Our model is of a ball rolling down a ramp.
Students can use this model to learn about different components of acceleration due to gravity when on an inclined plane. They can experiment with how much faster a ball will roll down a steep ramp versus a nearly-flat plane.
One of the key features that it provides is the ability to measure small differences in time. Without a very long ramp, it will be hard to get precise measurements on timing since a person probably isn’t accurate to tenths of a second using a stop watch.
However, we spent much more time on other things than this model. We started out wanting to do something modeling a social or aesthetic phenomenon rather than a scientific phenomenon. We came up with a lot of ideas (analyzing the colors in a picture book to see how, for instance, manga and kids books use different types of colors, analyzing conversations or other social dynamics, looking at school choice versus income level, and plenty of other worse ones). We even started implementing some of them (we got the video camera data to try to do an agent-based implementation of some photoshop features). However, none of these ideas seemed to fit the bounds of the assignment, so we settled for a ramp.
The design of the ramp was fairly simple. We soldered on some wires to a pressure sensor to give it some extra length and to allow the pressure sensor to fit in the gogoboard, and then we taped the pressure sensors on to the top and bottom of the ramp. The timer will start when the ball hits the top sensor and will stop when the ball hits the bottom sensor. One challenge was that the sensor is built for a lot more force than a light ball exerts, so we needed to use bigger objects. We also talked about using alternate sensors like a light sensor that the ball would go over, which would make the sensor much darker, or a sound sensor, or a motion sensor, but those seemed much more complicated than just using a larger object like a roll of tape.
When we were writing the code, we had to re-learn some physics to get the gravity and component-wise acceleration correct. That is one benefit of having the model: a child that doesn’t know enough physics or trigonometry to figure out that the acceleration of the ball down the ramp will be g * sin(theta) or the calculus to turn that into a velocity at any given time can still get the precise (ideal) number for the time.
We used a behavior space model to plot the time versus the incline. The x axis is degrees incline and the y axis is time for the ball to fall down a ramp of constant size with no friction. Students could do something like this to realize that time versus incline is inverse functional (which also opens up the door to talking about what it means for something to be inverse functional).
After we wrote that, we realized that even though our model was fairly close, it would be off with any very heavy objects or very rough surfaces because we didn’t take friction into account. Adding friction to the model also lets students use the model to weigh different objects, time how long it takes them to go down different ramps and then vary the coefficient of friction in the model to find out what the actual coefficient of friction between that particular ramp and ball is.