On 24 June 1994 at Fairchild Air Force Base, during practice for an air show, a low-flying B-52H aircraft banked its wings vertically and crashed. Emphasizing the activity of modeling drag and gravity, these notes examine the possibility of recovery with several models. First, with algebra, historical data lead to a model where in a free fall near…

The dynamics of a simple pendulum are often presented to undergraduate engineering students in introductory courses in dynamics. It is usually the first dynamic system considered by students that is modelled by a differential equation. This paper presents the standard material given to students. It is fair to say that students are accepting this…

The relativistic addition of velocities is usually introduced early in the study of Einstein's special theory of relativity. The equations are simple enough, but randomly chosen velocities lead to unwieldy calculations that can dishearten the student. This paper presents tables of velocity components in two dimensions, composed of five or fewer…

The question of the sources of electric and magnetic fields and their causes has been discussed extensively in the literature over the last decades. In this article, we approach this problem from the unified treatment of electromagnetic fields emphasizing the role of their sources in accordance with the cause-effect relationships. First, we…

Problems involving chains, cables, or ropes that are dropped, folded, or pass around pulleys attract ongoing interest, in part because they can become variable-mass situations if the chain is partitioned into sections for analysis. Less attention has been paid to trying to intentionally project the end of a string as far as possible. Here we…

We study the variation of the apparent weight of an object with height above the surface of a planet with a (buoyant) atmosphere. Interestingly, this variation depends on two competing factors--the reduced gravitational acceleration (which acts to reduce the weight with increasing height) and the reduced buoyancy force in the progressively less…

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…

The stately fall of magnets through conducting pipes is a favorite classroom and laboratory activity used in teaching electromagnetic induction, Lenz's law, eddy currents, electromagnetic braking, and even Newton's third law. When a neodymium magnet is used, the terminal velocity is reached in just a few milliseconds as the induced eddy currents…

Lissajous figures are parametric equations that deconstruct into equations of simple harmonic motion. They were a source of inspiration by artists and mathematicians alike, well before the digital age, due to their esthetic forms and simple equations that could be easily deconstructed. Here for the first time in literature, we present Lissajous…

A collision of one object with two or more objects is relatively complicated in general, but a simple example is provided by Newton's cradle since all the objects are identical and in line. In the present paper, an experiment is described where a heavy mallet collides head-on with two billiard balls. The two conservation equations indicate that…

An experiment is described where a pendulum bob was allowed to roll back and forth across an inclined plane. The period of oscillation is larger than that for oscillation in a vertical plane, in part because the effective value of "g" is reduced on an inclined plane. The experiment highlights the differences between all three common…

It is well known that Newton's work on mechanics depended in a crucial way on the previous observations of Galileo. The key insight of Galileo was that one can analyze the motion of bodies using experiments and mathematical equations. One experimental observation that roughly emerges from this work in modern terms is that two objects of different…

In order to describe the velocity of two bodies after they collide, Newton developed a phenomenological equation known as 'Newton's experimental law' (NEL). In this way, he was able to practically bypass the complication involving the details of the force that occurs during the collision of the two bodies. Today, we use NEL together with momentum…

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…

In this work, a simple rocking pendulum, in a circular arc shape, is presented. The idea is to put a rigid arc on a clean flat surface of glass and leave it to oscillate under the effect of a little impulse. Then, the periodic time of this arc pendulum's motion is experimentally determined. The mathematical analysis of the arc's motion is derived…