Day 29: More on Systems Thinking and Momentum

After our assessment, we tried some problems and did a little whiteboarding. A few things I learned from my students:

  • When students figure out momentum conservation on their own, they keep rediscovering it, and don't use a shortcut. They will calculate impulse on one object. Then they'd use Newton's Third Law to reason that the impulse on the other object is equal and opposite. And then they'd calculate the velocity of the second object. They'll also write momentum conservation in lots of interesting ways, including m₁∆v₁ = -m₂∆v₂. 
  • On the other hand, they really understand why momentum conservation works. They see that there's no net external force on the system, so they're no impulse on the system. That's why the total momentum doesn't change. I think this is worth it, especially since the biggest drawback is that they solve problems slower, which really isn't a drawback.
  • When students get stuck, they seem to stop. When I ask them to draw an SOS diagram (Sketch-Interaction Diagram-Sketch), they start working and then figure out their own way to solve the problem. It seems that they still don't realize how powerful drawing the picture is. 

Day 28: What Happens to Impulse if You Make the System Bigger?

After teaching the impulse-momentum relationship yesterday, I sent them off last night to try a few problems, telling them only that my new type of diagram for showing momentum transfer was an SOS diagram. The two S's stand for sketch, since, in momentum problems, knowing the direction of the momenta is so important. The O is, again, a interaction diagram (or system schema), where any net (non-negligible) external force will cause an impulse. So, instead of writing the impulse-momentum equation as F∆t=m∆v, we wrote it as mvi + Impulse = mvf.

We had a problem in the homework of two colliding railway cars. Without prompting, my students saw two railway cars as one system, and could figure out that the momentum of the whole system would be the sum of the momenta of the constituent parts. After about ten minutes of solidifying their comments, we were off to lab.

The lab I wanted to do wasn't working, because I couldn't get three PASCO probes work on a USB hub. (I'll detail that lab later when I get it to work.) So, instead, I had students set up their own labs. We put motion detectors on each end of the track, and we learned how to track the velocity of each cart on the track. Then, we learned how to have the computer calculate the momentum of each cart and the total momentum of the system. Then I asked them to break the model. Can you find a situation where there was no net external force but the total momentum changed? They couldn't. Here are some pictures I took of their most creative tries of making a cart-cart system that would break the momentum model:

Day 27: An Energy Experiment Gone Wrong (and Right)

I've done this lab, in various forms, at least ten times. I remember when Cathy Abbot, my physics mentor at Lexington High School, set up the scenario of bungee jumping over Yam Lake to appease the Yam gods. I've modified it many times, always trying to get it better. It's a model deployment lab; where should you drop a mass hooked to a spring so that it hits the surface of a pan of water but doesn't hit bottom? As a scientist, I expect students to find a model that seemed good, take a few measurements in lab, and then use the model and mathematics to come up with an answer that works in the real world, helping confirm the model.

I teach a class of engineers. I had a group study the model of the experiment in the front, which used a different spring and a different mass, to conclude that the distance from completely unstretched spring to equilibrium point is the the same as the distance from equilibrium point to maximum stretch. I had groups build replicas of the mass they'd have to drop to test, ignoring my instruction not to let anything drop from the spring. They wanted to test. They wanted to combine our physical models with approximations that work.

I'm impressed with their problem solving skills. But I'll never have any masses available when students do this lab in the future.

Day 26: Building the Momentum Transfer Model

We're finally ready to figure out what happens when you give an object a little push! Since last time we looked into the area of the force-position graph, this time, since the force hardly acts over any distance, we could look at the area of the force-time graph. A bigger force would do more, and so would more time that the force was applied. So, what does the area of the force-time graph tell us? We think it has something to do with the initial velocity of the cart, or the final velocity of the cart, or something.

So, we were off into lab. There were lots of different approaches. Some groups changed what surface was on the force probe. Other groups tried different initial velocities of the car. One group was sure that the average velocity predicts the area of the force-time graph. 

It was messy and it was great. By the time we wrapped up to look at the data, only two or three groups really felt comfortable with their data. But everybody had thought so much about the problem that it made sense why that data was best and why their conclusion should be believed. We defined impulse and momentum and started using our new model

Day 25: Test on UBFPM

Shortened periods. Long test (longer than I hoped). So there was no time to do anything else.

It made me a little sad. I like watching these students think, and while I'll have lots of evidence to mull over this weekend, it's different when you can hear them making changes in their thinking by talking to their peers. 

Day 24: Finishing Up Energy

We're back after another day off, this time for Yom Kippur. It's hard to get into my teaching groove this week, especially with the shorter classes, so again with no picture today. 

We worked on a few problems today. Many students instinctively started by drawing interaction diagrams and LOL diagrams, and these are the students who had the most success. I'm not sure if some of them saw the connection. Even though we drew diagram for twelve problems before it, if I don't ask for a diagram, they don't want to draw it. Some of them don't get the point of the diagrams yet. I gotta work on that.

We talked about the difference between work and pseudowork in class today. Work is when energy enters or leaves a system, and we can calculate that through the area of the force-position graph. Pseudowork is when energy transforms into thermal energy, some staying in the system and some leaving the system. We calculate it using the area of the force of friction vs. position graph, but while it looks like work, it isn't work. Not all that energy leaves the system.

Did a tiny bit on power today by having a short student and a tall student try to lift a heavy backpack 2.0 meters off the ground. They did the same work, but something was different. We called that difference power, and it's measured in watts. (What?)

Day 23: My Take on Energy Bar Charts

We worked on energy bar charts today. This year, I'm trying to make the interaction diagram to be useful no matter the model in mechanics we are working on. So I've turned the system O in the middle as a full-fledged interaction diagram. We've even written on the interaction diagram where the energy is being stored. Kinetic energy is just stored in the object; potential energies are stored in the interaction. Work then naturally makes sense as when energy enters or exits the system. We had a hard time decided where dissipated energy is in the friction interaction or floating outside, but we didn't want to put it with Ek, Eg, or Eel because it seemed like a different kind of energy--it wasn't mechanical energy.

Day 22: Longest Day of the Year

I talked so much today. Even though we have shortened periods this week for Spirit Week, everyone agreed that today seemed long. Lecturing is boring.

I didn't know how else to show how the interaction diagram can be used to show where the energy is stored and how it is transformed. We did energy pie charts today, and it caused a real debate. We came to the conclusion that both the normal force and the force of friction could cause energy to transform into dissipated energy. On to energy bar charts tomorrow!

Day 21: The area of the force-position graph

Concept first, then words. My students know nothing but that "the area under the force-position graph" means something. We figured out the relationship between the force of a spring and the compression or stretch of that spring. Then we tried to launch two cars so that, after the spring returned to its natural length, the two cars would be going the same speed. (Check out Kelly O'Shea's blog entry at Then we use this model to figure out how different areas of the force-position graph mean--as in, if a car starts at rest, what will its final velocity be given a certain area of the force-position graph? Again, Kelly O'Shea: And, we ended the day with three equations, all of which equal the area under the force-position graph. What does it mean? That's Monday. Have a great weekend, everybody!

Day 20: The Spring Force, By Accident

We went over our applications of our model of friction, which really went better than I expected. Then it was time to introduce a new force, the force of friction.

But it isn't really the time. Usually, I move from unbalanced forces to projectile motion. I had all those packets ready. But, somehow, I thought it was time to talk about the spring force. 

It wasn't what I planned, but it seemed to make sense. There's no reason we can't go back to projectiles when we know more about other tools to look at motion and force. And it was a great lab for where we are in our lab experience; I could let the students loose to use all the different tools at our disposal. (They all tried such different ways to do the lab; you can see that in the pictures.) It actually might be better to do projectile motion later, when we haven't just been focusing on kinematics for so long. It'll be a good way to reinforce and spiral back.

Or at least I hope. My subconscious made that decision, and now I'm going to try it.