It has long been suspected by general relativists that physicists who do not specialize in general relativity (GR) believe that special relativity (SR) is incapable of modeling dynamics within accelerated reference frames. Consequently, many physicists may conclude that certain phenomena, such as time dilation due to acceleration, can only be…

Most springs do not simply obey Hooke's law because they are constructed to have an initial tension, which must be overcome before normal elongation occurs. This property, well known to engineers, is universally neglected in elementary physics courses. In particular, the standard simple harmonic motion experiment omits any discussion of this…

There remains a strong movement for Introductory Physics for Life Sciences (IPLS) courses to better integrate physics and biology. Part of the challenge for IPLS educators is to introduce fundamental physical law while simultaneously establishing the relevance of physics to biological science. Life science relevant laboratory experiences are…

Energy and entropy are two of the most important concepts in science. For all natural processes where a system exchanges energy with its environment, the energy of the system tends to decrease and the entropy of the system tends to increase. Free energy is the special concept that specifies how to balance the opposing tendencies to minimize energy…

In physics, idealized models are often used to simplify complex situations. The motivation of the idealization is to make the real complex system tractable by adopting certain simplifications. In this treatment some unnecessary, negligible aspects are stripped away (so-called Aristotelian idealization), or some deliberate distortions are involved…

The ray tracing method is widely used in teaching geometrical optics at the upper secondary and university levels. However, using simple and straightforward examples may lead to a situation in which students use the model of ray tracing too narrowly. Previous studies show that students seem to use the ray tracing method too concretely instead of…

When students are first introduced to the idea of radioactive decay, a large conceptual hurdle must be overcome. The thought that an object's age has no bearing on the chance it will "die" (decay in this case) on a particular day is completely at odds with biological notions of life and death. Through the use of a simple…

On Aug. 13, 2011, at 8:45 p.m. country music fans were eagerly awaiting the band Sugarland to make its entry onto the main stage at the Indiana State Fairgrounds. Also competing for the fans' attention was an approaching storm. Sugarland never made their entrance. At 8:49 p.m. the stage rigging was hit by 59 mile/h (94 km/h) winds causing it to…

Modeling real-life situations is an important part of introductory physics. Here we consider the question "What is the largest weight of backpack a hiker can manage?" A quick perusal of the Internet suggests that as the weight of a healthy adult increases, the largest backpack weight W[subscript bp] also increases and should be about…

Early in their study of one-dimensional kinematics, my students build an algebraic model that describes the effects of a rolling ball's (perpendicular) collision with a wall. The goal is for the model to predict the ball's velocity when it returns to a fixed point approximately 50-100 cm from the wall as a function of its velocity as it passes…

There have been two articles in this journal that described a pair of collision carts used to demonstrate vividly the difference between elastic and inelastic collisions. One cart had a series of washers that were mounted rigidly on a rigid wooden framework, the other had washers mounted on rubber bands stretched across a framework. The rigidly…

One of the fundamental learning goals of introductory astronomy is for the students to gain some perspective on the scale and structure of the solar system. Many astronomy teachers have laid out the planets along a long strip of paper or across a school grounds or campus. Other activities that investigate the motion of the planets are often…

We present an experimental method to obtain the effective mass of an unloaded oscillating spring. We measure the period "T"("n") of the partial springs that result when hanging "n" of the total "N" coils of a given spring. Data are correlated with the expectation of a simple model for "T"("n") that takes into account the effective mass of the…

Students often wonder why polished metals are poor emitters of radiation when they are so shiny. Here I present a simple model that helps to explain this apparent paradox.

The Doppler shift is a frequency change of a repetitive effect, as measured by a receiver, due to the motion of the wave emitter, to the motion of the wave receiver, or both. A demonstration of the effect is provided by the sound of a car's horn that changes from a higher pitch to a lower pitch when a car drives past. Most derivations of the…