There has been and continues to be considerable discussion in the educational community about different ways of relating the concepts of work and energy in introductory physics.1 The present article reviews a consistent and streamlined treatment of the subject, drawing particular attention to aspects seldom covered in textbooks. The paper is intended to clarify the central equations for introductory courses and to put the wider literature in context. It is specifically designed to tie closely in terminology and order of presentation to standard texts, so that it complements rather than supplants them. In brief, the key point is that there are two major categories of work, center-of-mass work and particle work.2 After an overview of these two approaches, I illustrate them with a couple of instructive examples that can be used in group problem-solving sessions in class.
Topics
Educational aids
REFERENCES
1.
For example, see
A. J.
Mallinckrodt
and H. S.
Leff
, “All about work
,” Am. J. Phys.
60
, 356
–365
(April 1992
).2.
In partial agreement with
R. C.
Hilborn
, “Let's ban work from physics!
” Phys. Teach.
38
, 447
(Oct. 2000
), I encourage a careful verbal distinction between different kinds of work and an avoidance of the unsubscripted symbol W.3.
See the discussion of the “point-particle system” in R.W. Chabay and B.A. Sherwood, Matter & Interactions I: Modern Mechanics (Wiley, New York, 2002), Chap. 7.
4.
In this context, objects are assumed to be classical and to have mass. Thus, gravitational and electromagnetic fields, and massless particles, springs, strings, and rods are excluded; their role is limited to mediating the interactions between objects.
5.
A. B.
Arons
, “Development of energy concepts in introductory physics courses
,” Am. J. Phys.
67
, 1063
–1067
(Dec. 1999
).6.
This corresponds to a high-temperature specific heat per atom of (known as the Dulong-Petit rule), evident, for example, in Fig. 3 of
R. W.
Chabay
and B. A.
Sherwood
, “Bringing atoms into first-year physics
,” Am. J. Phys.
67
, 1045
–1050
(Dec. 1999
).7.
B. A.
Sherwood
, “Pseudowork and real work
,” Am. J. Phys.
51
, 597
–602
(July 1983
).8.
A particle is any object having no accessible internal degrees of freedom. It need not be microscopic. The rigid, isothermal, smooth, nonrotating blocks of introductory physics are a macroscopic example.
9.
There are no dissipative forces at the particle level. If there were, it would be possible for internal forces to change the energy of an isolated system! (Internal forces can change the net mechanical energy of two interacting macroscopic parts, but only with a compensating change in the internal energy of these same parts.) For example, the prototypical nonconservative force, friction, actually results from a sum over (conservative) electrostatic forces between the electron shells of the atoms in the contacting surfaces. In consequence, what is called internal work in
W. H.
Bernard
, “Internal work: A misinterpretation
,” Am. J. Phys.
52
, 253
–254
(March 1984
) is simply the negative of the change in the total (bulk plus internal) potential energy of the system.10.
Internal energy as used here is not identical with what thermodynamics texts usually refer to as internal energy. In the present context, it includes the energy of bulk rotations and other nonthermalized internal modes. See
M.
Alonso
and E. J.
Finn
, “On the notion of internal energy
,” Phys. Educ.
32
, 256
–264
(July 1997
).11.
Stored energy is traditionally divided into categories called “forms of energy” such as electric field energy, gravitational potential energy, chemical energy, and so on. But as argued in
G.
Falk
, F.
Herrmann
, and G. B.
Schmid
, “Energy forms or energy carriers?
” Am. J. Phys.
51
, 1074
–1077
(Dec. 1983
), why should one distinguish forms of energy any more than, say, forms of charge? It is only the carriers of the energy or charge, and not the energy or charge per se, that change.12.
For example, H.
Erlichson
, “Internal energy in the first law of thermodynamics
,” Am. J. Phys.
52
, 623
–625
(July 1984
) distinguishes work from heat on the basis of whether the force is macroscopic or microscopic. With the growing prevalence of microelectromechanical systems (MEMS), I think most physicists would be uncomfortable with this.A somewhat more common approach is that of
B. A.
Waite
, “A gas kinetic explanation of simple thermodynamic processes
,” J. Chem. Educ.
62
, 224
–227
(March 1985
), who distinguishes work and heat on the basis of whether the interaction is organized or random. While the logic behind this is evident for gases being acted upon by pistons or bunsen burners, it is far less helpful when thinking about dissipation via electrical resistance, kinetic friction, turbulent stirring, and the like.13.
M. W.
Zemansky
, “The use and misuse of the word ‘heat’ in physics teaching
,” Phys. Teach.
8
, 295
–300
(Sept. 1970
).Also see
R. H.
Romer
, “Heat is not a noun
,” Am. J. Phys.
69
, 107
–109
(Feb. 2001
);R. P.
Bauman
, “Physics that textbook writers usually get wrong: II. Heat and energy
,” Phys. Teach.
30
, 353
–356
(Sept. 1992
);G. M.
Barrow
, “Thermodynamics should be built on energy—Not on heat and work
,” J. Chem. Educ.
65
, 122
–125
(Feb. 1988
); andM.
Tribus
, “Generalizing the meaning of ‘heat’
,” Int. J. Heat Mass Transfer
11
, 9
–14
(Jan. 1968
).14.
H.
Erlichson
, “Are microscopic pictures part of macroscopic thermodynamics?
” Am. J. Phys.
54
, 665
(July 1986
) andS. G.
Canagaratna
, “Critique of the treatment of work
,” Am. J. Phys.
46
, 1241
–1244
(Dec. 1978
).15.
B. A.
Sherwood
and W. H.
Bernard
, “Work and heat transfer in the presence of sliding friction
,” Am. J. Phys.
52
, 1001
–1007
(Nov. 1984
).Also see the broken tailhook spring model in
R. P.
Bauman
, “Physics that textbook writers usually get wrong: I. Work
,” Phys. Teach.
30
, 264
–269
(May 1992
).16.
While the c.m. of the spool translates by L, the spool rotates through an angle of During this time, a length of string is unwound. The total displacement of point C is thus Note that this is consistent with the familiar results that point A (equivalent to ) has zero net velocity, point B has the c.m. velocity v, and point D has twice the c.m. velocity.
17.
As noted in
C.
Carnero
, J.
Aguiar
, and J.
Hierrezuelo
, “The work of the frictional force in rolling motion
,” Phys. Educ.
28
, 225
–227
(July 1993
), nonconservative forces need not be dissipative.18.
C. E.
Mungan
, “Acceleration of a pulled spool
,” Phys. Teach.
39
, 481
–485
(Nov. 2001
).19.
C. E.
Mungan
, “Irreversible adiabatic compression of an ideal gas
,” Phys. Teach.
41
, 450
–453
(Nov. 2003
).20.
H. S.
Leff
and A. J.
Mallinckrodt
, “Stopping objects with zero external work: Mechanics meets thermodynamics
,” Am. J. Phys.
61
, 121
–127
(Feb. 1993
).
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