Exploring balanced forces and the nature of locality with slinkies
I started this blog 2 years ago to mostly record the things I was doing in my physics classes. It’s been quite some time since I’ve written anything about physics teaching, so I thought I would take a moment to write up a fun lesson we did recently about slinkys.
First, stop everything and listen to this: Radiolab, What a Slinky Knows. This is a Radiolab podcast which features an interview with mathematician Steven Strogatz about a simple experiment with falling slinkys—what happens if you let a slinky hang vertically, come to equilibrium, and then release it from the top, like so:
I’ve done this demo many times before, but it wasn’t until I heard this podcast that I realized I could do so much more with this experiment and turn it into a lesson that shows very beginning physics students just how much they can explain with a few simple laws, and get to some pretty profound insights about what we can know in the process.
Don’t make them predict
Here’s how I used to do this demo:
me: Kids, see this slinky? What happens when I release it from rest? What will the bottom of the slinky do.
students: I bet it will fall?
me: sure, but when will the bottom start falling? The moment I let it go?
me: Ok, let’s test that out… (drops slinky)…bwhahaha it didn’t start to fall until the top of the slinky reached it…
students: physics is so confusing…
It took me a while to figure this out, but showing students a bunch of demos where the answers run counter to their intuition only serves to reinforce how difficult physics is and how wrong they are. They never really pick up the idea I wanted them to understand, that physics is counterintuitive, but with careful thought, they can understand it. And that’s likely because in a demo, I’m not giving them any time for careful thought—I’m just forcing them to make a off the cuff prediction which is almost certain to be wrong.
Start with a simpler question
So we start with a much simpler question. I take two common slinkys, break the class up into two groups and ask them to come up with a way to figure out how many links are int the slinky without having to count every individual link. One group gets a ruler, and the other group gets a slinky and a single link that I’ve cut from the slinky with a bolt cutter.
It doesn’t take long for one group to measure the height of the entire slinky and then the height of 10 rings, while the other group masses the individual ring and the entire slinky. Within a few minutes we come up with good agreement as a class, the slinky has about 50 links.
create a simpler system
Students realized that that the slinky is really just a giant spring. I proposed that we could simplify our analysis of it by modeling it as 3 links, the top, middle and bottom links, connected by two springs, the upper and lower springs.
Then I asks them to draw a system schema and the free body diagrams for each of the three coils at the moment just before the top coil is released. I get them started by asking them which one seemed simplest? Everyone agreed the bottom ring would be easiest to draw, since there are only two forces.
And I do have a conversation here with how we can calculate these forces, and get students to start to think about how big, relatively speaking the forces acting on the bottom coil are—we pass it around so that students can feel it in their hands.
Next I have them share their predictions for the middle ring, and everyone gets the right forces, but it takes some discussion to get to the idea that that the downward force of the lower spring on the middle ring is far, far greater than the gravitation force on the middle ring.
Next it’s a hop and skip to draw a free body diagram for the top coil, and by now, everyone is tuned in to the difference in sizes for the various forces.
I hold the slinky outstretched one more time, and the students can clearly see that links at the top are much more widely spaced than the links at the bottom, indicating that the tension in the slinky is greatest at the top and that it decreases as you move toward the bottom.
What happens when you let go?
Now that we have these 3 free body diagrams, everyone can see that before the top coil is released, all 3 coils have balanced forces. At this point in the year, the only major physics understanding we have is that balanced forces = constant velocity.
At the moment of release, when the force of the hand disappears, the top coil of the slinky will be experiencing a downward force some 50 times greater than its own weight. Even though we don’t have an understanding of unbalanced forces or acceleration, everyone can predict that this will mean the top part of the slinky will move downward much more quickly than if it were just falling, and this is something we can easily check with a quick experiment.
But while the top part of the slinky is falling, we look at the free body diagram for the middle coil and ask what is going there. The only way for the forces in this diagram to change is for the separation between the middle coil and its adjacent coils to change, and there’s no reason for this to happen since the top has just started to fall.
And once we think all this through, the students quickly come to agreement about the prediction that the slinky will collapse on itself, the top being quickly pulled downward by the spring force, and only once it is fully collapsed will the bottom link begin to fall with the rest of the slinky, just as we see in this great Veritasium video, which I then show to the students (after we test it ourselves).
After that, we listened to the first 5 minutes of the Radiolab episode from above, and I hoped I’d played enough to hook them to want to listen to the rest.
The Radiolab podcast is amazing since it explains that it isn’t just slinkys that fall in this weird way—people, pencils and basketballs do exactly the same thing—the bottom of a falling ball compresses just like a slinky, but the “springs” holding a basketball are much stiffer (and the distances often smaller) so that the compression time can be ignored and the object considered to be a single object. Radiolab also lays the foundation for thinking about extended objects down the road, by explaining to students that one part of an object has no idea what is going on with another part of the object. And this leads to a understanding of “locality”—we can only know about the things that are touching us directly (and a few special forces that work at a distance, like the gravitational force).
More and more, I think that the early part of mechanics to can feel pretty disconnected from the real world—it’s all frictionless carts on ramps, and massless pulleys with massless strings. If students watch even a few NOVA episodes before my class, they think physics is all string theory, black holes, and Higgs particles, but we mostly leave all of this stuff out of the introductory physics course because students don’t really have any ability to understand it.
What I love about this lesson, and the Radiolab podcast in particular, is that even in the earliest part of the year, when we don’t even have an understanding of Newton’s Second Law, we can examine a real world phenomenon, falling slinkys, and then see exactly why we want to model it in a more simplified physics-world way, so that we can use our understanding to correctly explain its behavior. And, thanks to Radiolab, this behavior tells us something profound about the universe, as Neil deGrasse Tyson says “we will forever be victims of the time delay between the information around us and our capacity to receive it,” or as Steve Strogatz puts it, “you’re always the bottom of the slinky.”