Section 14–1 Work

(The word “work” / Physical work / Physiological work)

In this section, Feynman discusses the word “work” and definitions of physical work and physiological work.

1. The word “work”:

“The physical word ‘work’ is not the word in the ordinary sense of ‘Workers of the world unite!,’ but is a different idea (Feynman et al., 1963, section 14–1 Work).”

Feynman explains that the word “work” does not have the same meaning as it is being used in a political slogan, “Workers of the world, unite!” In one of his Messenger Lectures, Feynman (1965) mentions that “physicists delight themselves by using ordinary words for something else (p. 84).” In his public lecture on QED, he adds that “[p]hysicists often use ordinary words such as ‘work’ or ‘action’ or ‘energy’ or even, as you shall see, “light” for some technical purpose. Thus, when I talk about ‘work’ in physics, I don’t mean the same thing as when I talk about ‘work’ on the street (Feynman, 1985, p. 10). However, some physicists advocate banning the word “work” from physics. They prefer to use the phrase “force-displacement product” or “force-displacement integral” (e.g., Hilborn, 2000).

It is worthwhile to mention a historical definition of work and to know how it was previously defined. In Calculation of the Effect of Machines, or Considerations on the Use of Engines and their Evaluation, Coriolis (1829) writes that “[w]e propose the appellation dynamical work, or simply work, for the quantity òPds… This name will not be confused with any other mechanical denomination. It seems suitable to give the right idea of the thing, by maintaining its common meaning of physical work… this name is then suitable to designate the union of the concepts, displacement, and force (Capecchi, 2012, p. 368).” Students should realize that physicists need to redefine work for more complicated problems in physics.

2. Physical work:

“Physical work is expressed as ∫F.ds, called ‘the line integral of F dot ds,’… (Feynman et al., 1963, section 14–1 Work).”

In general, physical work can be expressed as ∫F.ds and it means that if a force is in one direction and an object is forced to move in another direction, then only the component of force in the direction of the displacement contributes to the work done. Although the rule is simply “force times distance,” it is only the component of force in the same direction as the movement of the object times Δs or, equivalently, the component of displacement in the direction of the force (F) times the force. In certain mechanical problems, it is imprecise to define Δs as “the displacement of the object” or simply “the displacement.” Importantly, physicists need a more specific definition of Δs depending on the nature of a mechanical problem.

Some textbook authors simply specify Ds as the displacement of the point of application of the force. To be precise, the displacement of an object is not necessarily the same as the displacement of the center-of-mass of the object for a deformable or rotating object (Jewett, 2008). In complicated problems, one may need to redefine work or introduce terms such as “pseudo-work” or “center-of-mass work.” Interestingly, Mallinckrodt and Leff (1992) classify seven types of work that can be done on a system of particles interacting internally or with its environment. In essence, a definition of work is related to the nature of force (external or internal) and conditions such as an inertial frame of reference (frame dependent or frame invariant).

3. Physiological work:

“It is a fact that when one holds a weight he has to do “physiological” work (Feynman et al., 1963, section 14–1 Work).”

According to Feynman, there are two kinds of muscles in the human body: (1) striated or skeletal muscle is the type of muscle we have in our arms which is under voluntary control; (2) smooth muscle is like the muscle in the intestines which works very slowly. He adds that we have to generate effort for striated muscles to hold up a weight due to a need for enormous volleys of nerve impulses coming into the muscles. Biology students may disagree with Feynman’s classifications by describing a third kind of muscles that are known as cardiac muscles. However, physics teachers may elaborate that most of the muscles in the human body work like a third class lever systems (first class lever systems have the most mechanical advantage).

Another example of physiological work can be illustrated by a person pushing against a fixed wall. There is also no external work because the displacement of the wall is zero. In this case, a considerable amount of energy is expended in a human body to keep the muscles balanced during the act of pushing. On the other hand, the efficiency of the muscles is about 20% during cycling (Davidovits, 2008). In other words, about one-fifth of the chemical energy in the muscle is converted into useful work. Specifically, one may measure physiological work in terms of oxygen consumption and heart rate using a respirometer and cardio-tachometer.

Questions for discussion:

1. Should we use the phrase “force-displacement product” or “force-displacement integral” to replace the word work?

2. Is there a more rigorous definition of work in physics?

3. How would you explain the physiological work of holding a weight?

The moral of the lesson: physicists use ordinary words such as work that means ∫F.ds and it is called “the line integral of F dot ds”; the term ds needs to be redefined depending on the nature of mechanical problems.

References:

1. Capecchi, D. (2012). History of Virtual Work Laws: A History of Mechanics Prospective. Milan: Springer-Verlag Italia.

2. Coriolis, G. (1829). Du Calcul de l'effet des Machines, ou Considérations sur l'emploi des Moteurs et sur Leur Evaluation. Paris: Carilian-Goeury, Libraire.

3. Davidovits, P. (2008). Physics in Biology and Medicine (3rd Edition). Burlington: Elsevier.

4. Feynman, R. P. (1965). The character of physical law. Cambridge: MIT Press.

5. Feynman, R. P. (1985). QED: The strange theory of light and matter. Princeton: Princeton University Press.

6. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

7. Hilborn, R. C. (2000). Let’s ban work from physics!. The Physics Teacher, 38(7), 447-447.

8. Jewett Jr, J. W. (2008). Energy and the confused student I: Work. The Physics Teacher, 46(1), 38-43.

9. Mallinckrodt, A. J., & Leff, H. S. (1992). All about work. American Journal of Physics, 60(4), 356-365.