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18 March 2023

Mail Time: Does AP Physics 1 include rotational kinetic energy when rolling without slipping? And how carefully do I follow the AP1 course and exam description?

[Paraphrasing a correspondent...]

Dear Greg: I read online that, for AP Physics 1, "rolling kinetic energy is not required."  Is that correct?  What do AP1 students need to know about rolling?  Do you completely abide by the course and exam description in your AP1 course?

Rotational kinetic energy is definitely part of the AP Physics 1 exam!  Generally the problems involving rotation, like all AP1 problems, are qualitative and not quantitative.  That is, a student might be asked to describe the differences in energy conversion between a block sliding down a ramp, and a sphere rolling down a ramp; or, how an atwood's machine behaves differently with a massive vs. a low-mass pulley.  But here's the quotation I found in the course and exam description:

"A full dynamic treatment of rolling without slipping—for instance, using forces and torques to find the linear and angular acceleration of a cylinder rolling down a ramp—is not included in Physics 1."

A physics 1 student should be able to draw an energy bar chart for a cylinder rolling down a ramp, explain what forms of energy exist, and how we know they exist.  A Physics 1 student should be able to explain that the friction force of the ramp on the cylinder provides a torque around the cylinder's center of mass, and thus causes an angular acceleration, and thus causes the sphere to increase its rotational kinetic energy.  But the quantitative problem in which they write mgh = 1/2mv*2 + 1/2Iw^2, plug in w = v/R and the formula for the rotational inertia of a cylinder, and solve for v - that's an AP Physics C-mechanics question, not AP Physics 1.

I do cover everything in the course and exam description for physics 1, though in a unique order - for example, see this post or this post for examples of how I simplify concepts at the beginning of the course, and then add detail in the second half of the year.  And that course and exam description is not well written for an audience of teachers.  (It's much better as a guide for those who write the test, but for a teacher, it is too often impenetrable.)  For now, the best guide as to what you need to teach in your class is to look at recent exams; or, I've published my "fact sheet" in the 5 Steps to a 5 prep book.  That book is directly aligned to the exam, but everything is written in language that students and teachers can understand.

The College Board is publishing a new CED for the 2025 exam, or perhaps 2026 - no final word yet.  That one will be much more clearly written - I've seen a draft.  But for now, I'd use the 5 Steps book, or your own instincts from reading previous exams, as a guide for what's necessary in your AP1 course.

14 March 2023

Jurors wanted: 2023 Conceptual Physics Tournament, on May 21. We pay $100.

UPDATE May 10 - We are full - we've got enough jurors for 2023!  We will get you next year.

In my school's conceptual physics program, we give cumulative written tests after the first and second trimesters.  In lieu of a final exam*, we are once again running the Woodberry Forest Conceptual Physics Tournament!  This is a competition for 9th graders, to be held at 1:00 on Sunday May 21 2023.  We've done this before, including last year after a pandemic-enforced break.  We're happy to be back to annual.

*No, to be clear to all, we're not giving an A to the winner and an F to the person in last place.  That's silly.  We're just having a fun, competitive tournament, to determine a winner.  Jurors engage in discussion and conversation with participants about their problems.  Jurors then award scores and write comments for the participants; jurors aren't assigning grades!

How does this tournament work?

On May 1, I will reveal a slate of three problems to the 72 participants.  These problems will be in the style of AP Physics 1 "paragraph response" questions.  Except, rather than just answer in a paragraph, the students will spend the month of May setting up experiments to provide evidence for their answers. By tournament time, each student will be expected to be prepared to discuss the solution to two of the three problems, with both theoretical and experimental support.

At the tournament, each student will participate in two "physics fights."  Think of these physics fights like a miniature version of a graduate thesis defense.  Students will have a strict limit of two minutes to present their solution to a group of two or three jurors, who then will engage each student in conversation about the problem for five minutes.  The students are evaluated by the jurors not only on the quality of their solution, but also on their ability to discuss the solution, to confidently hold a conversation with the jury.

Importantly, jurors are explicitly instructed on their primary role - to find out how much the students DO know, not merely to expose what they don't know.  

How do the students prepare?

Starting on May 1, all conceptual physics classes the rest of the year will be devoted to tournament preparation.  They'll set up experiments in class, they'll be assigned to write up their solution as homework, they'll practice presenting.  

Most importantly, our AP physics classes will spend their final weeks of the school year serving as mentors to the conceptual students.  I will assign each AP student to lead groups of two or three 9th graders.  The AP students will dive into the problems with the conceptual class, helping to create and analyze experiments, helping the freshmen to understand the details of their presentations, and serving as mock-jurors in practice sessions.  This mentoring serves as the final project in lieu of the exam in the AP classes.

We need jurors.

The key, I think, to any class project is external assessment.  I and the other conceptual physics teachers will play the role of coach and advocate, always encouraging and helping the students to deepen their understanding of the problems and to improve their presentations.  Our relationship will be purely supportive, enthusiastic, positive.  

We can't then turn around and grill these same students as examiners!  That'd be like our football team's coaching staff refereeing the state finals.  Even -- especially -- if their officiating were fair, the coach-student relationship, both in before and after the game, would be irrevocably compromised.

So we need jurors.  We can pay.

Would you like to come to Woodberry on May 21 to be a juror?  We'd ask you to arrive at lunch time, like 11:30.  We'll have a meeting of all jurors in our beautiful dining hall over lunch.  

Then we'd ask you to be a juror for a couple of hours' worth of physics fights.  You'll be partnered with several other examiners over the course of the afternoon, getting to know a diverse set of fun folks from all over.  When all students have presented their two physics fights (to two separate juries), we'll gather the jurors for conversation, coffee, snacks, and their paycheck.

In any case, our goal is to be done by 3:30, or possibly 4:00 if there are logistical issues.  No later -- our students will be attending the final seated meal with their advisors that night followed by study hall, so we can't run late.

We will pay you $100 plus lunch for your time.  (If you're coming from more than a few hours away, we can put you up on campus on Saturday or Sunday night.) I think you'd find that the camaraderie among the jurors and the engagement with the students will make the trip worthwhile.

Who's eligible as an juror?

Anyone who has passed a college-level physics class.  This includes alumni of your advanced physics class, even if they're still juniors or seniors in high school - we've had several teachers bring a van of students, and they've had an awesome time.  We've had local college or graduate students on juries, we've had parents, alumni, colleagues who teach other subjects, grandparents, friends... Anyone willing to engage in conversation about physics at the high school level, as long as you can recognize good and bad physics, we'd love to have you.  We are looking for a diverse juror pool, which especially includes diversity in age - truly, we want folks in their teens as well as folks in their 70s, and everywhere in between. When I ran the USIYPT, I found the mixture of undergraduate / graduate / professor / high school teacher / industrial physicist / retired physicist on the juror panel allowed some amazing relationships to develop.  I'd love to create a similar vibe here.

How can I sign up?

Send me an email via greg dot jacobs at woodberry dot org.  I'll send you more information, including the three problems, and our current draft of the scoring rubric.

We would like to get 54 jurors - the first 54 who sign up.  I can't wait to see some blog readers!  I'll even introduce you and your students to my pet hippopotamus, Edna.  :-)


13 March 2023

Biology position open - know someone who wants to teach in my department?

Hi!  If you are reading this, you may know that I'm science department chair at Woodberry Forest School, a boarding school for boys in central Virginia.  Our long time biology teacher is retiring, and we're looking for someone to join our department.

Teaching at boarding school is, well, different from teaching in a day school - different in a way I find particularly appealing.  Our mandate is emphatically NOT to prepare students for a state or standardized test; nor to get students in to the right college that allows their parents to brag.  The fundamental job description is that we are to "know, challenge, and love" the students.  There's no state or other certification required, no formal checklist of prior experience.  We want people who enjoy being around and mentoring teenagers, teenagers from all over the US and the world, teenagers whose backgrounds are diverse in almost every way imaginable.  That's the whole job...

Our faculty are well taken care of.  Housing is provided, as is food, utilities, and even - if you live on dorm - satellite television and basic housekeeping service.  The school will pay for pretty much whatever professional development you'd like to undertake, at your discretion.  We work hard when the students are on campus, coaching (or an arts or sciences equivalent) two seasons, and standing dorm duty once every eight evenings; but know that is a far smaller commitment than is expected at many boarding schools.  Most importantly, we get more long, no-obligation breaks than at any other school I've seen: 1.5 weeks at Thanksgiving, 2-3 weeks at Christmastime, two full weeks for spring break, several four- or five-day weekends... and no summer obligations between the final faculty meeting on June 5 and the opening meeting on August 22.

In terms of biology teaching, our science faculty teach three full-year sections of 14 or so students each, usually with only one or two preps; plus one half-year section of "science thesis seminar."  The three biology sections could be the general 11th grade low-level introductory course, or could be our advanced course for top-end students, depending on the interest and ability of the candidate.  Then Science Thesis Seminar is an immersive course with 5-7 hand picked students, which can be truly anything you want, including research in an area of your interest, a deep dive into some aspect of science you enjoy, whatever.  Our goal throughout the science department is not merely to talk about science, but to *do* science.  We have all sorts of equipment such that laboratory activities can be the ground state of class rather than a rare event when the class absorbs high-energy photons.*

*Sorry, physics reference when pitching a biology position.  I am what I am, I guess.  :-)

Think of our school as a modern, secular monastery, where the "monks" come in all genders and family situations.  I do mean secular: the school was "founded on Christian principles," which in practice means that we are all asked to be kind to each other.  We have an honor system that actually works, such that students truly don't lie, cheat, or steal.  (On the rare occasion in which someone does these things, that someone is immediately asked to leave the school.)  Our academics are 100% evidence based.  We welcome, and our community includes, faculty and students of all sorts of religious persuasions.  

For this biology position, we're casting a very wide net.  In particular, we would be thrilled to take someone right out of college or graduate school who is excited to try their hand at teaching.  

I truly do mean it about casting a wide net.  I attended public school in Kentucky; I had never really heard of boarding schools other than in fiction; I'm not Christian; and I did not intend to make central Virginia my home.  Yet they sold me (and my then-fiance) from the moment we stepped onto campus.

Do you know someone who might be interested?  Have them contact me via greg dot jacobs at woodberry dot org.  I'd love to answer their questions, and to put them in touch with our Dean of Faculty.

12 March 2023

The Physics Adventures of Edna & Bertha - Episode 1

 


During the Pandemic, I did live AP Physics 1 exam prep shows on the College Board's Youtube channel.  Two audience members in particular maintained correspondence with me for a short time afterward: Liliana Gordan, and @aldescery.  The art above was drawn by @aldescery after I had joked in a show that there should be a spinoff called The Physics Adventures of Edna and Bertha.  She thought the idea had promise!  Then, Liliana arranged to zoom with me several times to help develop a plot outline for an "episode."  

Ideally, this would be an animated series based on @aldescery's artwork.  However, until a studio steps forward with a zillion dollar check, I'll stick with writing episodes as short stories.  

The episode below is based on the 2017 AP Physics 1 exam, problem 3.  Liliana came up with the framing device, including the human characters (other than Greg, of course!).  She wrote a first draft of the beginning.  I edited that, and wrote the rest.  

Hope you enjoy!


Emmy, Bri, and Andy lounged around the desks inside the physics classroom.  Their teacher was out making his lunch, but the trio stayed, scribbling notes to each other on scrap paper.  A debate was in progress.

“Look, can we take a break?” asked Andy.  “We’re talking in wider and wider circles.  I’m just gonna use mvr and be done with it.”  Emmy looked to the sky.

“OMG, Andy,” she said.  She actually said the letters, oh - em - gee.  “Your pet equation is just for a point object.  This is a rod!   How is a rod a point object?”

“I can point it at you, I can,” Andy said with a smile.  But he did pick up a meterstick and point it across the desks toward Emmy.  Emmy made a soft bear growl.

They both looked at Bri, who had been quiet for a while.  Emmy pled her case. “Come on, Bri, what do you think?  Shouldn’t we be using L = Iw for the rod’s angular momentum?”

Andy’s rebuttal: “Not only is Emmy using the wrong equation, she even wrote a doubleyou rather than an omega.  Look at the pointy bits!  It’s not “eye omega”, it’s mvr, I know it.”

Bri didn’t respond right away.  To her relief, the classroom door opened right then, cutting off Emmy’s forthcoming riposte.  The three physics students saw a determined little girl enter.  She had big brown eyes, a  blue and yellow floral, frilled skirt, two big buns, and a bright smile. She carried a worn, knitted green cloth grocery bag on her shoulder—something seemed to click inside it. She looked over at the group, beamed with a wide grin, and sprinted across the room to grab a chair at their table. 

She sat down.  “Hi!”

“Hi,” all three students said, laughing nervously. 

An awkward silence followed. Emmy, Bri, and Andy stared at each other.

‘Who is this kid?’ ‘Don’t look at me.’

The little girl broke the tension. She pointed at the paper on the table. “What’s that?”

“Our homework.” said Emmy. 

The girl giggled. “It looks really cool.”

“Thanks.”  Emmy continued to talk to the little girl, with Andy joining in. Both politely fished for clues. The girl’s answers seemed purposefully vague. Is she lost? No. Is she a teacher’s kid? Not exactly. 

Emmy and Andy became ever more unsure, the little girl ever more amused. 

Bri remained silent, observing the three jars in the little girl’s green bag: One seemed like a store-bought jar of pickled jalapeno peppers; the second, like a homemade jar of canned pickles; and the third, like it was half full of jelly beans. Bri looked at the girl with a distant familiarity. Then she remembered.

“Oooh!” Bri palmed her forehead. “Aren’t you Mr. Jacobs’ niece?”

“Yep,” she smiled

.“Yeah I remember him mentioning you and your collection.”

“Oh right!”  said Emmy. “Why didn’t I think of that? You’re the homeschool girl he’s always talking about.”

“Why didn’t you tell us that?” asked Anthony.

“I wanted it to be a game!”  The little girl giggled.

“What’s your name?” asked Bri. 

“Charley.” 

***

“My school is over today, but I get to come to physics class with the high schoolers!  I love physics, just like Greg does!  Nice to meet you Bri!  And who are you?”

“I’m Emmy, and this” —she gave an only sorta-playful punch— “is Andy.  Who were you talking to there?”

“This is my pet hippopotamus Edna.  Say hi to Edna!”

Emmy saw Charley remove what looked like three glass jars. She lovingly placed them on her desk as she talked softly to them.  Emmy saw that the two pickle jars had bows on the lids, one pink, one blue; and that the jelly bean jar was on its side.

“Hi, Edna,” said Emmy.

“And this is Bertha, who is a very nice elephant, and this is Anthony.  Edna says he’s a mean hippopotamus.”

“And why does she say that?”  asked Emmy.

Andy couldn’t hold his tongue any longer. “Because he’s a jar of jelly beans?”  Everyone looked at him.  Charley growled.  

“He’s a HIPPOPOTAMUS.  Not everyone can look beautiful like Edna and Bertha do.”

“But…” Bri glared at Andy, and Emmy punched his arm again, just a little bit too hard. “Okay, okay, I like your hippos, Charley.”

“And Bertha!  She’s an elephant, and she’s very smart.”

The bell rang for the start of class.

***

“Hi, all!  So, here’s the question you did for today.  In part (a), we’re asked where to hit the bar to produce more rotational speed—left or right of point C?”

“Left of point C, near the pivot!” says Andy.  “The pivot is the key spot! Hit it there!”

“Huh, said Charley softly, but not so softly that the other students couldn’t hear her. That’s what Anthony said!”  Other students laughed hesitantly at the idea of Anthony speaking.”

Emmy spoke up.  “But to apply more torque, you’d want a longer lever arm, so farther from the pivot!”  She sighed, and glared at Andy.

“Emmy’s right,” Bri said.  “We can also think of angular momentum conservation.  The angular momentum of the disk is mvr because it’s a point object, and that angular momentum is Iw of the rod/disk after collision.  To get a large omega, we need a big r—and r represents the distance from the pivot at collision.”

“Yeah, Bertha agrees with you, Bri! And she’s the best of my friends at physics.”

“You mean the best jar of pickles?”  Andy asked.  He wasn’t particularly happy about being disagreed with.

“Bertha is NOT a pickle!  She’s the best elephant in the world!  You be nice to her, Andy, or Edna will charge at you.  Hippopotamuseses are the most dangerous animals in the world when they’re angry.”

“Shut UP, Andy”, said Emmy.  “Be nice to the little girl and her pets.”

Charley turned her back to Andy as the bell rang to end class.

***

“Guys.  Pirate Larry is causing trouble again.  He’s trying to shut down the school.”  Bertha’s face seemed grayer than usual.  

“So?”  said Anthony.  “We get a day off of school.  I could use a break.”  

“Thinking of yourself as usual, eh, Anthony?  What about us?  What about Charley?!?  If Pirate Larry manages to shut the school down, she will be so lonely… she loves us, but she needs human friends, too.  Oy, Anthony, sometimes you are such a mean hippopotamus.”  Edna was not happy.

“But…” Anthony realized the truth of what Edna said.  “Humph.” he said.  Anthony folded his arms and sat quietly to listen to the rest of Bertha’s report.

“This time, he has a homemade snow machine.  He’s trying to dump a meter or more of snow on the Superintendent’s house so that school will be called off tomorrow!”

“Well, that’s easy enough to foil,” Edna said.  “I’m headed to Larry’s Lair to shut the stupid snow machine off.”  

“Yeah, sure, easy as that, right,” said Anthony.  How do you even know where Larry’s Lair might be?”

“Anthony, you know how hippopotomusses who aren’t lazy go on safari regularly?  See, there’s a watering hole in the abandoned rock quarry just out of town.  I saw Larry’s Lair’s lights one night, when he thought he was all alone.  Come on, we’ve got to get there while there’s still time.”

“Ooh, calling me lazy, eh?  I happen to be ready for action at any time!”  He pulled out a mask, plastic sword, and makeshift rubber helmet from his toy drawer. “Engarde! Il y a un poisson dans votre bibliothèque!”   

Edna rolled her eyes theatrically.  “You look like a bowling ball,” she told Anthony.  Come on, Bertha, at least I’m taking this threat seriously.  Let’s go stop the snow.  She headed east.  Bertha followed immediately.  Anthony looked around, realized they weren’t kidding about heading into danger; and that Charley was sound asleep, oblivious of the ungulates’ presence or absence.  So he, rubber helmet and all, rolled into action as well.  “Wait up!  I’m coming with!”

*** 

Pirate Larry’s plans were opaque to most people.  His lair was built into the highest layers of the quarry’s rock wall, visible only from the watering hole at the quarry’s bottom. 

Edna snuck nearer and nearer to the quarry.  Contrary to what many folks think, hippopotamuses can move quite stealthily.  She looked over the edge.

There he was.  Pirate Larry, the monster who had one day caused every fire alarm in the school to sound 30 seconds after anyone entered the stalls in the second floor bathroom in the science wing.  Who set the school bells in each classroom off by just the right amount such that the end of fifth period happened in a longitudinal wave that propagated across the school for 12 minutes.  Who had created a Ceiling Roomba to sweep Mrs. Smith’s room, raining down all 236 pencils that had been stuck there by Joey Jackson and his bored friends in the back row.

“He looks like a big onion. He can’t even walk! He hops around!”  Anthony was shushed by Edna.  More quietly, he asked, “How do you know he’s a pirate?  It’s not like he’s wearing an eyepatch or anything.”  

Bertha said, “You know how some people call you a jellybean?”

“Some people who are very wrong call me a whole jar of jellybeans!”

“Well, it’s the same for Pirate Larry.  Some people who are very wrong think he’s a harmless Vidalia Onion who can’t move or talk.  And that’s how he gets away with so much mischief.  People underestimate him.  Like they do us.”

“Shhh, Bertha!  He’s coming!”  

***

“Huh-HA!” shouted Larry. He stood at the entrance to a makeshift shed, inside which was a contraption.   “It’s ready, CrabbyCrabbyCrabbyCrabby!  See, the fancy ski resort up the mountain uses bespoke-engineered snow guns that fire high pressure water and air, properly designed for safety and functionality, making the snowmaking experience simple, wet, and white.

But sometimes, CrabbyCrabbyCrabby, sometimes, I wake up in a disused landfill, collect a decrepit box fan and a moldy fridge, hotwire ‘em both to a leaky methane-fueled generator, and create the budget ski lodge smelly localized snow storm that will… SHUT DOWN THE SCHOOL!  Huh-HA!

“Who the heck is he talking to?” whispered Anthony.  Bertha didn’t speak, she just pointed with her trunk.  Next to the onion-shaped pirate sat a horseshoe crab.  Or perhaps just a horseshoe crab skeleton?  It was hard to tell from this distance.  It must be a skeleton, right, because Larry’s Lair was hundreds of miles from the nearest saltwater.

With a huge, strong, onion-shaped muscle, Pirate Larry shoved the door to the shed.  It flew around its pivot, the generator hummed to life, and a cloud of snow shot out of the gun.  Way up in the air it fountained, toward a mansion several hundred yards from the quarry.  

“That’s the Superintendent's house!” Bertha said.  “Look, there’s already a few centimeters of snow on the lawn!  Oh, no.  This really is going to shut down the school!”

Larry picked up the crab, or its skeleton, and walked deeper into his lair.  “Let’s go get a soda, CrabbyCrabbyCrabbyCrabbyCrabby.  My plan has decommenced.  Or, commencated.  It’s underway, anyway.”

“I thought he had discovered us when he shoved the door,” Edna said quietly.  “Phew.  My heart can go back to normal hippopotamus frequency now.”

“I thought you like thrills, Edna,” Anthony said. “You’re always the daredevil who rides the physics demonstrations!”

“Yeah, but I trust that physics demonstrations work, because I understand the rules of physics.  Pirate Larry doesn’t have any rules.  Come on.”  Edna carefully sidled up to a shed door.  When she was sure Larry was nowhere near, she beckoned the others to join her.

“Look here, Bertha!  There’s a big photogate above the door—it gives an instantaneous speed readout on that screen.  Bertha waddled over to inspect the screen.

“Yup, and there’s the trigger speed—that big heavy door has to go 88 cm/s or faster through the photogate to turn the generator on or off.  Think we can do that?”

“Of course we can,” said Anthony.  Just shove the door near the pivot.  Easy.  Watch me!”  He did shove, the door did move… moved 13 cm/s.  “Oh.  That door is heavier than it looks.

Back came the door to its original spot.  “Time to try again,” said Edna, “but this time let’s be smart about the physics.  Larry can provide a lot of torque on the door about the pivot, because he’s so strong he can apply a large force.  We’re not as strong as Larry, but we can apply a force with a large lever arm!  That should make some serious torque!”  Edna pushed at the edge farthest from the pivot—still only 40 cm/s.  “Hrrummm,” said Edna, which is a fierce hippopotomus curse.

“Okay, I’m getting desperate.  If I run at the door instead of just shoving, then my angular momentum about the pivot will transfer to the door— that should make the door go faster!”

“Edna, what are you gonna do, run in circles?  Pshaw.  If you’re running in a straight line, you won’t have any angular momentum at all to cause a change in rotational speed.  Phthph.”  Anthony always was so sure of himself.

Edna opened her mouth to categorize this latest Anthony comment on the Mean Hippopotamus scale, but Bertha jumped in to keep the peace—and to keep the argument from escalating when they needed to be very, very quiet.  “Anthony, Edna’s right—a point object moving in a straight line has angular momentum mvr, with r the closest distance from the pivot.  Her idea could work.  Let her try it, and be quiet whether it works or not, okay?  We do NOT want to be captured by Larry.”  Even the brave and noble elephant shuddered visibly at the thought.

And so, Edna took a running start, grabbed the door at the far edge, swung through the gate… and only got 62 cm/s.  Edna’s eyes seemed a bit moist to the others as she let go and sat on the dirty ground, staring despondently at that glowing screen.

That’s when Edna saw the equation.  “Bertha!” she hissed.  Look at this!  I think this is an equation for the speed of the door as a function of other stuff!”

“What other stuff?” Bertha asked.  Into the room she came, instructing Anthony to stay outside on lookout.  “Make animal noises if something happens.  I need to see this equation.”

Bertha saw.  “Hey, the mass of the object colliding with the door is in the numerator.  That means, the heavier the colliding object, the faster the door will move.  I’m much more massive than you!  I’ll run at the door.”

“But Bertha, you know you don’t like riding things… look, I can put some rocks in my pockets. A few hundred ought to do it.  I’ll make it work.”

“Edna, it’s gotta be done.  Stand away from the door.  I’ve got this.”  And so the very large elephant dipped her blue bow low… and charged at the door.

Bertha leaped, grabbed onto the door, swung through with a great but inadvertent trumpeting… and the door did indeed move faster through the photogate.  Up to 75 cm/s.  

Not enough.

And now Bertha sat swaying on the dirt.  She couldn’t quite focus her eyes, but her brain kept a very focused focus on the serious nausea messages coming from her tummy.  Oh, oh, oh.  The other ungulates knew from long experience how susceptible Bertha was to motion sickness.  Elephant upchuck was possible at any moment now.  And the snow piled ever higher around the Superintendent’s house.

Edna and Anthony began to make whatever sounds they thought the local fauna made (“Hoot, hoot?  Nah, no owls, not enough trees.  “Wiggle wiggle?” “What animal makes that sound?”  “There are worms around here, I’ve seen them.” “And they say ‘wiggle’?  Oy.”)  around the quarry, frantically trying to alert Bertha to the incoming danger.  But if she heard, she could not physically act.  She sat there, now gray-green in the face, while her nemesis hopped inexorably from the soda room.

Pirate Larry stood before Bertha the Elephant.  His beady onion eyes seemed to bore into Bertha’s very elephant soul.  Bertha tried to stare back, but her eyes rolled.  She covered her mouth with her trunk, and stared instead at the dirty floor.

Pirate Larry taunted Bertha.  “Ah, Bertha.  Who entered my lair uninvited and unwanted.  Please do not remagurgitate—reguglitate—barf on my floor.  Pickle juice is so, so difficult to clean up.  Huh-HA!  But you’ll be doing the cleaning up, because you are in my clutches, Bertha who is nothing but a jar of pickled pickles.  

“You amost upset my grand plan, oh Bread and Buttered One.  Yes, you managed to figure out how my special snowing machine works, but you did not figure out how to stop it!  Oh, you might be good at physics, but what good is “good at physics” if you can’t prevent my insidiousness from insidiousing? 

"And now, you are helpless as the snow approaches three feet deep.  Huh-HA, Bertha the physics “elephant”, three feet, not a meter, because I use outdated units based on the size of a king’s foot.  And you don’t even have a feet, you have hooves!  Huh-HA!  Perhaps I should make the snow twenty elephant-ears deep!  

"My jury-rigged snow machine is WORKING!  Huh-HA!  I’m ready to turn it up, and to bury the Superintendent’s house. Yes, I’m ready!!  But first, I will taunt you a second time.

Edna broke down in tears.  All her, and Bertha’s, bravery had been for naught.  Poor Bertha!  Pirate Larry might do anything to her, once he ceased his obsession with the snow machine.  But Edna could do nothing.  She couldn’t make the door go any faster!  And she couldn’t figure out how to rescue her friend.  

Meanwhile, Anthony took stock of himself.  He heard Pirate Larry begin his second taunting.  He saw Edna’s hippopotamus tears.  He saw that he looked like a baby hippo in a Halloween costume, a costume so silly that the baby hippo himself must have made it.  The rubber helmet looked ever more ridiculous as the gravity of the situation caught up with Anthony.  He hadn’t been taking this adventure seriously at all.  And now his elephant friend was seriously in trouble.  

Anthony got mad.

With a Hrrummmm! so loud that even CrabbyCrabbyCrabby seemed to turn his head toward the sound, Anthony charged at the door.  His arms flailed wildly as he reared up in a final leap.  

But Anthony’s wavy wavy arms couldn’t grasp the door.  His body twisted midair, so in the event it was Anthony’s silly rubber helmet that hit the door, well, head-on.  

Anthony bounced backward, nearly as fast as he had been running.

The door swung.  Noticeably faster than even Bertha had managed.  The photogate triggered - 120 cm/s, it read.  The snow machine creaked, shook, and stopped.

The door kept swinging, though, by Newton’s first law for rotation.  It bopped hard into the onion tuchus of Pirate Larry as, mid-taunt, he stood over the retching Bertha.  Larry spun around involuntarily, rotating nearly 18 radians in barely a second before collapsing.  Now there were two sick beings on the floor of the lair.

While Anthony picked his stunned self off the floor, Edna alone kept her wits.  She raced through the door before it could reset.  Out came the emergency motion sickness tablets, which Edna always brought when she was with Bertha, the same way some folks carry epipens.  Bertha gratefully, but not gracefully, hauled herself off the dirt floor and staggered toward the lair’s entrance.  

A moment later Edna was supporting an elephant under one leg, and a mean but groggily heroic hippopotamus under the other, as the three ungulates swayed and lurched away from the quarry.

“Arrrrrrrrrrrrrrrrrrrrrrrrrrrrr!” came the sickly piratey moan of frustration from Larry’s Lair.

***

Edna helped Bertha lean against Charley’s bed, where Bertha fell asleep instantly.  Edna gently led Anthony to his full if slightly stagnant bathtub, where he took off his equipment and got in.  (Like all hippopotamuses, Anthony preferred to sleep underwater.)

Edna tried to stay on watch for a bit.  But she soon gave up and got into her own rather more sanitary sleeping pool.

***

“Good morning, Edna, who is a very nice hippopotamus!”  Charley helped Edna dry off, and then re-tied Edna’s pretty pink bow.  “You look like you had quite a night—your bow was very ruffled!  Please wake up Bertha and Anthony while I get dressed to go to school with Greg!”

Bertha was already up and about.  “Edna, what are we going to tell Charley!  She’s going to be so disappointed when she sees the weather report.  And the school closings.  Anthony’s brave charge may have stopped the snow and briefly stunned that terrible onion being, but all Pirate Larry had to do was trigger the photogate again.  He’s had time to put meters of snow on the Superintendent's house by now.  That’s impossible to dig out of!  Even if there’s no other snow in the city, the superintendent will close the school, cause she won’t be able even to see beyond her house!

“I don’t think the snow is as deep as you think,” Edna said.  

“Look, there’s the superintendent on television.  I wonder why they’re interviewing her?”

“You had told us school would be closed today.  Why did you change to only an hour delay?” asked the reporter. 

“What a weird night.  First the snow—smelly, brownish-white snow—piled up past my first-floor windows.  Then all of a sudden, it stopped snowing… and, well… I’ve never seen such a thing happen before.  I don’t know that I can even describe it.”

Edna turned off the television quickly, before the reporter could ask a follow-up question.  “Let’s not worry Charley.  School’s happening today.”  

“Edna, what aren’t you telling us?” Edna had moved just a bit too quickly, and Bertha the perceptive elephant noticed.

“Do you guys remember when both of you and Pirate Larry were all sitting stunned on the floor?  Well, before I rescued you, I may have blocked one of the photogate beams with CrabbyCrabbyCrabby’s carapace.”

“Oh!  Wow!  Great work, Edna!”

“Wait, what?  Why is that great work?  Are you trying to steal my lightning, Edna?  I’m the one who stopped the snow, remember!”  Anthony stuck out his chest proudly.

“Oh, Anthony, you are such a mean hippopotamus!  Don’t you see?  When Pirate Larry tried to start the machine again, the door only triggered the first photogate beam, after CrabbyCrabbyCrabby had already triggered the second one.  So the beams were blocked in reverse order!  Larry’s snow maker reversed its angular velocity, and vacuumed all the snow back off of the Superintendent’s house!  I imagine that Pirate Larry wailed rather intensely when he saw.”

Bertha and Anthony stared at Edna.  Edna thought they would stare right through her.  Which in fact they did—their eyes focused on Charley, who had entered the room behind Edna a moment earlier. 

“School’s on an hour delay.  That’s sad, but I get to go to Greg’s class eventually!  What are we not worrying me about, friends?  And who is Pirate Larry?  I do do do want to know!”

The ungulates looked at one another.  “Well, Charley, it’s a long story,” Bertha said.  “But I guess we have an hour to tell it now.”

***

Ding went the bell, and twenty students enthusiastically piled into the physics classroom. Bri, Emmy, and Andy headed to their seats, which were all together in the back of the room.  

“Charley!” called Emmy.  “Come sit with us!”

“Hi, Emmy!” The little girl gave Emmy a high-five, or at least the highest-five she could pull off at age 6.  “I’m so glad to see you!  We almost didn’t have school today—we foiled Pirate Larry’s snow, we did!  Hemph!  Well, by we, I mean they.”  Charley gestured to her three friends, that still looked for all the world to the teenagers like glass jars.  Though two of them had bows on their caps.

“Oh, your hippos?” said Andy.  “What did they do?”

“And Bertha, too, who is a very nice elephant.”

“Remember the problem Greg gave you yesterday?  It was just like that!!”  Charley was so excited she nearly jumped into the air.  She pointed to the diagram on the students’ paper.  “Anthony pushed the wrong side of point C, so he was unhelpful.  Edna says he’s a mean hippopotamus.  Edna and Bertha were so brave!  They transferred their angular momentum to the rod, but that wasn’t enough.  Bertha’s mass was in the numerator, so she almost made the rod go fast enough.”

“Bertha had the best plan.  But Pirate Larry captured her!  It was scary.  Then Anthony… he got so mad, he bounced back off the rod.  And the rod went fast enough to open!  The snow stopped, and everyone was saved!”

Bri and Emmy looked at each other.  “That’s a good story, Charley.” Bri said.  

“Not just a story! They were there!  It happened! 

Bri figured it out: “Of course!  Edna and Bertha gave the door all of their angular momentum.  But Anthony… not only was he running faster for more initial angular momentum; he BOUNCED OFF in the other direction!  So Anthony changed his momentum almost twice as much as Edna or Bertha did, meaning the door changed its momentum by much more and went really fast!”

Anthony saved the day with physics even if he didn’t quite know why.

“Maybe next time Anthony could trade his jelly beans for jumping beans, and he could bounce even faster,” Andy laughed, looking straight at Anthony.  “Don’t see where he’d put a rubber helmet if he had one.  Maybe he had 40 helmets, one for each jelly bean?”

Charley hung her head, and stifled a brief sob.  “He’s a hippopotamus.  It’s not his fault he’s not beautiful like Edna,” she said with quiet sadness.

“Okay, here’s the quiz,” Greg said.  Charley buried her head in her hands while the students worked.

In contrast to Charley’s demeanor, Bri, Emmy, and even Andy perked up immediately.  The last question on the quiz was familiar!

In case 1, the disk sticks to the rod.  In case 2, the disk bounces backward off of the rod.  In which case does the rod move with greater angular speed after collision?

The quiz question was exactly what Anthony had done! They all understood the problem as well as any physics problem they’d seen all year.

***

“Hey,” Andy said after the quiz.  “Sorry, Charley, that I called Anthony a jelly bean.  He really helped us out, and I appreciate it.”  

Charley’s face was still fierce.  “That’s all very friendly, Andy, but don’t apologize to me—talk to Anthony!  He is a hippopotamus with feelings, even if Edna thinks he is mean.”  She stared at Andy.  

Andy visibly balked.  He knew he shouldn’t have insulted Charley’s “pet” to Charley’s face, but, still.  Could he bring himself to talk directly to a jar of jelly beans?  Especially right In front of Bri and Emmy?  There was sorta no way out.  Okay, so we’re doing this.

Andy set in his mind that that jar of jelly beans was a friendly guy just like him.  “Yo, Anthony!” he said.  “Thanks for helping us out.  You saved our bacon on the quiz.  Great job, man.  I appreciate it.  And you’re a fine looking hippopotamus.”

Charley beamed.  “Yeah!” she said to the three high schoolers.  “He really is a fine hippopotamus!  Thanks for noticing!  Although Edna is a bit miffed that Anthony got the credit.  He just got lucky, Edna says.  Edna knew the physics!  She says he’s a mean hippopotamus.”

“He’s not mean, Edna,” Andy said, “Just a bit slow on the uptake sometimes.  See you ALL—” Andy’s expansive gesture took in Bri, Emmy, Charley, and especially Charley’s animal friends “—tomorrow in class.  Can’t wait.”

As the students went out the door, Charley listened to the continued banter among the ungulates.  “But he is a mean hippopotamus,” Edna was explaining.  “Bertha was actually captured by Larry!  She was so brave.  I could have changed my momentum by twice as much if I had thought of it, too!  And I would have known why!  And yet, it’s Anthony who gets the thanks?”  Bertha just shrugged.

11 March 2023

Which formula to find the width of a hair - single slit, or double slit?

I was asked to chime in on an ongoing debate: When using the diffraction pattern of a laser to determine the width of a hair... should you treat the hair as a single slit, or as a double slit?

The short answer: I don't know for sure; yet it won't matter in terms of your measurement.  The long answer is below.

Double slit diffraction is reasonably simple to explain conceptually.  At any point on a screen that's not directly across from the spot directly between the slits, light from one slit travels a wee bit farther than light from the other slit.  That extra distance traveled means that one beam is at a different spot in its wave cycle than the other beam.  If that extra distance is a wavelength - or any number of full wavelengths - than the interference is constructive, and you see a bright spot.  If that extra distance is a half-wavelength - or 1.5 wavelengths, 2.5 wavelengths, etc. - then the interference is destructive, and you see a dark spot.  The equation for the location of bright and dark spots is derived from straightforward trigonometry, which shows that the extra distance traveled by one wave is, with commonly defined variables, dsinθ (or dx/L for small angles).

But single slit diffraction is conceptually complex.  I've seen explanations that it's like double-slit diffraction, except with diffraction around the slit's edges rather than around two separate slits.  That's not at all correct, though, other than as a very hand wavey hint-of-the-truth discussion with a low-level first-year student.*  The derivation of the location of bright and dark spots begins with assuming an infinite number of point sources of light within the slit, and uses symmetry and trigonometric arguments to determine the locations at which most or all of these infinite point sources interfere constructively or destructively.  Not simple at all.

* Sort of like the planetary model of the atom

Yet, the fundamental equations for the locations of spots is the same: dx/L = mλ.  For a double slit, the central maximum is m = 0, the first dark spot is m = 0.5, the next bright spot is = 1, and so forth.  For a single slit, the central maximum is wider, such that m = 1 represents the first DARK spot away from the central maximum, m = 1.5 is the next bright spot, m = 2 the next dark spot, etc.

I do not know whether single or double slit approaches better model the behavior of a laser around a hair.  Are there effectively two beams, one on each side of the hair, that travel slightly different distances as in a double slit?  Or are there infinite point sources on either side of the hair, and do we need symmetry considerations to figure out where those infinite sources interfere con- and de-structively?  I suspect the argument could be settled by measuring the width of the central maximum compared to the dark-fringe-to-dark-fringe distance; or by using a light meter to very precisely measure the intensity as a function of position along a screen.

What it means for the hair thickness measurement:  I measure x along the screen by finding the distance from, say, one dark spot to the next to the next to the next until I reach, say, the sixth dark spot.  Then I divide that distance by 6 to get a value for x.

Look at the meanings of m three paragraphs up.  Whether the hair should be modeled as a single or double slit MAKES NO DIFFERENCE!!!  The value of x that I measured represents the distance between dark fringes.  Whether that means the distance from, say, m = 2 to m = 3, as for a single slit; or from m = 2.5 to m = 3.5, as for a double slit; doesn't matter.  We can use dx/L = mλ with the measured x  and m = 1.  The hair-to-screen distance is L, and the wavelength of the laser is λ.  Solve for d, and that's the width of the hair.


09 March 2023

Is it worthwhile to do low-level physics research projects? Yes.

I attended two Christmas concerts in the same day.

The first was my school's official Christmas Concert, including the concert band and string ensemble playing Christmas favorites.  The crowd of 300 students and parents applauded politely.

The second was Trans-Siberian Orchestra's The Ghosts of Christmas Eve tour - Christmas and classical music arranged in a rock-and-roll setting, complete with electric guitar riffs by long-haired men who might have been in the backseat of Wayne's car.  The crowd of 20,000 paying* fans screamed, shouted, applauded, and held their lit phones in the air.

* We paid for tickets, for parking, for ticketmaster's fees (how are they not an illegal monopoly, again?)... Somehow these fees weren't enough to hire anyone for basic traffic control around John Paul Jones Arena.  Two hours to make the 50 minute drive.  Oy.

Virtually all attendees at my school's concert had friends or relatives on the stage.  If they're honest, a large majority of the audience would acknowledge that their presence had far more to do with a social obligation to the performers than with a desire for entertainment.  And the vast majority of the on-stage performers won't play music professionally; in fact, most won't perform on their instrument ever again after high school.  

Though the high school concert compared to TSO as the Sun compares to a galactic cluster, even the most reluctant attendee watching their nephew hit most of the notes in "sleigh ride" could recognize the reasons that students performed their low-level concert.  Student musicians need an audience.  Music is part of a shared culture; the experience of rehearsing and performing music will enhance the performers' appreciation of professional performers.  The gulf in quality between students and highest-level professionals doesn't devalue the worth of the student performance.

You're nodding.  Of course - our JV baseball team plays, their families watch, then they pay elsewhere for the privilege of seeing real baseball at a major league game.  Rinse and repeat for any endeavor in the arts or athletics.

Why not academics?

I *do* have to convince people that student research in the context of an introductory physics class is worthwhile.  Near the end of even my lowest-level introductory class, students are presented with a problem that is a step beyond the level of problem they've been dealing with.  They're given time on the scale of weeks to investigate these problems experimentally and theoretically.  And then they're asked to present their results to an audience.  

Because I make this a Big Deal, and especially because I make this in lieu of an exam or written test, I get pushback.  Less and less pushback over time, because more people every year see the worth of these proto-research projects (and also because people give up complaining through sheer exhaustion - I'm not gonna end these projects).  But pushback nonetheless.  

Some of the pushback is reasonable.  All high school courses must find a niche within their school's ecosystem.  When facing grumbling about an assignment, it's not okay to just dismiss it all without due consideration.  Especially when the grumbling comes from respected colleagues or diligent students, it's important to listen in order to differentiate between "just kvetching" and legitimate beef.

One type of unreasonable pushback from colleagues comes from feeling threatened - physics students engage enthusiastically in their proto-research projects, and do them well.  Then when other classes give long cumulative written exams, students get tetchy - some of them like physics projects, but don't like cumulative math or history exams.  Nothing I can do there.  The soccer or football team shouldn't stop winning because their success might make other sports programs feel bad in comparison.  

A legitimate beef, though, comes from a fear of lost academic rigor.  It is absolutely true that the proliferation of project-based learning in the educational zeitgeist has led to all sorts of, shall we say, less than serious projects among the gems.  It's very hard for a non-science teacher to recognize the difference between "do cactuses like classical or rock music?" and "does the cart go faster when a projectile bounces off, or when it sticks?"  And if there's even one teacher in a department who gives out high marks for ridiculous "research" (or for parent-led research), then even the best low-level research project is gonna be a hard sell to colleagues.

But rigor doesn't mean Trans-Siberian Orchestra-levelThe school orchestra doesn't have to be professional level in order to make their concert worthwhile.  They just need to prepare carefully, and play to the best of their ability in front of an audience.  The existence of the audience is a significant motivating factor - participants know that friends and relatives are showing up to watch them.  Their audience doesn't expect to see Yo-Yo Ma, just a well-prepared best effort in which players don't have a flute up their nose.  

A 9th grade physics research project is not going to make a Nobel-level discovery, is not going to produce figures and mathematics publishable in Nature.  Yet the project can investigate physics one level beyond that of the year-long course.  The project can involve simple yet rigorous experimentation, simple yet rigorous explanation of theory.  And like the school Christmas concert, a low-level physics research project can be presented to an external audience who isn't expecting mind-blowing new science, but is happy to see a well-prepared best effort in which researchers don't try to swallow the motion detectors.

I'll be posting soon to request (paid) jurors to serve as our external audience for 9th grade physics research projects.  Even if, especially if, you or your colleagues are skeptical about the worth of low-level research, I encourage you to join us on May 21, 2023.  Don't expect to whoop and raise your lighted phone in response to a presentation!  But some presentations will be outstanding for the level of the course; and all will show a well-prepared best effort.  The mere existence of an audience, especially an audience tasked with giving feedback, will raise the quality of the experience for all participants.  




07 March 2023

5 Steps webinar March 2023 - put your questions, stories, and comments here - I'll respond

Folks, the live webinar associated with the 5 Steps to a 5 AP Physics 1 book took place at 3:30 on Tuesday March 7.  Here is the recording from the show!

I'm not on any social media!  But if you'd like to ask questions or share thoughts, please put them in the comments here.  They won't show up instantly... but I'll be happy to respond to people after the show!

And this thread will last a while.  Even if you watched the show on demand rather than live, still put your thoughts here!  I'll respond soon.

P.S. In the event, physics teachers Kristin Sumner and Nicole Murawski answered a LOT of the questions in the chat!  Thank you both!  

Greg