Posts Tagged: data
motion analysis: rolling
I love to do this lab or one similar to it in person, but you can also conduct an investigation about motion on your own. I’ve created some videos that you can use to collect data (and maybe these will inspire you to setup a situation from which to collect your own data) and I’ve also given you a little bit of video instruction to help out.
Here’s the basic idea: You want to figure out how to characterize motion, but all we can really measure directly is a position (“where”) and a time (“when”). We look for changes in these two things to describe motion.
I’ve just found a pool ball and a smooth table that the ball will roll on. (Like I said, you could do this as well, but it turns out I have a really nice setup for this.) You will want to compile some data about when (time) the ball is in different locations (positions). By getting this motion of the ball on video, you have the ability to repeat the same motion over and over and collect whatever data you need. In this case, I’m suggesting that you collect data for the time it takes to go from the start position of 0cm to another given position. I’ve marked increments of 10cm, so you can get the time it takes to get to the 10cm mark, the 20cm mark, the 30cm mark, and so on. The biggest distance I have marked on the video is 120cm. By replaying the video and running your stopwatch 12 different times, you can get 12 different data pairs of position and time.
I explain this here:
Then, you can jump into collecting data. Start with this video of the pool ball on a flat table. There’s two different versions of the motion, one in real time and the other in slow motion. Just pick one of these.
Like I said, you can pause and go back over and over, each time finding the time it takes the ball to go from 0cm to another mark on the table. Record those times with their corresponding positions in your notebook.
Then, you can do the same with this video of a ball rolling on a sloped table:
Once you’ve made all your measurements, your data can go into a spreadsheet or another table, and then from this you can create a graph. By tradition, and so that we can all compare our graphs to one another, your graph should have the positions on the vertical axis (“y-axis”) and the times on the horizontal axis (“x-axis”). So, a blank version might look like this:
But you’ll be filling this in with your own data. You can do this by hand, of course, but it’s also straightforward to have a spreadsheet (Excel, Google Sheets, etc.) make the graph for you as you input your data. To give you an idea of what I mean and to get you started, here’s a template for a spreadsheet that you can copy or download. You can then edit your own version to your heart’s content. I’ve set this up so that as you input data in the appropriate columns you should see the graphs form magically, all by themselves. You’re also welcome to change the settings for the graph, although I’ve tried to make it so you don’t have to.
Enjoy! I’m excited to see your data and the patterns your data create. You’ll be thinking about why it looks this way and we’ll talk about what this all means. Your assignment will tell you what I’m looking for in your report.
tricky tracks and scattered words
In class, we worked together to make sense of data. We usually think of “data” as something that comes in numbers and graphs, like it did with pendulums and with motion data collected in lab. But it can take many forms, like this example we imagined of indentations on some sandstone:
(This is taken from a lesson often referred to as “Tricky Tracks.” An example is here, though the idea goes back a long time. This version comes from the National Research Council1.)
The fun thing about revealing this bit by bit is that we can start to imagine the possibilities and where this collection of observations is going to lead us. We made some points in our discussion that, even though I asked “what do you see?” many times we start to go straight to what we interpret. We have to be careful about this distinction. At the same time, there’s a lot of power that our sense-making adds to the observations. We start to see patterns and possibilities, and the way that we connect these observations to other things we’ve seen (other big and small organisms, predator-prey relationships, parent-child relationships, not to mention the idea of dinosaur tracks or bird tracks in general). How we find meaning in these data is important. We have to rely on the data and be ready to change our ideas if we find new, contradictory observations; but we also get to construct a new idea that the observations don’t tell us directly.
That was the point of where I took you next, suggesting that you look at the following set of words as if they had been spilled on a parking lot and you had to reconstruct their origin:
This isn’t a real scientific situation, but it’s something that’s a lot like our Tricky Tracks scenario or the way that we figure out the Earth goes around the Sun or how we figure out how matter is made out of lots of small particles we can’t see directly. We take all this evidence and put it together into patterns, knowing about other patterns and using our knowledge of the data at hand. For example, we know that words often come from stories, and we can start to imagine how these ideas could have been strung together. We might have something out of order before we get more information; and we might even have something really backwards at some point. For example, “crane” is a piece of equipment but it’s also a bird, and it’s also a verb, something we might do with our neck and head. But in the context of movers and dangles, we start to put together a possible use of a tall crane dangling a piano. Oh, and the “stories” seem to fit well with this, as long as they’re referring to levels of a building rather than narratives and tales. Though it could be both.
We also had to know a little bit to make more sense of this. “Steinway” is a famous line of pianos, but that isn’t necessarily familiar to you. “April” could be a month or a name of a person, though we start to imagine it’s about the calendar and season when we combine it with snow—something that might be surprising and story-worthy, but still possible.
There are lots of other examples of how different meanings and interpretations can get pulled into this. We’d always want to be able to look for more data and see if those fit as well. We’d also want to be able to compare this data set to others and see if there are similar patterns. When Venus was first observed with a telescope, for example, Galileo was able to see that it went through phases, like the Moon. But the pattern of apparent sizes and phases it goes through is different than the Moon’s, and this tells us something really important about orbits and positions of planets.
One of the most interesting things about this exercise (to me, at least) is how we all come up with very similar stories based on these words, for the most part. (There’s always a new, creative solution to this puzzle, I’ve noticed. That happens in science, too; and it’s really important that we allow for these when the data support them.) Nature will never directly reveal to us the answers to all our questions—we can’t go back in time and really see what happened between the two creators of the footprints we observed—even though we get really consistent, testable explanations. In this case, though, I’m happy to reveal to you where these words came from. It’s one of my very favorite poems, written by Taylor Mali, an advocate for teachers and teaching. It’s called Undivided Attention.
I like this exercise a lot as a way to help us understand how we create explanations from observations, and how that is more interesting than you might first imagine. But I’ll admit that I love doing this in class so that I have a chance to read this poem. It’s hanging over my desk and it’s often the last thing I see before I step into a class.
- National Academy of Sciences (1998). Teaching about evolution and the nature of science. Washington, D.C.: National Academy Press, p. 89. ↩
getting into the swing of data collection
One of our first tasks has been to collect some data on an object known as a “simple pendulum.” There’s no perfect simple pendulum, but instead this term is used to describe something that swings back and forth with all of its mass stuck to the end that’s swinging. A yo-yo swinging back and forth is a good example, or maybe a tetherball at the end of its cord; but lots of things are really close to a perfect simple pendulum. In fact, I was counting on the fact that you could find something that would work, likely right there in front of you.
Here are the instructions I gave for setting this up:
Then, you each collected data from your own objects: keys at the end of a lanyard, the adapter at the end of an electrical cord, a weight at tied to the end of a string, etc. These all work — though you might wonder if it’s okay to all be using different things if we’re going to share the data with one another. That’s a good question, and we’ll get to this.
After everyone reported data for the length of their pendulum and the time it took to swing 10 times, I took all of that and made a graph. Here’s an example:
I love this graph for a few reasons. First and foremost, you each collected ONE piece of data, and that single piece of information didn’t tell you very much. But now we have it in the context of all the other data. You can see how yours compared to others. More important, you can see if there are any patterns in these data. To me, it looks like there are. I tried to sketch some of what I’m seeing right on the graph:
MOST of the data show that the shorter strings take the least amount of time to swing, and the longest strings take the greatest amount of time. In addition, it looks like those times change most drastically when we change the shortest strings, and they change less for the longer strings. This makes a kind of curve that seems to be getting flatter and flatter as you go from left to right (shorter to longer strings). There’s a pattern here, and your data likely fits right into it. But we needed lots of these experiments in order to see the bigger picture. In fact, now we can even imagine that this curve could be described mathematically. Nature actually abides by this mathematical relationship — or maybe it even invents the mathematical relationship for which we needed to invent the mathematics!
For now, I’ll leave you with a few questions:
- Seeing that there’s a pattern here, what do you think a shorter pendulum would do? A longer pendulum? In other words, does this graph/pattern tell us about other pendulums we didn’t collect data for?
- I never told you to use a specific kind of object, so people probably used objects that had different masses (or weights). They probably also had bigger and smaller swings. Since we didn’t account for those variations, what might that mean?
- Not everything fits the pattern perfectly, and there are definitely a few outliers. Why? What do you think happened? What does this tell us about collecting data, conducting experiments, and creating investigations? Or, maybe more broadly, what does this tell us about science? Can we trust it?