A study of physics textbooks from the 1860s up to the present reveals shortcomings of our contemporary approach to teaching the concept of energy. In response, this paper offers a coordinated set of conceptual definitions of force, work, and energy, which can provide a somewhat more accessible grounding on which to develop the subject pedagogically.
References
1.
See, for example,
B. A.
Lindsey
, P. R. L.
Heron
, and P. S.
Shaffer
, “Student understanding of energy: Difficulties related to systems
,” Am. J. Phys.
80
, 154
–163
(2012
);B. A.
Lindsey
,P. R. L.
Heron
, andP. S.
Shaffer
, “Student ability to apply the concepts of work and energy to extended systems
,” Am. J. Phys.
77
(11
), 999–1009
(2009
);J. W.
Jewett
, “Energy and the confused student. Part I–V
,” Phys. Teach.
46
, 38
–43
(2008
),J. W.
Jewett
, Phys. Teach.
46
, 81–86
(2008
),J. W.
Jewett
, Phys. Teach.
46
, 149–153
(2008
),J. W.
Jewett
, Phys. Teach.
46
, 210–217
(2008
),J. W.
Jewett
, Phys. Teach.
46
, 269–274
(2008
);C.
Singh
and D.
Rosengrant
, “Multiple-choice test of energy and momentum concepts
,” Am. J. Phys.
71
(6
), 607
–617
(2003
);H.
Goldring
and J.
Osborne
, “Students' difficulties with energy and related concepts
,” Phys. Educ.
29
(1
), 26
–32
(1994
);R. A.
Lawson
and L. C.
McDermott
, “Student understanding of the work-energy and impulse-momentum theorems
,” Am. J. Phys.
55
(9
), 811
–817
(1987
).2.
Richard P.
Feynman
, Robert B.
Leighton
, and Matthew
Sands
, The Feynman Lectures on Physics
(Addison-Wesley Pub. Co.
, Reading, Mass.
, 1963
), pp. 4
–2
.3.
Herman
Erlichson
, “Work and kinetic energy for an automobile coming to a stop
,” Am. J. Phys.
45
(8
), 769
(1977
);Claude
Penchina
, “Pseudowork and real work
,” Am. J. Phys.
46
(3
), 295
–296
(1978
);Bruce A.
Sherwood
, “Pseudowork and real work
,” Am. J. Phys.
51
(7
), 597
–602
(1983
);Hanna
Goldring
, “Energy revisited
,” Phys. Teach.
22
(5
), 318
(1984
);A.
John Mallinckrodt
and Harvey
Leff
, “All about work
,” Am. J. Phys.
60
(4
), 356
–365
(1992
);Robert
Bauman
, “Physics that textbook writers usually get wrong
,” Phys. Teach.
30
(5
), 264
–269
(1992
);Kenneth
Mendelson
, “Physical and colloquial meaning of the term ‘work
’,” Am. J. Phys.
71
(3
), 279
–281
(2003
).4.
René
Dugas
, A History of Mechanics
(Dover Pub., Inc.
, New York
, 1988
) <https://archive.org/details/historyofmachani000518mbp/page/n7>.5.
Reference 4, p.
128
.6.
7.
Eugene
Hecht
, “Kepler and the origins of pre-Newtonian mass
,” Am. J. Phys.
85
(2
), 115
–123
(2017
).8.
Paul G.
Hewitt
, Conceptual Physics
, 12th ed. (Addison-Wesley
, Reading, MA
, 2015
), p. G-10
.9.
Eugene
Hecht
, “There is no really good definition of mass
,” Phys. Teach.
44
(1
), 40
–45
(2006
).10.
Reference 6, p.
102
.11.
W. J.
Rolfe
and J. A.
Gillet
, Handbook of Natural Philosophy
(Potter, Ainsworth, and Co.
, NY
, 1869
), p. 275
.12.
13.
A.
Privat Deschanel
, Elementary Treatise on Natural Philosophy
(D. Appleton and Co.
, NY
, 1887
), p. 73
.14.
Robert
Millikan
and Henry
Gale
, A First Course in Physics
(Ginn & Co.
, Boston, MA
, 1906
), p. 162
.15.
16.
For example, see,
Erich
Hausmann
and Edgar
Slack
, Physics
(D. Van Nostrand Co.
, NY
, 1935
), p. 130
;Arthur
Beiser
, Physics
(The Benjamin Cummings Pub. Co.
, Menlo Park, CA
, 1978
), p. 842
;Edwin
Jones
and Richard
Childers
, Contemporary College Physics
(McGraw-Hill
, Boston, MA
, 1999
), p.181
.17.
For example, see,
Robert B.
Lindsay
, General Physics
(John Wiley & Sons
, London
, 1940
), pp. 88
–109
;Francis
Sears
and Mark
Zemansky
, University Physics
(Addison-Wesley Pub. Co.
, Reading, MA
, 1st ed. 1940), p. 117
(2nd ed., 1955
);Marcelo
Alonso
and Edward
Finn
, Fundamental University Physics
(Addison-Wesley Pub. Co.
, Reading, MA
, 1967
), pp. 195
–212
;Jerry
Wilson
and Anthony
Buffa
, College Physics
(Prentice Hall
, NJ
, 1997
), pp. 133
–141
;Richard
Wolfson
and Jay
Pasachoff
, Physics
(Addison-Wesley Pub. Co.
, Reading, MA
, 1999
), pp. 163
–187
;John
Cutnell
and Kenneth
Johnson
, Physics
, 5th ed. (John Wiley & Sons
, NY
, 2001
), pp. 151
–179
.18.
For example, see,
Hugh
Young
and Roger
Freedman
, University Physics
(Pearson
, San Francisco, CA
, 2004
), p. 207
;Raymond
Serway
and Cris
Vuille
, College Physics
(Cengage Learning
, Australia
, 2015
), pp. 127
–138
;19.
Raymond
Serway
and John
Jewett
, Physics for Scientists and Engineers
(Cengage Learning
, Australia
, 2014
), pp. 177
–202
.20.
Debora
Katz
, Physics for Scientists and Engineers
(Cengage Learning
, Australia
, 2016
), p. 215
.21.
22.
Randall
Knight
, Physics for Scientists and Engineers: A Strategic Approach
(Pearson Education
, Boston, MA
, 2017
), p. 207
.23.
Art
Hobson
, “Energy and work
,” Letter to the Editor, Phys. Teach.
42
, 260
(2004
).24.
Reference 8, p.
G-17
.25.
See, for example, Ref. 3,
A.
John Mallinckrodt
and Harvey
Leff
. Also see, Carl
Mungan
, “A primer on work-energy relationships for introductory physics
,” Phys. Teach.
43
(1
), 10
–15
(2005
);see also,
A. B.
Arons
, “Developing the energy concepts in introductory physics
,” Phys. Teach.
27
(10
), 506
–517
(1989
).26.
Reference 18, Giordano, p. 171; or Serway and Vuille, p. 133.
27.
28.
Albert
Einstein
, “On the relativity principle and the conclusions drawn from it
,” Jahrbuch Radioaktivität Elektronik
4
, 411
–462
(1907
).29.
30.
Clifford
Swartz
in “Why use the work-energy theorem?
” Letter to the Editor, Am. J. Phys.
72
, 1145
(2004
),agreed that “Work is just one way of transferring energy,”
Carl
Mungan
in “Work and energy
,” Letter to the Editor, Am. J. Phys.
73
, 197
(2005
) concurred: “it is correct to define work as an energy transfer.”;31.
Nancy
Hicks
, “Energy is the capacity to do work—or is it?
,” Phys. Teach.
21
(11
), 529
–530
(1983
);Robert
Lehman
, “Energy is not the ability to do work
,” Phys. Teach.
11
(1
), 15
–18
(1973
).32.
Eugene
Hecht
, “Energy and change
,” Phys. Teach.
45
(2
), 88
–92
(2007
).33.
34.
Compare Reference 8, 8th ed. p. 716 and 12th ed. p. G-6.
35.
Max
Planck
, Treatise on Thermodynamics
, 3rd English ed. (Dover
, NY
, 1945
), p. 41
. The idea that energy is “the capacity for producing physical change” goes back at least to the 1860s; see Ref. 12, Atkinson, p. 51.36.
Max
von Laue
, “Inertia and energy
,” in Albert Einstein Philosopher–Scientist
, edited by P.
Schilpp
(Harper Torchbooks
, NY
, 1951
), Vol. II
, pp. 503
–533
.37.
Eugene
Hecht
, “Relativity potential energy, and mass
,” Eur. J. Phys.
37
, 065804
(2016
);Eugene
Hecht
“An historic-critical account of potential energy: Is PE really real?
,” Phys. Teach.
41
(11
), 486
–493
(2003
).38.
Eugene
Hecht
, “Reply to a comment on ‘Relativity potential energy, and mass’
,” Eur. J. Phys.
40
, 028002
(2019
).39.
40.
41.
42.
John
Roche
, “What is potential energy?
” Eur. J. Phys.
24
(2
), 185
–196
(2003
).43.
Lev B.
Okun
, “The concept of mass (mass, energy, relativity)
,” Sov. Phys. Usp.
32
, 629
–638
(1989
);Lev B.
Okun
“The concept of mass
,” Phys. Today
42
(6
), 31
–36
(1989
);Gordon J.
Aubrecht
II, “Comment on ‘Apparatus to measure relativistic mass increase
’,” Am. J. Phys.
72
(7
), 970
–971
(2004
).44.
Albert
Einstein
and Leopold
Infeld
, The Evolution of Physics
(Simon and Schuster
, NY
, 1938
), p. 207
.See also
Carl G.
Adler
, “Does mass really depend on velocity, Dad?
,” Am. J. Phys.
55
, 739
–743
(1987
).45.
Albert
Einstein
, “The foundation of the general theory of relativity
,” in The Principle of Relativity
, translated by W.
Perrett
, and G. B.
Jeffery
(Dover Pub. Inc
, NY
, 1923
), p. 148
.46.
Dennis
Lehmkuhl
, “Mass-energy-momentum in general relativity. only there because of spacetime
,” Br. J. Philos. Sci.
62
(3
), 453
–488
(2011
).47.
Reference 36, p.
529
.48.
Eugene
Hecht
, “On defining mass
,” Phys. Teach.
49
(1
), 40
–44
(2011
).49.
Eugene
Hecht
, Physics In Perspective
(Addison Wesley Pub. Co.
, Reading, Mass.
, 1980
), p. 158
;Eugene
Hecht
, Physics: Algebra/Trig
, 3rd ed. (Brooks Cole Pub. Co.
, Pacific Grove, CA
, 2003
), p. 171
(1st ed. 1994, p. 278).For a philosophical discussion of energy as change see
Scientific Realism, Selected Essays of Mario Bunge
, edited by Martin
Mahner
(Prometheus Books
, Amherst, N.Y., 2001
), p. 51
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2019
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