The statics of fluids may seem simple at first but often poses problems for students when it comes to applying it to concrete cases. Despite its relatively simple laws, some subtleties, mainly related to the elastic characteristics of a fluid, must be noted. This elasticity allows the pressure exerted in a part of the fluid to propagate in its…

What happens when a perfectly elastic ball collides with a completely inelastic ball? It is shown that the outcome depends on the stiffness of each ball. A standard textbook problem in mechanics is to calculate the outcome of a head-on collision between two balls using conservation of momentum and kinetic energy. It is easily shown that the…

We propose a method to measure the speed of sound in air using a motion detector. The experiment is based on the principle of a motion detector used to measure distances. This device measures the time of flight of alternating ultrasonic waves between the observer and the target. By assuming a fixed speed of sound, the time of flight can be…

Simulations can provide opportunities for engaged exploration in physics teaching and learning. Beyond the two-dimensional world of screen-based simulations, abstract concepts like vectors (for example, of electric fields) can frequently be visualized better in a three-dimensional virtual reality (VR) environment. These visualizations can be…

In this note, the classical Doppler shift for some accelerated mechanical systems is considered under a common graphical approach. In one dimension, we study uniform accelerated motion and simple harmonic motion. In two dimensions, uniform circular motion and pendular motion are considered. In each case, an elementary treatment shows that the…

Friction is one of the most important forces studied in classical mechanics, and still is the subject of pedagogical literature. In a small series of problems stated below, we consider a particle sliding down a curve under the actions of gravity and kinetic friction. Unlike many of the referenced sources, we neglect the centripetal force arising…

There is a close connection between simple harmonic motion and uniform circular motion. This connection is widely taught and included in standard textbooks. Here, we exploit this connection to simultaneously derive two results from introductory mechanics: the period of a mass-spring system and the centripetal acceleration formula. Previously…

The trajectory of a ball in air is affected by aerodynamic drag and lift. In general, the trajectory needs to be calculated numerically since the acceleration varies with time in both the horizontal and vertical directions. If the trajectory remains approximately parabolic, then simple analytical solutions can be found, giving useful insights into…

During elementary physics courses, many examples in mechanics are studied without considering air resistance effects. We can mention, for example, projectile motion and free fall, among many others. Only brief studies of such systems in classical mechanics courses consider linear air resistance (F[subscript drag] [is proportional to] v), which is…

In this article, we construct a very simple double pendulum (the concept of a pendulum should be familiar to all beginning students of classical mechanics). Since a double pendulum has two degrees of freedom, we suggest that this pendulum can be used in the classroom environment to illustrate the concept of normal modes, and we use video software…

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…

Teaching special relativity to lower-division students is challenging because results such as time dilation, length contraction, and frame dependence of simultaneity are counterintuitive. The literature is extensive, so only a brief list is given here, with articles divided roughly between discussions of general principles and calculations applied…

In recent years, there have been a number of articles published concerning whether or not potential energy ("PE") as defined in mechanics is invariant under Galilean transformation. This essay addresses that issue in a different, more fundamental and elegant way than has been done thus far. It recognizes that a considerable change in the…

The conical pendulum is a classic introductory physics problem for teaching circular motion--a topic about which students frequently carry alternative conceptions. As teachers provide lessons to untangle these conceptions, it is good to allow students to practice their new knowledge in varied settings. This is one possible experiment that builds…

The study of the motion of a projectile, thrown at an angle to the horizon, is a wonderful classical problem. This issue has been the subject of great interest to investigators for centuries. Currently, the study of parabolic motion, in the absence of any drag force, is a common example in introductory physics courses. The theory of parabolic…