Sliding along downhill, uphill, and curved segments: A dynamical simulation exercise for a first course in physics or mechanics
In this paper we describe and review a specific simulation exercise in dynamics, developed at Elizabethtown College. It consists of simulating the dynamics of a manned sled along a number of downhill and uphill segments with different slopes, lengths, convexity/concavity and radii of curvature. Students are required to write the free body diagrams and to derive the kinematical equations of motion within each segment. Friction and air resistance are included. The non-uniformly accelerated motion is approximated by uniform acceleration within small path increments. The students (freshmen or sophomores) are requested to update the motion in a spreadsheet, while solutions with other software packages are assigned extra credit. Similarly, a variety of "what if" questions, some of them to be discovered, bring the students to critically analyze the results and find interesting solutions for specific initial or other conditions. We argue that this type of exercise/simulation, that requires students to intermix theoretical analysis with computer simulation and common-sense engineering data analysis, should become very important tools in physics and engineering. Such composite exercises do mimic in some sense "real-life" problems that graduating engineers find in their first job efforts, and do help prepare the students to the multifaceted requirements of graduate research. We analyze the performances and the attitudes of different classes and students to the sled problem and we report on a survey that reflects some of the students' thoughts on such type of challenges and their usefulness.