## 20170130

### Physics pre-lab: defending the model

Physics 205B, spring semester 2017
Cuesta College, San Luis Obispo, CA

Students have a weekly online pre-lab assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the pre-lab reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on "defending the model" of vehicle mileage versus weight.

Analyze the mathematical model (best-fit equation) derived from a small sampling of various vehicles' gas mileage G (in mpg) and weight (in lbs):

G = –0.0043·m + 60.

(For clarity the units for "0.0043" and "60" have been omitted.)

Selected/edited responses are given below.

Does the mathematical model make reasonable predictions for large independent variable values?(For an example of a typical heavy vehicle (in lbs), does the predicted gas mileage (in mpg) make sense? Cite a specific numerical example and discuss whether the mathematical model produces reasonable results or not.)
"For a 2017 Ford Focus, when I plugged in the weight of the car (2,935 lbs) I got a gas mileage of 47 miles per gallon. The actual average gas mileage is 30 mpg city, and 40 mpg freeway. So I would say this model does not produce reasonable results for light cars."

"No, it predicts that a car not weighing a single pound will still have a mpg of 60."

"The graph does make sense and predict reasonable results for small independent variables. A lighter car is imagined to have a higher mpg, but as the data approaches zero there is a minimum weight of a vehicle produced so the data should not go much lower than around 1,800 lbs."

Does the mathematical model make reasonable predictions for small independent variable values?(For an example of a typical light vehicle (in lbs), does the predicted gas mileage (in mpg) make sense? Cite a specific numerical example and discuss whether the mathematical model produces reasonable results or not.)
"For a large vehicle the data really does not make sense. Let's say our vehicle was 16,000 pounds, according to this data our gas mileage would be negative which is not possible."

"The model does represent large variables well, up until the weight exceeds 14,000 lbs, because all vehicles get more than 0 mpg."

"For a 2017 Chevy Silverado, when I plugged in the weight (4,510 lbs) into the equation I got 40 miles per gallon. The actual mpg is 18 city and 24 mpg freeway. Given that I would say this model does not produce reasonable results for heavy cars."

"This model will not work for large vehicles like semi-trucks that can weigh close to 80,000 pounds. For a standard car this model would work."

Is the mathematical model (here, linear) the simplest consistent with the data and its uncertainty? (Is this linear equation too simple, such that a more complex curve would be a better mathematical model; or is this linear equation "good enough." Cite specific numerical examples in your discussion.)
"At the initial point (0 lbs, 60 mpg) the data says a car can have a weight of zero. That is not the case. The trend is not unreasonable from 2,000 to 12,000 lbs but it needs some kind of leveling off. I would recommend a best-fit polynomial with this data."

"While the graph implies strictly that greater weight means less fuel efficiency, this is not the case. A 1,100 lb Fiat gets 32 mpg highway, and a 2,800 lb Corolla will get 40 mpg highway (both non-hybrid models)."

"Yes, as long the car as we test are within the same boundaries and characteristics the small sample is data was collected from we should be able to use this mathematical model."