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2.1: Untitled Page 13

  • Page ID
    18146
  • Chapter 2

    Units

    There are three things that every engineer should understand about units.

    First, the fundamental significance of units must be understood. Second, the conversion from one set of units to another must be a routine matter. Third, one must learn to use units to help prevent the occurrence of algebraic and conceptual errors. The second of these is emphasized by the following: In the Sacramento Bee, November 11, 1999 one finds the headline, Training faulted in loss of $125 million Mars probe, and in the article that follows one reads, “The immediate cause of the spacecraft’s Sept. 23 disappearance as it entered Mars orbit was a failure by a young engineer…...to make a simple conversion from English units to metric…..”

    Physics is a quantitative science. By this we mean that the physicist attempts to compare measured observables with values predicted from theory. There is basically only one measuring process and that is the process of counting. For example, the distance between two points is determined by counting the number of times that a standard length fits between the two points. Often we call this length a unit length. The business of measuring began with the Egyptians, but we are generally more familiar with the work of the Greek geometers such as Pythagoras. In physics, the process of performing experiments and measuring observables is often attributed to Galileo (1564‐1642). The process of measuring by counting standard units can be described as (Hurley and Garrod, 1978):

    “Since the measurement process is one of counting multiples of some chosen standard, it is reasonable to ask how many standards we need. If we need a standard for each observable, we will need a large Bureau of Standards. As a matter of fact, we need only four standards: a standard of length, a standard of mass, a standard of time, and a standard of electric charge. This is an extraordinary fact. It means that if one is equipped with a set of these four standards and the ability to count, one can ( in principle) assign a numerical value to any observable, be it distance, velocity, viscosity, temperature, pressure, etc.”

    Here we find that our confrontation with units begins with a great deal of simplicity since we require only the following four fundamental standards: 12

    Units

    13

    LENGTH

    MASS

    TIME

    ELECTRIC CHARGE

    The reason for this simplicity is that observables, in one way or another, must satisfy the laws of physics, and these laws can be quantified in terms of length, mass, time and electric charge.

    Although the concept of a standard is simple, the matter is complicated by the fact that the choice of a standard is arbitrary. For example, a football player prefers the yard as a standard of length because one yard is significant and 100

    yards represents an upper bound for the domain of interest. The carpenter prefers the foot as a standard of length since one foot is significant and the distance of one hundred feet spans the domain of interest for many building projects. For the same reasons, a truck driver prefers the mile as a standard of length, i.e., one of them is significant and one hundred of them represents a certain degree of accomplishment. It is a fact of life that people like to work in terms of standards that give rise to counts somewhere between one and one hundred and we therefore change our standards to fit the situation. While the football player thinks in terms of yards on Saturday, his Sunday chores are likely to be measured in feet and the distance to the next game will surely be thought of in terms of miles. Outside of the United States, a football player (soccer) thinks in terms of meters on Saturday, perhaps centimeters on Sunday, and the distance to the next match will undoubtedly be determined in kilometers.

    2.1 International System of Units

    In 1960 a conference was held in Paris to find agreement on a set of standards.

    From that conference there arose what are called the SI (Système International) system of basic units which are listed in Table 2‐1. Note that the SI system does not use the electric charge as a standard, but rather the electric charge per unit time or the electric current. In addition, the SI system of basic units includes three additional units, the thermodynamic temperature, the mole, and the luminous intensity. These three additional units are not necessary to assign numerical values to any observable, thus their role is somewhat different than the four fundamental standards identified by Hurley and Garrod. For example, a mole consists of

    23

    6.02209...  10 entities such as atoms, molecules, photons, etc., while the basic unit associated with counting entities is one. This point has been emphasized by Feynman et al. (1963) who commented that: “We use 1 as a unit, and the chemists use 6  1 23

    0 as a unit!” Nevertheless, a mole is a convenient unit

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