One way to develop a cross-curricular lesson is to select the most common mathematical formulas used in science and carefully develop and implement tasks that allow students to make connections between the mathematical representations and theoretical/physical science concepts. The slope-intercept formula, which is used to study relationships…

Light refracts as it travels from one medium to another. The angle of incidence "i" and the angle of refraction "r" are related by Snell's law, sin"i" ÷ sin"r"="k," where "k" is a constant. The diagram in Fig. 1 shows a geometric representation of the formula for light passing from…

End-pipe corrections seldom come to mind as a suitable topic for an introductory physics lab. Yet, the end-pipe correction formula can be verified in an engaging and inexpensive lab that requires only two supplies: plastic-tube toys called boomwhackers and a meter-stick. This article describes a lab activity in which students model data from…

This paper presents a simplified approach for the application of material efficiency metrics to linear and convergent synthesis plans encountered in organic synthesis courses. Computations are facilitated and automated using intuitively designed Microsoft Excel spreadsheets without invoking abstract mathematical formulas. The merits of this…

At our university, students in introductory physics classes perform a laboratory exercise to measure the range of a projectile fired at an assigned angle. A set of photogates is used to determine the initial velocity of the projectile (the launch velocity). We noticed a systematic deviation between the experimentally measured range and the range…

The standard for measuring fuel efficiency in the U.S. has been miles per gallon (mpg). However, the Environmental Protection Agency's (EPA) switch in rating fuel efficiency from miles per gallon to gallons per hundred miles with the 2013 model-year cars leads to interesting and relevant mathematics with real-world connections. By modeling…

Because mathematical formulae and problem solving are such prominent components of most introductory physics courses, many students consider these courses to be nothing more than courses in applied mathematics. As a result, students often do not develop an acceptable understanding of the relationship between mathematics and science and of the role…

The topic of coupled oscillations is rich in physical content which is both interesting and complex. The study of the time evolution of coupled oscillator systems involves a mathematical formalization beyond the level of the upper secondary school student's competence. Here, we present an original approach, suitable even for secondary students, to…

As students watched a compressional pulse bounce back and forth on the horizontally suspended Slinky[TM], shown in Fig. 1, we wrote down the formula for the speed of the pulse and promised that later in the course we would derive the formula. The problem is we did not keep our promise in the course. Here is where we are keeping the promise. As…

Students of General Physics often complain that the course is too abstract and remote from daily life. As teachers, we emphasize that the abstract concepts of physics are indispensable for understanding our daily experiences, and we try to give the impression that quantitative descriptions can be achieved by adopting concrete mathematical…

When examining complex waveforms by examining oscillograms from simple resonant circuits, interpretation problems occur. These problematic oscillograms are explainable by recognizing that the typical resonant filters pass significant amounts of several harmonics adjacent to the one intended. Adjacent harmonics effects are computed; resulting…