Posts in Category: course notes
bubble observations
This narrative describes our first task.
Walking into a first day of a science class, one of the proclamations that we’re conditioned to hear is about the power of the “scientific method.” There are plenty of first chapters of textbooks that devote themselves to describing a bit about what science is for, how it’s both an extension of things we naturally do, and a sharp contrast to other ways of knowing. And then there’s that scientific method. Each text is a little different on this point, but the essence is that we root out truth by testing our explanations against what we actually observe.
But I think we need to start somewhere else, back just a bit. I’m not sure that we really always agree on what it means to “observe.” And, it’s probably good to actually put this into practice. Observation is like any other skill.
For me, a sensible introduction to physical science is to begin with soap bubbles. This could be with a sink full of water and some dish detergent, or it could be some canister of stuff that you have left over from a summer birthday party. There are a few recipes that I like, but the basics of any of them include about 12 parts water and one part simple dish detergent. Put a wand, a straw, or even the end of a pipe or funnel into the solution so that a film stretches across one end, and then blow through the other.
What do you observe?
Get out your science journal. This could be a simple composition notebook, lined or unlined in any fashion you like. For me, the important part is that it’s a notebook that accompanies you and records ideas, observations, questions, and pursuits that may or may not lead to anything else. It’s not necessary that it’s pristine or even particularly well organized. You can display your edited genius in some other way, but this should be something that’s flooded with mistakes, ramblings, and snippets of ideas. It’s your blueprint of potential.
Find a page to start and document bubble observations. Having a partner in this pursuit is useful, not only because one person could be blowing the bubbles and the other could observe something closely, but because one person’s observation can lead to another. That said, there’s something about just sitting with an observation all to yourself. It’s up to you. (Often I’d have you start this in class, with a partner; and then you’d head home armed with your notebook and your bubbles to do more observations yourself.)
One of my favorite photos is this one of a girl playing with a giant soap bubble.
What do you observe?
It’s a good example of the many things that we could find in a soap bubble if we look closely. First, there’s the bubble itself, stuck to her hands. There are colors that are rainbow-ish, but not really the same colors that you see in a rainbow. Then, looking a little more closely, there’s a reflection of the sun at the top of the bubble, as well as another at the bottom of the bubble. There’s a big drop of bubble goo starting to form at the bottom, too. And there are hands — not just those holding the bubble, but reflected images of those hands at different places. Look some more and you’ll see that the photographer is in this image as well, reflected back from the front surface, his camera and hand towards the center, his legs and feet at the bottom. Each time I look at this image, I see something new.
Your first observations might be about how the bubbles form, how they fall or drift, what they do when they hit the ground, how they interact with one another, and on and on.
Keep observing. There’s no rush, and there’s plenty to see.
_____
The following essay, written by Samuel Scudder, was about his first experience in graduate school. He showed up to essentially begin his apprenticeship as a research scientist, ready to study insects. His professor greets Scudder and tasks the student with observing, of all things, a dead fish.
The Student, the Fish, and Agassiz,” by Samuel Scudder (1879).
Give this a read and consider what’s happening to Scudder and how he’s learning to observe. Go back to your own bubbles, again, and observe as Scudder might recommend to an apprentice scientist.
Go ahead, I’ll wait.
_____
What kinds of things do you observe with the bubbles now that you didn’t see before?
In general, we see more details that might seem more elaborate; we might take a pencil (like Scudder did) to start to observe through writing and drawing; and it might occur to you for the first time to note that the bubbles are round, just like fishes are symmetrical.
It should be no surprise that Scudder wasn’t the first nor the last person to observe a fish. Here’s another account:
“The Fish”, by Billy Collins (as published in the New York Times, along with some recipes)
Billy Collins is a notable poet, holding the position of U.S. Poet Laureate from 2001 – 2003. His observation of a fish is quite different — and not just because he’s at a restaurant in Pittsburg, although that’s clearly part of it.
Consider the perspective of a poet. Go back to your bubbles and observe again, still using that notebook, but now looking through the lens of a poet or perhaps even another artist. You don’t need to write your own poems (though no one is stopping you). Just observe from this new perspective.
Now, what do you see?
_____
The point of this exercise is two-fold:
First, observation is something that we take for granted as a practice and a skill. It’s at the very heart of what science does, where it starts. We don’t come up with questions or investigations or models or anything else until we’ve experienced phenomena in some way. Sometimes, the experience is in the mind’s eye, constructed from other things that we know, like with something as exotic as a black hole. Most of the time, though, I suspect that we start with an observation that’s very simple, seen but unobserved until we take the time to really delve into it.
Second, “observation” isn’t an action without context. The observations are different and differently directed if we look at something as a scientist rather than as a poet. As a scientist, we look for patterns that lead to an understanding of how things are put together, why they might move the way they do, how they function. As poets, we probably associate other meanings with what we see. Empathy and metaphors, statements about the human condition and how we can relate these to one another — these are all outside of scientific reach, but they’re still valuable in their own way and with their own purpose. The work of the scientist might impact the work of the poet (or the painter or the philosopher or the writer or anyone else), but it’s important to be clear about which of these lenses we’re wearing. Throughout this course, we’ll refine the lens we use as scientists, but this doesn’t mean the other lenses are less valuable. They just have different goals.
introductions
One of the very first tasks of this course is “introductions.” All the students in the class write a quick description of who they are, and I’m always impressed with people who can play water polo or bowl competitively; people who have complicated family lives that are really relatable or totally different from my own; people who aspire to be teachers but have an apprehension about science. People reveal all this stuff simply because I ask them, and I’ve found that as the semester goes by I get to learn more things about you, which only makes me realize that there’s still more that I don’t know. You’re all really interesting and complicated.
So, I figured that it’s only fair that I am at least as transparent about who I am. I’m a lot less complicated than you might think. And you probably don’t need to know anything about me in the first place, but I’ll offer it.
If you’re realizing right here on this line that you’d rather not take any additional time to learn any more about me, you can stop. I love teaching and the natural world and my family. Everything else derives from this. The end.
Here’s the rest:
Sometimes I have to give a presentation and someone will ask for a “bio,” or, I have to fill out a report an include what’s known as a curriculum vita or “CV.” I stow these kinds of things in the trunk of my university webpage, and I distill a few things onto a personal page, but a lot of that paints the same, plain picture. It’s just me in my khaki pants, maybe with my shirt sleeves rolled up.
Here’s a list of things that I like, in no particular order:
- I’m married to Karyn, and we have two kids. They used to be much smaller. The kids, I mean. Karyn’s about the same size as when I first met her. I really like going home.
- I love being outside on a trail. I try to do a long backpack trip each year (including this recent one to get a view of the solar eclipse from a pass in the Wind Rivers) as well as some shorter treks. Over the last few years I’ve started trail running, even though I used to believe that running is dumb. Now, a ten-mile run is one of my favorite things to do early on a Sunday morning.
- I play piano. Most people wouldn’t know this about me, but recently there’s been more opportunity to figure it out through this band that I’m in. I’m always struggling to get better at it, especially now that I play with other people. Making music has been really important for me to understand bigger things, like how we learn and how people can collaborate. But I also simply love playing jazz chord progressions with a band because it’s really, really fun.
- I founded a program where we get to play and do science with kids in Ogden City parks over the summer. I host a small conference in science education and I do a lot of other work with teachers around the state. I recently got involved with a dance|science project that actually put me on a stage and now has me collaborate to host workshops. I’m also working (slowly) on a project to document and describe more deeply what it means “to learn.” All of this is called “work,” which makes me giggle.
A summary of all this is that I really, really love to play with the natural world and try to figure out how we learn this stuff. I think that learning science is a form of really engaged play, and I think that learning science and doing science both take on that kind of playfulness. This isn’t to say that it’s easy. It’s hard. Really hard. So, when people come to a class like this and say that they’re intimidated by science or that they’re scared of this class, I can think of a million reasons why this could be the case. I’d like to remove a lot of those reasons, but I’m happy to honor the fact that it’s challenging—just like baking a good loaf of sourdough or playing a violin concerto or teaching fourth grade. That’s what the course is all about. We’ll untangle explanations about the natural world and look for the simple rules, and in the process we’ll figure out how this is done by everyone from particle physicists to 5-year-olds.
journals and wonders
Where do we start to do science? I think this is a good question because it is one of those that seems like it should have an obvious, maybe trivial answer. There’s this presumption that “science is nothing more than a refinement of every day thinking,” as Einstein is frequently quoted with saying. But, even as you continue to read more Einstein and other science thinkers, it’s clear that it’s not just an extension of the kind of thinking we may be used to doing, but some kind of thinking and doing that we’ve invented. Sure, we can all do it, but we have to work at it. This is why we have science classes, after all, and why I have a job.
There’s another even more important consideration, though. We don’t just think about and create science out of nothing. We have to have something to wonder about. There has to be a natural world to observe, and we have to do that observation. That’s where we employ the most important scientific tool in this history of humankind: the pencil. Of course, along with the pencil (or any other writing tool) comes paper. But the essence of it all is that we have to start making observations and making sense of them in a way that we can share the ideas with others and maybe even start to see the ideas laid out in front of us, letting them take on a new light.
I encourage you to have a notebook that’s dedicated to observations and making sense of the world. In fact, it’s likely that you’re taking a course from me that requires a dedicated notebook for the class. I like to carry a small journal or notebook around with me to make sense of the world, and recently I’ve been inspired by seeing how an artist, Lynda Barry, uses a composition notebook to craft, teach, and document her classes. Here’s her product next to my own composition notebook:
Adam’s and Lynda’s notebooks, side by side.
Lynda is an artist, and she sees the world and makes sense of it through an artist’s lens:
A sample of Lynda’s course pages, incorporated into her notebook.
But I don’t think that this means that the concept and tool is only for the artist. In my own notebooks, I’ve started to use the space of the page not only to record something I don’t want to forget, but to start to work through the idea. Based on the idea of a friend of mine, Andy Gilbert, I’ve had some teachers I work with promote these as “Wonder Journals” for themselves and with their elementary students. It’s not just a record, but a place to start to create questions and even to see new things.
My own wonder journal for the course, next to Lynda’s composition notebook as well as my own everyday notebook.
Your first step: Get yourself your own, dedicated notebook. I got a relatively fancy one with thick paper and “quad ruled” squares on it so that I could write in different directions as well as make graphs and other sketches. This cost me about $3.50 at the bookstore, but with options to spend even less or much more. It doesn’t matter — whatever suits you and your style and workflow. Then, start breaking it in. Put your name on it, crack the spine a little, and see how the pencil or pen feels on the page. Go ahead and write in it as you start to see and wonder things, but rest assured that we’ll start filling things in with vigor starting on our first day of class.
analysis of motion
In our work on elevators, we measured the forces that were responsible for changes in motion. In summary, we found that an extra force (“net force”) is necessary only if there’s a change in motion. This is Newton’s 2nd Law of Motion.
Now we’ll look at measurements from a slightly different angle. Instead of considering the forces and how they vary, we’ll analyze the motion due to these forces — and then think about the forces after the fact. In this case, we can look at the upward and downward motion of a ball tossed straight up into the air. We’ll use iPads and a program called “Video Physics” by Vernier, but you have a collection of additional options that you can look into yourself, including:
- Video Physics (Vernier Software) for iOS — This is what we typically use in class
- iTrack Motion lite and iTrack Motion for iOS
- VidAnalysis free and VidAnalysis for Android
- Logger Pro (Vernier Software) for Mac and Windows. (You may have access to a site license for this as a student.)
- Tracker (Open Source) for Mac and Windows.
With any of these pieces of software, the idea is that you can take your own video, identify a specific object or a piece of an object (like a tennis ball, or a point on someone’s shirt) and trace it frame by frame. You simply locate the position of an object for each frame of the video, and then the software will take care of showing what happens to that object’s position and velocity over time.
Of course, the point of a lab like this is to actually do this and see how these things go. What I’m writing here is a description of something you are probably already working on. If you haven’t done this already, go download yourself some software, have a friend toss a tennis ball up in the air (or, someone could jump, or something else entirely) and track the motion of that object with the software. Go ahead. I’ll wait.
An object that has been thrown up into the air or has jumped from the ground has a vertical (y) position versus time plot that could look like so:
This is for someone jumping, tracing out a spot in the middle of a striped t-shirt. We can see the position on the shirt go down for the first 0.4 seconds, and then there’s a sudden upward motion that peaks and falls back down until a landing at about 1.2 seconds. There’s lots to appreciate here. For our purposes, we’re really interested in that smooth arching pattern that takes place while the jumper (or tennis ball) is in the air. We can tell where the object is going upward (the slope is positive), where it reaches its highest height (the slope is zero, or the graph flattens out), and when the object is falling downward (the slope is negative). And, we get a sense for how this velocity is changing. Our software package probably shows us this velocity as it changes. It’s not new information, but it’s useful to display the values for the velocities:
This graph shows velocities. At 0.5 seconds, we see there’s a maximum upwards velocity, and at about 1.1 seconds, there’s a maximum downwards velocity. At about 0.8 seconds, there’s actually a zero velocity. This is also communicated by the position graph, but in a different way.
NONE OF THIS IS OBVIOUS. Go ahead and stare and ponder and pull on your hair. Undoubtedly, we talk about and analyze and agonize about this in class, but it took physics about 2000 years to make these connections and see these patterns. You should spend at least another 20 minutes on it.
The most beautiful and important part about this is that the velocity is continually changing in a very consistent way while the object is in the air. This is what we call freefall. It happens when the object is falling down, but also when the object is on its way upwards. Continually, the change in an object’s velocity is always negative, always getting less, always showing that negative slope. This change in velocity is, as you’ll remember, due to a force. Since there’s only one consistent change to the velocity, there must be only one force — and that’s what gravity is. We’ve discovered that an object moving up or down is only subject to one continual force, that of gravity.
Now, if something like a bowling ball that we rolled earlier in the class were analyzed in the same manner, we’d see a position versus time graph look like this:
This is an object that is continually moving at the same (or close to the same) velocity. It’s making the same progress in position which each moment of time, a constant velocity. It is not accelerating in this direction.
The graph above is actually taken from someone leaping across a video frame. This is just one dimension, from left to right. But we know that she’s also in “freefall,” so we’d expect the graphs of her up-and-down, vertical velocity to look just like what we’d had before:
This is perfectly allowable. An object can move left to right with a constant velocity, but be falling in the vertical direction. We see this all the time; and you’re used to those kinds of arch-like patterns as something flies through the air. You can probably think of a few.
Here’s the thing. What if you saw vertical motion graphs that looked like these?
Where there are a lot of similarities to our original graphs, but in these cases something happens right in the middle. There’s a leveling off in the position graph, and you see that we have almost zero up-and-down velocity. It’s as though someone is levitating, not moving up or down. That’s weird, right? It’s as though someone turned gravity off!
But this isn’t really possible. You know, based on the patterns and your analysis of them, that there must be something else going on. That’s the point of patterns: You now know what to expect, and when something doesn’t match the expected pattern, you know that something else strange happened. There must be another factor to consider.
In this case, the person who was leaping did something like this. You can imagine that as this dancer jumped and lifted up her legs into this leap, the mass of her legs made up for or compensated for the rest of her mass. If we were just tracing the top of her head as she raised her legs into the splits, we’d miss what the mass of her legs was doing in the overall motion. Her “center of mass” is rising with her legs, allowing her head to stay level. This makes the dancer look as if she’s levitating, momentarily. It creates a plateau in the graph and a horizontal, levitating motion in her leap. We see this aesthetic in both the graph and in the dance.
an elevator investigation
Investigate
Find yourself an elevator that’s reliable and, ideally, not too busy. Actually, the “too busy” part isn’t that important. It’s more fun to do this when others are watching.
Bring a standard bathroom scale on an elevator. The scale should be able to show you a continuous readout, so typically the scales with the old fashioned, analog dial are best. Stand on the scale while riding the elevator, in particular paying attention to the following conditions:
- Stopped, before any motion has occured
- Just starting to go upwards
- Going upwards, in between floors
- Coming to a stop as the elevator is going upwards
- Just starting to go downwards
- Going downwards, in between floors
- Coming to a stop as the elevator is going downwards
(In case you’re not in the vicinity of an elevator and/or you don’t have a bathroom scale or something similar, I’ve created this for you.)
Before you actually set off and make these observations, imagine what will be happening and think about what you expect will happen to the value on the scale.
When you’re on the elevator, make notes about what you observe and when you observe them, paying attention to the value that the scale reads under the different conditions, as well as any other oddities.
Reflect on your data and think about what these mean. Did the scale reading change in the way you were expecting? What do those scale readings actually mean — if they’re changing at all, it’s probably not due to your weight actually changing.
Debrief
When I first started teaching in the 6-story lab building of our campus, I quickly realized the potential in the infrastructure of the building. There are classic hypothetical problems and thought experiments about elevators, but it isn’t often that we actually put the absurd case studies to a test.
I love to put students on elevators, armed with their notebooks and a careful eye for what’s happening. And, they shoudl also be standing on scales. Alternatively, they could have a cart along with a grocery scale or perhaps a spring scale with a mass hanging from it. But the ideal is to be actually standing on the scale because this is the situation that we use to imagine the actual forces involved in going up and down.
When I first did this with a group of students early in my career, I had one who came back to me, dissatisfied and dismayed. He told me there was something wrong with the measurements: After they’d initially started, the weight he was reading was the same as his actual weight, even while the elevator was heading upwards. What did they do wrong, he wondered? If you’ve done the investigation, you realize that this is (hopefully) exactly the same result that you experienced. What does it mean?
The scale doesn’t necessarily tell you your “weight.” Rather, it tells you how much force the scale is pushing up with. When you’re at home weighing yourself, these two forces exactly balance one another, so you are assured that the reading on the scale is the same as your weight. This also holds true when you are moving at a constant velocity. It turns out, moving at a constant pace either in the upward or downward direction, that no extra forces are needed — the scale has the same reading as your weight. This tells us that constant velocity motion is natural, just as Newton’s 1st Law states. You don’t need any extra force pushing you in one direction or the other. Once you’re moving, you only need the force that’s necessary to balance your weight.
(This should feel counterintuitive in some ways. Go ahead and wrestle with it.)
However, in the elevator, there are instances where your motion changes. When the elevator slows down, speeds up, comes to a stop, or starts up, you have changes in the motion. It’s in these cases that an extra, net force is required. The scale has to push a little harder in the upward direction — more than just your weight — to produce changes in that direction. There is an upward change when you are just starting to go upward, but also when you are heading downward and coming to a stop. (Even if your motion is downward, you can still be changing towards the upward direction, just as you can pay money towards a loan but still be in debt.) The scale pushes with less force than your weight if the change in your motion is downward — as you’re heading upward and coming to a stop, or as you just start to head in the downward direction.
Elevators are an interesting case to me because many use them on a regular basis, but we still might not pay attention to how they’re exerting forces. I love the ridiculousness of standing on a scale in an elevator, but I especially like the simplicity of using the scale as a scientific instrument. It tells us something fundamental about motion, as well as about what conditions an extra force is required.