After day 1, of looking closely at what forces are and how to identify them, we spent the 2nd day looking more closely and Free-body Diagrams and what forces do.
On Day 1, we had shown that a constant force produced a constant acceleration. As a class we worked on a lab using a half-atwoods, with a force sensor to measure the force vs time and a motion detector to velocity vs. time. While we are aiming to find the relationship between acceleration and force, there are a few other practical goals here. First is having students identify what part of the force vs. time graph to select, and similar practicing this for the motion detector graph. I make sure that each of them can identify the part of the graph showing the force acting on cart before release, after release, and then after the crash, with the end stop)…
I model how to do this carefully for one trial. I then tell students that we are going to collectively get the data, so every group will just test 2 data points. One data point will be with 150 grams of mass pulling the string, and then each group will do a different point. And we will gather are data together.
I ask them what factors we will need to make the same across all our experiments, so that we are justified in pooling our data together. They came up with:
- Everyone needs to make sure their track is level
- Everyone needs to make to have same cart / mass
- Everyone needs to make sure the force sensor cable (attached to the cart) interferes as little as possible (i.e., stays slack) as the cart moves down the track.
Some ideas came up about starting the cart at the same location. In a not a great fashion, I argued that this shouldn’t effect the slope of the velocity vs. time graph, since it’s just a different position.
Anyway, groups were off to collect data. For groups that finished early, I asked them to either collect a new data point or to confirm an existing data point. One of thing I like about collective labs is that groups really care to make sure that one data point is as accurate/precise as possible. Also, groups are more likely to notice something like entering data in the table backwards, or a data point where the trend suggests a mistake was made. It also made the discussion about “control of variables” easy, because it was more obvious students that different apparatus would need to be as similar as possible.
We made our a vs. F graph from the common data, and compared it to the textbook’s graph. It was pretty similar (linear trend), although our graph did not have a perfectly zero intercept. I then showed them another graph from the textbook– three graphs were put up for same experiment done with 3 different masses. A clicker question was posed about which graph showed the heaviest of the three objects. This was hard for students, because the “lizard brain” wants to say, “heavy is more”, “steeper graph is more”… but students go to reasoning through that the heavier cart should accelerate less for the same amount of force.
By having them first reason about the fact that slope of an a. vs. F graph is related to mass, I hinted that next time we would use our data to determine the mass of cart without weighing it.
We ended the day practicing drawing Free-body diagrams, with individual forces in the FBD and a separate Fnet vector off to the side. We had lots of good conversations about Fnet, as “FBD show what the individual forces are doing, and Fnet as what the individual forces are accomplishing together as a team”