# DYNAMICS AS A PROCESS, HELPING UNDERGRADUATES UNDERSTAND DESIGN AND ANALYSIS OF DYNAMIC SYSTEMS

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3 report that a good predictor of future success is the ability to state a rule for solving a problem after an initial example. If procedural or rule based problem solving is important, is it necessary to provide students with the rules? Clearly the answer is no. It is possible for students to develop their own rules. Lewicki, Czyzewska and Hoffman 5 demonstrated that subjects could, it seemed, devise complex rules for predicting the outcome of perception tests. Though it is not clear that their experiment applies to technical problems, it, combined with practical teaching experience, suggests that students can develop their own procedures. In light of these studies, it seems reasonable that a procedural method of teaching Dynamics would: 1. facilitate commitment of the information to long-term memory, 2. facilitate conversion from example-matching to true understanding of the material, 3. result in greater performance by the students. Changing the way the material is presented is only one of the important alterations needed. Attention must also be placed on what is taught. What we want is to teach students, or rather give students practice with the truly high levels of thinking 6 and not bore them with the mundane. For example, we want students to formulate problems, to be able to ask the right questions and know how to respond to the answers. The students should know as much about why something is done as they do about what is done. Only by understanding why will they deal effectively with unique situations. A simple example of this concept in Dynamics is the case of belts and pulleys. Give a group of students an automobile engine running at constant speed, point to a fan belt and several pulleys under the hood. Let one of the pulleys be driving the fan or water pump and another be an idler pulley. Ask the students to draw freebody diagrams of the pump and idler pulleys. My hypothesis is that most of them will show equal tensions on either side of the pulley. Ask them why and they respond with something like, Tension on either side of a massless frictionless pulley is the same. This is of course wrong, what the students are demonstrating is an application of a memorized rule and not the application of a concept. They should apply the concept of equilibrium to arrive at the conclusion that the idler pulley has approximately equal tensions but the pump does not. What this indicates is that providing handy dandy rules and formulas, especially early in the course material can have a devastating effect. I suggest that by teaching process, rather than formulas, this difficulty and others can be avoided. Another area in which students are weak is design of Dynamic systems. The skills required for design are duals to those needed for analysis. For example, in analysis, one generally tries to make as few assumptions as possible then determine the resulting behavior. In design, one often makes many simplifying assumptions then applies intuition and memorized facts to reason what might happen. To be an effective designer one must have a ready supply of facts and correct intuition. The problem for the instructor is to make sure these facts and intuition are correct, and organized in some way to enable students to recall them. Hence a process is important. 3 Page

4 Finally, the current textbooks pose a real problem. Most texts are a collection of facts. For example, equations for rectilinear motion with constant acceleration are boxed and kinetics of a single rigid body rotating about a fixed point are separated from those for translation and general plane motion. Students learn quickly (and incorrectly) that Dynamics is a process of identifying the correct facts then applying the correct equation to compute some other desired fact. Likewise rather than incorporating work-energy methods into an overall scheme, they are often presented and treated as totally different methods of formulation exacerbating the faulty idea that there is a special equation for every case. In reality, work-energy can be thought of as an alternative method for relating force to motion and has a tie to all other problems. Impulse-momentum methods can be viewed as a method for handling complex forces which again leaves it potentially applicable to all problems. The Dynamic Process The process used for dynamic analysis consists of six major steps with some minor details in each step. The way the process is used in class is the six steps are listed early in the semester with very few details. Every new topic is placed in perspective using the process. As the semester progresses, the students obtain a more detailed perspective of the process. As new material is introduced, the process expands and remains expanded showing all the detail up to the current time. Since the present audience is most likely familiar with dynamic analysis, the entire process is listed here. Due to space limitations, the details are omitted. Detailed discussion of each step, examples of each one, and the course sequence for the class can be found by browsing the author's web site. The Process for Dynamic Analysis 1) Think About the Problem. Identify what is known, what is needed and what kind of solution is expected. Count the Degree of Freedom' Make necessary assumptions about the problem. Decide what assumptions to test first. 2) Choose Coordinates. Select variables, or coordinates, that will describe the object's motion. Decide if the problem requires a Force-Motion Relationship, discussed shortly, or if it is merely a Kinematic (relate motions only) problem. 3) Define the System. Determine what type of Force-Motion Relationship is needed. Determine how many objects or bodies you can expect to isolate and study. Typically you would study each object in the problem only once. So if there are three objects, you would expect a maximum of three isolated objects to study. Decide what object or body to study. Decide how to isolate objects wisely. Draw a freebody diagram or state diagram. 4) Apply a Force-Motion Relation. I use two laws, Newton's and Work-Energy. At this point, students compute acceleration (if required) and set it equal to forces. They perform 4 Page

5 the analogous operations for moment and work-energy. They understand that regardless of how they labeled motion variables, they must compute inertial motion. 5) Find Extra Equations. Find more objects to isolate and study. Relate motions kinematically. This involves thinking about the degrees of freedom and the information given in the problem statement. Find other relationships peculiar to the particular problem. As an example, the coefficient of restitution is extra information that describes the material behavior during collisions. Determine if the problem is ill-defined. If so, pose it differently. 6) Solve and Interpret. The solving step is relegated to computer tools whenever possible, but the students are often asked to interpret the solutions. Determine the required solution. Most dynamics problems have one of three types of solutions. These are: Given the motion NOW, determine some force NOW. Given force, solve a differential equation for motion in the future. Given a certain status NOW, solve a differential equation to find the status in the FUTURE. For example, determine the maximum force in an engine as it operates. Verify all assumptions. Students recognize that many assumptions involve assuming a constraint on a force or its corresponding motion. They learn to verify these constraints. Check to see that the solution is reasonable. RESULTS The process described in this paper was implemented in an undergraduate sophomore dynamics class of fifty students at Texas A&M in the Spring term The class is required of many engineering majors at Texas A&M. Typical of tough required classes, student classifications ranged from second term sophomores to graduating seniors. Of the 50 students enrolled, 2 dropped out by the end of the first week. I attribute that to the fact that the students were told the class would be out of the ordinary, which is disturbing to many students. Overall, the 48 students remaining in the class performed very well. The failure rate (D and F) was significantly below the average for other sections and there was a general sense of enthusiasm. The class attendance was always above 80%. Much of the time, attendance was very near 100%. The class is sufficiently different that it takes time for the students to adjust to the processoriented thinking. One individual after the second exam made the following comment: On problem XXX, I was lost. I didn't have a clue so I applied the process and it worked out real easy. The examinations were restricted to well defined problems. The problem statements left little to the student's imagination. Since vaguely worded and open ended problem statements often 5 Page

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The University of Tennessee, Memphis Writing Learning Objectives A Teaching Resource Document from the Office of the Vice Chancellor for Planning and Prepared by Raoul A. Arreola, Ph.D. Portions of this