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

Mental Images of the Act of Weighing

        The semantic representations of words often seem to include mental images (Jannedy, S., R. Poletto, and T. Weldon, 1994, 217). A word may thus conjure up a typical or ideal image. The typical image of bird might be a robin, eagle, or hawk, rather than a penguin or ostrich. What images are associated with the word "weight"? Being a quality, rather than an object, the image would probably involve an image of (a) the act of weighing something or (b) feeling weight when picking something up.
        GDC definition 3 above might, in fact, be interpreted as defining weight as the quantitative result of the act of weighing an object. We have already described the two most common methods for weighing objects on Earth: the balance scale and the compression scale. If there measurements are an integral part of the GDC definition, then we might ask ourselves whether those measurements are affected by location. What happens when we move a balance scale to a different location--a higher altitude or a different planet? Absolutely nothing. The SDC weight of everything changes in equal proportion, so the conditions to maintain balance--the "known" weights and their position on the lever--remain the same. The GDC weight, according to definition 3 using this kind of weighing machine, would give the same numerical value on the surface of any planet. The readings on a compression scale, however, will depend on location such that values on the Moon would be one sixth of what the machine registers on the Earth.
        The compression scale measure of weight is closely related to our second mental image of weight, the feeling of weight due to the downward pressure of our own body weight or the muscle tension necessary to hold a heavy object. These feelings and the readings of a compression scale are affected not only by gravity, but also by accelerations. Hewitt (1999, 186-187) acknowledges this "more practical" definition--"the force [an object exerts] against a supporting floor" rather than "the force of gravity that acts on [it]"--nine chapters after introducing weight and mass and illustrates it with an elevator ride. We feel a greater downward pressure when the elevator starts to go up, less when it starts to go down, and none (until we hit bottom) if the cable snaps sending us into a free fall. Similar accelerations can and do occur in horizontal directions whenever cars and trains accelerate or slow down, but weight seems to be considered a vertical phenomena only with direction determined by a single, dominant celestial body, usually at or close to its surface. Elevator rides and horizontal accelerations are temporary and artificial. There is, however, a slight, constant, natural acceleration due to the centrifugal force of the Earth's rotation (Hamburg, 1993, 20). It varies with latitude decreasing the weight of things located on the equator the most and less so towards the poles. And how should we treat buoyancy? When we step into some water does our weight decrease as we wade deeper becoming zero or even negative when we begin to float? Our downward pressure does decrease and may even become upward pressure. Hewitt does not make clear whether his "more practical" definition is valid within the SDC or simply an example of GDC practicality.
        We could say that the balance scale measures SDC mass, while the compression scale measures SDC weight. Yet both are used to "weigh" objects and find their GDC weight. There is no special verb associated with mass, as opposed to weight, in either the SDC or the GDC. In fact, the GDC usually uses the noun "mass" to describe an unquantifiable but large amount of matter itself rather than a specific quantity of heaviness. According to Webster's New World Dictionary of the American Language (Guralnik, 1980, 872):

Units of Weight and Mass

        We have been looking at some of the factors that influence the readings of scales that measure weight--looking, that is, at the numbers. The numbers for SDC weight and SDC mass of an object in a fixed location are always proportional, but uses different units (Hewitt, 1999, 49). The international scientific community and most of the world, including Japan, use the metric system: kilograms for mass and Newtons for force. In the United States, however, the amount of matter (i.e. mass) is described by its weight in pounds (Hewitt, 1999, 50). One kilogram exerts a force of 9.8 Newtons or 2.2 pounds (of pressure) at the surface of the Earth. Since SDC weight is prescriptively defined as gravitational force weight can be measured in Newtons or pounds. GDC weight is usually descriptively defined as a measure of heaviness, which is measured in pounds on scales in the United States and by kilograms on scales in most of the world (see table 3 below).

. . . . . . . country

word . . . . . . . .
United States Most Countries
GDC forcepound
(of pressure)
SDC force
and weight
GDC weightpoundkilogram
SDC massslugkilogram

Table 3 Units of Force, Weight, and Mass

        In physics the focus is on SDC mass and the motion of planets, cannon balls, and atomic particles. Whereas in the GDC focus is on amounts--size, volume, and GDC weight--of various economic commodities measured on the surface of a hard and apparently flat surface with a nearly uniform field of gravity. SDC mass for planets and atomic particles cannot be measured directly, it must be calculated from the motions that scientists observe. For cannon balls and other moderately sized objects, scientists could measure SDC mass on the basis of centrifugal forces by swinging them in horizontal circles or momentum by crashing them into other objects of known mass, but it is much easier and more common simply to weigh them on a scale. For the everyday objects around us SDC mass and GDC weight are measured in the same way.
        In Japan I step on a scale that measures my heaviness as 80 kilogams, in America a scale that measures it as 174 pounds. The scales are the same and could just as easily be calibrated in Newtons or slugs. All four values are proportional. It seems arbitrary to label two values, Newtons and pounds, as weight, the values in kilograms and slugs as mass, and treat them as two completely different entities. As long as all four measures remain proportional they can be considered measures of the same phenomenon--heaviness. The first, most salient meaning in the GDC for "heavy" (Guralnik 1980, 647) is "hard to lift or move because of great weight [italics added]" (Guralnik, 1980, 647). It is very interesting that both lift and move are used in this definition. The term "lift" seems to emphasize the role of gravity, while "move" (horizontally or in a gravity free environment) would seem to include the role of inertia. The constant of proportionality can be incorporated into any one of these units during the calibration of the measuring device.

Conclusions and
a Linguistic Solution

        The fundamental difference between SDC weight and mass is to be found in the mathematical expressions for each after they have been stripped of units and constant factors.

Object 1 Object 2
SDC massmM
SDC weightm (M / r 2) M (m / r 2)
GDC weightm (597 / 6,378 2)n.a.

Table 4 Formulas of Weight and Mass for a Binary Component

Mass has only one variable (m or M). It is a simple, single-object attribute. Weight requires at least two objects and three independent variables (m, M, and r) to characterize a binary component. More complex systems can be analyzed in terms of force vectors with each vector representing a component. Thus SDC weight should be considered a joint attribute of an independent binary entity. Traditionally a binary component consists of a relatively small object and a celestial body. For several reason binary components can be often be treated in isolation: (a) gravitation is an extremely weak force, (b) the mass of our solar system and universe are concentrated in oblong, almost spherical bundles called stars and planets, and (c) these celestial bodies are separated by large empty spaces.
        We can take advantage of this situation by treating each as a separate entity and giving them names. My total weight is really a composite of these components: my terrestrial weight, my lunar weight, et cetera. What happens to my weight if I travel to the Moon? The lunar component increases as the terrestrial component decreases. It is the lunar surface weight that is one-sixth of the terrestrial surface weight. This terminology makes it clear that we are comparing two very different entities. What about my solar weight? It is there but it escapes notice for two reasons: (1) it is very small, only 0.0006 of the terrestrial surface weight and (2) we, the Earth, and the Moon are all orbiting the Sun together. Since our masses are exactly proportional to our respective forces of gravitation, we all undergo the exact same accelerations and maintain the same velocities.

GeneralScientific Proposed
.SDC weight solar weight
terrestrial weight
lunar weight

surface weight
contact weight

GDC weightSDC mass terrestrial surface weight
GDC mass..

Table 5 Relationship of Terms

        When objects are falling or floating they do not feel their weight. You only feel your weight when you make contact with a surface that presses its weight against yours. The contribution of each object's mass is completely symmetric and indistinguishable from the other's. The weight of the Earth on my surface is the same as my weight on the surface of the Earth. It is when surfaces are in contact that we can feel the pressure their weight exerts and by slipping a scale between them measure that weight directly.
        The GDC concept of weight is a consequence of a flat-Earth mentality, which has worked quite well for centuries and continues to do so, because of the nearly uniform gravitational field at the surface of the Earth. There is some deviation from complete uniformity due to the oblateness of the Earth, but it is slight. There are also some extraneous forces that may distort the measurement and the feeling of weight. Because they are temporary, horizontal, or very slight they pose almost no threat to our flat-Earth state of mind, in which GDC weight and mass are indistinguishable. GDC weight and mass are the same as SDC terrestrial surface weight which can be thought of as the standard for SDC mass.
        It is only when we leave the surface of the Earth that the distinction between SDC weight and SDC mass becomes important. A spaceship Earth mentality brings with it a new image of weight. Not a single object resting on top of scale, but two objects, one very large and one very small, side by side with a compression scale between them measuring the pressure of their mutual attraction, otherwise known as weight.

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