Mail Time: What's your demo using kinematics with a spring?!?

Logan writes in:

Hi Greg,

What's the "energy of a spring demo with kinematics/energy" [on your class-by-class planner]?

Logan, 

I think you're talking about the demo where I hang a 1 kg object from a vertical spring of known spring constant, displace the object 5 cm, and predict  how fast the object is going at equilibrium.  I do this using Newton's second law and kinematics.  Yes, really.  

Then I do the experiment (a motion detector placed underneath makes a velocity-time graphs, and we look at the maximum vertical axis value).  Off by 40%.  What?  Physics didn't work?

But energy gives an accurate prediction.

Point is for students to recognize when kinematics are applicable, and not applicable.  And to practice energy bar charts, o'course.

Lincoln, Nebraska for the 2023 college soccer tournament 2nd round

Last weekend, I traveled to Lincoln, Nebraska for the second round of the college women’s soccer championship tournament.  The University of Nebraska hosted two games on Friday, and I attended both.  This trip was a part of my school “sabbatical”, in which I’ve been traveling the country to see women’s soccer.  I’ll also be heading to the College Cup semifinals in December in Cary, North Carolina.  

I’d been to Lincoln back in 1999-2004 for the AP physics reading.  I didn’t get very far off campus in those years, ‘cause we had everything we needed right there; because I didn’t have a car; because I didn’t have the money to do anything expensive, including eating at restaurants.  Good news was, the food in the dining hall was amazing.  Every year, the first night we arrived we were given the choice of shrimp scampi or a bacon-wrapped filet.  And my request of “both, please” was always met with an enthusiastic smile.  Ah, the good ol’ days.  

Back then, we were bussed in from Omaha, 1.5 hours away.  This time, I flew straight to Lincoln’s airport, so a 10-minute Lyft ride got me to the hotel that was a short walk from the stadium.

First game: Gonzaga vs. UC Irvine.  I went in rooting for the UCI Anteaters over the Gonzaga Bulldogs, just because of the mascot.  (If Gonzaga had been the Huskies, I would have supported them.)  UCI went up very early with a goal from Aveka Singh - a junior from New Delhi, India.  I’m pretty sure the assist came from midfielder Tati Fung, who seemed the best player on the pitch.  When she had the ball, I had confidence in the Anteater attack.  

It was cold in Lincoln, at least cold for an outdoor spectator sport.  I wore like a thousand long sleeve shirts, thermal underwear, a parka, and my elephant hat.  Yes, my wife has knitted several animal hats for me, my favorite of which has elephant ears and a proboscis sticking out of the forehead.  Many, many Lincolnites admired my hat, but a good fraction thought it was an anteater in honor of UC Irvine.  

One man successfully identified the elephant, though, and told me so - he said he was a professor (of sociology) at UC Fullerton, whose mascot is an elephant.  He very much liked my hat.  Yet his daughter had become an anteater.  Go figure. 

The Anteater fans as a group - as a group of maybe 20 - were positive, enthusiastic, and kind.  They greeted their team enthusiastically after the game in the same way as a European team’s visiting support do, though with less drunken chanting.

UC Irvine had defeated national #1 UCLA in the first round, and were the underdog in this game against #8 Gonzaga.  Nevertheless, the Anteaters dominated the first half, slurping up a second early goal from Lilli Rask.  Gonzaga then grew into the game, finally breaking through five minutes before the half from freshperson Katelyn Rigg.*

*In the early 1990s, it seemed that a full third of the women I met at college were named some form of Cindy, or Cindi, or Cynthia, or Syndi, or similar.  Well, the same phenomenon in the 2020s seems to have shifted to Caitlyn, or Kaitlin, or… I suspect the latter to often be the offspring of the former.

It was a different first-year player, though, who was the danger woman for Gonzaga.  Emelia Warta kept gaining possession in advanced positions in midfield, after which she would rampage into the box.  Every time she touched the ball I expected her to create a chance. Warta and her team controlled the game more and more as the second half went on.

Yet the Anteaters weathered the storm, including a storm in which they themselves seeded the clouds - some dangerous passing under pressure in the back led to a giveaway and a ball cleared off the line with the goalkeeper out of her area.  Phew.  For the most part, UCI headed crosses away, got the ball to Fung in midfield, and passed out of trouble before trouble came right back toward them.

Tension mounted palpably as the clock ticked down* and Warta terrified the Anteaters as if she were a jaguar rather than a Bulldog.  In the last 15 minutes or so, the ball barely left the Anteaters’ half.  Yet a couple of final clearances through Fung sealed the deal.  And a couple dozen fans cheered.

*Yes, the college soccer clock counts down rather than up, ‘cause the NCAA knows better than the entire rest of the world how the game should work.  Phthphth.

Second game: Tennessee vs. Nebraska.  This was a home game for the Cornhuskers, who packed the stadium with a second-highest-all-time attendance of 2100 fans.  That’s like one of every 100 residents… whereas Portland gets one of every 25 residents at a Thorns game to make attendance figures more than 10 times larger.  (For comparison, Nebraska gridiron football gets something like one of every three residents to show up.  Football isn’t religion in Nebraska - it’s much more important than that.)

Perhaps because it was an NCAA tournament game, the stadium made a pretense of neutrality, playing the Tennessee fight song as the Volunteers entered.  It was fun to hear their entire team point in the air and “woooo” audibly - It’s good, old, Rocky Top (woooo!).  

Thing is, even though Nebraska was the highest of the four seeds, this game seemed of less quality than the first.  Both teams played helter-skelter, causing the wannabe-coach middle-aged men in the crowd to holler “settle!” with increasing intensity, becoming audibly angry when the players didn’t obey.  On occasions when the teams did settle possession in the midfield, neither could complete a pass to the forwards.  Seemingly every pass was too heavy, intercepted, out of touch, or simply astray.  

Seconds before the half, Tennessee keeper Ally Zazzara slipped as she took a goal kick.  Oy.  The ball ran straight to Nebraska’s Sarah Weber, who punished the mistake that wasn’t even Zazzara’s fault.  Of course the crowd cheered, and they should!  No one taunted or laughed at the keeper’s misfortune.  But as a quasi-neutral, I cringed.  Cheering felt dirty.  The poor woman slipped!  The Tennessee team avoided their keeper, who was the last one into the locker room accompanied only by her (presumably) goalkeeper coach.  This surprised me - I thought the team would surround Zazzara, try to boost her confidence for the second half to come.  They did not.

And then the Tennessee players didn’t woooo when they returned after the half down 1-0. Rocky Top without the “woooo” sounds uncannily incomplete, like “shave and a haircut” without “two bits.”  I thought the team were finished.  Yet UT equalized moments into the second half.  

The game became tense, but never really picked up in quality.  Passes didn’t connect; fouls stopped attacking action.  

I was initially rooting for Nebraska.  I’d spent many weeks of my life in Lincoln; I own a hat shaped like an enormous ear of corn.  I wanted to celebrate with a crown of supporters.  The problem is, too many of these supporters were sorta toxic and probably inebriated middle-aged men.  

I mean, I understand and accept that when a call goes against the home team, the fans will howl.  When two players collided in the box after a Nebraska forward headed over the bar, the crowd ignorantly brayed for a penalty.  That’s part of tribalism.  When two players tussled at midfield and both went down, the crowd screamed bloody murder when the foul went Tennessee’s way.  These aren’t the fan reactions that bothered me; in fact, I’d probably be disappointed if the fans were not invested enough to howl at these incidents. 

As the game mounted in intensity, though, the drunk men turned their wrath toward the referee.  “Whaddaya mean that ball was out?  Are you blind?  What game are you watching?”  Every minor decision brought forth more whining, more intense personal attacks on the ref. Not after 50-50 foul calls, but offside decisions, which way the throw-in went, niggling complaints.  

I’ve had a number of conversations with colleagues about the boundary between legitimate tribalism and over-the-top abuse of opponents/referees.  I’m a referee myself; but I willingly accept the home team howling as an important part of the game.  I’m a commentator for my school’s sports teams, where I am always utterly respectful of the opponent; yet I also am supportive of student banter about who is gonna win, or about who won last year, etc.  Separating the in-game passion from the post-game handshake is, to me, a critical part of learning to function in a society in which many of us are often on different “teams”.  I still don’t exactly know where that line sits.  Yet I do know that these obnoxious Husker fans crossed it.

I finally snapped when the arsehole to my left screamed at the referee with five minutes left.  The ref stopped play and indicated a head injury - he asked the Nebraska athletic trainer to take a player off for treatment who seemed to show symptoms of a concussion.  This dude - and a few of his like-minded fans around him - went berserk.  “Let them play!”  “She’s fine!” “The game’s not about you!”  “Go back to the YMCA, butthead!”  “You’ve been a butthead all game!”  And the personal abuse toward the referee got progressively worse.  No one shut these folks up.

This is the bystander problem that we try to address with the 14 year olds in my care.  If you say nothing, you’re complicit.  “Well, he might have been out of line, but *I* didn’t do anything wrong, so I can’t be blamed for anything that happened” is simply unacceptable.  Did you speak up?  Did you leave the area?  Or did you just grin and grab the popcorn while someone, even someone in absentia, was abused?  

I wish one of this man’s relatives or friends had spoken up.  “Hey, that’s going too far” coming from a family member can do wonders.  Or “come on, man, cheer for our team and shut up about the ref” from a fellow Cornhusker - preferably one who’s been leading the “HUSKER! POWER!” chants all night - would have helped.  

I was in no position to say anything.  I had no prior relationship with the nasty man; I was not in any way part of Husker Nation.  I was just a weird guy with an elephant on my head.  So I moved to a different seat to watch the last few minutes.  

And oh, what a last few minutes.  The game looked to be heading to extra time.  But with less than a minute to play, defender Ella Guyott - who had earlier in the game repositioned as a forward due to a substitution - stayed calm at the far post when a cross went over everyone else’s heads.  She slotted the ball into the net with a finish that looked so-easy-anyone-could-do-it but I would likely miss 9 of 10 times.  And that was that.  Nebraska 2, Tennessee 1.  

The players took a victory lap around the stadium, giving the front row high fives - that right there is so much of what I love about women’s soccer.  The players show overt, enthusiastic thanks for their fans’ support.  The teams huddled together, in wondrous shock and catatonic shock, respectively.  And the crowd raced to their cars to beat the awful traffic surrounding the stadium.  Glad I could walk.

I planned to spend the next morning walking around town, finding a cafe in which to grade my trimester exams.  Unfortunately, I had chosen the hotel in a rundown strip mall next to the “MEAT & BEER”.*  No coffee, unless you count McDonalds.  

*At night, the lights for the ampersand and T didn’t work, so the store became MEA BEER.

I did eat at the strip mall’s Runza, that wonderful fast-food empire that only exists within 600 miles of Lincoln.  They serve fast-food meat pies that are part calzone, part Hamburger-Helper-in-a-bread-wrap.  I was first exposed to Runza in 2000, when the AP physics readers were served Runzas for lunch.  Runza Rex, their tyrannosaurus mascot, handed me a Runza baseball cap which I still own.  I ate three of these large sandwiches.  After which I fell asleep during the afternoon grading session - the only time I’ve ever fallen asleep at the reading.  (Since that day, I’ve not eaten any lunch at all during the AP reading.)

Eventually, a twenty minute walk brought me to an excellent coffee shop in the UNL “Innovation campus”.  No clue what they’re innovating, or whether they’re gonna rename the rest of the university the “stuck in the past campus.”  Guh.  But the coffee was good, the barista was friendly, the tables were spacious and clean with lots of windows.  Exams got graded.  

Directions of motion are "toward the detector" and "away from the detector".

A fundamental principle of teaching first year physics students is to never trust a student with a negative sign.  The linked post details ways that I avoid negative signs wherever possible.  

My conceptual class never gets to the full-on kinematic equations - for them, all motion either is constant speed, using d = vt; or starts/ends at rest, making d = (1/2)at^2 or d = v^2/2a valid.  Since we never discuss computationally an object that changes direction of motion, we can dispense with the negative signs!

AP-level algebraic kinematics is one place where I haven't found a way to avoid a negative sign.  Yet!  Before we ever touch computation with kinematics equations, my AP class learns about position-time graphs, velocity-time graphs, and the definition of acceleration without any negative signs.  In fact, both classes begin with the exact same facts and exercises.  For position-time graphs, the facts are:

The steeper the position-time graph, the faster the object is moving.

A position-time slope like a front slash / means the object is moving away from the detector.

A position-time slope like a back slash \ means the object is moving toward the detector.

To determine how far from the detector an object is located, look at the vertical axis of the position-time graph.

After a number of in-class laboratory exercises with motion detectors, students are used to relating the way a position-time graph is sloped to whether a cart moves toward or away from a detector.  This takes about a day of class for AP, about three days of class for conceptual.  They're ready for the next step.

A daily quiz question eventually asks, "A motion detector points north.  The position-time graph it produces is sloped like /.  Which way is the object moving?"

When we grade this quiz together, I cite the fact: "A position-time graph sloped like a front slash means the object is moving away from the detector.  Count the question correct if the student wrote 'away from the detector,' or even just 'away.'"  

But I go on. I call a student to the front of the room and hand them a motion detector.  "Please place this detector on the track and point it north."  I usually have to help the student figure out that "north" is different from "toward the ceiling."

Next  I call a different student up.  "Here is my pet hippopotamus Edna.  Please help her move along the track away from the detector."  The student does so.  "Which way was Edna moving, north or south?"  Now it's obvious that Edna was moving north.  "So, the best answer to this question is that the object moves north.  If a student wrote "north" as their answer, count it correct AND add one bonus point."

"From now on, if a question indicates the direction the motion detector is pointing, answers should no longer state just 'toward' or 'away from' the detector.  Your answers should be north, south, east, west, left, right, up, down, etc."  And I hold students to that.

The only difference for AP is, eventually they get to computational kinematics with changing direction of motion.  So we talk about defining directions as "positive" and "negative" so the math works out.  And we define that the direction "away from the detector" is the "positive" direction, by definition.

Interestingly, despite this roundabout and indirect way of introducing what "positive" and "negative" mean in the context of kinematics, my AP students don't generally have difficulty interpreting an exam question that does use negative signs to indicate direction!  They perform way above the national average on the exam, including on the unit 1 kinematics questions.  And those who do take calculus-based physics transition to using coordinate systems as if they were native Cartesians.

Students work at different paces. Let them.

By November, I've generally established a positive, authentic class culture in which everyone is working as a team to learn a difficult subject.  This class culture will look different for different teachers, different school ecosystems.  Point is, now the class clowns have been brought into the fold or at least neutralized; the folks who'd rather whine or lawyer up than learn have similarly changed their priorities - or left the class.  

So we're doing a lot of laboratory work and problem solving in class now, and for the remainder of the school year.  A typical class day starts with a 3-5 minute quiz, after which students work on a list of activities.  Each activity must be checked with me for completeness and correctness.  A typical day's "order of work" might look like:

• One position-time exercise
• Experimental graphs worksheet
• Power in a bulb exercise
• Test 2 corrections
• Test 3 corrections
• Two more position-time exercises complete
• Two circuit graphing exercises complete
• “Graph that motion” interactive

And this list might be substantially unchanged for a week or two.  This is "teaching like a video game" - students feel like they level up when they complete each item in the list.

The question I'm often asked is, how do I handle the class when some students are on level 8, but others are on level 2?

Remember - I'm comfortable with our class culture and that each student is working in good faith.  I must support a student who took two days to finish a single position-time exercise and is now struggling with the graphs worksheet, the same way I support the student who, in those same two days, is nearing the end of the list.  They're both working at their respective ability levels.

Firstly, I can subtly slow down fast students and speed up slow students.  I don't mean artificially!  A student who is good at physics and does everything right should be allowed and encouraged to proceed quickly through the order of work.  But after the first 20 minutes, I'll probably be a bit more exacting about the standard of evidence a fast student presents me; and I'm more likely to let a slower student move along despite minor errors of reasoning.  

Next, since we've built a good team atmosphere, a faster student often slows down naturally.  Everyone knows that the price of my assistance on a problem is to pay it forward - the next person who needs help on that problem gets sent to the student I helped previously.  Helping classmates takes time!  It's time extraordinarily well-spent, because teaching others is the best way to learn physics.  Fast students often recognize how much they're learning by teaching, and so keep teaching.  Or, they get a nice ego boost by being the go-to person for their classmates.  Sometimes deep friendships are built around in-class collaboration, as physics can be a great social leveler - the universe doesn't care how socially cool or uncool you are, just whether your predictions are right.  Helping classmates is good for physics achievement, but it's also kind, friendly, and the right thing to do.

But in the end, I'm always gonna have a few folks who, comparatively, barely make progress.  That's okay.  At some point, the class moves on to new material - at which point, my order of work resets to new activities.  It's important that I do NOT insist that everyone finish every activity!  

I prioritize test corrections - these absolutely must be finished. And I'll bring in students to extra help time, or assign corrections as homework, to meet this goal.  For everything else, though, we just move on when it's time to move on.  Some students will have finished everything.  They will have been given a next-level challenge, or just allowed to do work for other classes while they wait for their classmates to catch up.  Others may barely progress, because they're bogged down in corrections, or in an exercise that's just not clicking.  No worries!  Not everyone even got to level 8 in Super Mario 3, let alone beat the level.  Not everyone makes the state playoff final.  We move on - to the next sports season, to the next Mario release.  

The stated goal for all students is that they work hard, take care of each other, and get better every day.  Nothing in there about the pace of their work.  As long as students are meeting these three goals, they get as much done as they can, without complaint from me.