SNL "Posters" - Marcello Hernández was cheated

"Posters" has been a recurring skit on Saturday Night Live. It originally featured guest Emma Stone and cast member Pete Davidson, with additional cast members Mikey Day, Kenan Thompson, and Kate McKinnon. It seems to be resurrected whenever Stone hosts.

Last night, "Posters" was staged again, this time with Marcello Hernández and Ego Nwodom alongside Stone, Day, and Thompson. The talking posters assured Hernández that physics was—in fact—relevant.

The punchline stinger at the end of the skit is always a graphic showing the subsequent failed exam.

I posted the skit to Twitter/X (@phyzman) for the benefit of my #ITeachPhysics colleagues. Dan Burns (@kilroy22) quickly noticed that Marcello actually got the correct answer on the most difficult question of the three shown, Question 3.

The recoil height depends on the ball's recoil speed. Conservation of momentum for a perfectly elastic head-on collision with a twice-as-massive body is 1/3 of the impact speed. With 1/3 the impact speed, conservation of energy reveals the ball will rise 1/9 the launch height: 1/9 h. Marcello's answer is correct.

That made me take a look at Question 2. The road must exert a forward force to match the force of air resistance while also exerting a centripetal force equal to mv²/r. Taken together, the forward force and radially inward force result in F(B). Marcello's answer is correct on that one, too.

Dan and I dismissed Question 1 as "not even wrong" since it's not even a physics question. It's a pure math question involving unit conversions. Invoking Avogadro's number in a physics exam is distasteful. 

If we allow this faux pas, 1/12 of Avogadro's number is 5 × 10²². Convert that from seconds to hours by dividing it by 3600 (the number of seconds in an hour). Convert that to days by dividing by 24. Convert that to the never-used-in-a-physics-class unit of weeks by dividing by 7. That's 8.26 × 10¹⁶ weeks. Not an option. So divide that by 52 to convert it to years. 1.59 × 10¹⁵. Once again, Marcello's answer is correct.

It's picking nits to complain that the formatting of Question 1's answer options don't match those of Questions 2 and 3. Or that X was used instead of the correct symbol, ×.

Marcello aced this exam. Kudos to the talking posters. And who is Marcello's physics instructor?

Is a tape measure a constant force spring?

I recently came across a video of tape measures "racing" along a board of wood as they retract. Who doesn't love extending the tape as far as you can and recklessly letting it fly in? It obviously accelerates dramatically. Like any physics-minded person I got to wondering if the force is constant. How might we assess?

I'm home for the summer, a summer I desperately needed, and away from some of my usual tools. No probeware. No students to help. First I put a small bucket with a handle on a food scale from our kitchen. I extended the tape measure and used it to pull up on the scale. The force was somewhat constant, but not as steady as I would like. A force probe would have been handy to average many data points and see the force graphically.

Perhaps it would be simpler to measure acceleration, rather than measuring force directly. We could replicate the original video. But what about friction? I've also noticed that tape measures sometimes stick when used in this position. What if we pulled a cart of known mass and analyzed the video? The toy cars at my disposal were all too light—or had too much friction—to provide a motion that was slow enough and consistent enough to satisfyingly measure with the tools on hand.

But there it was staring me in the face: the air hockey table. I put the tape measure on its side, so that the weight of the extended tape doesn't cause it to rub as much against the tape (tape retracts more smoothly). Lego base plate floats beautifully on table. A few Lego bricks are placed on one end of the plate to hold the hook of the tape measure during retraction.  

Teeeeter Totr

Just a quick balanced torque puzzle. It's really a test of whether or not one truly accepts the concept of center of mass.

Nothing exotic going on. The meterstick is uniform. Sufficient information is provided to solve the puzzle. It can be confounding to students.

Teeeeter Totr - HTML export | movie export

UPDATE: Among the many things I can count on in life is that virtually any mechanics demo I might share here has already been done better by the inimitable Dan Burns. For example:

RT;DL Things That Go Bump!

Which involves more force: stopping or bouncing? Let's demonstrate.

I inherited a stop/bounce dart when I arrived at my school in 1986. You arrange the dart as a pendulum and swing it into a wood block. Back in those days, you ran the unadorned nail point into the block for the stop, and attached a rubber stopped to the nail point for the bounce.

Since then, the advent of "happy" and "sad" balls improved this demo. And happy/sad pendula/mallets have been commercially available (help me out with a link if you know one).

Arrange the dart so that it barely knocks over the block using the happy ball on the tip. Then switch to the sad ball and allow for predictions and arguments. Then proceed with the reveal.

Things That Go "Bump" [Virtual Demonstration] at Teachers Pay Teachers

RT;DL Blowout—Newton's Laws Edition

My use of Pasco's Lenz's Law demonstrator as a blowgun to explore the equations of motion is discussed in a previous post. That's an activity I don't do in my regular Physics class, because number puzzles aren't a priority there.

In this activity, I introduce the blowgun to Physics, do a quick speed determination, and then detail how Newton's laws of motion apply to the various portions of the Hero's Marker's Journey.

How are Newton's third, first, and second laws relevant to when the marker (bullet) was in the tube (barrel)? Between the barrel and the box? When caught by the catch box?

I do this after all three laws have been taught in class. It's a nice review.

For example, when the marker is in the tube, Newton's third law is relevant in that the air pushes the marker forward while the marker pushes the air backward. 

Newton's first law is relevant in that the marker at rest would have remained at rest, but was acted on by an unbalanced, external force applied by the air. 

And Newton's second law tells us the acceleration of the marker will be proportional to the force that the air applies and inversely proportional to the mass of the marker. 

In the end, we ponder how to make a faster-moving bullet based on Newton's laws. I can't blow any harder. So we modify the bullet. 

Is this demonstration activity really just an excuse to do another blowgun activity in class? I mean... what are you even talking about right now? That's ridiculous! Why would you even suggest such a thing?

It really is a nice review of Newton's laws. 

Blowout Newton [Virtual Demonstration] at Teachers Pay Teachers

Here's the accompanying HTML presentation. As always, the presentation was designed to accompany to the student document rather than to stand on its own.

RT;DL The Newtonian Shot

I'm embarrassed to confess that I don't remember the name of the physics teacher who shared this demo at the January 1986 MSTA Meeting in Lansing. I do recall driving past many cars that had slid into the ditch on the road from Ann Arbor that morning. It was windy and icy. And cold.

But the demo stayed with me, and I worked it into my curriculum early on. It was my first Show & Tell at an NCNAAPT Meeting (Spring 1992, American River College, IIRC). 

I think it's a great demo for the Newton's Law unit. There have been times when securing toy dart guns was a challenge. They can last for many cycles, but they were built as inexpensive toys, not precision science apparatus. Here's one I found online in 2025; use your search engine/AI skills as needed.

I wrote a post about this demo previously, when I recorded some nice high-speed video of it. It includes a few more specifics.

The Newtonian Shot at TPT (Students document, Answer Key, link to presentation)

HTML Preso: Demo - The Newtonian Shot (including convenient Zoom participant reaction instant poll)

As ever, my presos are designed to support my storytelling and do not stand on their own terribly well. (Like a backup band with no lead singer.) And you can see I use aluminum support rods to help with the simultaneous launch. I launch the darts from ceiling-level down to my countertop so students can see the landing point. I protect my concrete countertop with a wood plank.

RT;DL Cannonball - Ball dropped from moving ship

Another classic demo that can elicit excellent classroom discussion. A cannonball is dropped from the mast of a moving boat. Where will the ball land? This nicely confronts our inner Aristotle.

In my version, the premise is laid out, the landing point options are described, and students are asked to produce arguments supporting three of the five possible landing sites: one that they believe, and two they could convince others of (as good attorneys).

A straw poll is conducted (now with Zoom participant reactions), then students are asked to defend their various positions. After the classroom discussion/debate, a final vote is taken. 

I warn them to vote carefully. "Physics is a democracy, and whichever outcome gets the most votes will  be correct. The universe will accede to our wishes. Please vote responsibly!" [Update: at some point Zoom made participant reactions ephemeral, so they lost their value as an instant polling tool.]

Then we see the actual outcome. First in my animation; eventually in the classic Project Physics footage from 1968. In face-to-face instruction, I also carry it out using a discontinued Pasco product (Ballistic Cart Accessory with Ball Drop Attachment). So sad to see that combo go.

Lastly, I ask students how the demo could be altered so that the ball would land at the other locations that were offered in the premise. The 1968 footage shows one such modification. I leave it to students to think of the others.

Cannonball [Virtual Demonstration] free resource at Teachers Pay Teachers

Includes

Student document (Google Docs file on Google Drive)

Presentation link embedded in student document

Answer key

The HTML export from Apple Keynote had a few wee quirks this time. Mostly in that while most of the splash sounds are muted, the audio from the 1968 video (muted in my preso) comes through loud and clear in the export.

Here's the HTML presentation: Cannonball. It's intended for use with the TPT student document.

Further discussion in the comments.

RT;DL The Clever Dumbbell - Tension & Inertia Demo

A classic and popular demo. I do it in Conceptual Physics, Physics, and AP Physics 1. And I use a 5-lb dumbbell and kite/packaging cotton string. For years, I used a cast-iron dumbbell. But I broke floor tiles on occasion, and there was that one time the wheel-like nature of the dumbbell ends allowed it to roll onto a student's open ... toes. So I found rubberized hexagonal-end dumbbells. And I use a cardboard catch-box with scrap paper to protect the tiles.

After posing the initial question: Which string will break when the bottom string is pulled, I have them work through some leading questions.

Instead of having students predict which string will break, I have them request a string for me to break. Once they understand this paradigm shift, they request the bottom string. And I oblige. Eventually I break the top string, too. This can be navigated in the preso, alone. But I prefer to do the demo in my empty classroom because I can.

The efficacy of this demo lies in the dependence of the outcome on the presenter's technique. If it were a 50-50 coin flip each time, the demo would not have any pedagogical value. Some ponderables are offered post-demo, too.

As is a continuing theme in my RT;DLs, the student sheet is a Google Doc and the preso is an Apple Keynote preso, exported to HTML. These exports work delightfully on computers. Less well on tablets or phones. 

This one takes a bit of practice to navigate. 

Things shown in images but not in words: strings break when they are stretched beyond their limit by tension greater than the sting can withstand. A rapid pull stretches the bottom string through its limit before the dumbbell moves very much, thus keeping the top string from being stretched. A slow pull allows the top string to be at greater tension than the bottom string, allowing it to reach its limit before the bottom string does.

Clever Dumbbell [Virtual Demonstration] at Teachers Pay Teachers

Includes

Student document (Google Docs file on Google Drive)

Observations presentation (linked to on student document)

Answer key

RT;DL Blowout: A tour through the equations of motion

Near the close of the last century, I wrote an article for The Physics Teacher extolling the unadvertised virtues of Pasco's Lenz's Law Demonstration tube. 

Sure, you could use it to demonstrate Lenz's law, but that fine aluminum tube seemed pricey, so I was keen to justify the expense. You can tap it with a mallet (or on the ground) while holding it at various places to produce different notes. The Q of aluminum is great for this. You can stand it up on its end in your classroom to demonstrate unstable equilibrium. 

But for my notion of classroom theatrics, the best unintended use for the tube was as a blowgun. 

For this RT;DL I prepared a tour through the equations of motion with the blowgun acting as my vehicle. it is very much up to the task. I do this in my AP Physics 1 course only. Regular Physics students don't really need the exercise in number puzzles that the equations of motion afford. The year's too short.

In any case, I blow a marker pen through the tube and arrange two photogates near the muzzle to help determine the exit speed. It's over 60 mph!

Once the exit speed is determined, we figure out the acceleration of the marker while it was in the tube. Over 20 g's.

We also figure out how long it took the marker to exit the tube once its motion began. Then we investigate where the marker was when it was at the half way point (in time) along its journey through the tube.

The preso is enhanced with photos and high-speed videos. And an instructive(?) blooper at the end.

Blowout Kinematics [Virtual Demonstration] at TPT

Here's the accompanying HTML presentation: Blowout Kinematics. It's intended for use with the TPT student document.

Exploratorium friends, Don Rathjen and Paul Doherty, turned the blowgun idea into a nice Snack: Marshmallow Puff Tube.

RT;DL The Great Bullet Race

I run this demo in AP Physics 1. I don't run it in Physics. Why? Projectiles is not a topic I teach in Physics. We tend to spend more time in kinematics than kinematics is due. It wasn't a big topic in California Science Standards Physics (RIP). It's not that big a deal in AP Physics 1. It's virtually non-existent in NGSS Physics. If you are among the few, the happy few—the band of brothers and sisters—who teach a year-long AP Physics C-Mechanics, have at it!

But physics teachers of all stripes love, embrace, and perhaps cling to our kinematics. Maybe after a decade of NGSS Physics and a generation of retirements, kinematics' star will begin to fade. I have my doubts. Kinematophilia seems to have inordinate inertia. </soapbox>

In any case, we still regard this demo as a classic. [We don't seem to have a universally agreed-upon name for it. Or if we do, I don't know what it is.] So when it came up this year, I spent some time in my empty classroom trying to get some useable high-speed footage. 

Here's the student sheet and preso I cobbled together. (The Mythbusters segment is included.) Oh, and where a prediction is called for, Zoom participant reactions are solicited (yes, no, go slower, etc.).

The Great Bullet Race at TPT

HTML Presentation: Demo - The Great Bullet Race

I found the embedded videos in this HTML export to be a bit cantankerous—practice before using in class. Arrow keys to advance. Clicking in a video activates a scrub bar at the bottom and allows you to scrub forward/backward in that video.

Maybe you can get some use out of these; maybe your district won't let you use it. Guns and bullets are discussed, modeled, and used.

[RT;DL is remote teaching; distance learning]

RT;DL Inertia in Action

[RT;DL is remote teaching; distance learning. Where we show our attempts to bring extant lessons into the COVID-19 era.]

In the old days of face-to-face, in-class teaching, we did a station lab activity involving inertia experiences. It was called "Inertia in Action."

I retooled it into a video-based demo in which small groups could view segments, discuss prompts, and record their ideas on a Google Doc. It may not be your cuppa. But it works for me, given the circumstances. 

Inertia in Action [Virtual Demonstration] at Teachers Pay Teachers

Includes

Student document (Google Docs file that lives on Google Drive)

Observations presentation (link embedded in student document)

Answer key

Here's the presentation. It makes more sense with the prompts in the student document.

https://phyz.org/phyz/BOP/2-NEWTON/inertia/#0

Some students had trouble with the HTML presentation, so I exported it as a video. Again, intended for use with the student document. 

https://youtu.be/9QJ6MphQ80A

Slow your roll

If you're not following Frank Noschese (@fnoschese) on Twitter, why even be a physics teacher with a Twitter account?

And if you get useful mileage out of constant velocity buggies (such as these from Arbor Scientific) but wish you had a convenient, reliable way to curb their enthusiasm, Frank tweets this:

These homemade battery spacers are amazing! Better than anything else I've tried (foil, paper clips, etc) to make a slow moving buggy.
* One flat-head machine screw (#6-32 x 2"))
* Two fender washers (1/8" x 1")
* Three #6-32 hex nuts#iteachphysics #modphys pic.twitter.com/r5gCvpSGJw

— Frank Noschese (@fnoschese) October 25, 2019

Spring demo set-up

I joke with my classes that the last class of the day gets the best version of me. At least today it only took one period for me to get this worked out.

My AP Physics C are studying simple harmonic motion and the most common type is a block attached to a spring on a horizontal friction less surface. Surprisingly our book does not touch upon springs in series and parallel. Students did a quick activity using PhET's Hooke's Law simulation the other day, leading them to the equations to find the equivalent spring constant if series and parallel pendulums. We ran out of time that day to show it to them live so I set it up for the next day.

I had two identical springs of spring constant 20 N/m +10% that I hung from a horizontal support attached to two large ring stands. I used a pegboard hook to link the two springs when working in parallel which made it easier to hang one mass from it. For the first class of the day I hung a 500 gram mass from a single spring, then the two springs in series and then in parallel so the class could see the difference. The series elongation was very easy to see the difference but the parallel elongation was harder for those in the back. So I added to it between classes.

I used bright post-its and labeled the natural length of one spring, where it stretched to in parallel and in series. I taped a measuring tape in line with the top of the spring so if I wanted to, I could do calculations. It made for a much better visual for the students.

After the fact I realized I wanted to add a marker for the natural length for the two in series since the new length is much larger than twice the stretch of the single spring because of the additional length of the second spring. If I had enough springs of the same spring constant I would want to have all three setups up at the same time. Add that one to the wishlist I guess.

Challenge Accepted: 2019 Top Safety Picks

On Wednesday, The Insurance Institute for Highway Safety (IIHS) released its 2019 list of Top Safety Picks and Top Safety Picks+, it's two highest ratings for vehicle safety.

"Challenge Accepted" is the title of their report; IIHS increases the rigors required for vehicles to earn the top ratings. They keep the goalposts moving to compel manufacturers to better protect occupants each year. IIHS hopes that the 57 models that qualified for this initial list will be joined by more models as 2019 moves forward.



Years ago, Griff Jones worked with the IIHS to create the classic, Understanding Car Crashes: It's Basic Physics. It's an excellent capstone for instruction in mechanics. As mentioned in a previous post, I developed a fairly robust single-period lesson around vehicle safety and Jones' video.

YouTube Physics—Understanding Car Crashes: It's Basic Physics @ TPT 

It brings the physics home to the students and gets them talking about vehicles they ride in or might aspire to own. I hope the lesson plants a seed that will get them to make vehicle safety and crashworthiness a primary factor when they consider a vehicle purchase.

As a native of Michigan, I was disappointed to see only one American model listed as a Top Safety Pick. Japanese, South Korean, and German makes and models proliferate these lists. I hope US nameplates step up their game, but their track record does not nourish my hope.

#AAPTSM18: Using physics to win a tug-of-war

I will post as many gems as I can from the American Association of Physics Teachers Summer Meeting held in Washington, DC July 28-August 1, 2018. On Twitter, that's #AAPTSM18. The items may be new or classic; simple or complex. Here's one such gem.

At the "30 Demos in 60 Minutes" session, Colorado State's Brian Jones—director of The Little Shop of Physics and author of College Physics by Knight, Jones, and Field—showed us his secret to winning a tug-of-war.

Brian Jones Tug-of-War


I love it: so simple!. Two concerns:

Those once-ubiquitous single-use plastic bags may be an endangered species as voters outlaw them out of concern for the growing plastic islands and gyres in the oceans. It should work equally well with the thicker multiple-use bags that are now coming online.

I wonder if this will work as well on tile as it does on carpet. It clearly works like a charm on carpet. I guess I'll find out soon enough how well it works on tile.

Catch and Splash: Grass Omelette XVII

After a few year's dalliance with Energy before Momentum, I have switched back to Momentum before Energy. Please don't flame!

One benefit to the return is that our annual egg toss competition, Grass Omelette, has returned to late October/early November. And that increases the likelihood of nice weather.

We conduct the event prior to any discussion on impulse so that we can refer to it during or after our lessons on F∆t = m∆v.

I shoot the catches at 120 fps so that I can pull half-decent still images of "splashes" to give to the individual students who were brave enough to don the plastic ponchos and kilts. I'm currently using a Panasonic Lumix DMC-FZ200. Maybe in the future, I'll shoot normal-speed 4K video to get better stills. At some point, consumer high-speed 4K will be available. I know the Sony RX10 iv can shoot 24 fps at full resolution (as well as 960 fps lower-res high-speed).

In any case...

Egg Toss 2017 Catches

Egg Toss 2017 Splashes

When I had 5 sections of Physics (no AP anything and no Conceptual Physics) in 2013, I had enough to produce an amusing compendium set to Vangelis' Chariots of Fire.

Egg Toss 2013

Simple demo big gains

I have noticed a big difference in student comprehension when the problems become real to them. Simple visuals can have a big impact on the students "getting it." I can't count the number of times I've tossed a tennis ball around to make a point. Somehow holding the tennis ball at different heights or just tossing it up to catch it again can lead to "Oooh now I see what's happening!" So I have several simple demos that help students visualize their problems, a block or two hanging from the ceiling with spring scales, a stuffed toy in a bucket, etc. 

When we studied springs I found a Pasco spring demo set with five springs all of the same length but different spring constants. The first stage was to hang a 20 g mass from the red spring and see it barely settle above the table. I asked students what would happen if I were to hang a 500 g mass then from the green (which they assumed was identical). They were surprised at its shorter elongation and when I asked why they all said "it has a larger spring constant."

For the next stage I set up two large ring stands with another bar clamped horizontally between them. I dramatically assure students it is level with the springs hanging at their relaxed length. Then I hang a 500 g mass from each and they can see the slight differences in elongation. Then the 500 g masses are switched out for 1 kg and the difference between them becomes more pronounced (left). Applying this to Hooke's Law they could all calculate the spring constant for each spring. But this made it way more interesting than five given forces and elongation lengths to calculate the spring constant from a word problem. 

When my AP Physics C class started center of mass, many could calculate the center of mass with equations but had a hard time visualizing what that actually meant. A common problem involves materials of different densities stuck together, for example a piece of aluminum and a piece of iron. To make a real life version I found a piece of Styrofoam that was the same thickness as a piece of scrap wood. I drilled three holes in the wood, stuck three dowels into the holes and stuck the dowels into the Styrofoam. I wrapped the whole thing in paper to make it appear uniform but I did tell students it was made of two different materials. I showed it to students and asked what information they would need to solve for the center of mass. Of course I play with them a bit and after each response I say, "Ok, now you can solve it right?" to which they predictably respond, "No, we need XYZ too!" Eventually, I give them the dimensions of the whole thing and let them solve for it. The dimensions are listed on the paper below (the "total mass" includes the paper in case they ask).

They are not surprised that the center of mass is closer to the wood side but they are surprised that for this particular arrangement it's actually on the wood. It's a simple practice problem but once they're done I can balance the piece on my hand at (almost) the exact position they predicted, about 5 cm in from the wood side. Students that struggle with this homework problem were successful with this in-class practice problem. 

Another simple one my colleague Jessie Chen shared with me can be done by every student in your class on the cheap. Like less than $1 cheap. Most dollar stores sell packs of cards for $1, or even a double pack if you're lucky. Each student will need one plastic playing card (or index card) folded at a right angle along the length of the card. Place it on the corner of the table with one corner hanging off the edge of the table. Place two pennies on the card so that one is on the portion on the table and one is on the portion hanging off the table. You can use a pen or pencil to press on the card so that when it moves it pivots around that point. Flick the vertical part of the card on the side that is hanging off the table. This causes the card to move so that it is no longer supporting the penny hanging off the table and it will fall straight down due to gravity. On the other side the vertical portion of the card will push forward, applying a horizontal velocity to the penny and making it shoot off the table in a half a parabola shape. You can hear (and see) the two pennies hitting the ground at the same time. Many of us have a fancy machine that demos this for us, sometimes called a "Drop/shot" or a Newton's Second Law machine, and those work great, don't get me wrong. But to be able to hand these to my students and have them try it, nothing can be better than that! 

Reining in the kilogram once and for all

It seems we're been here before. More than once. The kilogram: a pesky unit of measure that hasn't been behaving itself.

Derek Muller goes deep into the explanation of the newly redefined kilogram. The task is not trivial. I may need to rewatch this robust explainer a couple of times before it all sinks in. Have a seat and prepare to get your geek on: there will be mathematics!

How We're Redefining the kg

Understanding Even More Car Crashes

I posted a lesson to accompany the IIHS "classic", Understanding Car Crashes a few years ago. If that post doesn't ring a bell, click here. Links to the video and lesson can be found in that original post.

A related story percolated up through my social media feed a few days ago. National Public Radio's Goats and Soda produced a story about the Latin New Car Assessment Program (NCAP). NCAP ran a crash test that pitted entry level Nissan vehicles against each other: The American Versa vs. the Mexican Tsura.

Crash Test Dummies Show The Difference Between Cars In Mexico And U.S.

Here's the video:

2015 Nissan Tsura vs. 2016 Nissan Versa


[Executive summary: The American passenger fares much better than Mexican passenger.]

When news of the test went public, Nissan announced that Nissan Mexico would discontinue sales of the Tsura in a few months.

It could be that the timing of Nissan's announcement coinciding with NCAP's test was... coincidental. That is a real possibility.

On a tangentially related oldie-but-goodie, some folks think cars from yesteryear were tanks that would decimate today's light-weight counterparts. An instuctive crash test pits a 2009 Impala against a 1959 Bel Air. Watch the video to see how that one turned out.

2009 Chevrolet Impala vs. 1959 Chevrolet Bel Air


If you're a classic car enthusiast, drive carefully!

The lesson I constructed includes an exercise in which students look up the IIHS safety test of the car they drive (or are commonly driven in).

Forces Match Graph: The Presidential Election Challenge

I developed an activity using force sensors to create a visual representation of Newton's Third Law.

The activity includes a brief exploration of the force sensor, then engages students within lab groups to conduct miniature tug-of-war sessions using the force while the computer records force vs. time data to plot a real-time graph.

The symmetry of the plots revels that whenever one object exerts a force on a second object, the second exerts a force on the first that is equal in magnitude and opposite in direction.

The plot also resembles the "probability of winning" graphs produced by Nate Silver's FiveThirtyEight team.

So I challenged early finishers of the lab to try their hands (literally) at reproducing the Presidential graph using force sensors. I thought the students did a fine job of it.



Here's the student sheet for the activity. It's adapted from the one included in the Conceptual Physics lab manual authored by Paul Hewitt and me.

The Force Mirror

Nate Silver's graphs can be found at FiveThirtyEight.