For a few years now I’ve been building the momentum transfer model using an empirical approach, but this year I decided to have students try to derive conservation of momentum first. I did this for two reason; first, time (we have had 6 snow/cold days this year). Secondly, I also did this for time reason during projectile motion, and I found that students really like the idea that they can use their prior knowledge of models to figure out something new.
To do this I walked around and asked groups lots of questions, guiding them to get to conservation of momentum. Once groups got to the point of attempting free body diagrams, I had a group present and we had a great time re-learning Newton’s 3rd Law (it’s still amazing to me how strongly their misconceptions are rooted: “but if one has a bigger mass, it MUST exert a bigger force!”). From there students went back into groups to finalize, and we had presentations at the end as well, particularly to discuss why the change in time must be the same for both objects.
I missed pictures for the Area vs. change in height lab, but here’s from last year and here’s my writeup for the entire 5 days. Today we collected data to see how the area under the force vs position graph (still haven’t named it…) correlates with velocity. Results below. When students graph A vs. v, it is usually either non-correlated (a variety of possible errors) or, more often than not, pretty obviously not linear. When they linearize it as A vs. v^2 it turns out nice, as shown.
Today we started investigating the mysterious integral of a force position graph and how it seems to make predictions for stuff (more detail here). Today I had students pick a start and end point on a ramp. They had to pull the carts from their start to end point, starting and ending at rest, in any way they wanted without going backwards. They could go fast, slow, accelerate, jerk (though jerking is hard to do without letting the cart go backwards), or anything else they could think of. The end results are below and speak for themselves. A couple groups tried going backwards, and predictably got negative integrals of the same value, which was neat.
Today we started the Energy Transfer Model. The first day I copied from Kelly. The students above are at the point of trying to find spring displacement values such that the carts will be launched with the same area under the F vs x graphs. Below is at first when the students are tying to find positions such that the forces acting on the springs are the same (which awesomely leads to the weaker spring launching the cart faster!) After this I continue for a couple more days by empirically exploring how work affects a couple different situations.
Today we collected centripetal acceleration vs. speed data using spinny chairs, Labquest accelerometers, and lots of masking tape. Tomorrow we analyze data.
Today students presented a claim and their data supporting it for whether speed, surface area, weight/mass, or surface type affected friction. The results for the two classes are shown below (as multiple groups did each one). I forgot to take a pic of first hour, but they had a dissenter in SA thinking it did not affect friction. The far right list of Yes and No is the ‘right’ answer.
I was disappointed with the results, but I learned a valuable lesson; good data can’t be rushed. I am under the gun at this point to finish up unbalanced forces by winter break, so we did this experiment very quickly, with no time for revision and with very little actual data. It is very difficult to get good data for this, particularly the speed experiment. When I did the demo lab after we had compiled their data, I put a motion detector up as well as the force detector, so students could see whether I was pulling at a constant velocity (which you have to in order for the force probe reading to equal the force of friction). I legitimately tried to pull with a constant velocity on the medium speed trial, and it wasn’t even close. I’m confident that they found that speed increased friction only because they were actually accelerating the object. I think the surface area experiment is simply prone to lots of random uncertainty. I have seen it done well when I let them talk almost a week to complete it, but I don’t have that time anymore. Which is kind of sad.
Today we started investigating friction. I was inspired to have students design their own experiments by John in this post, and I’m looking forward to comparing notes with him and Frank (see the comments of John’s post).
We started this process by going through the Friction Investigations page in my UBFPM packet here. The graph above was produced for #4. I was pretty happy with how this guided students towards the idea that static friction only acts as much as it has to (does anyone have a better way to say that, btw?), and that kinetic friction tends to be constant. After we finished up with listing then culling the possible variables to affect friction, I gave them some brief instructions on how to use the force detectors in this case and set them loose. I asked them to investigate qualitatively (if they were changing the speed, do a slow, medium, and fast trial), mostly because of lack of time.
I must admit I am conflicted here a bit because I am crunched for time to finish Unbalanced Forces before winter break. I know some groups are going to get the ‘wrong’ answer from their lab, and I would like to have all the groups follow up with either extensions or re-doing their lab (as Frank suggests in the comments), but I’m out of time. So unfortunately I think I’ll just demo the experiments (as I’ve done in the past) to show the “right” answer. But I hope I don’t have to and the data will speak for itself. We’ll see tomorrow.