Using Geogebra to develop Newton’s 2nd Law

I have been following as closely as possible the Modeling Physics approach with my regular physics students this year. My schedule during the summer has kept me from attending a workshop, so much of what I am doing is just an approximation of the real thing, as close to what I understand from the notes on the Modeling instruction website as I can get. We just finished the constant velocity unit last week, and were ready to look at some dynamics of objects. I am starting by looking just at the balanced force particle model before going to the constant acceleration model.

I started the particle force model unit by giving students a chance to play with a cart on an air track with some fans either turned on, or turned off. I had them make observations of what they saw. When they made assertions of constant velocity, I asked them to measure and verify their assertions. They asked to use the ultrasonic detector – I was more than willing to oblige their request. They collected some data, made some graphs, and talked about constant velocity, but they had trouble getting the detector to detect the cart without getting noise in their data. They were pretty sure that they could look past the noise in the ultrasonic detector data and create a constant velocity model. We also thought about taking a video and using Tracker, but given the odd interactions I’ve seen with Tracker and Mac OSX Lion, I opted not to endorse that without looking more into the problems that arose (Xuggle just not installing in one case, two computers becoming unbootable in another, and my own laptop suddenly getting its setting wiped and wireless obliterated until a rest of the system configuration. I digress – a discussion for another day.)

We then talked about drawing system schema and the ideas of forces as interactions between objects before heading off for the day. I knew we needed something to play with to help develop the connection between net force and constant velocity for the next class. My old standby, Geogebra, was there to help.

I created the Geogebra applet above at http://geogebratube.org/material/show/id/17438 and had my students go through the steps of making the object appear to travel at constant velocity by adjusting the magnitudes of the forces.

The steps:
• Adjust the sizes of the forces so that the object appears to move at constant velocity.
• Turn on the position versus time graph using the check box to confirm that it is actually traveling at
constant velocity. What should you be looking for?
• Create three different situations of constant velocity by changing the magnitudes of forces AND the initial velocity. Write down the settings you used for F1, F2, m, and v0 so we can compile them in one place when you are done.

Turning on the position vs. time graph, the students could then check and see if it was constant velocity using their knowledge from the last unit. I was really pleased that getting students to see the graph and figure out how to make adjustments took no prompting. The time we spent on constant velocity paid off, as they did a great job of then matching the graph to their observations and adjusting the forces as needed.

Before long, they had started talking themselves about how the object travels at constant velocity when the forces are equal. They asked if they could just take screenshots of the situations of constant velocity rather than just writing down their values for force, mass, and initial velocity. This made it easy to go one by one through their configurations and see what they had in common. We developed together the definition of net force, and then they adapted it to what they had figured out to come up with the static version of Newton’s 2nd.

I was especially impressed when I had them work individually to answer the following questions – their explanations came more naturally than ever before as non-chalant statements of fact, and without the “yeah, but…” moments that have shown up every other time I introduce the idea of net force.

The questions:

I am a big believer in having real objects in front of the students to manipulate and observe. I also like when the equipment works well enough to make it easy to make the measurements and observations students want/need to take. I thought this was a nice compromise between having an ideal, noise free (virtual) environment and giving enough flexibility for the students to play around themselves with the different parameters for the problem.