1. Pulling force
2. Mass of the cart
3. Angle of the pull
4. Angle of the ramp
We looked at the boards and found out that there was a linear relationship between pulling force and acceleration. In addition there was an inverse relationship between mass and acceleration. These were the two expected results and they came out quite good despite the trepidation of the groups about the wonky lab procedures. They didn't think that pushing or pulling the cart with a spring scale would give good enough data to model the actual physical laws.
But the data came out great - WHAT'S UP NOW! To be honest, this isn't my first rodeo! This was enough to move on to generate the law, but we still had two more situations to examine.
Next came the pull angle. We looked at their data and my question was - if you break up the pulling force into it's "shadow arrows" the component forces, which one is responsible for the acceleration. AND which one is the unbalanced force? We looked at a couple of the situations and it turned out that the horizontal component was the unbalanced force and responsible for the acceleration. In addition, it changes with the angle. So we looked at a couple of situations (30 and 60 degrees) and asked the questions how does the unbalanced force change and how does the acceleration change?
I was very specific here to make note of the unbalanced force which I called the Funbal. The participants immediately started calling it the FunBall; which I love! This is WAY better than Fnet or Sum of the Forces because it ground the understanding in the language.
I decided to ignore the angle of the ramp. Mostly because we didn't yet have any context in which to analyze the forces of a cart on a hill. More on that tomorrow.
Once we got to the point of seeing that the the pull force and the mass were the only real factors that affected the acceleration we used the mathematical structure of those relationships to create one equation that related all three variables:
a = (coefficient)Funbal/mass
The participants then set up their stations to solve for the coefficient. With the exception of one group (who ti think had faulty equipment) each group found a coefficient very close to 1.0 and we settled on that and wrote the law.
From there we talked about what the Funbal meant in a few different situations and I set them on unit 5 worksheet 1 the elevator problems. They worked on these but had significantly more difficulty that I thought they would. That, however, is very positive. It means that they were either in a very good "student mode" or that they need the content help. Both work for me.
This is kind of where the wheels fell off the cart. One of the questions asks what would happen if the elevator cable broke. At that moment I realized that we never measured a free fall acceleration. This is because in my class I don't do things in the prescriptive modeling order and I would have done free fall before this. But I forgot! So we went back and talked about what happened to the acceleration of the cart when you increased the angle of the ramp. And it its max angle do we know the acceleration?
They set up the situation and measured the free acceleration of various objects, a book, a ball, anything they could drop. Asked them to get the acceleration after a drop AND after an object was thrown upward a little bit. They found and white boarded this data and we agreed upon a free acceleration of 10 m/s/s.
Then I asked them to ride the elevator and find the 4 accelerations. One group used a bathroom scale, one group put a 5 N mass on a spring scale. Two groups used data taken with LabQuests.
We then asked them to find the acceleration of the elevator using their actual data.
This was a little challenging but worth the effort.
I then asked then to relate the force diagrams, the acceleration of the rider to how you feel (heavy light or normal).
The point of the discussion is that:
Our bodies are not speedometers - they are accelerometers!
When they finished that activity we decided to finally talk about the readings. The first reading was from Hake and was on the SDI labs that he ran at IU. The participants liked the dialogue and felt that it well reflected what Laura and I are trying to do in the class. I tried to emphasize that we are not promoting the SDI labs but highlighting the importance of the Socratic Dialogue in the classroom.
I have an idea that in order to create the constructivist science classroom you need two aspects:
1. Inquiry lab experiences
2. Socratic Dialogues
Neither one by itself will lead to the promised land, but together they can be very powerful!
The second reading we talked about was from Arons. He asked the differences between gravitational mass and inertial mass. The participants were like, "Forget the differences, what ARE gravitational and inertial mass?" I was like, "forget gravitational and inertial, WHAT IS MASS?" Do we have an operational definition for mass?
No, really, do we have an operational definition for mass? In all of the years that I've been teaching I never have come up with anything that made sense. We have an idea of mass (at least we can say if an object has more mass than another) and even measure it in kilograms. But what it is?
I've had to rely on the circular reasoning argument that "all matter is made of atoms and has mass" and then "mass is the amount of matter contained in an object". These statements, unfortunately, make so sense at all! We still don't have a good definition of mass. WTF!
To make matters worse it turns out that we have no way to directly measure the mass of an object! I asked in class and they suggested a balance - but that is a comparison between an already known mass based on a gravitational force; how did you establish the first mass? Then they suggested the "inertial balance" which puts you in a position to measure the frequency of a vibrating mass and inferring the value for the mass. Someone suggested we just push with a force and measure the acceleration; again inferring the mass.
We don't have a way to measure the mass of an object! I am not sure that the participants have thought that deeply about mass as a concept before but we still have a long way to go with it.