Deriving relativistic momentum and energy. II. Three-dimensional case

We generalise a recent derivation of the relativistic expressions for momentum and kinetic energy from the one-dimensional to the three-dimensional case.Comment: 7 page

Fixing the shadows while moving the gnomon

It is a common practice to fix a vertical gnomon and study the moving shadow cast by it. This shows our local solar time and gives us a hint regarding the season in which we perform the observation. The moving shadow can also tell us our latitude with high precision. In this paper we propose to exchange the roles and while keeping the shadows fixed on the ground we will move the gnomon. This lets us understand in a simple way the relevance of the tropical lines of latitude and the behavior of shadows in different locations. We then put these ideas into practice using sticks and threads during a solstice on two sites located on opposite sides of the Tropic of Capricorn.Comment: Published version available at http://cms.iafe.uba.ar/gangui/didaastro/#Publication

Coordination of Mathematics and Physical Resources by Physics Graduate Students

We investigate the dynamics of how graduate students coordinate their mathematics and physics knowledge within the context of solving a homework problem for a plasma physics survey course. Students were asked to obtain the complex dielectric function for a plasma with a specified distribution function and find the roots of that expression. While all the 16 participating students obtained the dielectric function correctly in one of two equivalent expressions, roughly half of them (7 of 16) failed to compute the roots correctly. All seven took the same initial step that led them to the incorrect answer. We note a perfect correlation between the specific expression of dielectric function obtained and the student's success in solving for the roots. We analyze student responses in terms of a resources framework and suggest routes for future research.Comment: 4 page

Chemistry vs. Physics: A Comparison of How Biology Majors View Each Discipline

A student's beliefs about science and learning science may be more or less sophisticated depending on the specific science discipline. In this study, we used the physics and chemistry versions of the Colorado Learning Attitudes about Science Survey (CLASS) to measure student beliefs in the large, introductory physics and chemistry courses, respectively. We compare how biology majors -- generally required to take both of the courses -- view these two disciplines. We find that these students' beliefs are more sophisticated about physics (more like the experts in that discipline) than they are about chemistry. At the start of the term, the average % Overall Favorable score on the CLASS is 59% in physics and 53% in chemistry. The students' responses are statistically more expert-like in physics than in chemistry on 10 statements (P lesser-than-or-equal-to 0.01), indicating that these students think chemistry is more about memorizing disconnected pieces of information and sample problems, and has less to do with the real world. In addition, these students' view of chemistry degraded over the course of the term. Their favorable scores shifted -5.7% and -13.5% in 'Overall' and the 'Real World Connection' category, respectively; in the physics course, which used a variety of research-based teaching practices, these scores shifted 0.0% and +0.3%, respectively. The chemistry shifts are comparable to those previously observed in traditional introductory physics courses

Sticky physics of joy: On the dissolution of spherical candies

Assuming a constant mass-decrease per unit-surface and -time we provide a very simplistic model for the dissolution process of spherical candies. The aim is to investigate the quantitative behavior of the dissolution process throughout the act of eating the candy. In our model we do not take any microscopic mechanism of the dissolution process into account, but rather provide an estimate which is based on easy-to-follow calculations. Having obtained a description based on this calculation, we confirm the assumed behavior by providing experimental data of the dissolution process. Besides a deviation from our prediction caused by the production process of the candies below a diameter of 2 mm, we find good agreement with our model-based expectations. Serious questions on the optimal strategy of enjoying a candy will be addressed, like whether it is wise to split the candy by breaking it with the teeth or not