Recently I have been doing a lot of whiteboarding via whiteboard speed dating as well as problem solving without presentations. Today I decided to go back to presentations just to change things up, and I learned two things. 1) Presentations are worth the time, both because of the conversations but also because I learn what misconceptions students have and can guide them in the right direction. 2) Lecture is bad.
I say lecture is bad because of this group above. I had done an example yesterday to introduce solving problems using momentum bar charts, and in doing so I did a problem where two carts stuck together at the end of the problem. I showed students that because they had the same velocity, you could combine the two bars together to make one bar with the total mass as the height and the velocity as the width. The group above generalized that particular scenario and thought they should always draw the bars together. Students will, at no fault of their own, take what I say and misconstrue it as it is applied to other scenarios. They tend to do this far less with clever solutions and diagrams that their peers present, however.
Always good to be reminded of why I teach the way I do.
Today, as part of my technology integration job, I was able to help and observe as my friend and colleague used Vernier Labquests to do a titration. This way students can watch the titration curve unfold in real time. They were investigating qualitatively today, tomorrow they will perform the experiment quantitatively. I re-learned a lot of Chemistry today!
Today some groups finished up their data collection while others worked on problems. The first group is looking at collisions of pool balls from both energy and momentum standpoints, and the second is going to try to find the coefficient of friction between the cart and the track using an energy analysis.
Instead of lecturing about how satellites can be analyzed using circular dynamics and Newton’s Universal Law of Gravitation, I made it a goalless problem. Each class had a couple of groups get to this point, and other groups did cool stuff too. One group (below) calculated the distance required for Earth’s gravity to be negligible, which they defined to be 0.1 N.
Today we worked on one of my favorite problems, it goes something like this.
“Let’s say there are two people dancing a healthy 1 meter apart. We want to ensure that they stay a healthy 1 meter apart such that no one must take part in grinding. Let’s find an approximation for the coefficient of friction required to keep them separated.”
The kids love it, and it’s perfectly in time for prom.
Today we started regular physics with groups attempting to summarize the relationship between the two masses and changes in velocities for carts involved in a collision. Many groups had variations on the same theme; more below.
We got to a point where some students suggested something resembling conservation of momentum but with the masses paired with the wrong velocities (see the last two pics above); I asked everyone to verify it. One group mentioned that it seems the masses should be switched. We tried it and about half the class seemed to agree that it worked for their data.
Here’s where I’m stuck; I believe that the half that didn’t agree probably thought so because of poor data collection, which is difficult for me to fix in real time particularly because of the relatively large class vs relatively small number of effective setups. Thus I decided to take a different tack, and so far I’m glad I did.
I usually give a quick mention of the difference between empirical and theoretical methods of building models, and this is a perfect place for it. I mentioned that we have something that seems to work for some people based on data. Let’s find out if we can figure something close to it based on theory as well.
We started with drawing free body diagrams for three snapshots, which was good to cycle back to anyway (it’s been a while); the carts traveling on their own before the collision, during the collision, and after the collision. We did two rounds of whiteboard speed dating, my current favorite flavor of whiteboarding, and by the end all but one or two of the groups had something resembling this;
This is where we left off; tomorrow we’ll pick up here to try to derive conservation of momentum, then compare with our empirical model. I hope to start momentum diagrams tomorrow as well, first time!
After college physics went through the process of designing their own lab using Energy conservation, we moved on to where they can design a lab to verify anything we have currently studied. The final step is to do a larger investigation (a capstone, if you will) of a situation of their choosing, where they should have to extend what they have learned in class. The picture above is a group trying to verify the so-called ‘range’ equation.
Below is a group testing impulse-momentum. See the force detector?
I believe the group below is investigating projectiles launched at a downward angle.
This group is modeling the classic ballistic pendulum using dynamics carts.
This group is looking at how the speed and radius of a rotating platform are related to when a penny slips as it rides on the platform.