Tags: falling

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  1. 2020-Beeken, Paul - First Order Differential Equations - AirResistance

    26 Mar 2020 | Contributor(s):: Brian Winkel

    Beeken-FirstOrderDifferentialEquations-AirResistanceBeeken, 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...

  2. 2010-Chicone, C. - Mathematical Modeling and Chemical Kinetics. Notes

    26 Mar 2020 | Contributor(s):: Brian Winkel

    2010-Chicone-MathModelingANDChemicalKineticsChicone, 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...

  3. 3-015-S-StyrofoamBallFall

    24 Mar 2020 | | Contributor(s):: Brian Winkel

    We are given data on a falling Styrofoam ball and we seek to model this motion.

  4. 2003-Bohren, 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): 534-537.See http://pages.erau.edu/~reynodb2/ps303/Bohren_2004_AJP_DimensionalAnalysis.pdf .Abstract: Dimensional analysis is a simple,...

  5. 1-083-S-FallingMeteorites

    24 Aug 2019 | | Contributor(s):: Lyle Clifford Smith

    After introducing the solution to the ordinary differential equation which models a falling object with drag (first-order, non-linear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus is on creative identification of factors. Students...

  6. 3-009-S-BallDropInWater

    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.

  7. 1-063-S-ThreeHoleColumn

    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.

  8. 2018-Schneebeli,Hans R. - Modeling Falling Bodies

    01 Mar 2018 | | Contributor(s):: Hans Rudolf Schneebeli

    Modelling falling bodies is discussed using a computer algebra system-calculator 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,...

  9. 2017-Groetsch, 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: 3-7.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...

  10. 2017-Vas, 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...

  11. 2017-Benaka, 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...

  12. 1-115-S-ModelingWithFirstOrderODEs

    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

  13. 3-017-S-StackedCoffeeFiltersFalling

    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.

  14. 2014-Groetsch, 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): 499-505.Article Abstract: This article, inspired by a 17th-century woodcut, validates empirical observations of Marin Mersenne...

  15. 1999-Brauer, 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): 437-440.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...

  16. 3-070-S-FallingInWater

    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 -...

  17. 3-044-S-DeepWell

    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.

  18. 1994-Gruszka, 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): 442-444.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...

  19. 3-019-S-ShuttlecockFall

    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...

  20. 3-013-S-WhiffleBallFall

    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.