Catálogo de publicaciones - revistas

<jats:p>[Media: see text]</jats:p><jats:p> We present a simple, low-cost activity for students in a university-level introductory physics course. The main objective of the activity is to calculate and experimentally measure the center of mass of a 2D Tangram figure using complementary techniques. First, the algebraic and numerical results for the center of mass of the Tangram pieces are checked analytically and using mathematical software. Students then create their own Tangram figure and calculate its center of mass using formulas from physics tables. CAD software is also used to obtain the figure's center of mass. Finally, the center of mass is measured experimentally, and a comparison with the theoretical results is made. The modularity of the activity allows instructors' flexibility to design an ad hoc activity to emphasize individual subjects according to the needs of their course. </jats:p>

<jats:p> We revisit the golfer's curse, which is the possibility that a golf ball can emerge from the cylindrical hole into which it has entered. Our analysis focuses on three constants of the motion. One of these is the energy, because we assume that the ball rolls without slipping on the inner wall of the hole, losing only a small amount of energy to rolling resistance; the other two are related to the angular momentum about the contact point of the ball with the inner wall of the hole. We develop an analysis of the motion of the ball and report measurements of the moment of inertia of a real golf ball. Solving the equation of motion along the vertical direction, we address the question of whether or not the ball could complete a vertical oscillation without reaching the bottom of the hole. We also present measurements of the dynamical friction for a golf ball and discuss dissipation in slip conditions. We conclude by proposing a challenge to golf players: to find a way to send a ball into a hole in order to make it emerge. </jats:p>

<jats:p> A fundamental problem in spacecraft mission design is to find free-flight paths from one place to another that satisfy various design criteria. We explore the geometry of free-flight paths between departure and arrival points for Kepler's problem. Newton showed that these paths are conic arcs. We find the parameters for all conic paths between a departure and an arrival point as a function of one key variable called the inside angle. Once the paths are written in terms of this single parameter, then it is straightforward to find the path that takes a specified travel time (the Lambert problem) or to perform other optimizations such as minimizing the fuel costs. </jats:p>