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.

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
, and
P. 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.
Jennifer
Coopersmith
,
Energy the Subtle Concept
(
Oxford U.P.
,
Oxford
,
2010
), p.
61
.
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.
E.
Atkinson
,
Elementary Treatise on Physics
(
William Wood and Co.
,
NY
,
1886
), p.
50
.
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.
Ervin S.
Ferry
,
General Physics
(
John Wiley & Sons
,
Reading, NY
,
1928
), p.
104
.
16.
For example, see,
Erich
Hausmann
and
Edgar
Slack
,
Physics
(
D. Van Nostrand Co.
,
NY
,
1935
), p.
130
;
F.
Bueche
,
Principles of Physics
(
McGraw-Hill
,
NY
,
1972
), p.
90
;
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
;
Douglas
Giancoli
,
Physics
, 5th ed. (
Prentice Hall
,
NJ
,
1998
), pp.
145
167
;
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
;
Nicholas
Giordano
,
College Physics
(
Cengage Learning
,
Australia
,
2010
), pp.
165
176
.
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.
Jearl
Walker
,
Fundamentals of Physics
(
John Wiley & Sons
,
NY
,
2014
), p.
149
.
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.
James C.
Maxwell
,
Matter and Motion
(
Dover Pub. Inc.
,
Mineola, NY
,
1991
), p.
56
.
28.
Albert
Einstein
, “
On the relativity principle and the conclusions drawn from it
,”
Jahrbuch Radioaktivität Elektronik
4
,
411
462
(
1907
).
29.
Enrico
Fermi
,
Thermodynamics
(
Dover Pub. Inc.
,
Mineola, NY
,
1936
), pp.
12
15
.
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.”;
See
H. B.
Callen
,
Thermodynamics
(
John Wiley & Sons
,
New York
,
1962
), p.
7
.
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.
Frank
Wilczek
,
The Lightness of Being
(
Basic Books
,
New York, NY
,
1963
), p.
24
.
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.
Robert
Mills
,
Space, Time and Quanta
(
W. H. Freeman
,
NY
,
1994
), p.
151
.
40.
L. D.
Landau
and
E. M.
Lifshitz
,
Mechanics
(
Pergamon Press
,
Oxford
,
1960
), p.
7
.
41.
Albert
Einstein
, “
E = Mc2
,” in
Ideas and Opinions
(
Dell
,
New York
,
1976
), p.
330
.
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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