
3027SBobbingDropping
10 Jul 2020   Contributor(s):: Brian Winkel
We present two exercises from a differential equations text in which we ask students to model (1) falling object experiencing terminal velocity and (2) bobbing block of wood in liquid. We model the motion using Newton's Second Law of Motion and Archimedes' Principle.

1128SRocketFlight
04 Jun 2020   Contributor(s):: Brian Winkel
We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its fall to earth.

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...

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

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.

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

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,...

2006Loyd, Alun L. and Dominik Wodarz  Drug Resistance in Acute Viral Infections: Rhinovirus as a Case Study.
18 Sep 2017   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.See http://www4.ncsu.edu/~allloyd/pdf_files/resistance_preprint.pdf . Accessed 18 September 2017.Abstract: The emergence and spread...

1994Minton, Roland  A Progression of Projectiles  Examples from Sports.
12 Sep 2017   Contributor(s):: Brian Winkel
Minton, Roland. 1994. A Progression of Projectiles  Examples from Sports. The College Mathematics Teacher. 28(5): 436442.See https://www.maa.org/programs/facultyanddepartments/classroomcapsulesandnotes/aprogressionofprojectilesexamplesfromsports .There is a progression...

2017Unknown  Calculus for Engineers IISample Problems on mathematical modeling with differential equations
10 Sep 2017   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...

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...

3075SRLCCircuit
17 May 2017   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.

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...

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...

1994Gruszka, T.  Balloon Experiment in the Classroom
01 Mar 2017   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...

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

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 ...

1999Brauer, F.  What Goes Up Must Come Down
20 Jun 2015   Contributor(s):: F. Brauer
Brauer, F. 1999. What Goes Up Must Come Down. American Mathematical Monthly. 108(5): 437440.See https://www.tandfonline.com/doi/abs/10.1080/00029890.2001.11919770 .This paper is a wonderfully general analysis of the following, “It is natural to ask whether a...

1999Meade, Douglas B. and Allan A. Struthers  Differential Equations in the New Millennium: The Parachute Problem.
20 Jun 2015   Contributor(s):: Douglas B. Meade, Allan A Struthers
Meade, Douglas B. and Allan A. Struthers. 1999. Differential Equations in the New Millennium: The Parachute Problem. International Journal of Engineering Education. 15(6): 417424.See https://www.ijee.ie/articles/Vol156/ijee1097.pdf .Article Abstract: Introductory...

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...