The appendix has long been supposed to be a vestigial, useless organ. But a 2007 study suggests that it might have had — and may still have in many developing countries — an important role in digestion. It may provide a refuge for helpful, commensal bacteria to repopulate our guts after we purge when we get sick (Bollinger et al., 2007):
The organs of the lower digestive system. The appendix is located in the lower left, near where the small and large intestines meet. Image from Wikipedia.
… the human appendix is well suited as a “safe house” for commensal bacteria, providing support for bacterial growth and potentially facilitating re-inoculation of the colon in the event that the contents of the intestinal tract are purged following exposure to a pathogen.
The shape of the appendix is perfectly suited as a sanctuary for bacteria: Its narrow opening prevents an influx of the intestinal contents, and it’s situated inaccessibly outside the main flow of the fecal stream.
A ball rolling down a ramp hits a car which moves off uphill. Can you come up with an experiment to predict how far the car will move if the ball is released from any height? What if different masses of balls are used?
Students try to figure out the relationship between the ball's release height and how far the car moves.
For my middle school class, who’ve been dealing with linear relationships all year, they could do this easily if the distance the car moves is directly proportional to height from which the ball was released?
The question ultimately comes down to momentum, but I really didn’t know if the experiment would work out to be a nice linear relationship. If you do the math, you’ll find that release height and the maximum distance the car moves are directly proportional if the momentum transferred to the car by the ball is also directly proportional to the velocity at impact. Given that wooden ball and hard plastic car would probably have a very elastic collision I figured there would be a good chance that this would be the case and the experiment would work.
It worked did well enough. Not perfectly, but well enough.
One of the middle-school projects is to build a little solar water heater. By simply pumping water through a black tube that’s sitting in the sun, you can raise the temperature of the water by about 15°C in about 15 minutes.
The solar water heater in action.
Next year I want to try building an actual solar water heater, similar to the passive air heater my students built two years ago, with the tubing in a greenhouse box to see just how efficient we can make it.
The discussion started off with projectiles. If you’re floating in space — zero gravity — and throw something, like a basketball, away from you, you’ll be pushed off in the opposite direction. In fact, if you throw something that has the exact same mass as you do away from yourself, you’ll move off in the opposite direction with the exact same speed as the thing you threw.
Then I brought up rockets, and how they’re expelling gas to move them forward. I think it was the phrase, “expelling gas” that did it. The next question, which the student brought up somewhat circumspectly, sidling around the issue and the language, was (more or less), “So if you expel gas in space will you move off in the other direction?”
The simple answer, appropriate to that stage of the discussion, was, of course, “Yes.”
Which lead to to, “What about spitting?”
“Yes.”
“What about, you know, peeing?”
“Yes, except …”
At that point I thought it would be wise to rein it in a little, and make a further point about the whole action-reaction thing.
“You see, if you expel anything, wouldn’t it just be stuck in your spacesuit with you? Then you’re not really expelling it, it’s still attached to you, so you wouldn’t really move. What would be more useful would be to collect it in something like a spray can or a squeeze bottle. Then you can just squirt it out opposite the direction you want to go in to control your movement.”
This produced a moment of thoughtful silence as they figured out the logistics.
Notes
I thought this was a useful conversation to have. The students were interested and animated. And I believe it’ll be memorable too.
An artist's concept depicts the Deep Space 1 probe with its ion engine operating at full thrust. Image via NASA.
P.S.: I’d wanted to talk about ion drives, which operate on the same reaction principle, but are much cooler (after all they’re used in Star Trek). Instead of burning fuel to create the propulsive force ion drives generate an electric field that ejects charged particles; we’d been talking about ions and charged particles earlier in the day. However, I decided on the day that it would just complicate what was a new issue. I’ll probably bring it up this week though as we recurse through Newton’s Laws.
Waiting, observing, and recording as the snow melts on the hot plate.
Though it might not sound much more interesting than watching paint dry, the relationships between phase changes, heat, and temperature are nicely illustrated by melting a beaker of snow on a hot plate.
A light, overnight snowfall, lingers on the branches that cross the creek.
This week’s snowfall created an opportunity I was eager to take. We have access to an ice machine, but closely packed snow works much better for this experiment, I think; the small snowflakes have larger surface-area to volume ratio, so they melt much more evenly, and demonstrate the latent heat of melting much more effectively.
Instructions
My instructions to the students are simple: collect some snow, and observe how it melts on the hot plate.
I also ask them to determine the mass and density of the snow before (and after) the melting, so I could show that throughout the phase changes and transformations the mass does not change (at least not a lot) and so they can practice calculating density1,2.
Procedure
I broke up my middle school students into groups of 2 or 3 and had them come up with a procedure and list of materials before they started. As usual I had to restrain a few of the over-eager ones who wanted to just rush out and collect the snow.
A 600 ml beaker filled with (cold) snow. A thermometer is embedded in the ice.
I guided their decision-making a little, so they would use glass beakers for the collection and melting. Because I wasn’t sure what the density of the packed snow would be, I suggested the larger, 600 ml beakers, which turned out to work very well. They ended up with somewhere between 350 and 400 grams of snow, giving densities around 0.65 g/ml.
When they put the beakers on the hot-plate, I specifically asked the students to observe and record, every minute or so, the changes in:
temperature,
volume
appearance
I had them continue to record until the water was boiling. This produced the question, “How do we know when it’s boiling?” My answer was that they’d know when they saw the temperature stop changing.
They also needed to stir the water well, especially when the ice was melting, so they could get a “good”, uniform temperature reading.
Results
We ended up with some very beautiful graphs.
Temperature Change
Changing temperature with time as the beaker of snow melted into water and then came to a boil. Graph by E.F.
The temperature graph clearly shows three distinct segments:
In the first few minutes (about 8 min), the temperature remains relatively constant, near the freezing/melting point of water: 0 ºC.
Then the temperature starts to rise, at an constant rate, for about 20 minutes.
Finally, when the water reaches close to 100 ºC, its boiling point, the temperature stops changing.
Volume Change
The graph of volume versus time is a little rougher because the gradations on the 600 ml beaker were about 25 ml apart. However, it shows quite clearly that the volume of the container decreases for the first 10 minutes or so as the ice melts, then remains constant for the rest of the time.
The change in volume with time of the melting ice. Graph by E.F.
Analysis
To highlight the significant changes I made copies of the temperature and volume graphs on transparencies so they could be overlain, and shown on the overhead projector.
Melting Ice: Latent Heat of Melting/Fusion
Comparison of temperature and volume change data shows that the temperature starts to rise when the volume stops changing.
The fact that the temperature only starts to rise when the volume stops changing is no coincidence. The density of the snow is only about 65% of the density of water (0.65 g/ml versus 1 g/ml), so as the snow melts into water (a phase change) the volume in the beaker reduces.
When the snow is melted the volume stops changing and then the temperature starts to rise.
The temperature does not rise until the snow has melted because during the melting the heat from the hot plate is being used to melt the snow. The transformation from solid ice to liquid water is called a phase change, and this particular phase change requires heat. The heat required to melt one gram of ice is called the latent heat of melting, which is about 80 calories (334 J/g) for water.
Conversely, the heat that needs to be taken away to freeze one gram of water into ice (called the latent heat of fusion) is also 80 calories.
So if we had 400 grams of snow then, to melt all the ice, it would take:
400 g × 80 cal/g = 32,000 calories
Since the graph shows that it takes approximately 10 minutes (600 seconds) to melt all the snow the we can calculate that the rate at which heat was added to the beaker is:
32,000 cal ÷ 10 min = 3,200 cal/min
Constantly Rising Temperature
The second section of the temperature graph, when the temperature rises at an almost constant rate, occurs after all the now has melted and the beaker is now full of water. I asked my students to use their observations from the experiment to annotate the graphs. I also asked a few of my students who have worked on the equation of a line in algebra to draw their best-fit straight lines and then determine the equation.
The rising temperatures in the middle of the graph can be modeled with a straight line. Graph by A.F.
All the equations were different because each small group started with different masses of snow, we used two different hot plates, and even students who used the same data would, naturally, draw slightly different best-fit lines. However, for an example, the equation determined from the data shown in the figure above is:
y = 4.375 x – 35
Since our graph is of Temperature (T) versus time (t) we should really write the equation as:
T = 4.375 t – 35
It is important to realize that the slope of the line (4.375) is the change in temperature with time, so it has units of ºC/min:
slope = 4.375 ºC/min
which means that the temperature of the water rises by 4.375 ºC every minute.
NOTE: It would be very nice to be able to have all the students compare all their data. Because of the different initial masses of water we’d only be able to compare the slopes of the lines (4.375 ºC/min in this case, but another student in the same group came up with 5 ºC/min).
Furthermore, we would also have to normalize with respect to the mass of the ice by dividing the slope by mass, which, for the case where the slope was 4.375 ºC/min and the mass was 400 g, would give:
4.375 ºC/min ÷ 400 g = 0.011 ºC/min/g
Specific Heat Capacity of Water
A better alternative for comparison would be to figure out how much heat it takes to raise the temperature of one gram of water by one degree Celsius. This can be done because we earlier calculated how much heat is being added to the beaker when we were looking at the melting of the ice.
In this case, using the heating rate of 3,200 cal/min, a mass of 400 g, and a rising temperature rate (slope from the curve) of 4.375 ºC/min we can:
The amount of heat it takes to raise the temperature of one gram of a substance by one degree Celsius is called its specific heat capacity. We calculated a specific heat capacity of water here of 1.8 cal/ºC/g. The actual specific heat capacity of water is 1 cal/ºC/g, so our measurements are a wee bit off, but at least in the same ballpark (order of magnitude). Using the students actual mass measurements (instead of using the approximate 400g) might help.
Evaporating Water
Finally, in the last segment of the graph, the temperature levels off again at about 100 ºC when the water starts to boil. Just like the first part where the ice was melting into water, here the water is boiling off to create water vapor, which is also a phase change and also requires energy.
The energy required to boil one gram of water is 540 calories, which is called the latent heat of vaporization. The water will probably remain at 100 ºC until all the water boils off and then it will begin to rise again.
Conclusion
This project worked out very well, and there was so much to tie into it, including: physics, algebra, and graphing.
"Seasoning" a cast iron frying pan creates a non-stick coating. (Image by Evan-Amos via Wikipedia).
Back in the day, if you wanted a non-stick cooking skillet, your best option was to do it yourself by seasoning a cast metal pan. Sheryl Canter has an excellent post describing the science behind the “seasoning” process. The key is to bake on a little bit of oil to create a strong cross-linked polymer surface. This is a nice tie into our discussion of polymers and polymerization in the middle school science class; although I’m not sure how many of my students have actually seen a cast iron pan, or even know what cast iron is.
Normal polymers are long molecules made up of smaller molecules linked together, much like a paperclip chain.Cross-linked polymers are created when the long chained polymers are linked together by cross-links. It makes for a much sturdier molecule.
To season, you coat the pan with a thin layer of oil and bake it for a while (without anything in it). Baking releases free radicals from the metal that react with the oil to create a cross-linked polymer that’s really hard to break down or wear out, and prevent food from sticking to the pan. Different, cross linked polymers are used in car tires for their durability, but probably not for their lack of stickiness.
Apparently, linseed oil is the best seasoning agent, but it might be a bit hard to find.
Most non-stick, artificial surfaces, are also made of polymers of hydrocarbons, silicon oxides and other interesting chemicals.
Making a cross-linked polymer with borax and polyvinyl alcohol.
A selection of (as yet) unidentified fungi from the school campus in eastern Missouri.
It’s remarkable how interest drives motivation and motivation gets things done. We’re in an intercession right now and ten students signed up with me to do a biological survey of the school grounds. With a small creek on one side, and a fairly tall ridge on the other, the school has a nice variety of biomes.
Now, to be clear, I’m not a biologist. In fact, that’s why I was so interested in the biological survey. Everything in this area is new to me. But it also means that I approached this project as a novice. Mrs. E. was nice enough to lend me a veritable library of reference books, covering everything from the wildflowers of Missouri to the amphibians of the mid-West, but she was off teaching another batch of students how to cook, so I was on my own.
All the students in the group were volunteers, but a fair chunk of them just wanted to get outside, even though it was overcast and threatening rain. To get the students more engaged I let them choose either the environment they’d like to survey, or the types of organisms they’d like to specialize in. I also gave them the option of working independently or in pairs.
The Creek
The Creek team collected a pair of amphibians. They were documented, photographed, and then released.
One pair choose to canvas the small creek that runs past the school. I’d set a minnow trap the night before to collect fish for our tank, and they hauled that in. The stream water was somewhere around 14°C, while our tank was closer to 23°C, so, to prevent the fish from going into thermal shock, we left the minnows in a bucket so it could, slowly, thermally equilibrate. They monitored the temperature change with time, and I think I’ll use their data in my physics and calculus classes.
They also collected a pair of amphibians, which we photographed and then released. They tried to catch some crawfish, but were unsuccessful, despite the fact that one of them searched for “how to catch crawfish” on their phone; unfortunately they did not have time to follow the detailed video instructions they found on the web that described, in detail, how to build a crawfish trap.
Trees and Shrubs
Collected leaf specimens PL01 and PL02.
Because of the incipient rain, we did not take our reference books out with us. Instead, we collected leaves and sketched bark patterns so we could do our floral identification later.
Berries from an (as yet) unidentified bush.
A number of students really got into that. So we have a fairly large collection, though almost all of which come from the riparian area that bounds the creek. I would have liked a broader survey, but we only had so much time.
Unidentified wildflowers.
Mushrooms
Part of our mushroom collection.
More than a few students were interested in looking for mushrooms – even one of the tree specialists came back a mushroom sample – but one student really got into it, canvasing all the dead logs from the creek, through the meadow, and up past the treeline on the side of the hill.
The underside of this fungi looks a bit like a brain coral.
And we now have quite the collection of fungi. They’re as yet unidentified, but they’re elegant bits of biota. Our fungi specialist is interested in coming back in and sketching them.
Identification
We had two hours. Not even enough time to do a complete survey, so we barely got started on identification. It will probably go slowly.
While our methods were not systematic, and our coverage of the grounds incomplete, this exercise was a good start to cataloging the local biology. I don’t know if I’ll be able to expand on the survey any time soon, but this type of project would be a great for middle school science next year when we focus more on the biological sciences, particularly on taxonomy.
They’re a bit noisy, and would probably benefit from being reproduced in a more interactive format (Flash maybe), but they’re still a useful resource for talking about life cycles.
They’re a less dramatic presentation which can supplement the advocacy of the Story of Stuff video.
