Enrico Fermi is remembered for his many contributions to theoretical and experimental physics, but from an educational point of view he also popularized the use of the kind of questions we now call "Fermi problems" (or "Fermi questions"). Fermi problems (FPs) are back-of-envelope problems that arose from the need to make order…

We will present a problem-solving method for the dynamics of a projectile that has two perpendicular acceleration vectors through rotation of the axes. This methodology of reparameterizing the two-dimensional system simplifies the speed optimization calculus.

The cross diagram is a way to illustrate and plan the solutions for all kinds of constant-acceleration kinematics problems--including projectile motion, multistage, and multiple-object problems. The cross diagram arranges the kinematic variables in a logical way, making the kinematic relationships between them easy to identify. Combined with a…

This paper describes two examples of teaching situations in which the idea of infinity arises, and supports the conclusion that infinity is not a physical reality but a very powerful and useful mathematical device which facilitates modelling and the solution of problems in physics.

The article describes a methodology for studying Fresnel diffraction with the active involvement of students in discussing the results of a demonstration experiment. To create a clearly visible model of Fresnel zones, a centimeter radio wave range was chosen, in which the first zone is about 10 cm in size. This makes visible the created…

What does it mean to "make sense" of physics? It's not a simple question. Most people have an intuitive feeling for when things do (or do not) make sense to them. But putting this feeling into words--especially actionable words--is another task entirely. Generally speaking, there are two ways in which we commonly use the term "make…

In a typical first physics class, homework consists of problems in which numerical values for physical quantities are given and the desired answer is a number with appropriate units. In contrast, most calculations in upper-division undergraduate physics are entirely symbolic. Despite the need to learn symbolic manipulation, students are often…

When authoring physics problems, professors may develop an intuition for how much information they need to provide such that the problem has a unique answer and is not over constrained. It is an open question as to whether using intuition leads to a sufficiently broad range of problems. In this paper we discuss a systematic way of authoring…

Students often use incoherent strategies in their problem solving involving force and motion, as revealed, e.g. when they are asked to draw force diagrams for amusement rides involving circular motion, whether in horizontal or vertical planes. Depending on the questions asked, assignments involving circular motion can reveal different types of…

The principle of relativity is of fundamental importance in practice when we are solving problems in physics since the axiom states that the result of any physical experiment is the same when performed with identical initial conditions relative to any inertial coordinate system. Hence, conceptual knowledge of coordinate systems is central in any…

The Widlar current source is one of the basic current sources that undergraduate students encounter throughout their learning process on electronics courses. The Widlar current is actually given in terms of a transcendental equation. Although an analytical solution exists in terms of the Lambert W function it might not be that useful for students…

The motion equations of a body under gravity and resistance linearly dependent on speed are usually analysed by solving differential equations. In this paper we report a derivation not explicitly involving differential equations but instead based on some elementary mathematical operations. The derivation uses only knowledge covered in a typical…

Students in introductory college physics often have wide ranges of preparation, making it challenging to deliver effective instruction for all. While numerous educational products and strategies have been shown to be broadly effective, there is a need for research-based online materials that support personalized learning and focus specifically on…

This paper shows how the freely downloadable software package called "SMath Studio" can be used to solve the time-independent Schrödinger equation using a simple step-wise approximation. The solution is illustrated with reference to the hydrogen atom for which trial eigenvalues are supplied by the energy level formula of the Bohr atom.

On August 16, 1960, at 7:12 a.m., United States Air Force Captain Joseph W. Kittinger Jr. looked out from his balloon gondola at a height of over 19 miles and… jumped. Kittinger's altitude and free-fall speed record lasted until Felix Baumgartner's jump from a height of nearly 24 miles on Oct. 14, 2012. Baumgartner broke several records, including…