We have found that incorporating computer programming into introductory physics requires problems suited for numerical treatment while still maintaining ties with the analytical themes in a typical introductory-level university physics course. In this paper, we discuss a numerical adaptation of a system commonly encountered in the introductory physics curriculum: the dynamics of an object constrained to move along a curved path. A numerical analysis of this problem that includes a computer animation can provide many insights and pedagogical avenues not possible with the usual analytical treatment. We present two approaches for computing the instantaneous kinematic variables of an object constrained to move along a path described by a mathematical function. The first is a pedagogical approach, appropriate for introductory students in the calculus-based sequence. The second is a more generalized approach, suitable for simulations of more complex scenarios.
Finally, it's worth noting that for introductory physics problems it is common place to ignore air resistance when doing projectile motion problems.
problems: A Taxonomy of Introductory Physics Problems”, Phys
The use of the work–energy relationship is intended to inform the students’ understanding of protein biology. To say that a protein is in a “stable” energy state means that, in order to move it out of this state, energy would need to be added by doing work on the molecule. Bringing the biological context of protein energy landscapes and protein stability into contact with the physics in the problem may also enhance the students’ understanding of the work–energy relationship. As we mentioned above, the ability of external work to cause a change in an object's kinetic energy is often the only context in which work is explored in traditional introductory physics problems. However, in this task, students encounter a situation in which the work done on the protein does not impact the translational motion, but rather the shape, and therefore the stability, of the protein. Because the internal structure of a biological molecule is crucial to its functioning in a way that may not be true for a nonbiological system (particularly for systems typically explored in a standard introductory physics problem), it is perhaps more apparent in this context than in traditional physics contexts that structural changes must be considered. The work done on the protein changes the protein from a more stable (folded) to a less stable (unfolded) form. Focusing the task on protein stability forces students to consider relationships among forms of energy that they might not typically encounter in a traditional work–energy physics task, thus providing the students an opportunity to refine their ideas about the relationship between work and energy.