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Modeling Scenario

3-070-FallingInWater-ModelingScenario

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: data water resistance falling buoyancy mass

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Abstract

Resource Image We model a small canister with ballast to keep it vertical as it falls through water in a graduated cylinder filled with water. We suggest several models in terms of resistance due to the media and estimate appropriate parameters.

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Article Context

Resource Type
Differential Equation Type
Qualitative Analysis
Application Area
Technology
Approach
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Bloom's Cognitive Level

Description

We model a small canister with ballast to keep it vertical as it falls through water in a graduated cylinder filled with water. We suggest several models in terms of resistance due to the media and estimate appropriate parameters. We then ask students to compare models using the Akaike Information Criterion which we define and reference.

In the iconic differential equation text Braun, M. 1978. Differential Equations and Their Applications, Second Edition. New York: Springer Verlag, there is a section on modeling a falling canister of nuclear waste in the ocean to determine the velocity that the canister might have upon striking the bottom of the ocean. This is due to concern that the canister might break open and the lead containment surrounding the nuclear material might fail.

Model the fall of our own canister in a cylinder of water as shown in in our own small little ``ocean'' as we place it in the water using the setup and video found at YouTube from which we took data used here. 

Article Files

Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

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