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Pendulum as a culturally rich topic to teach physics Igal Galili Science Teaching Center The Hebrew University of Jerusalem Pendulum is a traditional item in physics curriculum 1. Pendulum is used to practice measurements 2. Pendulum is used to test students’ understanding of force-motion relationship Questions asked in matriculation examination: Show/calculate the forces on the bob in… Show/calculate the acceleration of the bob in… Show/calculate the velocity of the bob in… Calculate the period… l T 2π g Example: Question from the matriculation examination of 1998 The focus is on the formalism and procedural knowledge The required knowledge: Huygens’ formula Example: Question from the matriculation examination of 1991 The term (conical) pendulum is not even mentioned Example: Question from the matriculation examination (Phys.lab.) Galileo’s experiment with this setting is not mentioned Example: Question from the matriculation examination (Phys.lab.) Students empirically investigate physical pendulum without any theory and identification Features of the current presentation Used: Missed: Pendulum presents the case of vertical movement on a circular path Mathematical Pendulum is isochrornic (harmonic) only approximately Mathematical (mandatory) and physical (elected) pendulums are addressed. Pendulum can measure time Pendulum can provide operational definition of time Understanding of the force-motion relationship is tested Pendulum represents falling of bodies (Galileo) “When period is asked then the formula of Huygens is applicable” Conical pendulum “explains” nonfalling of bodies - imitates satellite (Hooke) Pendulum What is it? What is it included for? What does it represent? Object… System… Model… Theory … The status of scientific knowledge is ignored (hierarchy, importance…) • A holistic view is neither provided nor required What can be suggested? Teaching physics as a discipline-culture rather than a discipline. Physics as a Discipline-Culture body nucleus periphery Nucleus (center) – elements identifying the paradigms, concepts, principles, axioms, rules of knowledge production Body area – elements of knowledge which are produced basing on the rules of the nucleus Periphery (margins) – elements of knowledge which are at odds with the nucleus Holistic view on the subject of pendulum within the discipline-culture framework: 1. What is the contribution of pendulum to the principles of classical physics? (nucleus) 2. What other conceptions of pendulum are possible, were dismissed, and so on? (periphery) 3. Usually standard problem solving is trained and assessed (body) Periphery Body Nucleus Examples of materials which could be introduced Collision of two views on the nature of science Nucleus Galileo Guidobaldo del Monte 1607-1545 Newton Two conceptions: Galileo’s versus Newton’s Which one do we teach? Is Mathematical Pendulum isochrornic (harmonic) ? ... it must be remarked that one pendulum passes through its arcs of 180°, 160°, etc., in the same time that the other swings through its 10°, 8°, etc. …if two persons start to count the vibrations, the one the large, the other the small, they will discover that after counting tens and even hundreds they will not differ by a single vibration, not even by a fraction of one. Galileo, Dialogues Concerning Two New Sciences (1638) Pendulum can measure time (three meanings) Timekeeping (eventual) Time-meaning (operational) Time-measuring (instrumental) Nucleus • What makes pendulum moving? Aristotle: air Periphery Philoponus: impetus Galileo: gravity as a quality of bodies Descartes: vortices of ether Newton: Gravitational force Einstein: Space Time curvature • Pendulum entered science in the Medieval European science of the 14th century Jean Buridan (1290-1360) Albert of Saxony (1316-1390) Nicole Oresme (1320-1382) Thought Experiment of falling bodies The first explanation of the pendulum motion was provided within then new theory: the Theory of Impetus Albert of Saxony Questions on the Four Books on the Heavens and the World of Aristotle According to this [theory], it would be said also that if the earth were completely perforated, and through that hole a heavy body were descending quite rapidly toward the center, then when the center of gravity (medium gravitatis) of the descending body was at the center of the world, that body would be moved on still further [beyond the center] in the other direction, i.e., toward the heavens, because of the impetus in it not yet corrupted. And, in so ascending, when the impetus would be spent, it would conversely descend. And in such a descent it would again acquire unto itself a certain small impetus by which it would be moved again beyond the center. When this impetus was spent, it would descend again. And so it would be moved, oscillating (titubando) about the center until there no longer would be any such impetus in it, and then it would come to rest. • Changing the paradigm of permanent motion Pendulum presented an intermediate stage in the transition of the perception of “natural motion” between circular and linear motions Giovanni Batista Benedetti’s (1530-1590) demonstration of the instant nature of the rest in a periodic motion True motion of a planet P Pedagogical potential: Concepts Instant velocity, the split between acceleration and velocity a p Conception Harmonic motion Observer b Apparent motion of the planet Non-asked questions: A P B - Describe the movement at the terminal point(s) of pendulum motion A, B - Describe the movement at the top point P of a tossed body - Characterize the sate of the body in points A, B, and P? Pendulum and the concept of weight: L mg T 3mg T Surprise: mg To appreciate this result change the setting to a swing The result is independent on L What do we feel on a swing? What force do we perceive? Why do people like swinging? What do we feel at the extreme points? Swing can serve a setting to introduce the understanding of weight as a concept different from the gravitational force weight is a result of weighing • Galileo’s approach to Pendulum This approach yields T L Galileo’s law of the chords Huygens’ formula for mathematical pendulum A B A D C D TAD= TAD=TBD=TCD=…= 2 R/g π R/g 2 T1/4 2 R/g Galileo π T1/4 R/g 2 Huygens π 2 2 Educational benefit Surprise • The discrepancy between the circular and linear paths is essential. It is regardless how close the chord approaches the line. L T 2π g gπ 2 T L 2 Is this an easy way to define units? T1 sec L 1m Foucault pendulum What does it prove? Common view: Earth’s rotation Common misconception: absolute motion Conclusion • The common account of pendulum is formal and instrumental • The conceptual knowledge of pendulum is often ignored and this significantly impoverishes students’ knowledge of physics • Cultural issues (history of physics, interdisciplinary aspects) both beneficial and enjoying are ignored • The chance to learn about the nature of science (philosophical aspects) is missed תודה רבה
