frontiers of fundamental physics (ffp14) - hps can...
TRANSCRIPT
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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
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Plan of the talk
1. On the concept of force
2. On the law of inertia
3. Problem-solving
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Plan of the talk
1. On the concept of force
2. On the law of inertia
3. Problem-solving
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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.
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Kinds of definitions of force
= m𝐚
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
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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/𝐚
Def. of force: F=ma
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HS: Mach 1868
Criticism:
m=W/g
W=mg
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Force-effort
=m𝐚
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
on the bodies”
F
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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
or philosophical.
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The most common concept of force
= m𝐚
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
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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)
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Criticism
D’Alembert 1743, L. Carnot 1803,
Kirchhoff 1876, Hertz 1894, Poincaré 1897,
Hamel 1912, Platrier 1954, Ludwig 1985,
Wilczek 2004-5.
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Criticism
=m𝐚 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
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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).
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Force-cause
There is a logical reason for this concept of force.
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Plan of the talk
1. On the concept of force
2. On the law of inertia
3. Problem-solving
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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
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The link with force
Free body ⟹ constant velocity
P ⟹ Q
(P ⟹ Q) ⟹ (-Q ⟹ -P)
LI ⟹ (- const. velo. ⟹ - free body)
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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
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Free body ⟹ constant velocity
P ⟹ Q
(P ⟹ Q) ⟹ (-Q ⟹ -P)
LI ⟹ (- const. velo. ⟹ - free body)
⟹
- const. velo. - free body
a F m
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A Problem with the law
Voigt 1901, Planck 1916, Nielsen 1935, Becker
1954, French 1971, Budò 1974, Bergmann &
Schaefer 1990, Nolting 2005 (Coelho 2012).
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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”.
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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”.
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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?”
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Stachel 2005
“The presence of gravitation effectively
nullifies the distinction between forced and
free-motions” (p. 24).
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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).
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HS: a motion of reference?
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HS: a motion of reference?
rectilinear and uniform (Newton)
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HS: a motion of reference?
rectilinear and uniform (Newton)
non-rectilinear or non-uniform
- (P ˄ U) = -P ˅ - U
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HS: a motion of reference?
least curvature and uniform (Hertz)
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HS: a motion of reference?
least curvature and uniform (Hertz)
non-least curvature or non-uniforme
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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
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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
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Logical connection
Motion of reference:
Path ˄ How it is covered
Force:
- P ˅ - U
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Plan of the talk
1. On the concept of force
2. On the law of inertia
3. Problem-solving
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2004
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The problem presented
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HS: Poggendorff
1854
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Peter & Neal Graneau 2006
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Experiment
4.9 N
4.704 N
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Experiment
Image displayed by the monitor connected to the force sensor
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Problem
Solving Strategy
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4.704 N
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4.704 N
4.704 N
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4.704 N
4.704 N
4.9 N
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a=0.2m/s2
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For pedagogical reasons
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Poggendorff - Atwood
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Pogg. 3 – Pogg. 4
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Pogg. 4 – At. 4
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A Problem for textbooks
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The ontological meaning of
force and the Atwood machine
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Atwood At Atwood 1784
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19th Century
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20th Century
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Acting
force
Body
acted
upon
Accelerati
on caused
FED F = m a
Atwood
machine
Mg-mg = M+m a
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Is this the cause of
acceleration?
Acting
force
Body
acted
upon
Accelerati
on caused
Atwood
machine
Mg-mg = M+m a
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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
of inertia.
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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.
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Th.y
Thank you very much for your attention.
Ricardo LC
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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 Nagel E (1961) Structure of science: problems in the logic of scientific explanation.
Harcourt, Brace & World, New York
Newburgh, R., Peidle, J., & Rueckner, W. (2004). When equal masses don’t balance.
Physics Education, 39(3), 289–293.
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.
Planck, M. (1916). Einfu¨hrung in die Allgemeine Mechanik. Leipzig: S. Hirzel.
Poggendorff, J. C. (1854). U¨ ber eine Aba¨nderung der Fallmaschine. Annalen der Physik
und Chemie, 168, 179–182.
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).
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
Wolfson R. & Pasachoff JM (1990) Physics. Scott, Glenview, Ill