
4039SFallingDarts
21 Jan 2022   Contributor(s):: Jacob Paul Duncan
Most projectile motion and free fall models are based on the assumption that gravity is the only force acting on the object. Here we develop, solve, and analyze a second order nonhomogeneous differential equation model for free fall which incorporates air resistance. Students will solve the model...

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.

2013Doboszczak, Stefan and Virginia Forstall  Mathematical modeling by differential equations Case study: Traffic flow.
09 Sep 2017   Contributor(s):: Brian Winkel
Doboszczak, Stefan and Virginia Forstall. 2013. Mathematical modeling by differential equations Case study: Traffic flow. PowerPoint Slides. 52 slides. University of Maryland. See www.norbertwiener.umd.edu/Education/m3cdocs/Presentation2.pdf . Accessed 8 September...

2017Pennel, Steve  Differential Equations First Order Applications  Notes
09 Sep 2017   Contributor(s):: Brian Winkel
Pennel, Steve. Differential Equations: Applications of First Order Differential Equations. Notes. 44 p. Universiyt of Massachusetts, Lowel.This is a set of modeling activities with derivations, Matlab code, and mathematical details covering the following topics: Newton’s Second...

1980Peastrel, M., R. Lynch, and A. Armenti, Jr.  Terminal velocity of a shuttlecock in vertical fall
01 Mar 2017   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...

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

1050SBargingAhead
10 Feb 2016   Contributor(s):: Timothy Pennings
As captain of a barge, you need to determine how fast to transportyour barge up river against the current in order to minimize the expended energy.Since expended energy is proportional to the force, and since the force is proportional to the speed, traveling too fast is inefficient. However, if...

1980Peastrel, M., R. Lynch Lynch, and A.Armenti, Jr.  Terminal velocity of a shuttlecock in vertical fall.
20 Jun 2015   Contributor(s):: M. Peastrel, R. Lynch, A. Armenti
Peastrel, M., R. Lynch Lynch, and A.Armenti, Jr. 1980. Terminal velocity of a shuttlecock in vertical fall. American Journal of Physics. 48(7): 511513.See https://ui.adsabs.harvard.edu/abs/1980AmJPh..48..511P/abstract .Article Abstract: We have performed a straightforward vertical...

1999Long, Lyle N. and Harold Weiss  The Velocity Dependence of Aerodynamic Drag: A Primer for Mathematicians
20 Jun 2015   Contributor(s):: Lyle N. Long, Harold Weiss
Long, Lyle N. and Harold Weiss. 1999. The Velocity Dependence of Aerodynamic Drag: A Primer for Mathematicians. The American Mathematical Monthly. 106(2): 127135.See https://www.tandfonline.com/doi/abs/10.1080/00029890.1999.12005019 .This paper is exactly what it says it is,...