In the years after Joule's experiment on the equivalence of heat and work, it was taken for granted that heat and work could be independently defined and that the change in energy for a change of state is the sum of the heat and the work. Only with the work of Caratheodory and Born did it become clear that heat cannot be measured independently,…

Participants estimated the imagined elongation of a spring while they were imagining that a load was stretching the spring. This elongation turned out to be a multiplicative function of spring length and load weight--a cognitive law analogous to Hooke's law of elasticity. Participants also estimated the total imagined elongation of springs joined…

Some physicists have pointed out that we do not know what force is. The most common definition of force in textbooks has been criticized for more than two centuries. Many studies have shown that the concept of force is a problem for teaching. How to conceive force on the basis of the concepts and criticism of force in the works of Newton, Euler,…

This paper was first motivated by the following question: "A pair of twins, R and S, each gives the "same" hard push on a block. R's block is on a rougher floor than S's. Who does more work?" It is shown that S will do more work on his block if there is no constraint on the distance over which the force is applied. On the other hand, if the…

For both casual and avid fans alike, Olympic and other sporting events can provide a wealth of data for simple physics analyses. One of the most impressive performances in recent Olympic history is that of Usain Bolt in the track-and-field sprinting events during the 2008 Summer Games. Over a seven-day span, Bolt set world records in the 100-m and…

The earliest mechanical clocks appeared in Europe in the 13th century. From about 1250 CE to 1670 CE, these simple clocks consisted of a weight suspended from a rope or chain that was wrapped around a horizontal axle. To tell time, the weight must fall with a slow uniform speed, but, under the action of gravity alone, such a suspended weight would…

Several years ago a student asked why so many things in the solar system were round. He noted that many objects in the solar system, although not all, are round. The standard answer, which he knew, is that the mutual gravitational attraction of the molecules pulls them into the shape that gets them as close to each other as possible: a sphere.…

Fill an ordinary latex balloon with helium gas and you know what to expect. Over the next day or two the volume will decrease noticeably as helium escapes from the balloon. So what happens when a latex balloon is filled with carbon dioxide gas? Surprisingly, carbon dioxide balloons deflate at rates as much as an order of magnitude faster than…

Recently, there has been an increasing emphasis in discussions on science education on the potential and advantages of stories and narratives in teaching situations. From this, one might conclude that simply starting to use stories in science classrooms is a good thing, "per se". Yet, as I will argue in my paper, things do not appear to be that…

We present an analysis on the locus formed by the set of maxima of the trajectories of a projectile launched in a medium with linear drag. Such a place, the locus of apexes, is written in terms of the Lambert "W" function in polar coordinates, confirming the special role played by this function in the problem. To characterize the locus, a study of…

It is well known that the speed [image omitted] is obtained in the process of defining SI units via action-at-a-distance forces, like the force between two static charges and the force between two long and parallel currents. The speed c[subscript u] is then physically different from the observed speed of propagation c associated with…

Toward the end of the AP[R] Physics C Mechanics course, I challenge my students to integrate many of the concepts they have learned in both the classroom and laboratory by completing the "Bola Lab." The title is based on the Argentinean gaucho (cowboy) herding tool, the "boleadora," or "bola" for short (see Fig. 1), which consists of two heavier…

We analyse two-mirror resonators in terms of their fractional Fourier transform (FRFT) properties. We use the basic ABCD ray transfer matrix method to show how the resonator can be regarded as the cascade of two propagation-lens-propagation FRFT systems. Then, we present a connection between the geometric properties of the resonator (the g…

The Landau-Zener formula provides the probability of non-adiabatic transitions occurring when two energy levels are swept through an avoided crossing. The formula is derived here in a simple calculation that emphasizes the physics responsible for non-adiabatic population transfer. (Contains 2 figures.)

Physics is not immune to questioning by supporters of nonscientific propositions such as "intelligent design" and "creationism." The supporters of these propositions use phrases such as "it's just a theory" to influence those unfamiliar with or even fearful of science, making it increasingly important that all students and in particular science…