Today was very similar to last weeks class but instead of having the cart move at constant velocity, we wanted constant acceleration. Following in the steps of Galileo we inclined the track by placing a few blocks under one end, giving an angle of only a few degrees. Data was taken with the Video Physics app and then moved to the Graphical Analysis app by Vernier. The Graphical Analysis app gives you more control on how your graph looks, and it can perform a best fit of your data (find the slope of the best line that describes your data). We calculated slopes by hand last week but this time I let them use the app. Everyone had very nice linear graphs of velocity as a function of time (blue line below). We took data as the cart traveled up the track, slowing down, until it stops and then accelerates down the track. You can see on the photo above the red data points marking the position of the cart for each time step. Just by looking at the smaller distances between the dots at the high end of the track you know the cart was moving slower. Before the kids took data they made predictions of what they thought the position vs time, velocity vs time and acceleration vs time graphs would look like. Most of them knew the velocity vs time graph would be linear and the acceleration vs time graph would be a horizontal line (constant!) but it can be hard to visual what that means for the position vs time graph. By taking data with the cart going in two directions, I’m hoping their data helped get it across that the acceleration was the same the entire time even though the velocity changed direction (went from negative velocity to positive velocity – increasing at a constant rate). When they had their graphs printed out and their acceleration reported with correct units and uncertainty, I had them look back at their graph predictions and see how they did.
When we were done with the lab, I introduced a bit of a calculus, explaining how finding the slope of a line is the same as taking a derivative in calculus. None of these students are in calculus though a few are starting pre-cal, so we won’t be using calculus in this class, but I want them to see how its used so when they do start seeing it in math, they’ll understand why its useful. I also worked some problems in class and tried to demonstrate that when working on physics problems, you start by sketching the problem… stick figures come in to play a lot, and by writing down all the things you do know and what you are looking for. For example, if the problem says you drop a pebble, then you know the initial velocity is zero and its going to be accelerating downward. If the problem says the pebble is thrown, then you know the initial velocity is nonzero.
Next week we cover Chapter 4 – forces. The experiment we did today could also be done with a marble on a track, you don’t need the air track to do this.