HPS Can Improve Problem- Solving Ricardo Lopes Coelho Faculdade de - - PowerPoint PPT Presentation

HPS Can Improve Problem- Solving

Ricardo Lopes Coelho Faculdade de Ciências

Universidade de Lisboa &

Centro de História das Ciências e Tecnologia

FFP 14

University of Aix Marseille, July 2014

Plan of the talk

 1. On the concept of force  2. On the law of inertia  3. Problem-solving

Plan of the talk

 1. On the concept of force  2. On the law of inertia  3. Problem-solving

On students’ misunderstandings

 McClelland 1985; Halloun & Hestenes 1985;  Bliss & Ogborn 1994; Hijs & Bosch 1995;

Rowlands et al. 1999; Lozano & Cardenas 2002

 On the relationship between force and motion:

Peters 1985; Halloun and Hestenes 1985; Galili & Bar 1992; Lombardi 1999; Carson & Rowlands 2005; Smith & Wittmann 2008

 Teaching strategies developed: Arons 1990;

Hestenes 1992; Rowlands et al. 1998; Stinner 2001; Galili 2001; Seker & Welsh 2006.

Kinds of definitions of force

 = m𝐛  Force is the cause of acceleration  Force is the effort felt by the pulling or pushing of

an object

 Force is the product of mass and acceleration

F

Force-product

 Fließbach 2007: “Newton’s second axiom

embraces the following definitions and affirmations:

 Definition of mass;  Definition of force  […]” (p. 13-14).  Def. of mass: m=F/𝐛  Def. of force: F=ma

HS: Mach 1868

 Criticism:  m=W/g  W=mg

Force-effort

 =m𝐛  Nolting 2005: “The concept of force can only be

defined indirectly through its effects. If we want to modify the state of movement or the shape of a body, for example, using our muscles, then an effort will be necessary […] This effort is called force […] We observe everywhere in our environment changes in the states of motion of certain bodies […] We see their causes equally in forces, which in the same way as our muscles, act

• n the bodies”

F

HS: Reech 1852

 Andrade 1898: ‘‘Certain spirits despise the

common idea of force, as furthermore, they despise the notion of muscular force. This disdain does not seem justified to me, since the only common notion of force is the fruitful notion; mechanics, we admit clearly, is essentially anthropomorphic’’.

 Poincaré 1900, the anthropomorphism cannot

provide the foundation of anything truly scientific

• r philosophical.

The most common concept of force

 = m𝐛  Feynman 1974: “If an object is accelerating, some

agency is at work" (§ 9-4).

 Wolfson & Pasachoff 1990: "Why are we so

interested in knowing about forces? Because forces cause changes in motion" (p. 76). F

Force-cause

 Euler 1736, Lagrange 1787-8, Poisson

1833, Coriolis 1844, F. Neumann 1883, Thomson & Tait 1890, Voigt 1901, Webster 1904, Planck 1916, Lenard 1936, Sommerfeld 1947, Schaefer 1962, Budo´ 1974, Eisberg & Lerner 1981, Hestenes 1987, Alonso & Finn 1992, Knudsen & Hjorth (1996), Sears & Zemansky 2004, Gerthsen 2006, Kuypers 2008, …(Coelho 2010)

Criticism

 D’Alembert 1743, L. Carnot 1803,

Kirchhoff 1876, Hertz 1894, Poincaré 1897, Hamel 1912, Platrier 1954, Ludwig 1985, Wilczek 2004-5.

Criticism

 =m𝐛  Hamel 1912: ‘‘Force itself, however, we do not

define as cause of motion, force is a thing of thought and not a natural phenomenon’’.

 Platrier 1954: ‘‘In fact, force is only a human

concept and we have no knowledge of the profound cause of motions’’.

 Wilczek 2004: ‘‘By comparison to modern

foundational physics, the culture of force is vaguely defined, limited in scope, and approximate’’ (p. 12). Assumptions concerning force are ‘‘a sort of folklore’’ (2005, p. 10). F

Carson & Rowlands 2005 (ST)

 “The problem is that we do not observe or

experience ‘force’ as such” (p. 474).

 “it is difficult to see how force can be

abstracted from experience” (p. 479).

Force-cause

 There is a logical reason for this concept of force.

Plan of the talk

 1. On the concept of force  2. On the law of inertia  3. Problem-solving

• 2. The law of inertia

 Newton’s first law:

“Every body perseveres in its state of resting or of moving uniformly in a straight line, as far as it is not compelled to change that state by impressed forces” (1726, p. 13).

 LI: ‘a free body has constant velocity’  Free body ⟹ constant velocity

The link with force

 Free body ⟹ constant velocity  P ⟹ Q  (P ⟹ Q) ⟹ (-Q ⟹ -P)  LI ⟹ (- const. velo. ⟹ - free body)

The link with force

 Free body ⟹ constant velocity  P ⟹ Q  (P ⟹ Q) ⟹ (-Q ⟹ -P)  LI ⟹ (- const. velo. ⟹ - free body)  ⟹

• const. velo.
• free

body acceleration force mass

 Free body ⟹ constant velocity  P ⟹ Q  (P ⟹ Q) ⟹ (-Q ⟹ -P)  LI ⟹ (- const. velo. ⟹ - free body)  ⟹

• const. velo.
• free

body

a F m

A Problem with the law

Voigt 1901, Planck 1916, Nielsen 1935, Becker 1954, French 1971, Budò 1974, Bergmann & Schaefer 1990, Nolting 2005 (Coelho 2012).

Planck 1916: “The first question that we want to answer is the following: how does a material point move […] when it is completely isolated [...] this experiment cannot be carried out […] It can even be doubted, if the question asked above has some meaning”.

Planck 1916: “The first question that we want to answer is the following: how does a material point move […] when it is completely isolated [...] this experiment cannot be carried out […] It can even be doubted, if the question asked above has some meaning”. Scobel, Lindström & Langkau 2002: “a free particle is fiction”.

Planck 1916: “The first question that we want to answer is the following: how does a material point move […] when it is completely isolated [...] this experiment cannot be carried out […] It can even be doubted, if the question asked above has some meaning”. Scobel, Lindström & Langkau 2002: “a free particle is fiction”. Matthews 2009 (ST): “we never see force-free behaviour in nature, nor can it be experimentally induced, so what is the source and justification of our knowledge of bodies without impressed forces?”

Stachel 2005

 “The presence of gravitation effectively

nullifies the distinction between forced and free-motions” (p. 24).

Nagel 1961 (PS)

 “Why should uniform velocity be selected

as the state of a body which needs no explanation in terms of the operation of forces, rather than uniform rest or uniform acceleration (such as motion along a circular orbit with constant velocity) […]?” (p. 177).

HS: a motion of reference?

HS: a motion of reference?

rectilinear and uniform (Newton)

HS: a motion of reference?

rectilinear and uniform (Newton) non-rectilinear or non-uniform

• (P ˄ U) = -P ˅ - U

HS: a motion of reference?

least curvature and uniform (Hertz)

HS: a motion of reference?

least curvature and uniform (Hertz) non-least curvature or non-uniforme

HS: a motion of reference?

rectilinear and uniform (Newton) non-rectilinear or non-uniform least curvature and uniform (Hertz) non-least curvature or non-uniform

HS: a motion of reference?

• rectilinear and uniform (Newton)
• geodesic and uniform (Euler)
• circular and uniform (Lagrange)
• least curvature and uniform (Hertz)

Path and How the path is covered

Logical connection

 Motion of reference:

Path ˄ How it is covered Force:

• P ˅ - U

Plan of the talk

 1. On the concept of force  2. On the law of inertia  3. Problem-solving

2004

The problem presented

HS: Poggendorff 1854

Peter & Neal Graneau 2006

Experiment

 4.9 N  4.704 N

Experiment

Image displayed by the monitor connected to the force sensor

Problem Solving Strategy

4.704 N

4.704 N

4.704 N

4.704 N

4.704 N 4.9 N

a=0.2m/s

2

For pedagogical reasons

Poggendorff - Atwood

• Pogg. 3 – Pogg. 4

• Pogg. 4 – At. 4

A Problem for textbooks

The ontological meaning of force and the Atwood machine

Atwood At Atwood 1784

19th Century

20th Century

Acting force Body acted upon Accelerati

• n caused

FED

F = m a

Atwood machine

Mg-mg = M+m a

Is this the cause of acceleration?

Acting force Body acted upon Accelerati

• n caused

Atwood machine

Mg-mg = M+m a

 Poincaré said that to say ‘force is the cause of

acceleration‘ is talking metaphysics.

 Matthews (2009) added ‘‘as every physics class

talks of force being the cause of motion, then there is metaphysics lurking in every classroom, just waiting to be exposed’’ (p. 706).

 We understand those who defended force as the

cause of acceleration, since they admitted the law

• f inertia.

Final Remarks

 The law of inertia cannot be tested – a motion of

reference

 Force: a deviation from that motion.  Poggendorff‘s experiment – the concept of force is

not adequate regarding the Atwood machine.

 This experiment leads us to solve problems in a new

way.

 All this comes from the HS.

Th.y

 Thank you very much for your attention.  Ricardo LC  rlc@fc.ul.pt

References



Alembert J. d’ (1758) Traité de Dynamique, 2nd edn. Paris, Johnson Reprint Corporation, New York, London, (Republished 1968)



Carson, R., & Rowlands, S. (2005). Mechanics as the logical point of entry for the enculturation into scientific thinking. Science & Education, 14, 473–493.



Carnot L (1803) Principes fondamentaux de l’équilibre et du mouvement. Deterville, Paris



Coelho, R. L. (2010). On the concept of force: How understanding its history can improve physics

• teaching. Science & Education, 19, 91–113.



Coelho, R. L. (2012). Conceptual problems in the foundations of mechanics. Science & Education 21 (9), 1337-1356.



Coelho, R.L. (2013) “Could HPS Improve Problem-Solving?” Science & Education 22, 1043- 1068.



Graneau, P., & Graneau, N. (2006). In the grip of the distant universe: The science of inertia. New Jersey: World Scientific.



Hamel G (1912) Elementare Mechanik. Teubner, Leipzig, Berlin



Hertz H (2003/1899) The principles of mechanics presented in a new form, Trans. by Jones DE and Walley JT, Dover Publications, Nineola, New York



Mach E (1868) Ueber die Definition der Masse. Repertorium Experimental-Physik 4, 355–359



Matthews, M. R. (2009). Teaching the philosophical and worldviews components of science. Science & Education, 18, 697–728.



Nagel E (1961) Structure of science: problems in the logic of scientific explanation. Harcourt, Brace & World, New York

References

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Nagel E (1961) Structure of science: problems in the logic of scientific explanation. Harcourt, Brace & World, New York

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Newburgh, R., Peidle, J., & Rueckner, W. (2004). When equal masses don’t balance. Physics Education, 39(3), 289–293.

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Newton, I. (1972 [1726]). Isaac Newton’s Philosophiae Naturalis Principia Mathematica (3rd ed.). In A. Koyre´ & I. B. Cohen (Eds.). Harvard: Harvard University Press.



Nolting, W. (2005). Grundkurs: Theoretische Physik 1: Klassische Mechanik (7th ed.). Braunschweig, Wiesbaden: Vieweg.

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Planck, M. (1916). Einfu¨hrung in die Allgemeine Mechanik. Leipzig: S. Hirzel.

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Poggendorff, J. C. (1854). U¨ ber eine Aba¨nderung der Fallmaschine. Annalen der Physik und Chemie, 168, 179–182.

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Poincaré H (1900/1901), Sur les Principes de la Mécanique. In Ier Congrès international de Philosophie, Tome 3. Paris, pp 457–494. Kraus Reprint Limited, Nendeln, Liechtenstein (Republished 1968).

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Reech F (1852) Cours de Mécanique d’après la nature généralement flexible et élastique des corps, Carilian-Goeury et Vor Dalmont, Paris



Wilczek F (2004) Whence the force of F = ma ? I: culture shock. Phys Today 57N10:11–12



Wilczek F (2005) Whence the force of F = ma ? III: cultural diversity. Phys Today 58N7:10–11

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