Working Papers

High School Physics Revisited: Weight and
Mass from a Linguistic Point of View

R. Jeffrey Blair

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From Quality to Quantity
Scalar Numbers and Vectors

Discourse Communities
Measures of Amount
Semantic Complexity in the GDC

Semantic Complexity in the GDC

        The prescriptive SDC definitions of weight and mass designate proper use (see Jannedy, Poletto, and Weldon, 1994, 216) of the given terms in the field of science. To avoid ambiguity, a single definition has been agreed upon for each term. Similarly we will use definitions from Webster's New World Dictionary of the American Language (Guralnik, 1980) as a description of meanings in the GDC. Because the GDC has a much larger, more diverse population and very little linguistic control, our dictionary has not one, but seventeen definitions for weight and ten for mass. In the "real" world multiple definitions are the norm and there is a great deal of overlap in these definitions. The overlap makes it hard to distinguish exactly where one definition ends and another begins.

Since each of the verb definitions is associated with one or more of the nouns, we can probably eliminate them as majors source of semantic overlap and confusion in favor of the associated nouns. The specialized uses in definitions 9-12 occur in such restricted circumstances that they, too, are unlikely candidates for source of confusion. It is hard to see how figurative uses of weight--such as the weight of responsibility or a matter of great weight--could possibly be applied in the physical sciences. This leaves us with the first six core definitions of weight. Definitions 4-6, unlike the SDC definitions, refer to heavy objects or loads themselves, rather than the heavy quality of those objects and can thus be discarded. This leaves us with three remaining definitions

        Let us examine these three GDC definitions more closely to see how they might differ from the SDC definition of weight discussed above. Definition 1 stipulates objects of a definite weight. Yet SDC weight requires two objects (m and M) and depends on their distance apart (r). When I say my weight (m is me) is 80 kg (to people in Japan) or 174 pounds (to people in America), it has to be assumed that I am talking about my terrestrial weight (M is the Earth) on the surface of the Earth (r is 6,378 km from the center, ignoring my contribution of 0.000915 km). Balance scales and compression scales used to measure weight depend on a supporting surface. Throughout history until the twentieth century such a surface has had to be on or very close to the surface of the Earth. Until Armstrong took his "step for Mankind" on the Moon, airplanes cabins, the tops of high mountains, and space vehicles during the brief period of re-entry were as far as human weight was able to get away from the Earth's gravitational domination. Due to the lack of a supporting surface orbiting weight (see discussion below) has to be calculated, rather than measured. The human experience with lunar weight has been extremely brief, very few people and only from 1969 to 1972. While scientists tend to acknowledge the obvious and lawyers even build a great deal of redundancy into contracts and cross-examinations, the GDC usually tries to "be brief". Linguists refer to this as Grice's 3rd Maxim of Manner (Jannedy, Poletto, and Weldon, 1994, 238). It provide one possible explanation for why weight is treated as if it were an attribute of a single object. Everyone naturally assumes that any discussion of weight refers to terrestrial surface weight. Almost all non-scientists further assume that the the Earth is a sphere and the gravitational field at the surface is uniform. In reality the distance from the center of the Earth to its surface varies by about 21.7 km (13.5 miles) causing about a 0.5% variation in weight: heavier at the poles which is closer than the equator (Hamburg, 1993, 20). To be completely accurate about weight, we should specify what the latitude is.
        It would seem that location is simply not a factor in the GDC's notion of weight.

An alternate interpretation, however, is that GDC weight actually is independent of location. When someone says that they would weigh 29 pounds on the Moon, they are talking figuratively not literally. They are really talking about apparent weight. It would seem as if they weighed 29 pounds. The figurative meanings of weight in definitions 6-8, give such a metaphorical interpretation ample legitimacy. It is, of course, exactly this fuzzy kind of metaphorical use of key terms that the SDC seeks to avoid when fashioning their own precise prescriptive definitions.

        Definition 2 also ignores any influence that location might have until adding the GDC definition of the SDC meaning after the "physics" heading, where the force of gravity and the acceleration of gravity are literally factored in. This inclusion could have profound implications for use since both force and acceleration, like velocity, are vector quantities.

SDC Weight of Moving Objects

        So far we have considered only the weight of objects which are held stationary (a) on the surface of Earth or the Moon by the Earth or Moon's gravity or (b) in space by a balance of gravitational forces. The use of "acceleration" in the (GDC) definition of SDC weight, however, compels us to consider the weight of moving objects. Let us now consider the case of an orbiting object. If an object, like an artificial satellite, is in a stable orbit around the Earth at a high altitude, what is its SDC weight?
        The Earth's gravity certainly exerts a force upon the object and that accelerates the object toward the center of the Earth, so it has some (SDC) weight. The force of gravity and that acceleration are less than they would be close to the surface of the Earth because the force of gravity decreases as the distance from the center of the Earth increases (radius of the Earth plus altitude). For simplicity's sake we are disregarding the much smaller gravitational forces of the Moon, the Sun, and other distant celestial bodies. There is no balance of gravitational forces here. Yet the object maintains a fixed altitude (a stable orbit) because the gravitation force, perpendicular to the direction of the object's motion around the Earth produces a change in direction that matches the curvature of Earth. The orbiting object is actually in a free-fall situation--falling around and around the Earth but never hitting the surface. That is the geocentric perspective. From the satellite's perspective, the direction of the vectors of force would rotate around it canceling each other out with each complete orbit.
        According to either view, as long as the altitude remains fixed, the scalar weight of the satellite is constant, less than it would be at the Earth's surface but greater than zero, while its vector weight continually rotates around it. Astronauts may be weightless in GDC discourse, but they are NOT weightless according to our SDC definition.
        Semantic features can be used to analyze the varying degrees of this overlap in meaning and bring some order to an otherwise chaotic situation. Here is a list of some possible semantic features that might be useful in teasing through the various definitions of weight:

. . . . . . . definitions

features . . . . . . . .

1 . . . . . 2 . . . . . 3

the object
- + - - -
quantity +-?++
vector +----

Table 2 Semantic Features

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