I want to present demonstrations from the front of the room.  

I *do* mean to suggest that if you're going to use energy bar charts as a teaching tool, I think it's worth setting up some form of physical bar chart rather than just drawing on paper.  I'm gonna have to try these.