We are migrating our materials to QUBES. Please pardon the construction. Close

OER Materials

Modeling Scenario

3-015-StyrofoamBallFall-ModelingScenario

Author(s): Brian Winkel

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

Keywords: football resistance gravity falling body sum of square errors Newton's Second Law of Motion sum of forces styrofoam

23 total view(s), 1 download(s)

Abstract

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

Citation

Researchers should cite this work as follows:

Article Context

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

Description

We propose two models for y(t) the distance fallen by the Styrofoam ball in meters at time $t$ in seconds in which positive distances and velocities are downward.

  1. The ball meets with resistance due to the air which is proportional to velocity, y'(t). We model this with - a y'(t) where we presume a is positive.
  2.  The ball meets with resistance due to the air which is proportional to velocity squared, y'(t)2. We model this with - a y'(t)2 where we presume a is positive.

In both cases (1) and (2) we seek to determine the parameter a such that the model fits the data best in the sense of minimizing the sum of square errors between the observed data and the model over all data points.

Article Files

Authors

Author(s): Brian Winkel

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

Comments

Comments

There are no comments on this resource.