Teaching Physics - University of Waterloo [PDF]

Phys13news UNIVERSITY OF

WATERLOO

Department of Physics & Astronomy University of Waterloo Waterloo, Ontario, Canada N2L 3G1

Fall 2010

Number 136

Teaching Physics

Cover:

Contents

A demonstration of centre-of-mass using a lighted throwing stick. See page 9 to learn how to make this demonstration. Reprinted with permission from Physics in Canada.

Teaching is both rewarding and challenging. It is an activity that can try our patience to the limit and at the same time provide us with a level of inspiration few other human endeavours can match. This issue of PHYS13 centres on teaching physics. We have put together several articles that speak to various aspects of physics teaching at a variety of levels. An article written by a winner of last year’s Award for Excellence in High School Physics Teaching describes her experiences with “Hands-On” physics teaching, telling how she modified her approach in the classroom to better communicate the exciting developments in physics today. We also have an article by Oersted Medal winner Lillian McDermott that outlines the research she has done in Physics Education. You might be surprised to learn what kinds of things are effective (and not) in helping students understand the subject. We also have an article showing how to make a lively and fun demonstration to illustrate the concept of centre of mass. Our student corner features an article by a recent Waterloo doctoral graduate, Chanda PrescodWeinstein, about the relationship between dark matter and cosmic acceleration. You might find a few interesting nuggets here to share with your students. Last, but certainly not least, is a reminder about the upcoming 2011 Awards for Excellence in High School and CEGEP Physics Teaching. Perhaps you know of a worthy nominee! Robert Mann

Contents What do Dark Matter Haloes Teach us About Cosmic Acceleration? by Chanda Prescod- Weinstein………….…3 Our student corner this issue discusses the relationship between the dark matter in galaxies and the accelerating expansion of our universe

Hands-on Modern Physics by Roberta Tevlin…………………………….......7 Some tips from an award-winning teacher on how to engage your students in physics

How to Make a Lighted Throwing Stick by Forest Fyfe……………………………………9 This demonstration of the centre-of-mass is one that you can make with readily available materials.

Oersted Medal Lecture 2001: ‘‘Physics Education Research—The Key to Student Learning’’ by Lillian Christie McDermott ………………...11 Find out some insights as to the learning processes students undergo when studying physics.

Puzzles, Problems and Solutions SIN BIN ...........……………………………….…...….17 Find the Laureates Puzzle ……………………..........18 Solution to Double Nobel Laureate Sudoku Puzzle from Issue #134 ………………………………………19

Phys13news / Fall 2010

Phys13news is published four times a year by the Department of Physics and Astronomy at the University of Waterloo. Our policy is to publish anything relevant to high school and first-year university physics, or of interest to high school physics teachers and their senior students. Letters, ideas and articles of general interest with respect to physics are welcomed by the editor. You can reach the editor by paper mail, fax or email. Paper:

Fax: E-mail:

Phys13news Department of Physics and Astronomy University of Waterloo Waterloo, ON N2L 3G1 519-746-8115 [email protected]

Editor:

Robert Mann

Editorial Board: N. Afshordi, B.-Y. Ha, D. Hawthorn, Y. Leonenko, Q.-B. Lu, R. Melko, K. Resch Publisher: Judy McDonnell Printing: UW Graphics

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What do Dark Matter Haloes Teach us About Cosmic Acceleration? by Chanda Prescod- Weinstein Structure formation provides a strong test of any cosmic acceleration model because a successful dark energy model must not inhibit the development of observed large-scale structures. Traditional approaches to studies of structure formation in the presence of dark energy or a modified theory of gravity implement the Press & Schechter formalism. I explore the potential for universality in the Press & Schechter formalism and what dark matter haloes may be able to tell us about cosmology.

Introduction Observations of Type Ia supernovae [1, 2] and cosmic microwave background anisotropy measurements [3] seem to have converged on an extraordinary observation: the universe is not only expanding – it is accelerating. In other words, not only most galaxies in the universe are moving away from each other, but also their motions are speeding up. The simplest way to explain this is to assume that the matter-energy content of our universe is dominated by a strange component that can be described as a vacuum energy with negative pressure. While we traditionally expect attractive gravity to be the dominant force on large-scales, this “energy” pushes outward, challenging Newtonian gravity’s hegemony. Explaining the source of this acceleration is the great cosmological question of our era. Approaches to the cosmic acceleration question are as varied and strange as the problem itself. The first of these is the introduction of a “simple” vacuum energy whose value is called the cosmological constant, which is often referred to as Λ. However, Λ is in fact a problem itself, one that, as we shall see, is independent of the cosmic acceleration issue. This has been known for decades as the cosmological constant problem. An alternative explanation of cosmic acceleration is quintessence, which proposes a new type of matter- energy called a scalar field as This proposed an additional stress-energy source. new source of energy modifies the Einstein equations that describe the expansion of our universe so as to generate cosmic acceleration. The term quintessence is often used interchangeably with the more general term “dark energy”. None of these models adequately address the cosmological constant

Phys13news / Fall 2010

problem. A third approach involves changing the way that gravity -- manifested as spacetime curvature -interacts with the energy content of the universe. Such models are known as modified gravities (MGs). Discovering which of these models best fits the data is now central to the cosmological research enterprise. Finding tests for these models can be a challenge, since the techniques used to discover cosmic acceleration do not allow us to distinguish between general relativity and modifications to general relativity such as quintessence and MGs. Moreover, depending on one’s assumptions at a technical level, MGs are indistinguishable from quintessence models because MGs can look like an effective dark energy [4]. A natural way to distinguish between the MGs and quintessence is to see whether the theory looks more “natural” as a modified gravity or a quintessence in the context of structure formation at large scales, i.e., the formation of galaxies and galaxy clusters. In fact, the study of structure formation can provide a powerful, independent test of models of cosmic acceleration [5]. My most recent re- search efforts focus on ways to improve methods that use models of large-scale structure to differentiate between models of cosmic acceleration.

The Expanding Universe In 1929, Edwin Hubble made a momentous discovery that would dominate, if not begin, progress in cosmology for the entirety of the 20th century right into the 21st. While studying the movements of galaxies, he noted that the recession velocity of a galaxy was proportional to its distance [6]. The proportionality factor came to be known as the Hubble Constant, H , and the relation as Hubble’s law:

r

r

υ = H 0r

(1)

In other words, we can describe the expansion of the universe as the increase, with time, of the proper distance between galaxies. This is not to say that gravitationally bound systems such as galaxies are expanding. In fact, the tension between the expansion and the tendency of matter to gravitationally attract leads to interesting effects such as structure formation, which will be discussed more in depth below. Although initially rejected by Einstein, Hubble’s observations have been confirmed repeatedly during the several decades since and are

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a cornerstone of experimental evidence for Einstein’s General Relativity. Indeed, as mentioned in the introduction, in 1998 an interesting twist in the narrative was introduced by Supernova Type Ia data which seemed to suggest that the universe is not only expanding but that very expansion is accelerating.

2.

The Weak Cosmological Constant Problem: Just as we do not understand why the value of Λ is so small, we also do not understand why it is so close to zero but not exactly zero. Current cosmological observations, paired with relativity theory, indicate that there may be a vacuum energy density of order 10-120 g/cc.

3. The New Cosmological Constant Problem: Curiously, the current value of the energy density associated with Λ is comparable to the present mass density. This is also known as the coincidence problem.

Fig. 1: This diagram, from Hubble’s original paper, shows a strong correlation between the distance of galaxies and their recession velocities [6]. The simplest explanation for this acceleration is the presence of a cosmological constant in Einstein’s equations, describing a non-zero vacuum energy. But as I shall describe later, this explanation leaves a lot to be desired. Cosmological Constant In the context of the cosmic acceleration, we can na¨ıvely assume that Einstein’s equations continue to satisfactorily describe the universe’s cosmology if we merely recall his famed blunder, the cosmological constant or Λ (Einstein first added Λ to his equations to explain a static universe, but this became obsolete with Hubble’s discovery of cosmic expansion). Physically, this means we assume the presence of a vacuum energy whose value is set by experiment, for example the value necessary to cause observed cosmic acceleration. Relativity cannot tell us how to deduce this value from theoretical considerations. However, the cosmological constant is unsatisfactory because it leaves several questions unanswered. As outlined by Weinberg [7, 8] and many others, the cosmological constant comes with its own set of problems that are independent of cosmological issues. Three major questions arise when talking about Λ, with or without the presence of cosmic acceleration: 1.

The Old Cosmological Constant Problem: There is a severe mismatch between the measured Λ and the expected value from particle physics.

Phys13news / Fall 2010

The old cosmological constant problem is so named because its existence predates observations that indicate the existence of a vacuum energy. In fact, before the discovery of cosmic acceleration it was a problem that had worried particle physicists for decades. The missing energy could not be accounted for in experiment, and it was not clear why. The 1998 discovery of cosmic acceleration added an additional constraint and mystery in the form of the weak cosmological constant problem. The old problem, instead of being eliminated, was compounded by the discovery of an apparent vacuum energy that is incredibly close to zero but just large enough to be noticeably non-zero. It also introduced astrophysical concerns more directly into the phenomenological discussion about vacuum energy. Reconsidering the old cosmological constant problem in the context of the weak problem could be taken to imply that these questions are tied to the larger discussion of how quantum field theory is related to general relativity. In other words, it could be seen as one edge of the multifaceted quantum gravity problem. From a phenomenological perspective, a particularly attractive model of cosmic acceleration that could better address the aforementioned three issues would supplant Λ in cosmological models. While quintessence could potentially explain the cosmic acceleration, addressing the weak cosmological constant problem and the new cosmological constant problem requires fine-tuning of the quintessence field. This is nearly as unsatisfactory as the cosmological constant itself.

Structure Formation An important part of the effort to explain cosmic acceleration and the cosmological constant problem is testing proposed models in the context of what are, at this stage, better-established physical pictures. Structure formation could prove to be an incredibly useful phenomenological method for

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distinguishing models of cosmic acceleration. It is currently believed that large-scale structure formation has its seeds in small quantum fluctuations in the early universe (e.g. [9]). The current model for structure formation is elegant in its fundamental simplicity. Random inhomogeneities, artifacts of cosmic inflation, create a runaway effect in which overdense regions attract more matter, thus becoming more dense and leading to galaxies, stars, and planets. Better understanding of this process is independently an intriguing enterprise in the field of cosmology. In my doctoral work, I focused on the relationship between the cosmic acceleration and structure formation. More specifically, different cosmological pictures (cosmologies with differing causes of acceleration, such as a cosmological constant, dark energy, or modifications of Einstein gravity) might have expansion histories that are similar to one another but leave different imprints on large-scale structures, and in particular on galaxy clusters. Therefore, structure formation provides a unique testing ground for models of cosmic acceleration ([10-12]). The relationship between dark energy and structure formation, i.e., the evolution of small-scale inhomogeneities, manifests via the cluster mass function (CMF). The CMF gives abundance of galaxy clusters as a function of mass. It has been noted that the CMF can help to constrain the vacuum energy density as well as other cosmological parameters [13, 14]. In other words, understanding the correlation between galaxy cluster density and dark energy can provide a powerful test of the dark energy as cosmological constant. The first step in this direction is to revisit how the Press-Schechter formalism [15] (PSF) is used to predict the cluster mass function. Press and Schechter [15] have argued that the number density of dark matter haloes (or galaxy clusters) of mass M is related to the variance of linear overdensity in spherical regions of mass M at the same time, and the function describing this relation is often referred to as f (σ). I highlight the fact that the PSF relies on linear overdensities because structure formation by its very nature is inherently nonlinear. While the PSF successfully predicts the broad features of the simulated cluster mass functions, it proves too simplistic for detailed model comparisons required for precision cosmology. Consequently, several authors including Sheth & Tormen [16], Jenkins et al. [17], Evrard et al. [18], Warren et al. [19], and Tinker et al. [20] have refined the function to better match the simulated mass functions in N-body simulations.

Phys13news / Fall 2010

For example, [19] and [20] propose a fitting formula, which tries to find a curve that fits best the simulated data. While most of this work is based on fitting formulae to simulated mass functions, Sheth & Tormen [21] argue that an approximate implementation of ellipsoidal collapse can account for most of the deviations from the PSF. However, a more pressing question for cosmological applications is whether the function f (σ) is universal, or rather can vary for different cosmologies or cosmic acceleration models. In other words, could the same modified PSF be used to accurately predict halo abundance in cosmologies with different cosmological parameters? While earlier studies failed to find such dependence, Tinker et al. [20] first noticed a systematic evolution of f (σ) with redshift, implying a breakdown of universality (also see [22]). In my doctoral thesis, I contribute to the effort to better understand the role and limits of universality in the cluster mass function by introducing a new parameter that appears to be universal across cosmological models. In particular, the PSF relies on σ(M), the rootmean-square of linear density fluctuations at the time of observation, when in reality, observed clusters are very non-linear objects with overdensities exceeding 200. We thus seek to calculate a universal time in the past when we could make a connection between the non-linear structures that we observe in the present and the linear structures that existed in the past, since all structures go through a linear phase. Our basic strategy is to find the time in the past at which the linear density of the structures that collapse today show minimum dispersion, as we vary cosmologies. The result was to discover that regardless of cosmological model (i.e. variations in the value of the cosmological constant or the equation of state parameter for dark energy), at 94% of the collapse time, all models experience the same linear density (see Fig. 2). In other words, we found more evidence for universality. Conclusion I have provided an overview of the cosmic acceleration and cosmological constant problems. Additionally, I have described the way models of structure formation may be used to test potential resolutions of these problems. The universal behaviour of the cluster mass function allows us to derive the history of linear structure formation, allowing us to refine how structure formation is used to understand cosmological dynamics. As in the case of other endeavors mentioned in this section, the work is extendable and is by no means concluded here.

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Fig. 2. Relative change in δL (t/tcollapse) in cold dark matter cosmologies (with fractional vacuum energy density ΩΛ = 0.1, 0.2, …, 0.7), with respect to the Einsteinde Sitter Universe. Tcollapse is calculated for spherical overdensities. The curves seem to intersect at t/tcollapse = 0.94, and a calculation of the point of minimum variance between the lines confirms this.

[1] Adam G. Riess et al. Astron. J., 116:1009–1038, 1998. arXiv: astro-ph/9805201, doi:10.1086/300499. [2] S. Perlmutter et al. Astrophys. J., 517:565–586, 1999. arXiv:astro-ph/9812133, doi: 10.1086/307221. [3] D. N. Spergel, R. Bean, O. Dor´e, M. R. Nolta, C. L. Bennett, J. Dunkley, G. Hinshaw, N. Jarosik, E. Ko- matsu, L. Page, H. V. Peiris, L. Verde, M. Halpern, R. S. Hill, A. Kogut, M. Limon, S. S. Meyer, N. Ode- gard, G. S. Tucker, J. L. Weiland, E. Wollack, and E. L. Wright ApJS, 170:377–408, June 2007. arXiv:astro-ph/0603449, doi:10.1086/513700. [4] E. Bertschinger and P. Zukin. Phys. Rev. D, 78(2):024015–+, July 2008 arXiv:0801.2431, doi:10.1103 / PhysRevD. 78.024015. [5] E. Bertschinger. ApJ, 648:797–806, September 2006. arXiv:astro-ph/0604485, doi: 10.1086/506021. [6] E. Hubble. 15:168–173, March 1929. doi:10.1073 /pnas.15.3.168. [7] S. Weinberg 61:1–23, January 1989 doi: 10.1103 /RevModPhys.61.1. [8] S. Weinberg, The Cosmological Constant Problems (Talk given at Dark Matter 2000, February, 2000). ArXiv Astrophysics e-prints, May 2000. arXiv:astroph/0005265. [9] V. F. Mukhanov, H. A. Feldman, and R. H. Brandenberger Phys. Rep., 215:203–333, June 1992. doi:10.1016/0370-1573(92)90044-Z. [10] M. Ishak, A. Upadhye, and D. N. Spergel, Phys. Rev. D, 74(4):043513–+, August 2006. arXiv:arXiv:astro-ph/0507184, doi:10.1103/ Phys. Rev. D 74 043513. [11] V. Acquaviva, A. Hajian, D. N. Spergel, and S. Das. Phys. Rev. D, 78(4): 043514–+, August 2008. arXiv:0803.2236, doi:10.1103 / PhysRevD.78.043514. [12] A. Vikhlinin, A. V. Kravtsov, R. A. Burenin, H. Ebel- ing, W. R. Forman, A. Hornstrup, C. Jones, S. S. Mur- ray, D. Nagai, H. Quintana, and A. Voevodkin. ApJ, 692:1060–1074, February 2009. arXiv: 0812.2720, doi:10.1088/0004-637X/692/2/1060.

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[13] N. A. Bahcall and X. Fan, ApJ, 504:1–+, September 1998 arXiv:arXiv:astro-ph/9803277, doi: 10.1086/306088. [14] G. Holder, Z. Haiman, and J. J. Mohr. ApJ, 560: L111–L114, October 2001 arXiv:arXiv: astroph/0105396, doi:10.1086/324309. [15] W. H. Press and P. Schechter ApJ, 187:425–438, February 1974. doi: 10.1086/152650. [16] R. K. Sheth and G. Tormen. MNRAS, 308:119– 126, September 1999. arXiv:arXiv:astro-ph/9901122, doi:10. 1046/j.1365-8711.1999.02692.x. [17] A. Jenkins, C. S. Frenk, S. D. M. White, J. M. Col- berg, S. Cole, A. E. Evrard, H. M. P. Couchman, and N. Yoshida, MNRAS, 321:372–384, February 2001. arXiv: arXiv:astro-ph/0005260, doi:10.1046/ j.1365-8711. 2001.04029.x. [18] A.E. Evrard, T.J. MacFarland, H.M.P. Couchman, J.M. Colberg, N. Yoshida, S. D. M. White, A. Jenkins, C. S. Frenk, F. R. Pearce, J. A. Peacock, and P. A. Thomas, ApJ, 573:7–36, July 2002 arXiv: astro-ph/0110246, doi:10.1086/340551. [19] M. S. Warren, K. Abazajian, D. E. Holz, and L. Teodoro, ApJ, 646:881–885, August 2006 arXiv:astroph/0506395, doi:10.1086/504962. [20] J. Tinker, A. V. Kravtsov, A. Klypin, K. Abazajian, M. Warren, G. Yepes, S. Gottl¨ober, and D. E. Holz, ApJ, 688:709–728, December 2008. arXiv:0803.2706, doi:10.1086/591439. [21] R. K. Sheth, H. J. Mo, and G. Tormen, MNRAS, 323:1–12, May 2001. arXiv:arXiv:astroph/9907024, doi:10.1046/j.1365-8711.2001.04006.x. [22] S. Bhattacharya, K. Heitmann, M. White, Z. Luki´c, C. Wagner, and S. Habib. Mass Function ArXiv e-prints, May 2010.arXiv: 1005.2239. Chanda Prescod-Weinstein [email protected]

can

be

reached

at:

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Hands-on Modern Physics by Roberta Tevlin I am a high school teacher at Danforth Collegiate and Technical Institute in Toronto. I have been teaching here for thirteen years. It is an old school with a very eclectic student body that is never dull. This school has the usual range of academic courses and it also has a fabulous selection of technical courses; the autobody shop is across the hall from my room and the new stateof-the-art kitchen for our awarding winning chefs is just down the hall and around the corner. I have been teaching high school physics for a long time and I thought I had it all figured out. However, in 2005 - the year of physics - two events caused me to radically change my approach to teaching. In the summer I attended the Einstein Plus Workshop at the Perimeter Institute of Theoretical Physics1. After that experience, I couldn't wait to start adding more modern physics in my classes. Secondly, I read Carl Weiman's article in Physics Today called "Transforming Physics Education" which was all about Physics Education Research (PER)2. It made me realize that the techniques that I had been using were well-meaning but largely ineffectual. I needed to present physics in a way that the students were better motivated to talk about and use physics. I found Eric Mazur’s Peer Instruction3 was the easiest PER technique to incorporate into my existing lessons. In this technique, the class is asked a conceptual question in a multiple-choice format. The students have small four-page booklets with large A, B, C, D’s on them. You ask the students to hold up the letter corresponding to their answer and you can immediately see how well the class understands the question. Next, instead of asking one person to explain things to the whole class, you have the students turn to find someone with a different answer. Now everyone is involved. The confused students get private tutors and the ones who understand the situation, end up understanding it even better because they had to explain it to someone else. Whiteboards are another great tool4. These only require a question and not a set of prepared multiplechoice answers and are great for problems using diagrams, i.e., freebody diagrams. Each pair of students works on one diagram and learns from each other. You’ll see a variety of solutions and so you have them show their boards to each other and the discussions ensue. Most importantly, whiteboards let you see what your students are thinking. This easy assessment allows you to modify your next comments, hints or questions appropriately.

Phys13news / Fall 2010

These PER techniques and others like them5 have completely altered the culture in my classroom. Rather than planning what I will say, I plan what I will ask. The students are comfortable working together on problems that don’t have an immediate easy solution. They are thinking, talking and questioning. They are doing physics. Now, what about the modern physics? This was much harder to bring into my classroom. There are very few physics resources that deal with modern physics and which also involve the students as active learners. Most of the PER resources deal with classical physics and places like Fermilab and CERN have modern physics resources but very few of these engage the students as active learners. However, there are some resources that do both. The PhET website6 of the University of Colorado at Boulder is a huge collection of free, easy to use simulations that allow students to experiment and help them visualize key phenomena in modern physics like the double-slit experiment, the photoelectric effect and radioactive decay. The Perimeter Institute of Theoretical Physics7 has put out several great free resources that help students explore such topics as general relativity and dark matter with simple hands-on demonstrations. CERN has a treasure trove of bubble chamber photographs and I have used these to develop some guided inquiry worksheets in which students apply five simple rules to become “Bubble Chamber Detective.” I have put together a web site8 containing all the resources that I have found or developed which teach modern physics using student-centered learning.

Left: A typical diagram derived from bubble-chamber data

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The following demonstration of a bubble chamber can be presented in 5 minutes. A bubble chamber consists of liquid hydrogen at a temperature just below its boiling point. The pressure is suddenly reduced so it is no longer stable. Bubbles are formed where the hydrogen is disturbed by moving charges. While early models used beer, you can demonstrate the physics with a bottle of soda water. Remove the label so the students can see the clear liquid. Unscrew the cap and suddenly there are bubbles everywhere. If you shake some salt into the soda water, visible trails will form. To show how magnets can bend the path of charged particle, bring a strong magnet (like one from an old speaker) near a black and white TV. Don't do this with a colour TV! I am always interested in hearing from other teachers with suggestions and questions. I can be reached at [email protected].

3

For a full understanding of the technique you might want to read Peer Instruction: A user’s manual, Eric Mazur, Prentice Hall, 1997. A set of good concept questions organized by topic can be found here http://www.physics.umd.edu/perg/role/PIProbs/ProbSubj s.htm 4

Dan MacIsaac is a great promoter of whiteboards. You can get more information at his website. http://physicsed.buffalostate.edu/AZTEC/BP_WB/index. html

5

Other great techniques are Interactive Lecture Demonstrations, Context Rich Problem Solving and the simulations of Physics Education Technology.

6

http://phet.colorado.edu/en/simulations/

7

http://www.perimeterinstitute.ca/Outreach/General/Teach ers/ 8

http://roberta.tevlin.ca

1

These workshops are one-week long, fabulous and completely free. http://www.perimeterinstitute.ca/en/Outreach/General/Te achers/ 2

C. Wieman, K. Perkins, Physics Today, November (2005) p. 36You can find a pdf of the article at http://cecelia.physics.indiana.edu/journal/physics_educati on.pdf. It is a great short introduction to PER. The best book for this is Randall Knight’s Five Easy Lessons: Strategies for Successful Physics Teaching, Benjamin/Cummings Pub Co 2002

Phys13news / Fall 2010

Roberta Tevlin is a winner of the 2010 Award for Excellence in Teaching High School Physics, given annually by the Canadian Association of Physicists. To find out more about next year’s award see page 10.

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How to Make a Lighted Throwing Stick by Forest Fyfe Illustrating the concepts of centre of mass and centre of mass motion to an introductory physics class can be a challenge to a physics instructor. The topic can be very mathematically complex and is not necessarily intuitively obvious. A device that demonstrates how the centre of mass of an object moves as compared to the motion of a point on the object away from the centre of mass would provide an excellent qualitative illustration of this. At Dalhousie University we have constructed just such a device, our lighted throwing sticks (see Fig.1). These throwing sticks are long rods with lighted bands located at one end and at the centre of mass of the rods.

far from the centre of gravity. Each light has an on/off switch. Fig, 4 shows the layout of the stick. Landings are very harmful to the throwing stick. We felt we were doing well if a stick survived 10 throws without failing. We usually operated in lectures with two spares.

Things that helped sticks survive are: 1. We used flexible, braided wire. 2. We used AA cells with solder tabs. 3. We twisted, soldered and taped all electrical joints. 4. We wrapped the pipe insulation with transparent first aid tape. 5. A rubber stopper in each end of the pipe helped but never stayed in place very long.

Fig. 1: Lighted Throwing Stick

By throwing such a rod with the centre of mass lights on, the students see a smooth trajectory of the centre of mass motion, while the end lights demonstrate the complicated motion of points away from the centre of mass (see Fig. 2) Jeff Dahn demonstrated our lighted throwing sticks at the 2009 Canadian Association of Physicists Congress in Moncton, NB.

Fig. 3: LED details

How to use: Throw the stick with only the off-centre light switched on and you see a complex tumbling path. Switch on only the light at the centre of gravity. Throw the stick with a tumbling motion and the light will follow a simple parabolic path, demonstrating that the centre of mass is a special place. Throw the stick with both lights on and you see both motions as shown in Figure 2.

Supplies: We bought LED's (in packages of 100) and slide switches from Jameco Electronics, Belmont, California. Everything else came from local hardware stores or pharmacies.

Fig. 2: Stick thrown with both lights on

At Dalhousie we made throwing sticks from white water pipe (3/4" outside diameter). The lights are made from about 10 to 30 LED's, soldered around the circumference of two rings as in Fig. 3. The pipe is padded with 3/4" id foam pipe insulation. The LED's are protected by potting them in clear caulking. A steel mass near one end ensures the centre of gravity is not at the centre of the pipe. One light is at the centre of gravity; the other is

Phys13news / Fall 2010

Fig. 4: Cross-section of Throwing Stick

(Article reprinted with permission from Physics in Canada)

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Phys13news / Fall 2010

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Oersted Medal Lecture 2001: ‘‘Physics Education Research—The Key to Student Learning’’ by Lillian Christie McDermott Research on the learning and teaching of physics is essential for cumulative improvement in physics instruction. Pursuing this goal through systematic research is efficient and greatly increases the likelihood that innovations will be effective beyond a particular instructor or institutional setting. The perspective taken is that teaching is a science as well as an art. Research conducted by physicists who are actively engaged in teaching can be the key to setting high (yet realistic) standards, to helping students meet expectations, and to assessing the extent to which real learning takes place. Introduction Physics education research differs from traditional education research in that the emphasis is not on educational theory or methodology in the general sense, but rather on student understanding of science content. For both intellectual and practical reasons, discipline-based education research should be conducted by science faculty within science departments. There is evidence that this is an effective approach for improving student learning (K– 20) in physics. The emphasis in the discussion here is on introductory students and K–12 teachers and, to a lesser extent, on graduate students in their role as teaching assistants. However, insights obtained through research have also proved to be a useful guide for instruction in more advanced physics courses. Perspectives on Teaching as an Art and as a Science Many physics faculty think of teaching solely as an art. This traditional view was clearly expressed in 1933 in the first article in the first journal published by the American Association of Physics Teachers1. In Physics is Physics, F.K. Richtmyer, who considered teaching very important, argued that it is an art and not a science. He quoted R. A. Millikan in characterizing science as comprising ‘‘a body of factual knowledge accepted as correct by all workers in the field.’’ Professor Richtmyer went on to say: ‘‘Without a reasonable foundation of accepted fact, no subject can lay claim to the appellation ‘science.’ If this definition of a science be accepted—and it seems to me very sound— then I believe that one must admit that in no sense can teaching be considered a science.’’

Phys13news / Fall 2010

Although this definition of science is somewhat limited, we may challenge the implication that it is not possible to build ‘‘a reasonable foundation of accepted fact’’ for the teaching of physics (and, by extension, other sciences). The Physics Education Group treats research on the learning and teaching of physics as an empirical applied science. Results from our research support the premise that teaching can be considered a science. Students in equivalent physics courses with different instructors are remarkably similar in the way they respond to certain kinds of questions, both before and after standard instruction by lecture, textbook, and laboratory. We have found that there are a limited number of conceptual and reasoning difficulties that students encounter in the study of a given topic. These can be identified, analyzed, and effectively addressed through an iterative process of research, curriculum development, and instruction. Although students vary in the way they learn best, learning is not as idiosyncratic as is often assumed. Student difficulties and effective strategies for addressing them are often generalizable beyond a particular course, instructor, or institution. When the results are reproducible, as is often the case, they constitute a ‘‘reasonable foundation of accepted fact.’’ There is by now a rapidly growing research base that is a rich resource for cumulative improvement in physics instruction.2 Publicly shared knowledge that provides a basis for the acquisition of new knowledge is characteristic of science. To the extent that faculty are willing to draw upon and to contribute to this foundation, teaching can be treated as a science. Insights from Research and Teaching Experience in Nonstandard Physics Courses The Physics Education Group has two major curriculum development projects: Physics by Inquiry (Wiley, 1996) and Tutorials in Introductory Physics (Prentice Hall, 1998).3 Both owe much to our research and teaching experience in nonstandard physics courses. For more than 25 years, we have been conducting special courses during the academic year and in NSF Summer Institutes to prepare prospective and practicing teachers to teach physics and physical science by inquiry. Another group whom we have been able to teach in relatively small classes are students who aspire to science-related careers but whose prior preparation is inadequate for success in the required physics courses. Close contact with students in these special courses has provided us with the opportunity to observe the intellectual struggles of students as they try to understand important concepts and principles. We have found that students better prepared in physics often encounter the same difficulties as those who are not as well prepared. Since the latter are usually less adept in mathematics, it is easier to identify and probe the

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nature of common difficulties. Day-to-day interaction in the classroom has enabled us to explore in detail the nature of specific difficulties, to experiment with different instructional strategies, and to monitor their effect on student learning. Below, we briefly illustrate the type of research that underlies the development of curriculum by our group. The context is electric circuits. In the question in Fig. 1 (a), students are asked to rank the brightness of identical bulbs in three circuits. This question has been used in many different classes over many years. It has been given either before or after the usual treatment of this topic in lecture, textbook, and laboratory. Since the results have been essentially the same before and after standard instruction, they have been combined. As shown in Table I, only about 15% of more than 1000 introductory students have given the correct ranking (A=D=E>B=C). Similar results have been obtained from high school physics teachers and from university faculty in other sciences and mathematics. Only about 70% of the graduate teaching assistants have given a correct ranking. Analysis of the responses has re-vealed the widespread prevalence of two mistaken beliefs: the battery is a constant current source and current is ‘‘used up’’ in a circuit. Among all populations, the basic underlying difficulty seems to be the lack of a conceptual model for an electric circuit.

particularly unsuitable for a typical introductory physics course in which fewer than 5% of the students will major in physics. For most, it is a terminal course in the discipline. Although faculty hope that they are helping students develop scientific reasoning skills, the type of problem solving that takes place in a typical introductory course is not consistent with this objective. Often the effect is to reinforce the common perception that physics is a collection of facts and formulas and that the key to solving physics problems is finding the right formulas. However, even correctly memorized formulas are likely to be forgotten after the course ends. An understanding of important physical concepts and the ability to do the reasoning necessary to apply them is of greater lasting value.

Insights from Research and Teaching Experience in Standard introductory Courses The topic of electric circuits is only one of many in which we have examined student understanding. Our investigations have spanned many topics at several levels of instruction with special emphasis on introductory physics. Instructors expect that, in the process of learning how to solve standard physics problems, students are developing important concepts, integrating them into a coherent conceptual framework, and developing the reasoning ability necessary to apply the concepts in simple situations. It is also assumed that students are learning to relate the formalism of physics to objects and events in the real world. There is ample evidence from research, however, that students do not make nearly as much progress toward these basic goals as they are capable of doing. Few develop a functional understanding of the material they have studied. The gap between the course goals and student achievement reflects a corresponding gap between the instructor and the students. In teaching introductory physics, many instructors proceed from where they are now or where they think they were as students. They frequently view students as younger versions of themselves. This approach is

Phys13news / Fall 2010

Fig. 1. Circuits used on questions given (a) after standard instruction on electric circuits and (b) after students had studied the material through guided inquiry. Students are asked to rank the bulbs from brightest to dimmest and to explain their reasoning. In both cases, they are told to treat the bulbs as identical and the batteries as identical and ideal.

Research-based Teaching

Generalization

on

Learning

and

Our experience in research, curriculum development, and instruction has led to several generalizations on learning and teaching.5 These are empirically based in that they have been inferred and validated through research. The early research and development of Physics by Inquiry formed the initial basis for the generalizations. Our later experience with PbI and Tutorials in Introductory Physics confirmed their validity and provided additional insights that broadened their applicability. The generalizations serve as a practical model for curriculum development by our group.

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Fig. 2. Questions used to probe student understanding of diffraction after standard instruction in large introductory physics courses: (a) quantitative question  and (b) qualitative question.

A. Research-based learning

generalizations

on

student

Examples from our research are given below as evidence for a few of the generalizations on student learning. Others are supported more broadly from our research base. 1. Facility in solving standard quantitative problems is not an adequate criterion for functional understanding. Although experienced instructors know that there is a gap between what they teach and what is learned, most do not recognize how large the gap can be. The traditional measure for assessing student understanding is performance on standard quantitative problems. Since a significant portion of a typical class receives grades of A or B, instructors may conclude that students have understood the material at an acceptable level. However, the ability of students to obtain correct answers for numerical problems often depends on memorized algorithms. Liberal awarding of partial credit also may conceal lack of understanding.

Questions that require qualitative reasoning and verbal explanation are essential for assessing student learning. The importance of qualitative questions is demonstrated by all of our research. As illustrations, we consider some examples from physical optics. As part of our investigation, we tried to determine what students who have studied physical optics in a standard course can and cannot do. The two questions below pose essentially the same problem. a. Quantitative question on single-slit diffraction. The question in Fig. 2(a) was given on an examination to about 130 students. They were told that light is incident on a single slit of width a=4λ. The students were asked to state if any minima would appear on a screen and, if so, to calculate the angle to the first minimum. Since the slit width is larger than the wavelength, minima would occur. The required angle can be obtained by using the equation a sin θ=λ, which yields θ=sin-1 (0.25) ≈ 14°. Approximately 85% of the students stated that there would be minima. About 70% determined the correct angle for the first minimum. (See the first column in Table II.) b. Qualitative question on single-slit diffraction. For the question in Fig. 2(b), students were shown a single-slit diffraction pattern with several minima. They were told that the pattern results when a mask with a single vertical slit is placed between a laser (wavelength λ) and a screen. They were asked to decide whether the slit width is greater than, less than, or equal to λ, and to explain their reasoning. They could answer by referring to the equation for the angle θ to the first diffraction minimum. Since minima are visible, the angle to the first minimum is less than 90° and a sin θ = λ. Therefore, since sin θλ.

Phys13news / Fall 2010

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About 510 students, including the 130 who had been given the quantitative question, were asked this question after they had completed standard instruction on single-slit diffraction. Performance was poor. About 45% of the students made a correct comparison. Only 10% gave a correct explanation. (See the second column of Table II.) c. Comparison of results from qualitative and quantitative questions. The difference in the way that the introductory students treated the two questions above provides some insight into what they typically can and cannot do. As can be seen from Table II, the success rate on the qualitative question was much lower than on the quantitative question. The 130 students who had previously been given the quantitative question performed at about the same level as those who had not had this experience. Apparently, the ability to solve numerical problems is not a reliable indicator of conceptual understanding. 2. Connections among concepts, formal representations, and the real world are often lacking after traditional instruction.

The ability to use and interpret formal representations (algebraic, diagrammatic, and graphical) is critical in physics. The responses to the qualitative question on single-slit diffraction demonstrate that many students could not relate the formula that they had memorized (or had available) for the location of diffraction minima to the diffraction pattern. Two examples that provide additional evidence of a failure to make connections between the phenomena and formalism of physical optics appear under the next generalization. 3. Certain conceptual difficulties are not overcome by traditional instruction. Advanced study may not increase understanding of basic concepts.

Research has shown that certain conceptual difficulties persist in spite of instruction. The two examples below indicate deep confusion about the different models for light and the circumstances under which a ray, wave, or particle model applies. All the students involved had received explicit instruction on at least the ray and wave models but seemed to have great difficulty in interpreting the information. a. Qualitative question on double-slit interference. The students were shown a photograph of the central portion of a double-slit interference pattern in which all the maxima are of similar intensity. [See Fig. 3(a).] They were asked to sketch what would appear on the screen if the left slit were covered. To respond correctly, they needed to recognize

Phys13news / Fall 2010

that the minima are due to destructive interference of light from the two slits and that each slit can be treated as a line source. After the left slit is covered, the interference minima would vanish and the screen would be (nearly) uniformly bright. This question was asked in several lecture sections of the calculus-based course (N~600) with similar results before and after standard instruction. No more than about 40% of the students answered correctly. Overall, about 45% gave answers reminiscent of geometrical optics. Many claimed that the pattern would be the same, but dimmer. Others predicted that the maxima on one side would vanish, leaving a dark region, or that every other maximum would vanish. [See Fig. 3(b).] b. Individual demonstration interview on single-slit diffraction. In addition to the written questions on single-slit diffraction, we conducted individual demonstration interviews. Of the 46 students who participated, 16 were from the introductory calculus-based course and 30 from a sophomore-level modern physics course. All were volunteers and had earned grades at or above the mean in their respective courses. During the interviews, students were shown a small bulb, a screen, and a small rectangular aperture. They were asked to predict what they would see on the screen as the aperture is narrowed to a slit. Initially, the geometric image of the aperture would be seen. Eventually, a singleslit diffraction pattern would appear. In responding to this and other questions, students from both courses often used hybrid models with features of both geometrical and physical optics. For example, some students claimed that the central maximum of the diffraction pattern is the geometric image of the slit and that the fringes are due to light that is bent at the edges. Another difficulty of both introductory and more advanced students was the tendency to attribute a spatial extent to the wavelength or amplitude of a wave. Many considered diffraction to be a consequence of whether or not light would ‘‘fit’’ through the slit. Some of the introductory students claimed that if the width of the slit were greater than the amplitude of the wave, light would be able to pass through the slit, but that if the slit width were less, no light could emerge. [See Figs. 4(a) and 4(b).] Some modern physics students extended these same ideas to photons distributed along sinusoidal paths. (See Fig. 5.) Their diagrams indicated that the photons would not get through the slit if the amplitude were greater than the slit width. In physical optics and other topics, we have found that study beyond the introductory level does not necessarily overcome serious difficulties with basic material. Unless explicitly addressed in introductory physics, these difficulties are likely to persist.

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Fig. 3. (a) Question used to probe student understanding of double-slit interference. (b) Common incorrect diagrams drawn by students in response to the written question.

B. Research-based generalizations on teaching The generalizations on student learning have implications for teaching. Our experience in developing curriculum and testing its effectiveness with students has led to a corresponding set of research-based generalizations on teaching. Below, the generalizations on student learning are repeated. Each is followed by one on teaching [in bold italics]. 1. Facility in solving standard quantitative problems is not an adequate criterion for functional understanding. Questions that require qualitative reasoning and verbal explanation are essential for assessing student learning and are an effective strategy for helping students learn.

As has been discussed, the traditional forms of instruction seem to be inadequate for helping most students develop a functional understanding of basic topics in physics. Hearing lectures, reading textbooks, solving quantitative problems, seeing demonstrations, and doing experiments often have surprisingly little effect on student learning. We have found that an effective instructional approach is to challenge students with qualitative questions that cannot be answered through memorization, to help them learn how to respond to such questions, and to insist that they do the necessary reasoning by not supplying them with answers.

Phys13news / Fall 2010

2. Connections among concepts, formal representations, and the real world are often lacking after traditional instruction. Students need repeated practice in interpreting physics formalism and relating it to the real world. Most instructors recognize that students need help in relating the concepts and formal representations of physics to one another and to physical phenomena. However, illustrative examples and detailed explanations are often ineffective. Analogies obvious to instructors are often not recognized by students. For example, in developing our curriculum on physical optics, we found that many students needed explicit guidance in transferring their experience with two-source interference in water to double-slit interference in light. 3. Certain conceptual difficulties are not overcome by traditional instruction. (Advanced study may not increase understanding of basic concepts.) Persistent conceptual difficulties must be explicitly addressed in multiple contexts. Some difficulties that students have in learning a body of material are addressed through standard instruction or gradually disappear as the course progresses. Others are highly resistant to instruction. Some are sufficiently serious that they may impede, or even preclude, development of a functional

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understanding. For example, the belief that the amplitude of a light wave has a spatial extent or that the wave is a carrier of photons makes it impossible to develop a correct wave model for light. (See Figs. 4 and 5.) Our experience indicates that warning students not to make particular errors is ineffective. For most students, assertions by an instructor make no difference. Avoiding situations likely to evoke errors by students, or providing algorithms that they can follow without thinking, may conceal latent difficulties that will surface at some later time. If faulty reasoning is involved, merely correcting an error is useless. Major conceptual change does not take place without a significant intellectual commitment by students. An instructional strategy that we have often found effective for securing the mental engagement of students can be summarized as: elicit, confront, and resolve. The first step is to create a situation in which the tendency to make a known common error is exposed. After the students have been helped to recognize a resultant inconsistency, they are required to go through the reasoning needed to resolve the underlying difficulty. Since single encounters are seldom sufficient for successfully addressing serious difficulties, it is necessary to provide students with additional opportunities to apply, reflect, and generalize. A word of caution is necessary because frequent use of the terms ‘‘misconceptions’’ and ‘‘misconceptions research’’ has trivialized the intellectual problem. The solution is not a matter of identifying and eradicating misconceptions. The intellectual issues are much deeper. Misconceptions are often symptoms of confusion at a fundamental level.

Conclusion

 

Research in physics education can provide a guide for setting standards for student learning that are more rigorous than the generally accepted criterion of success in solving quantitative problems. It is possible to help students meet higher standards than most instructors often tacitly accept. As already mentioned, there is considerable evidence that time spent on developing a sound qualitative understanding does not detract from, and often improves (sometimes significantly), the ability to solve quantitative problems. Students should be expected to develop a coherent conceptual framework that enables them to determine in advance  the  type  of  answer that they should obtain  in a quantitative problem. Therefore, the types of intellectual goals that have been set forth, both explicitly and implicitly, do not represent a ‘‘dumbing down’’ of standards, a charge often levied at attempts to modify traditional physics

Phys13news / Fall 2010

instruction. On the contrary, an increased emphasis on qualitative reasoning means that we are setting much higher standards. Research can be the key to student learning. Without a sound base for informing the development of curriculum, we lack the knowledge necessary to make cumulative progress in improving instruction. We need to increase our understanding of how students think about traditional and contemporary topics. This information can provide a basis for designing instruction to achieve the specific goals of physics courses. Research on how students learn can also lead to insights about how to promote the development of some more general intellectual goals. We would like to help students understand the nature of scientific models and the scientific method through which they are developed. We want them to know the difference between what is and what is not a scientific explanation and to be able to distinguish between explanations based on scientific reasoning and arguments based on personal belief or popular opinion. Students need to recognize the kinds of questions that they must ask themselves to determine whether they understand a concept or line of reasoning and, if they do not, to formulate questions that can help them improve their understanding. Being able to reflect on one’s thinking and to learn on one’s own is a valuable asset that transcends the learning of physics. The study of physics offers many opportunities to cultivate the ability to engage in scientific, critical, and reflective thinking. Thus, research can be the key to setting higher (yet realistic) standards, to helping students meet expectations, and to assessing the extent to which the goals for student learning are met. We can be greatly encouraged by the positive change that has occurred in the physics community within the last decade. Research in physics education has had an increasing influence on the way physics is taught. Faculty have drawn upon the results in producing new textbooks and revised versions of established texts. Research has also had a direct impact on the development of innovative instructional materials that have been shown to be effective. The results have been reported at professional meetings and in readily accessible journals. At meetings of professional organizations, sessions on research are well attended. We have come a long way and, with research as a guide, can look forward to continued progress in physics education. Acknowledgments This Oersted Medal is the result of my collaboration with many members of the Physics Education Group, past and present. Special thanks are due to the current faculty in the group: Paula R. L.

Page 16

Heron, Peter S. Shaffer, and Stamatis Vokos. I would like to recognize the early intellectual influence of Arnold B. Arons and the invaluable support of Mark N. McDermott. I also want to express my appreciation to the Department of Physics and the University of Washington. I am grateful to the National Science Foundation for enabling our group to conduct a coordinated program of research, curriculum development, and instruction. 1 F. K. Richtmyer, ‘‘Physics is Physics,’’ Am. Phys. Teach. 1 (1), 1–5 (1933). 2 For an overview, see L. C. McDermott and E. F. Redish, ‘‘Resource Letter: PER-1: Physics Education Research,’’ Am. J. Phys. 67, 755–767 (1999). The Resource Letter emphasizes research conducted among university students and contains relatively few entries below the college level. 3 L. C. McDermott and the Physics Education Education Group at the University of Washington, Physics by Inquiry (Wiley, New York, 1996);L.C. McDermott, P. S. Shaffer, and the Physics Education Group at the University of Washington, Tutorials in Introductory Physics, First Edition (Prentice Hall, Upper Saddle River, NJ, 2002). 4 L. C. McDermott and P. S. Shaffer, ‘‘Research as a guide for curriculum development: An example from introductory electricity. I. Investigation of student understanding,’’ Am. J. Phys. 60, 994–1003 (1992); Printer’s erratum to Part I 61,81 (1993); and P. S. Shaffer and L. C. McDermott, ‘‘Research as a guide for curriculum development: An example from introductory electricity. II. Design of instructional strategies,’’ ibid. 60, 1003–1013 (1992). In addition to the examples given in these papers, reference is made to some of the research reported in L. C. McDermott, P. S. Shaffer, and C. P. Constantinou, ‘‘Preparing teachers to teach physics and physical science by inquiry,’’ Phys. Educ. 35 (6),411–416 (2000).

interference and diffraction of light,’’ Phys. Educ. Res., Am. J. Phys. Suppl. 67, S5–S15 (1999). In addition to the specific examples in these papers, reference is made to some of the research reported in B. S. Ambrose, P. R. L. Heron, S. Vokos, and L. C. McDermott, ‘‘Student understanding of light as an electromagnetic wave: Relating the formalism to physical phenomena,’’ Am. J. Phys. 67, 891– 898 (1999); S. Vokos, B. S. Ambrose, P. S. Shaffer, and L. C. McDermott, ‘‘Student understanding of the wave nature of matter: Diffraction and interference of particles,’’ Phys. Educ. Res., Am. J. Phys. Suppl. 68, S42– S51 (2000). © 2001 American Association of Physics Teachers. [DOI: 10.1119/1.1389280] Reprinted with permission from the author ______________________________________________

SIN BIN #136 by Rohan Jayasundera The British Concorde (BC) and the French Concorde (FC) flew around the world in considerably less than 80 days. Each plane covered 40,000 km. The BC covered half its flight distance at a supersonic speed of 2,500 km/hr and the other half at a subsonic speed of 1,000 km/hr. The FC spent half its flight time at 2,500 km/hr and the other half at 1,000 km/hr. Don’t worry about time zones or date lines, and leave the pollution question up in the air. How did the trip times compare? (A) (B) (C) (D) (E)

Both trips had the same flight time. BC beat FC by 496 minutes. BC beat FC by 309 minutes. FC beat BC by 496 minutes. FC beat BC by 308 minutes.

5

L. C. McDermott, ‘‘Guest Comment: How we teach and how students learn—A mismatch?,’’ Am. J. Phys. 61, 295–298 (1993). The discrepancy between teaching and learning is also discussed in L. C. McDermott, ‘‘Millikan Lecture 1990: What we teach and what is learned— Closing the gap,’’ ibid. 59, 301–315 (1991), as well as in other articles by the Physics Education Group. 6 B. S. Ambrose, P. S. Shaffer, R. N. Steinberg, and L. C. McDermott, ‘‘An investigation of student understanding of single-slit diffraction and double-slit interference,’’ Am. J. Phys. 67, 146–155 (1999); K. Wosilait, P. R. L. Heron, P. S. Shaffer, and L. C. McDermott, ‘‘Addressing student difficulties in applying a wave model to the

Phys13news / Fall 2010

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FIND THE LAUREATES PUZZLE #7 by Tony Anderson

Hidden in the above table of 144 letters are the surnames of 30 Nobel Prize winning physicists and chemists, who are listed alphabetically below. You will find them by reading in one of eight ways: left to right, right to left, up, down, or 4 different diagonals. If you check off the names as you find them and also circle all the letters in these names (many are used more than once, so don’t cross them out!), you will eventually find 9 unused letters. Now read these sequentially in the usual way (left to right, top line first), and they will form the name of another Nobel Laureate. Who is he?

(Solution on page 20)

Biographies and further information on these Nobel Laureates can be found on the website of the Nobel Foundation: http://www.nobelprize.org

Phys13news / Fall 2010

In the list below, P indicates Physics and C indicates Chemistry, with the year of the award in brackets:

Kurt ALDER, C (1950); Hans BETHE, P (1967); Max BORN, P (1954); Elias COREY, C (1990); Clinton DAVISSON, P (1937); William GIAUQUE, C (1949); Jerome KARLE, C (1985); Max von LAUE, P (1914); David Lee, P (1996); Lars ONSAGER, P (1968); Jean PERRIN, P (1926); Frederick REINES, P (1995); Emilio SEGRE, P (1959); Jack STEINBERGER, P (1988); Martinus VELTMAN, P (1999);

Francis ASTON, C Neils BOHR P Paul BOYER, C Eric CORNELL, P Riccardo GIACCONI,P Vitali GINZBURG, P Henry KENDALL, P Leon LEDERMAN, P George OLAH, C Wolfgang PAUL, P Isidor RABI, P Heinrich ROHRER, P Jens SKOU, C Henry TAUBE, C Eugene WIGNER, P

(1922); (1922); (1997); (2001); (2002); (2003); (1990); (1988); (1994); (1989); (1944); (1986); (1997); (1983); (1963).

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Solution to Double Nobel Laureate Sudoku Puzzle Issue #134 (apologies for omission from the previous issue)

The two physics laureates hidden in the grid are Niels Bohr (1922) and Wolfgang Pauli (1945)

Solution to SIN BIN #135 Ball bearings are graded as to size and quality from their behaviour in a nearly elastic collision with a hard smooth steel plate. The ball bearings run down a trough, drop for a short distance, bounce off the plate and, if they are just the correct size and are exactly spherical (within extremely fine tolerances), they will just pass through a small hole in a wall. Assume a ball bearing of mass m has just passed the test. When dropped vertically on the steel plate, it bounces to 9/10 of its original height. If the velocity of the ball at A is Vo3 how high is the hole in the wall if the ball bearing passes through it horizontally? (A)

9 ⎡ V sin θ ⎤ H = ⎢h + 0 10 ⎣ 2 g ⎥⎦

(B)

2 9 ⎡ V0 sin θ ⎤ H = ⎢h + ⎥ 10 ⎢⎣ g ⎥⎦

(C)

2 2 9 ⎡ V0 sin θ ⎤ H = ⎢h − ⎥ 10 ⎣⎢ g 2 ⎦⎥

Phys13news / Fall 2010

9 ⎡ V02 sin 2 θ ⎤ h+ 10 ⎢⎣ 2 g ⎥⎦

(D)

H=

(E)

10 ⎡ V02 sin 2 θ ⎤ H = ⎢h + ⎥ 9 ⎣ g ⎦

Wasn’t that a dirty trick not to let you eliminate all the wrong choices by dimensional analysis? However, A and C are obviously wrong because V/g and V2/g2 cannot have the required dimensions of H. B and E can also be ruled out since they give H>h for V0=0, a rather neat way to solve world energy problems if it were possible. This leaves D as the only possibility, but you probably want to verify it. The vertical component of the ball’s velocity at the start is V0 sinθ downwards and it falls a distance h with an acceleration of g. Hence, the vertical downward velocity component just before collision obeys

V12 = V02 sin 2 θ = 2 gh. 2

The collision decreases V1 by a factor of 9/10. This is based on the fairly reasonable assumption that horizontal effects of the collision will not alter the vertical effects. There are conditions you could imagine where this would not be true, but these are ball bearings striking a smooth steel plate. Hence, the vertical upward velocity just after collision must obey

V22 = 9 /10 (V02 sin 2 θ + 2 gh ) This vertical velocity then decreases to zero in a distance H under a deceleration of g, so

9 2 2 (V0 sin θ + 2 gh ) = 2 gH . 10 ⇒

H=

9 ⎡ V02 sin 2 θ ⎤ h+ 10 ⎢⎣ 2 g ⎥⎦

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SOLUTION to Find the Laureates Puzzle #7 pg 18 Aleksandr PROKHOROV, P (1997).

Phys13news / Fall 2010

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