Volume 49, Issue 5, May 2011
 PAPERS


Equations as Guides to Thinking and Problem Solving
View Description Hide DescriptionScience is the study of nature's rules. The most basic of these are the laws of physics, most of which are expressed in equation form. Physics equations show how concepts connect to one another. But does a study of these equations enhance student understanding? Not always, for too often in an introductory course students are tempted (or even encouraged) to memorize equations or keep them in a handy list and then, when confronted with a problem, to look for what might be a relevant equation and plug numbers into it. Little understanding results. Or worse, equations may take a backseat in an introductory course and get little or no attention at all (as some popular physics books boast no equations).

An Inexpensive Mechanical Model for Projectile Motion
View Description Hide DescriptionAs experienced physicists, we see the beauty and simplicity of projectile motion. It is merely the superposition of uniform linear motion along the direction of the initial velocity vector and the downward motion due to the constant acceleration of gravity. We see the kinematic equations as just the mathematical machinery to perform the calculations. What do our students see? Likely, most see no deeper than the operational understanding needed to use the kinematic equations. Described below is a device (shown in Fig. 1) that illustrates the physicist's view of projectile motion. It can be used as a classroom demonstration or as a project for your students, and it costs less than three dollars to make.

Rolling the Black Pearl Over: Analyzing the Physics of a Movie Clip
View Description Hide DescriptionIn the third movie (“At World's End”) in the Pirates of the Caribbean series, Jack Sparrow and his crew need to roll their ship (the Black Pearl) over in order to bring it back to the living world during a green flash at sunset. They do so by running back and forth from one side railing to the other on the top deck. In addition, Captain Barbossa orders that 18 cannons and a pile of barrels on the lower deck be cut loose to add mass to the running crew. In the movie they overturned the ship, but would they succeed under the same circumstances on a real galleon? In this paper, a numerical analysis using simple approximations is developed that suggests that what occurs in the movie is in fact realistic. Analyzing a popular film clip in this manner is a good way to arouse student interest, to teach about physics and numerical methods, and to model scientific reasoning when a situation is not as neatly defined as in a typical textbook problem.

A Simple, Successful Capacitor Lab
View Description Hide DescriptionCapacitors are a fundamental component of modern electronics. They appear in myriad devices and in an enormous range of sizes. Although our students are taught the function and analysis of capacitors, few have the opportunity to use them in our labs.

Teaching Physics (and Some Computation) Using Intentionally Incorrect Simulations
View Description Hide DescriptionComputer simulations are widely used in physics instruction because they can aid student visualization of abstract concepts, they can provide multiple representations of concepts (graphical, trajectories, charts), they can approximate realworld examples, and they can engage students interactively, all of which can enhance student understanding of physics concepts. For these reasons, we create and use simulations to teach physics,^{1,2} but we also want students to recognize that the simulations are only as good as the physics behind them, so we have developed a series of simulations that are intentionally incorrect, where the task is for students to find and correct the errors.^{3}

“FindtheFlaw” Problems
View Description Hide DescriptionA physics teacher assigns problems to his or her students not to keep them indoors during sunny days, but to strengthen and deepen their understanding of the universe. Every problem has not only an answer, but also a “moral to the story”—a reason why that question and that answer are interesting and probing. It is an unfortunate fact that our rush to find the answer can obscure the moral and, even worse, obscure the very idea that a moral exists. For more than a decade, I have assigned “findtheflaw” physics problems in which the answer to the problem is given and where the only point of the problem is to build “moral of the story” insight.

Pressure Oscillations in Adiabatic Compression
View Description Hide DescriptionAfter finding Moloney and McGarvey's^{1} modified adiabatic compression apparatus, I decided to insert this experiment into my physical chemistry laboratory at the last minute, replacing a problematic experiment. With insufficient time to build the apparatus, we placed a bottle between two thick textbooks and compressed it with a third textbook forced down from above. We discovered that approximately one in three trials exhibited a damped pressure oscillation after compression, as shown in Fig. 1 below, making it difficult to determine the true peak pressure. We discarded these trials and used only those without oscillation. I subsequently have had time to build a version of Moloney and McGarvin's apparatus. Using this apparatus, my students and I have recently performed numerous adiabatic compression trials with three different gases, with very few instances of oscillation.

Adding a Bit More History to Science Courses
View Description Hide DescriptionThe usual science course is not meant to be a history course and the usual science book is not meant to be a history book. However, most science books do include some historical information. Unfortunately, the history part is usually so brief that it is far from interesting and often so oversimplified that it is totally wrong. Introductory physics books often present the history of physics as a dull, cold, logical progression of discoveries and theories. As a result, the student might think that one day Sir Isaac Newton said to himself, “I think I'll produce a theory of gravitation.” Then he sat down, wrote it all out, published it, received universal acclaim, and then was included in all physicstextbooks. This view of science can look pretty dull and unappealing to students.

A Teachable Moment Uncovered by Video Analysis
View Description Hide DescriptionEarly in their study of onedimensional 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 this point initially. They are told to assume that the ball's velocity does not change while it rolls to or from the wall—that the velocity change all happens very quickly and only at the wall. In order to evaluate this assumption following the data collection, I have the students analyze one such collision using video analysis. The results uncover an excellent teachable moment about assumptions and their impact on models and error analysis.

Measuring Electrical Current: The Roads Not Taken
View Description Hide DescriptionRecently I wrote about the standard Weston meter movement^{1,2} that is at the heart of all modern analogue currentmeasurements. Now I will discuss other techniques used to measureelectric current that, despite being based on valid physical principles, are largely lost in technological history.

Revisiting the Ladder on a Wall Problem
View Description Hide DescriptionThe problem of a ladder leaning on a wall has been a staple of introductory physics for years. It is discussed in numerous physics textbooks and in journals.^{1–4} Now, it even has an Internet presence. Postings from students seek help for “ladder on a wall” problems. A quick review of those postings would show that they all deal with frictionless walls. This is also how the situation is presented in most textbooks. One may get the impression that the friction between a ladder and a wall is always negligible, or that dealing with it is so difficult that it should be left out of the realm of introductory physics. The truth of the matter is that the magnitude of the friction coefficient between a ladder and a wall is not much different from that with the floor, and that friction with the wall is an important part of the conditions for having a static ladder. This paper derives a simple relationship between the friction coefficients of the ladder with the floor (μ_{1}) and with the wall (μ_{2}), when the ladder is in static equilibrium. Figure 1 shows the forces that act on a ladder that leans on a wall.

The Cramster Conclusion
View Description Hide DescriptionIn a recent TPT article,^{1} I wrote about a website called “Cramster” (www.cramster.com), which provides students with solutions to homework problems from many textbooks in math and science. I proposed the following question: Could giving students the answers to their assigned homework problems be an effective way of teaching them physics? This paper summarizes my findings after providing each of my students with solutions to every assigned homework problem over the course of one academic year.

Physics Labs with Flavor II
View Description Hide DescriptionThis paper was inspired by the numerous requests from TPT readers to expand the number of examples of “recurrent study” lab exercises described in my previous paper “Physics Labs with Flavor.”^{1} I recommend that readers examine it first in order to better understand this one as my attempt here is to be brief. In that paper, one can find details that are not included in this paper; here I aim to present how the essence of the recurrent method is applied to different labs. The examples used in this paper are based on the labs traditionally offered in lab manuals^{2–4} commonly used for introductory physics courses.

Writing for Nonscientists about Physics1
View Description Hide DescriptionPhysicists should communicate their knowledge to the general public because, as the American Association for the Advancement of Science puts it, “without a scientifically literate population, the outlook for a better world is not promising.” This article discusses what I've learned about writing for nonscientists from working on my physicstextbook for nonscience college students,^{2} as well as from my hometown newspaper column and other writings.^{3} Lessons learned include tips for writing effective prose, do's and dont's when writing for nonscientists, choice of subject matter, being relevant to the needs of nonscientists, unifying one's book by using general themes, and the process of organizing and writing a textbook. Many of these lessons should be helpful in all scientific writing regardless of the target audience.

Studying Hooke's Law by Using a Pogo Stick
View Description Hide DescriptionPerhaps the pogo stick was little Robert Hooke's favorite childhood toy, consisting of a stiff spring inserted in a tube fixed at the upper end and connected to a moveable rod at the other. Hand grips and a foot rest are connected to the tube. The idea is to jump on it taking advantage of the force provided by the spring when it is compressed. Figure 1 shows a schematic of a pogo stick.

Special Relativity in Week One: 3) Introducing the Lorentz Contraction
View Description Hide DescriptionThis is the third of four articles on teaching special relativity in the first week of an introductory physics course.^{1,2} With Einstein's second postulate that the speed of light is the same to all observers, we could use the light pulse clock to introduce time dilation. But we had difficulty introducing the Lorentz contraction until we saw the movie “Time Dilation, an Experiment with MuMesons” by David Frisch and James Smith.^{3,4} The movie demonstrates that time dilation and the Lorentz contraction are essentially two sides of the same coin. Here we take the muon's point of view for a more intuitive understanding of the Lorentz contraction, and use the results of the movie to provide an insight into the way we interpret experimental results involving special relativity.

SwitchedOn Physics: If you can dream it, you can do it
View Description Hide DescriptionAs classroom science teachers, we are all often reminded of the inevitable and sometimes not small challenges that face us in captivating and keeping the interest of our students. To give additional relevance and life to my teaching of physics, I decided to integrate global, handson projects into my approach. I decided from the onset that the projects had to be innovative, spectacular, and creative, and they must include input from students and colleagues from their inception. This chosen course of action resulted in the development of a dynamic threeyear physics odyssey culminating with the SwitchedOn Physics Project. In this paper, I describe the program and encourage other teachers to consider engaging in projects that capture their interest and that of their students.

Adding Value to Force Diagrams: Representing Relative Force Magnitudes
View Description Hide DescriptionNearly all physics instructors recognize the instructional value of force diagrams, and this journal has published several collections of exercises to improve student skill in this area.^{1–4} Yet some instructors worry that too few students perceive the conceptual and problemsolving utility of force diagrams,^{4–6} and over recent years a rich variety of approaches has been proposed to add value to force diagrams. Suggestions include strategies for identifying candidate forces,^{6,7} emphasizing the distinction between “contact” and “noncontact” forces,^{5,8} and the use of computerbased tutorials.^{9,10} Instructors have suggested a variety of conventions for constructing force diagrams, including approaches to arrow placement and orientation^{2,11–13} and proposed notations for locating forces or marking actionreaction force pairs.^{8,11,14,15}
