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3-020-ChordPathTime-ModelingScenario

Author(s): Brian Winkel

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

Keywords: Unit Circle path falling gravity chord Netwon's Second Law of Motion

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Abstract

Resource Image Using Newton's Second Law of motion we can determine the time it takes for a mass to slide along a chord of a vertical circle from high point to any point along the circle. Initially, the result is nonintuitive and challenging to understand.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

A mass particle starts from rest at the highest point, O = (0,1), of a vertical circle and slides along a chord only effected by the acceleration due to gravity to another terminal point A on the circle.

What can you say about the time(s) it takes for the mass to hit the terminal points in terms of a changing angle of the chord with the perpendicular Reflect on your answer and make comments on the reasonableness and interpretations we might offer for your solution. This modeling opportunity appears in a number of textbooks. However, we believe the use of elementary vector mathematics to obtain a differential equation and then solve the equation and interpret the solution is a worthy modeling task.

 

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Authors

Author(s): Brian Winkel

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

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