Inducing causal relationships from observations is a classic problem in scientific inference, statistics, and machine learning. It is also a central part of human learning, and a task that people perform remarkably well given its notorious difficulties. People can learn causal structure in various settings, from diverse forms of data: observations…

The bicycle provides a context-rich problem accessible to students in a first-year physics course, encircling several core physics principles such as conservation of total energy and angular momentum, dissipative forces, and vectors. In this article, I develop a simple numerical model that can be used by any first-year physics student to…

To find the point between two massive spherical bodies at which their gravitational fields cancel is an apparently simple problem usually found in introductory physics textbooks. However, by noting that such a point does not exist when the distance between the spheres is small and one of the masses is much smaller than the other--e.g., between the…

In this paper, a procedure is presented that will allow (i) the power and (ii) the energy of a pulsed and tuneable TEA CO[subscript 2] laser to be optimized. This type of laser represents a significant improvement in performance and portability. Combining a pulse mode with a grating tuning facility, it enables us to scan the working wavelength…

Utility companies generate three-phase electric power, which consists of three sinusoidal voltages with phase angles of 0 degrees, 120 degrees, and 240 degrees. The ac generators described in most introductory textbooks are single-phase generators, so physics students are not likely to learn about three-phase power. I have developed a simple way…

There is a growing consensus that introductory physics courses should help students develop general scientific reasoning abilities that transform them into lifelong learners, preparing them for careers and citizenship in a rapidly evolving world. Despite the sometimes daunting nature of this challenge, activities developed by various physics…

The aim of physics education is to generate understanding of physics and there is considerable anecdotal evidence that passing examinations in physics is not the same as understanding the subject. This paper describes how the areas of difficulties in understanding of physics were determined for pupils in Taiwan aged 13-15. Test material which…

The flight trajectory of a water rocket can be reasonably calculated if the magnitude of the drag coefficient is known. The experimental determination of this coefficient with enough precision is usually quite difficult, but in this paper we propose a simple free-fall experiment for undergraduate students to reasonably estimate the drag…

The Sun's atmosphere is a highly structured but dynamic place, dominated by the solar magnetic field. Hot charged gas (plasma) is trapped on lines of magnetic force that can snap like an elastic band, propelling giant clouds of material out into space. A range of ground-based and space-based solar telescopes observe these eruptions, particularly…

We discuss three methods of measuring the density of air most commonly used in a teaching context. Emphasis is put on the advantages and/or difficulties of each method. In particular, we show that the 'rubber balloon' method can still be performed with meaningful physical insight, but it requires a very careful approach. (Contains 4 figures and 3…

In this experiment, physical science students measured the mass of several soda cans, measured the mass and volume of water displaced when these cans were placed in water, and determined whether these cans sank or floated in water. Then, the students plotted graphs of the mass of displaced water versus the volume of displaced water, the mass of…

During a recent unit on characteristics of animals in different environments, "backyard safari" trips around the schoolyard provided opportunities for students to describe ways that animals are adapted to their unique environments. This led to a discussion of how polar bears have adjusted to living in the arctic. Therefore, students' questions…

The null result of the Michelson-Morley experiment and the constancy of the one-way speed of light in the "rest system" are used to formulate a simple problem, to be solved by elementary geometry techniques using a pair of compasses and non-graduated rulers. The solution consists of a drawing allowing a direct visualization of all the fundamental…

A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…

A small mechanical device, the atomic force microscope, measuring a force and the distance over which this force is applied, can be used on a single polysaccharide molecule to obtain the Gibbs energy of a conformational change within the polysaccharide. This well-defined conformational change within certain types of polysaccharide molecules is…