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Modeling Scenario

3-009-BallDropInWater-ModelingScenario

Author(s): Brian Winkel

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

Keywords: resistance gravity falling body terminal velocity buoyancy

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Abstract

Resource Image 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.

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Article Context

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

Description

Derive and defend a mathematical model for a falling ball in liquid using a Free Body Diagram and Newton's Second Law of Motion. The latter says that for a body of mass m its mass times its acceleration is equal to the sum of all external forces acting on the body.

Identify all the forces in this situation and then build the differential equation which models the position beneath the surface of the ball.

Article Files

Authors

Author(s): Brian Winkel

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

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