Frontiers of Fundamental Physics (FFP14) - HPS Can...

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

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

= 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

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

HS: Mach 1868

Criticism:

m=W/g

W=mg

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

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.

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

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

=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

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



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


P ⟹ Q

(P ⟹ Q) ⟹ (-Q ⟹ -P)

LI ⟹ (- const. velo. ⟹ - free body)

The link with force


P ⟹ Q

(P ⟹ Q) ⟹ (-Q ⟹ -P)


⟹

- const. velo. - free body

acceleration force mass


P ⟹ Q

(P ⟹ Q) ⟹ (-Q ⟹ -P)


⟹

- 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”.





meaning”.

Scobel, Lindström & Langkau 2002: “a free particle is fiction”.





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?


rectilinear and uniform (Newton)



non-rectilinear or non-uniform

- (P ˄ U) = -P ˅ - U


least curvature and uniform (Hertz)



non-least curvature or non-uniforme



non-rectilinear or non-uniform


non-least curvature or non-uniform


- 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



3. Problem-solving

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/s2

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

on caused

FED F = m a

Atwood

machine

Mg-mg = M+m a

Is this the cause of

acceleration?

Acting

force

Body

acted

upon

Accelerati

on 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

of 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

[email protected]

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).

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corps, Carilian-Goeury et Vor Dalmont, Paris

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

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