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Session 3268

Problem Solving in Statics and Dynamics: A Proposal for a Structured Approach

Gary L. Gray, Francesco Costanzo, Michael E. Plesha The Pennsylvania State University / The Pennsylvania State University / University of Wisconsin–Madison Abstract

It has been the authors’ experience that, even with the most careful presentation, students perceive the solutions to problems in statics, and especially dynamics, to be a “hodgepodge” of techniques and tricks. This is also born out by feedback the author’s have received from colleagues and from the approximately 50 expert reviewers of the statics and dynamics books that the authors are currently writing. Interestingly, this state of affairs has changed little in the more than 40 years since the publication of the first editions of Meriam 1952, Shames in 1959, and Beer and Johnston in 1962 changed the way engineering mechanics was taught. In this paper, we present a formal procedure that we are using in the statics and dynamics texts we are writing. The procedure we are using is not new in that it derives from the approach used in more advanced mechanics courses in which the equations needed to solve problems derive from three areas or places: 1. balance laws (e.g., momentum,∗ angular momentum, energy, etc.); 2. constitutive equations (e.g., friction laws, drag laws, etc.); and 3. kinematics or constraints. On the other hand, it is new in the sense that we are applying it in freshman and sophomore-level mechanics courses. We will close with several examples from statics and dynamics for which we use our approach.

Introduction

Engineering courses in mechanics differ from their companion courses offered by physics departments in that, in engineering, there is a strong emphasis on issues concerning engineering standards and design on the one hand and on the acquisition of effective problem solving techniques, on the other. In this paper we focus our attention on how problem solving is treated and fostered in current freshman/sophomore-level mechanics books in statics and dynamics. Specifically, we are interested in investigating the notion of structured problem solving, where, by structured problem solving, we mean an approach to problem solving that can be applied almost universally to mechanics problems and helps the student in avoiding a trial and error approach to the assembling of the equations governing a problem’s solution. Our motivation is that, in our experience, students perceive the solutions to problems in statics and, especially, dynamics to be a “hodgepodge” of tricks ∗ ˙ Of course, the balance of momentum as given by Euler’s First Law for a particle, i.e., F = p, where p is the particle’s momentum, contains the “equilibrium equations” of statics as a special case.

Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright © 2005, American Society for Engineering Education

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Plesha, M., & Gray, G., & Costanzo, F. (2005, June), Problem Solving In Statics And Dynamics: A Proposal For A Structured Approach Paper presented at 2005 Annual Conference, Portland, Oregon. 10.18260/1-2--15371