Transformation Project
Overview
For this project, we had to determine two certain functions that were linear and non linear, meaning if you were to graph it, it would end up going in a straight line or not. The main idea of the project was to get better familiarized with what makes an equation linear or non linear. To achieve this, we had to first figure out what is linear and what isn't. For the project, my partner and I decided to select temperature conversion for our linear growth, and the flight pattern of an SA-7 surface to air missile for our non linear growth, which was related to our physics project, constructing a model of an SA-7 missile.
To represent both of these growths, we decided to create an interactive thermometer that measured in Fahrenheit and Celsius and to represent the flight pattern of the missile, we decided to make an interactive display of newton's second law F=ma.
To represent both of these growths, we decided to create an interactive thermometer that measured in Fahrenheit and Celsius and to represent the flight pattern of the missile, we decided to make an interactive display of newton's second law F=ma.
Processes of the Project
The first thing that we had to accomplish was figuring out what my partner and I decided to do the project on. At first we wanted to do electricity bills for our linear growth and the flight pattern of a SAM as our non linear growth, but unfortunately, the electricity bills were non linear as well so we went with something that was obvious that it was linear, temperature conversion. Then we had to record our data and learn how to convert Fahrenheit to Celsius and found that if to do the conversion, you must deduct 32, multiply by 5, then divide by 9. For the SAM flight pattern non linear growth, we had to fit the numbers into slope-intercept form in order to graph it and the final equation we got was y = 5,000x2 / (9.8 - 0.28x). We then had to embellish it somehow and out idea was that we should make both of the functions interactive. What we had in mind for the temperature conversion was to create a diagram of sorts that had two wheels, one larger than the other, connected with a belt, so that if you rotate one the other rotates at a different speed, which is valid when it comes to Fahrenheit and Celsius because Fahrenheit generally raises and lowers faster than Celsius. For our non linear relationship, we wanted to interactively showcase newtons second law, and to do that, we constructed a box which had a foam core square cut out attached to four rubber bands on each corner to show that the more force is applied on the board, the slower the board retracts.
Why we did What we did
We decided to create our final creative pieces to be interactive because we felt that it was easier to demonstrate what other people could see and because few other people were creating interactive displays. We wanted ours to be different than most so that our really popped out to the audience of people we were portraying all of our work to.
Graphs
Why it is Linear(Left)
The temperature conversion function is linear because, as you can see from the graph, the slope is constant and you can draw a straight line throughout all of the points
Why it is Non Linear(Right)
The Surface to Air Missile function is just barely non linear as you can see from the graph on the right. The reason it is non linear is because a missile does not fly at a steady rate, therefore making an inconstant slop, therefore making it possible to only draw a straight line between a couple points.
Reflection
I would have to say that a lot of things went well for this project. For example, our final products turned out very nice and were worthy to be displayed during exhibition and many people liked our work. The only thing that I would have to say didn't go well would be trying to figure out how to properly construct the belt to work properly, but in the end, we overcame that issue with Velcro and elbow grease. One Habit of a Mathematician I used well was being confident and persistent because it took a lot of that to complete our final product. One thing I would do differently next time would be to bring in more materials because we were low on materials like Velcro, foam core, glue etc many times.