
3009TBallDropInWater
16 Dec 2018  Modeling Scenarios  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.

3009SBallDropInWater
16 Dec 2018  Modeling Scenarios  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.

2008WillHansenExamplesOfODEsInPhysics
09 Dec 2018  Potential Scenario Ideas  Contributor(s): Brian Winkel
WittHansen, Ole. 2008. Examples of the Differential equations of Physics. www.olewitthansen.dk. Contents1. The dependence of pressure with altitude.............................................................................. 12. Radioaktive chains of decay...

2004PhoebusReilyTheParachuteProblem
09 Dec 2018  Potential Scenario Ideas  Contributor(s): Brian Winkel
Phoebus, Ronald and Cole Reilly. 2004, Differential Equations and the Parachute Problem. Presentation 10 May 2004. https://mse.redwoods.edu/darnold/math55/DEproj/sp04/coleron/presentation.pdf .Abstract: The parachute problem is a classical first semester differential equations problem...

Modeling Falling Bodies
01 Mar 2018  Articles and Publications  Contributor(s): Brian Winkel
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,...

Pretty Good Physics
13 Nov 2017  Potential Scenario Ideas  Contributor(s): Brian Winkel
We were introduced to PrettyGood Physics by a high school physics teacher colleague, Paul Beeken, Physics, Byram Hills High School, Armonk NY USA. He has posted some very nice materials there on differential equations. All the material at this website is free and...

2006LoydWodarz Drug Resistance in Acute Viral Infections
18 Sep 2017  Potential Scenario Ideas  Contributor(s): Brian Winkel
Loyd, Alun L. and Dominik Wodarz. 2006. Drug Resistance in Acute Viral Infections: Rhinovirus as a Case Study. Preprint. 21 pp. http://www4.ncsu.edu/~allloyd/pdf_files/resistance_preprint.pdf . Accessed 18 September 2017.Abstract: The emergence and spread of drug...

1994MintonProgression of Projectiles  Examples from Sports
12 Sep 2017  Potential Scenario Ideas  Contributor(s): Brian Winkel
Minton, Roland. 1994. A Progression of Projectiles  Examples from Sports. The College Mathematics Teacher. 28(5): 436442.There is a progression of complexity and issues in projectile motion modeling from no rsistance, to resistance proportional to velocity, then to velocity...

Math Modeling with Differential Equations  Interesting Tank Problem
12 Sep 2017  Potential Scenario Ideas  Contributor(s): Brian Winkel
Math Modeling with Differential Equations  Interesting Tank ProblemMath Modeling with Differential Equations  Interesting Tank Problem . Class Notes on five problems.,Several models are workd out including exponential decay, bullet traveling with resisitance, This material contains a solution...

Calculus for Engineers IISample Problems on mathematical modeling with differential equations
10 Sep 2017  Potential Scenario Ideas  Contributor(s): Brian Winkel
Calculus for Engineers IISample Problems on mathematical modeling with differential equations. https://www.maths.tcd.ie/~manuela/Sample_1.pdf . Accessed 10 September 2017.Five modeling activities involved with emptying various tanks, projectile motion with resistance, and population growth and...

2017GroetschHammerANDFeather
09 Sep 2017  Potential Scenario Ideas  Contributor(s): Brian Winkel
Groetsch, C. W. 2017. Hammer and Feather: Some Calculus of Mass and Fall Time. Mathematics Magazine. 90: 37.The paper opens this way,“Does a heavy object fall faster than a lighter one? In 1971 NASA astronaut Dave Scott, Commander of the Apollo 15 lunar mission, used a hammer and a...

3075TRLCCircuit
17 May 2017  Modeling Scenarios  Contributor(s): Brian Winkel
We introduce the basics of RLC circuits, defining the terms of inductance, resistance, and capacitance in a circuit in which an induced voltage created a current running through these devices. We build a differential equation using Kirchhoff's Law and solve and interpret our solutions.

3075SRLCCircuit
17 May 2017  Modeling Scenarios  Contributor(s): Brian Winkel
We introduce the basics of RLC circuits, defining the terms of inductance, resistance, and capacitance in a circuit in which an induced voltage created a current running through these devices.

3002TModelsMotivatingSecondOrder
30 Mar 2017  Modeling Scenarios  Contributor(s): Brian Winkel
We introduce several basic, but substantial, approaches to modeling the motion of a spring mass system using a standard second order, linear, constant coefficient differential equation obtained from Newton's Second Law of Motion and a Free Body Diagram. We do this using a set of data...

3017TStackedCoffeeFiltersFalling
11 Mar 2017  Modeling Scenarios  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 a resistance term proportional to velocity, velocity squared, or velocity to some general power. Parameters need to be estimated and models compared.

What Goes Up Must Come Down
02 Mar 2017  Articles and Publications  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 height...

Terminal velocity of a shuttlecock in vertical fall
01 Mar 2017  Articles and Publications  Contributor(s): Brian Winkel
Peastrel, M., R. Lynch, and A. Armenti, Jr. 1980. Terminal velocity of a shuttlecock in vertical fall. American Journal of Physics. 48(7): 511513.Article Abstract: We have performed a straightforward vertical fall experiment for a case where the effects of air resistance are important and...

Balloon Experiment in the Classroom
01 Mar 2017  Articles and Publications  Contributor(s): Brian Winkel
Gruszka, T. 1994. A Balloon Experiment in the Classroom. The College Mathematics Journal. 25(5): 442444.We quote from the article,“The following experiment involves a balloon, a stopwatch, and a measurement device such as a meter stick. . . . The goals of the experiment include fostering...

3065TUpDown
05 Oct 2016  Modeling Scenarios  Contributor(s): Brian Winkel
We model the height of a launched object which is subject to resistance proportional to velocity during its flight. We ask questions about the motion as well, e.g., highest point or apex and terminal velocity.

3065SUpDown
05 Oct 2016  Modeling Scenarios  Contributor(s): Brian Winkel