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A Structured Approach to Problem Solving in Statics and Dynamics: Assessment and Evolution

Introduction

It has been the authors’ experience that, in spite of even the most careful presentation, students often perceive the solutions to problems in dynamics to be a hodgepodge of techniques and “tricks”. Interestingly, to address this perception problem, only limited resources can be found in textbooks published during the 50 years since the first editions of Meriam in 1951, Shames in 1959, and Beer and Johnston in 1962 that initiated a complete change in the way engineering mechanics was taught. Specifically, up until two years ago, little could be found in textbooks that one could use to teach a systematic approach to problem solving in Statics and Dynamics. As a result, we wondered why the approach used in more advanced mechanics courses (and often in sophomore-level Strength/Mechanics of Materials) is not used in Statics and Dynamics. This approach is much more structured and it is based on the idea that the equations needed to solve problems derive from three areas: 1. balance laws (e.g., force, moment, momentum, angular momemtum, energy, etc.); 2. constitutive equations (e.g., friction laws, drag laws, etc.); and 3. kinematics or constraints. Since we didn’t see any reason why this approach can’t and shouldn’t be applied to problems in Statics and Dynamics, we developed a structured approach to problems in these courses based on the classes of equations listed above and this approach was presented at the 2005 ASEE Annual Conference.1 At the time, a similar approach had just appeared for the first time in Statics and Dynamics textbooks,2, 3 though we were not aware of it when we developed ours. Since then, we have taught Dynamics using our structured approach to problem solving and have discovered a number of interesting aspects of it that we will discuss in this paper. In particular, we will: discuss our original approach, the reasoning behind its structure, and present an example of how we implemented it in the classroom, describe our experience using it in teaching Dynamics in the spring 2007 semester, present feedback from students who took our Dynamics course during the spring 2007 semester, discuss how and why we modified our approach based on our experience teaching with it, and discuss why we think this is the future of teaching problem solving in introductory mechanics courses.

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Costanzo, F., & Gray, G. L. (2008, June), A Structured Approach To Problem Solving In Statics And Dynamics: Assessment And Evolution Paper presented at 2008 Annual Conference & Exposition, Pittsburgh, Pennsylvania. 10.18260/1-2--4259