
2020Beeken, Paul  First Order Differential Equations  AirResistance
26 Mar 2020  Contributor(s):: Brian Winkel
BeekenFirstOrderDifferentialEquationsAirResistanceBeeken, Paul. First Order Differential Equations as applied to Air Resistance. Byram Hills High School.This is a nice and gentle introduction to air resistance modeling.From the Introduction"The problem of air...

2010Chicone, C.  Mathematical Modeling and Chemical Kinetics. Notes
26 Mar 2020  Contributor(s):: Brian Winkel
2010ChiconeMathModelingANDChemicalKineticsChicone, C. 2010. Mathematical Modeling and Chemical Kinetics. Notes. 14 pp.Motivated by physical science motion laws the author moves into kinetics and life science applications of differential equations.From early section...

3015SStyrofoamBallFall
24 Mar 2020   Contributor(s):: Brian Winkel
We are given data on a falling Styrofoam ball and we seek to model this motion.

2003Bohren, Craig F  Dimensional analysis, falling bodies, and the fine art of not solving differential equations
13 Mar 2020   Contributor(s):: Brian Winkel
Bohren, Craig F. 2003. Dimensional analysis, falling bodies, and the fine art of not solving differential equations. Am. J. Physics. 72(4): 534537.See http://pages.erau.edu/~reynodb2/ps303/Bohren_2004_AJP_DimensionalAnalysis.pdf .Abstract: Dimensional analysis is a simple,...

1083SFallingMeteorites
24 Aug 2019   Contributor(s):: Lyle Clifford Smith
After introducing the solution to the ordinary differential equation which models a falling object with drag (firstorder, nonlinear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus is on creative identification of factors. Students...

3009SBallDropInWater
16 Dec 2018   Contributor(s):: Brian Winkel
We conduct an analysis of a falling ball in liquid to determine its terminal velocity and to ascertain just what radius ball for a given mass density is necessary to attain a designated terminal velocity.

1063SThreeHoleColumn
15 Dec 2018   Contributor(s):: Brian Winkel
We consider a column of water with three holes or spigots through which water can exit and ask students to model the height of the column of water over time.

2018Schneebeli,Hans R.  Modeling Falling Bodies
01 Mar 2018   Contributor(s):: Hans Rudolf Schneebeli
Modelling falling bodies is discussed using a computer algebra systemcalculator and introducing various traditional and elementary methods from calculus as well as numerics for dealing with the resulting ordinary differential equations.This article is in German under the title,...

2017Groetsch, C. W.  Hammer and Feather: Some Calculus of Mass and Fall Time
09 Sep 2017   Contributor(s):: Brian Winkel
Groetsch, C. W. 2017. Hammer and Feather: Some Calculus of Mass and Fall Time. Mathematics Magazine. 90: 37.See https://www.tandfonline.com/doi/abs/10.4169/math.mag.90.1.3 .The paper opens this way,“Does a heavy object fall faster than a lighter one? In 1971 NASA...

2017Vas, Lia  Modeling With Differential Equations  notes
05 Sep 2017   Contributor(s):: Brian Winkel
Vas, Lia. Notes: Modeling With Differential Equations. 8 pp. http://liavas.net/courses/math422/files/Differential_eq.pdf . Accessed 5 September 2017.This is a set of class notes for Lia Vas in which examples from population, falling objects, tank mixing, growth and threshold, are...

2017Benaka, Jan and Sona Ceretkova  Free fall in a vacuum and in the air – calculating limits using a real example and demonstrating the limiting process to high school students using Excel.
05 Sep 2017   Contributor(s):: Brian Winkel
Benaka, Jan and Sona Ceretkova. 2017. Free fall in a vacuum and in the air – calculating limits using a real example and demonstrating the limiting process to high school students using Excel. Spreadsheets in Education. 9(1): Article 3.Abstract: The paper gives the result of an...

1115SModelingWithFirstOrderODEs
04 Sep 2017   Contributor(s):: Michael Grayling
Several models using first order differential equations are offered with some questions on formulating a differential equations model

3017SStackedCoffeeFiltersFalling
11 Mar 2017   Contributor(s):: Brian Winkel
Data on free falling 2, 4, 6, and 8 stacked coffee filters is offered for analysis. Students first form a model using resistance terms. Parameters need to be estimated and models compared.

2014Groetsch, C. W. and S. A. Yost.  Vertical Projection in a Resisting Medium: Revelations on Observations of Mersenne
02 Mar 2017   Contributor(s):: Brian Winkel
Groetsch, C. W. and S. A. Yost. 2014. Vertical Projection in a Resisting Medium: Revelations on Observations of Mersenne. The American Mathematical Monthly. 21(6): 499505.Article Abstract: This article, inspired by a 17thcentury woodcut, validates empirical observations of Marin Mersenne...

1999Brauer, F.  What Goes Up Must Come Down
02 Mar 2017   Contributor(s):: Brian Winkel
Brauer, F. 1999. What Goes Up Must Come Down. American Mathematical Monthly. 108(5): 437440.Article Abstract: NONEThis paper is a wonderfully general analysis of the following, “It is natural to ask whether a particle propelled upwards takes longer to fall to earth from its maximum...

3070SFallingInWater
04 Mar 2016   Contributor(s):: Brian Winkel
This is a study of modeling a falling object in liquid. We provide a video (in two versions  .mov and .mp4) which will enable you to collect data on a falling object in water to compare with your model and to estimate parameters using data you can collect from the video. VIDEO Version 1 ...

3044SDeepWell
30 Aug 2015   Contributor(s):: Brian Winkel
We drop a pebble in a deep well. Given the time elapsed from release of the pebble until we hear the splash determine the depth of the well.

1994Gruszka, T.  A Balloon Experiment in the Classroom
20 Jun 2015   Contributor(s):: T. Gruszka
Gruszka, T. 1994. A Balloon Experiment in the Classroom. The College Mathematics Journal. 25(5): 442444.See https://www.tandfonline.com/doi/abs/10.1080/07468342.1994.11973649 .We quote from the article,“The following experiment involves a balloon, a stopwatch, and a...

3019SShuttlecockFall
30 May 2015   Contributor(s):: Brian Winkel
We are given data on the time and position of a shuttlecock as it falls to the ground from a set height. We attempt to model the falling object and we confront the different resistance terms and models. Finally, we introduce a new way of comparing models, the Akaike Information Criterion, and...

3013SWhiffleBallFall
30 May 2015   Contributor(s):: Brian Winkel
We are given data on the time and position of a whiffle ball as it falls to the ground. We attempt to model the falling ball and we confront the different resistance terms and models. Finally, we introduce a new way of comparing models, the Akaike Information Criterion, and apply it to our models.