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Using History to Teach Mechanics

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Abstract

History of mechanics can contribute to the teaching of mechanics in two major ways. It can help students to learn about the nature of science and it can provide illustrations, stories and experiments which assist the teacher in overcoming some of the misconceptions students appear to share with scientists of the past. In this chapter a brief overview of the history of mechanics is presented in which emphasis is placed on the different types of motion which have been of interest during this history. This is followed by a discussion of issues which arise from this history and are relevant to teaching. Some of the ways history of mechanics can be used to address problems which students have with mechanics are then presented followed by a brief consideration of the science education literature relating to the teaching of mechanics. To conclude recommendations are made about future directions for research and development in this area.

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Notes

  1. 1.

    I thank the anonymous reviewers whose insightful comments led to significant improvements in the content and the structure of this chapter.

  2. 2.

    For Aristotle “motion” was a term that covered all types of change and what we call “motion” was a change of place – movement from one position to another – called by him “local motion” or “locomotion”.

  3. 3.

    See Cohen and Drabkin (1958, pp. 221–3) and Wolff (1987).

  4. 4.

    If the void were thought of as space with zero density, Aristotle’s relationship would imply that bodies would move through it with infinite speed which Aristotle considered to be impossible.

  5. 5.

    See Aristotle, Physics, 5.6; 6.7; 8.9 and Heavens, 1.8; 2.6.

  6. 6.

    See Cohen and Drabkin (1958, pp. 217–21), Moody (1951b, p. 360), and Wolff (1987).

  7. 7.

    See Dijksterhuis (1961, pp. 190–1). This relationship means, in our terms, the following: when the speed, S, doubles, the ratio, motive force (F)/resistance (R), is squared or, more generally, when K = S 1 /S 2 ,

    \( \frac{F_2}{R_2}={\left(\frac{F_1}{R_1}\right)}^k \). In modern terms this means \( S\kern0.36em \propto \log \kern0.36em \left(\;\frac{F}{R}\right) \).

  8. 8.

    In days 3 and 4 of his Discourses (pp. 158–9), Galileo indicated a lack of interest in extrinsic, efficient causes such as forces (Machamer 1978) and sought firstly to describe the motion of a falling body. For Descartes and Newton the search for such causes was much more central to their investigations.

  9. 9.

    A younger contemporary of Galileo, Marcus Marci, also developed a theory of impact (Aiton 1970).

  10. 10.

    See Ariotti (1968), Erlichson (1994, 2001), Gauld (1999), MacLachlan (1976), and Naylor (2003).

  11. 11.

    Further details about the pendulum in history and teaching can be found in Matthews et al. (2005).

  12. 12.

    See Arons and Bork (1964), Dijksterhuis (1961, pp. 464–77), and Erlichson (1995).

  13. 13.

    Time does not appear in Newton’s second law because in a collision the duration of the forces on the two bodies involved is the same.

  14. 14.

    See Gauld (2010, equation (3)), Pourciau (2011), and Westfall (1971, pp. 481–91). In Book 1 of the Principia, Newton developed the implications of his three laws for the action of central forces on bodies which experience no resistance (other than that of the “force of inertia”). It is in this book that he derived Kepler’s laws of planetary motion from an inverse square of force. In Book 3 Newton applied the insights of Book 1 to observation made on the motion of planets, the moon and comets. In Book 2 his Laws are applied to a variety of other situations including the motion of bodies through resisting mediums, fluid flow and waves. Densmore (1995) is an excellent guide to the Principia. Pourciau (2011) presents a different view of the nature of Newton’s second law than that presented here.

  15. 15.

    See Herival (1965), Newton and Henry (2000), Stinner (2001), and Westfall (1971, pp. 353–55).

  16. 16.

    See Principia, Book 2, Sect. 6, Gauld (2009, 2010).

  17. 17.

    See Hankins (1965), Iltis (1970, 1971, 1973), Laudan (1968), and Papineau (1977).

  18. 18.

    See Mach (1893/1960, pp. 303–07; 319–24), but see also Bunge (1966).

  19. 19.

    Coelho (2012) provides a detailed analysis of conceptual issues in mechanics.

  20. 20.

    d’Alembert’s approach to the solution of problems of motion is still alive today in some engineering contexts (see Newburgh et al. 2004). See also the discussion of inertial forces by Coelho (2012), and Galili (2012).

  21. 21.

    Gabbey (1980) argues that, in Newton’s Principia, there are two concepts of vis inertiae that associated with the persistence of motion and measured by mv and that associated with the change of velocity and measured by mΔv.

  22. 22.

    Following his definition of naturally accelerated motion, Galileo’s postulate in his Discourses related to motion down inclined planes: I assume that the degrees of speed acquired by the same moveable over different inclinations of planes are equal whenever the heights of those planes are equal (Discourses, p. 162). This postulate would not have been self-evident to Galileo’s contemporaries and later in the Discourses he deduced it as a theorem!

  23. 23.

    Galileo’s notion of inertial motion was expressed in similar terms (see Discourses, p. 197), but for him the path was not a straight line but a circle around the earth (Dialogue, pp. 147–8). On the status of Newton’s first law among physicists over the last two centuries, see Whitrow (1950).

  24. 24.

    Hanson (1963) pointed out that it is impossible to consider the motion of an isolated body without a fixed reference frame and, for this, one needs the existence of at least one other body. However, as soon as this second body is introduced, the first is no longer isolated so that it appears that Newton’s first law refers to an impossible state of affairs.

  25. 25.

    The device known as Newton’s cradle provides another example of illegitimate idealisation (Gauld 2006; Hutzler et al. 2004).

  26. 26.

    Matthews (1994, pp. 163–74) has given a number of examples of contemporaries who were on opposite sides of this divide.

  27. 27.

    It is interesting to note that in the discussion which took place on day 4 of Discourses, Galileo dealt with two-dimensional trajectory motion but presented no experimental data although it was evident from his working papers that he had carried out a series of experiments to show the parabolic nature of these trajectories. While he tried as far as possible to reduce impediments, he was not aware of the effect of rotation on the acceleration of a rolling ball and no doubt noticed the rather significant discrepancies between his results in his unpublished working papers and what he expected to find (see Sect. 3.5.3.2).

  28. 28.

    Galileo’s working papers can be viewed at the website: http://mpiwg-berlin.mpg.de/Galileo_Prototype/index.htm.

  29. 29.

    See Hall and Tilling (1975–1977), Herival (1965), Scott (1967), Turnbull (1959–1961), and Whiteside (1967–1981).

  30. 30.

    See Gauld (2010), Herival (1965), Smith (2001), and Westfall (1971).

  31. 31.

    See Drake (1973, 1974, 1975a, b, 1978, 1990).

  32. 32.

    See Naylor (1974a, b, 1976, 1977, 1980, 1983).

  33. 33.

    See, for example, Brown (1989), Clement (1982), Doménech et al. (1993), Galili and Bar (1992), Gunstone (1984), Halloun and Hestenes (1985), Ioannides and Vosniadou (2002), Lythcott (1985), McCloskey (1983), Montanero et al. (1995), Steinberg et al. (1990), Twigger et al. (1994), Viennot (1979), and Whitaker (1983).

  34. 34.

    See also Eckstein (1997), Nersessian and Resnick (1989), and Ioannides and Vosniadou (2002).

  35. 35.

    See Galili (2009), Gendler (1998), and Helm and Gilbert (1985). Of course the truth of the outcome of a thought experiment depends on the truth of the premise.

  36. 36.

    Other thought experiments not discussed here include Galileo’s use of two inclined planes to show that an unimpeded moving body would continue to move with undiminished speed on a “horizontal plane” around the earth (see Dialogue, pp. 145–8) and Archimedes’, Galileo’s and Mach’s thought experiment to establish the principle of the lever (Galileo, Discourses, pp. 109–12; Goe 1972; Mach 1893/1960, pp. 13–8).

  37. 37.

    Another possibility for Stevin’s arrangement is that the chain moves from one state to another identical state and so keeps moving forever. Stevin ruled this out because he denied that perpetual motion was possible. Of course, perpetual motion is impossible because energy is dissipated through friction, but in Stevin’s arrangement friction is necessarily absent.

  38. 38.

    These include the investigation of the motion of the simple pendulum (MacLachlan 1976; Matthews 2000, pp. 245–8), the use of Escriche’s inclined pendulum to vary the effective value of the acceleration due to gravity (Vaquero and Gallego 2000; Mach 1893/1960, pp. 207–9) and experiments based on Newton’s investigation of the resistance to motion of air and water (Gauld 2009, 2010). Blair (2001) and O’Connell (2001) encourage the use of ancient technological devices as aids in teaching about motion in the classroom.

  39. 39.

    See Drake (1973, 1990, pp. 9–15), MacLachlan (1976), Naylor (1974b), Settle (1961), Sherman (1974), and Straulino (2008).

  40. 40.

    Use of this method in a classroom is shown on the website http://www.youtube.com/watch?v=ZUgYcbBi46w.

  41. 41.

    See Naylor (1974b, 1976, 1980, 1983).

  42. 42.

    The problem Galileo apparently encountered with this experiment was that when H was equal to the height of the table on which the inclined plane was situated, he expected that D would equal 2H. Instead, his value for D was only 80% of what he expected. Today we can account for this discrepancy by appealing to the rotational kinetic energy of the ball which reduces D to 5/7 (or 85%) of Galileo’s expected value.

  43. 43.

    Nersessian (1992, p. 71) suggested that one of the reasons for the success of thought experiments is that they are set in an attractive narrative context.

  44. 44.

    See, for example, Stinner (1989, 1990, 1994, 1995, 1996, 2001) and Stinner and Williams (1993).

  45. 45.

    See Adler and Coulter (1978) and Moody (1951a, b); for an alternative reconstruction, see Franklin (1979).

  46. 46.

    A re-enactment of this story can be seen at the website http://youtube.com/watch?v=_Kv-U5tjNCY. The discussion by Erlichson (1993) is also helpful in considering the truth of this story.

  47. 47.

    See Holton (1952), Holton and Brush (2001), and Holton and Roller (1958).

  48. 48.

    See Cassidy et al. (2002); see also Holton (2003).

  49. 49.

    For example, Arons (1988); Galili (2012); Monk and Osborne (1997); Rosenblatt (2011); Stinner (1989, 1994, 1995).

  50. 50.

    Journals included in the analysis were American Journal of Physics (17), International Journal of Science Education (4), Journal of Research in Science Teaching (1), Physics Education (16), Research in Science Education (3), Science & Education (41), Science Education (0), The Physics Teacher (20) and The Science Teacher (2). The period covered was 1992–2011 and the number of articles in each journal is shown in parentheses.

  51. 51.

    See, for example, Galili and Tzeitlin (2003) and Wörmer (2007).

  52. 52.

    See Stinner (1989, 1994, 1995, 2001).

  53. 53.

    See, for example, Kokkotas et al. (2009), Kubli (1999), and Teichmann (1999).

  54. 54.

    See Kalman and Aulls (2003) and Seker and Welsh (2006).

  55. 55.

    There are, of course, more sophisticated contexts in which the history of mechanics can be used such as in tertiary courses on the history of science, but the greatest exposure to mechanics occurs in the secondary school whether for future specialists of physics or for science for non-specialists.

  56. 56.

    See also Arons (1988), Rosenblatt (2011, Chap. 6), Stinner (1994), and Stinner and Williams (1993).

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Gauld, C. (2014). Using History to Teach Mechanics. In: Matthews, M. (eds) International Handbook of Research in History, Philosophy and Science Teaching. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7654-8_3

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