Today we finally were able to have the post-lab discussion on the collisions experiment. It was a bit of a different style of discussion. I had each group prep a WB with a description of each collision it studied, they demonstrated each one and we viewed the movie the group posted. I also had the group provide the initial and final momenta values for each collision, then we looked at the pooled data from all of the classes for that type of collision. For the most part our results were pretty decent. We had wanted a slope of 1.0 to establish the conservation of momentum. The inelastic collisions were the most accurate. I think this is because there is only 1 ‘thing’ (the connected) carts to determine the velocity for. Next year I think I need re-enforce the concept that we really need the instantaneous velocity right where the carts collide. I had a few groups put on a linear fit so the velocity was a bit off. Tomorrow we will compare the total initial kinetic energy and total final kinetic energy. As the homework for tonight, each group needed to simply add a column or three to the spreadsheet so the kinetic energies could be calculated.
Today we had the WB discussion on the Hooke;’s Law experiment with the springs. For some reason, this time around, quite a few groups had significant intercepts… I even had a few groups re-gather the data with the same results. Interesting enough, the slope values were pretty much spot on with the given values. Tomorrow, we are planning to practice with the spring constant concept by asking a few ranking task and quantitative questions.
Spring Break in Neenah has come and gone… now it’s the final push to the end of the year. I always get mixed feelings after spring break. Panic… sooo much yet to cover (well to learn); Pride– all the students (well most, … no all) have grown so much and are much better (physics) students than they realize; Sadness… this group of students will be moving on, that’s sad (for the most part); Frustration… I still have not figured out how to reach a few students. No matter what I try, it just does not seem to work.
Today was to be the day we had the post – lab discussion for the collisions experiment we started on the Thursday before the spring break. It seems to be taking longer this year. I did a few new things this time around. Each group shot a quick movie of collisions they studied. Here is an example:
And one more.
I also required the students to use a spreadsheet (or Logger pro with calculated columns) to complete all the calculations. All of the data will be pooled and dumped into one Logger pro file to create a graph of total initial momentum vs. total final momentum. If the slope turns out to be equal to 1.0, then we know that momentum is conserved. The new part for me was setting up a google spreadsheet for the (CAPP) students that were required to complete the analysis of a 2D collision using our hover pucks or our air hockey table. I’m a bit ashamed to admit it, but this is the first time I have used a google spreadsheet with my classes. It is awesome to sit and watch the data get entered. Hopefully we will be able to see momentum conserved in both the x and the y directions. I will probably not go into any detail about the center of mass of a system aspect unless the opportunity presents itself. In my experience, conserving momentum in two separate directions.
SIDEBAR: In my mind I am wrestling with my sequence. I have been teaching momentum( and impulse) AFTER Energy and dynamics. As of late, though I have read more about teaching momentum (and impulse) BEFORE energy and even before some aspect of dynamics. I’m just not sure if there is a pedagogical advantage one way or the other.
Today we discussed the Energy bar chart (LOL’s) assessment they took the day before we went on break. We also had the pre-lab discussion for the Hooke’s Law experiment. I do not do the traditional Hooke’s Law Experiment with masses being hung on a vertical spring. I phrase the purpose to include something like this:…. determine the relationship between the force exerted on a spring and the change in length of the spring. I find it makes it easier for the students to transition to a compression spring because the ‘change in length’ could be a ‘get longer change in length’ (like our extension springs) or a ‘get shorter change in length (like a compression spring that will be used with the Pasco cart launchers). Here is a picture of how the data is gathered:
The spring are pulled horizontally so there is no confusion about any gravitational affects. This also makes it much easier to transition to the compression spring and determine it’s spring constant. Each group did two springs to see that the slope of the linear graph does depend on the spring AND to have its data confirmed.
Today we did a pre-lab discussion for the two remaining energy assets, kinetic and gravitational. The discussion centered around how we could use the knowledge we have of elastic energy to study kinetic and gravitational energy. It was an easy discussion because most of the students saw pretty quickly that we could use a spring to launch a cart. To study the kinetic asset, we just need to choose the initial condition (for the energy bar graphs) when the spring has been compressed but the cart is at rest, and the exact instant the spring is no longer compressed (so all the elastic is now kinetic) for the final condition. For the gravitational, just launch the cart up a ramp, and use the maximum height as the final conditional so all the energy is gravitational.
We have two main springs to use to launch the carts. The first is the one built into out Pascar’s. The second is the launcher available from Pasco that looks like this:
Both experiments start with a quick Hooke’s Law experiment to create the Force vs. change in length graph and or (depending on how the group chooses to quantify the energy). I helped each group use a WDSS Fore sensor and Motion detector at the same time to directly create the ‘Hooke’s Law’ Graph.
Having just discussed N2L, and using the Giant Lab Cart of Physics, we turned to connecting N2L to N1L and N3L. We accomplished this by using our two giant hovercrafts of physics:
The two examples had the same series of questions… 1. Which person exerted the greater force ? Explain, 2. Which person had the greater acceleration? Explain, and 3. Which person has the greater velocity after the interaction.
Over the last 3.5 days of class (yes, another 1/2 in there), the students completed and independent research experiment related to Hooke’s Law. Essentially they came up with one change they wanted to make to a spring/spring system, made a hypothesis about how the change would affect the spring constant, then gathered and analyzed the data to verify the hypothesis. They also posted their results on a shared Schoology discussion and made at least three comments regarding other experiments. Now, truth be told, some of the experiments reached conclusions that may not be accurate, but I’m OK with this because the focus was on the freedom to just explore and be creative, not necessarily scientifically accurate. In short, I think is was awesome. I had 2 groups compare the ‘k’ value in air and in water… yep, into our pool to gather data. Groups look at temperature… room temperature vs. -17F (~-30F with the windchill). I need to allow more of this.. just need to find the time.
Today we connected Hooke’s law back to energy. We discussed how when we exert a force to cause a change in length of a spring, we are also storing elastic energy in the spring. We plotted force as a function of change in length (the traditional Hooke’s Law graph), but did not have any energy into the graph yet. We discussed where the energy might be hiding. After looking at the energy bars for several changes in length and the Hooke’s Law graph, we defined the area trapped as the (working) elastic energy.
The next step was to plot a graph of elastic energy as a function of change in length. To determine the energy values, we used the integral feature of Logger Pro to find the energy at 8 changes in length. We did not use our original Hooke’s Law graph, we used a new one plotted from the Hooke’s Law EOL and generated change in length values. We did this to ‘smooth’ the data and to provide more to work with. Tomorrow is the post ‘lab’ discussion on this.
Tomorrow we will have the post lab discussion for the Modified Atwood machine experiment that develops Newton’s 2nd Law.It is essentially the same experiment the advanced students completed, but the general students only complete one part, either acceleration as a function of mass (with a constant net force) or acceleration as a function of net force (with a constant mass system).