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3-027-BobbingDropping-ModelingScenario

Author(s): Brian Winkel

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

Keywords: drug resistance directed buoyancy free fall static equilibrium displacement

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Abstract

Resource Image We present two exercises 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.

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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

Dropping

A body of weight 32 lb is dropped from rest from a height of 100 ft in a medium offering resistance proportional to the velocity.

If the limiting or terminal velocity is 400 ft/sec, find the velocity and displacement at any time. Find the time at which the velocity is 200 ft/sec.

Bobbing

A 360 lb block of wood in the form of a 2 ft cube is floating in liquid which has a density of 60 lb/ft3.

If the cube is depressed, so that its upper face is level with the surface of the liquid, and then released, find the differential equation of its motion. Solve the differential equation and find the period of the motion

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Authors

Author(s): Brian Winkel

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

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