Peter Ganatos and Benjamin Liaw
The City College of The City University of New York
The software which these modules are based on is called Working Model and is commercially available from Knowledge Revolution, San Francisco, CA. The software allows the user to create two-dimensional mechanical systems on the screen containing devices such as springs, masses, pulleys, dampers, motors and actuators. Various types of forces may be simulated including gravitational, frictional and electrostatic forces. Clicking a RUN button animates the experiment. Controls may be introduced which allow the user to vary physical parameters such as initial position, velocity, and acceleration of objects, magnitude and direction of applied forces and torques, etc. Physical quantities such as velocity, acceleration, linear and angular momentum and kinetic energy may be measured and displayed while an animation is in progress.
Several illustrative modules have been developed covering a variety of topics. In addition, as the students became acquainted with the software, they were given specific topics and asked to develop their own modules. This paper describes some of the modules developed and the students' reactions to this learning experience.
In many physical science and engineering courses, students have difficulty visualizing some of the theoretical concepts presented. Textbook homework problems are helpful but even then, a student may have difficulty visualizing what a mathematical solution to a problem means. If students are provided with the means to experiment and apply the theory to real world situations, this can only lead to a better visualization and understanding of the theoretical concepts.
Toward this end, two approaches have been developed in the Department of Mechanical Engineering at CCNY. The first approach, used in our Heat transfer and Fluid Mechanics courses, has been to have the students perform simple home experiments using materials which can readily be found in the home. This teaching methodology has proven to be highly successful and the results have been reported elsewhere [1]. The present paper focuses on a second approach which is the use of computer animation as the vehicle for experimentation. The latter approach has successfully been used in our Engineering Mechanics (Dynamics) course over the past year.
A computer laboratory facility was set up containing ten 486 PC's and three inkjet printers for student use. The platform which supports these modules is called Working Model and is commercially available from Knowledge Revolution, San Francisco, CA. The software is menu driven and permits the user to construct two-dimensional mechanical systems on a computer screen consisting of masses, springs, dampers, ropes, pulleys, motors, actuators and many other objects with a mouse. The user does not have to rely on heavy mathematics or tedious programming. The software has the capability of dealing with real-world interactions such as collisions, gravity, wind resistance and electrostatics and allows the user to experiment with different scenarios and situations.
Initially, three computer-animated teaching modules were developed, each with the purpose of illustrating or clarifying some theoretical aspect of the course.
The first module, bsktbl.wm, is illustrated in Fig. 1. In this
module, a basketball player shoots a ball at a basket which is at height
m. For a given distance L and shooting angle
, the
student is asked to determine the initial velocity
needed
to get the ball through the hoop. As a first attempt to develop a mathematical
model, the student writes the differential equations of motion and solves
them subject to the initial conditions to determine the position of the
ball as a function of time. By requiring that at a certain time T
the ball be at the position of the basket leads to an expression for the
velocity needed to get the ball to the position of the basket. A plot of
the locus of such solutions is shown in Fig. 2. The student tries out the
solution for
(
m/s) and discovers
that the ball bounces off the hoop without passing through. After a few
more runs, the student realizes that in order for the ball to pass through
the hoop, it must arrive at the basket with a certain minimum slope. Thus
the student must modify his/her model to calculate the slope of the trajectory
at the basket and select only solutions having the required minimum slope.
In the process of this exercise, the student has not only gotten a better
understanding of the theory involved, but has also discovered that mathematical
models of a physical situation are not perfect and can always be improved.
