Machinery's Handbook, 31st Edition
158 Mechanics Use of Metric SI System in Mechanics Calculations.— The SI system is a development of the traditional metric system based on decimal arithmetic; fractions are avoided. For each physical quantity, units of different sizes are formed by multiplying or dividing a single base value by powers of 10. Conversions can be made simply by adding zeros or shifting decimal points. For example, the meter is the basic unit of length; kilo meter is a multiple (1000 meters); and milli meter is a sub-multiple (1/1000 of a meter). In the older metric system, the simplicity of a series of units linked by powers of 10 is an advantage for plain quantities such as length, but this simplicity is lost as soon as more complex units are encountered. For example, in different branches of science and engineering, energy may appear as the erg, calorie, kilogram-meter, liter-atmosphere, or horsepower-hour. In contrast, the metric SI provides only one basic unit for each physical quantity, and universality is thus achieved. There are seven base units, and in mechanics calculations three are used, which are for the basic quantities of length, mass, and time, expressed as meter (m), kilogram (kg), and second (s). The other four base-units are ampere (A) for electric current, kelvin (K) for thermodynamic temperature, candela (cd) for luminous intensity, and mole (mol) for amount of substance. The SI is a coherent system. A system of units is said to be coherent if the product or quo tient of any two unit quantities in the system is the unit of the resultant quantity. For exam ple, in a coherent system in which the foot is a unit of length, the square foot is the unit of area, whereas the acre is not. Further details of the SI, and definitions of the units are given in the section MEASURING UNITS starting on page 2831 , near the end of the Handbook. Additional units of physical quantities are derived from the base-units. For example, the unit of velocity is meter per second (m/s), which is a combination of the base-units of length and time. The unit of acceleration is meter per second squared (m/s 2 ). By applying Newton’s second law of motion, force is proportional to mass multiplied by acceleration: The unit of force is obtained, which is kg·m/s 2 . This unit is the newton, or N. Work, the product of force and distance, has units of kg·m 2 /s 2 , which is the joule, or J. (1 J = 1 N·m) and energy is also expressed in these terms. Power, or work per unit time, has units of kg·m 2 /s 3 , which is the watt, or W. (1 W = 1 J/s = 1 N·m/s). Information on Newton’s laws may be found in Newton’s Laws of Motion on page 182 . The coherence of SI units has two important advantages. The first, that of uniqueness and therefore universality, has been explained. The second is that it greatly simplifies technical calculations. Equations representing physical principles can be applied without introducing such numbers as 550 in power calculations, which, in the English system of measurement have to be used to convert units. Thus, conversion factors largely disappear from calculations carried out in SI units, with a great saving in time and labor. Mass, Weight, Force, Load: SI is an absolute system (see Unit Systems on page 157 ), and consequently it is necessary to make a clear distinction between mass and weight. The mass of a body is a measure of its inertia, which is unaffected by gravity whereas the weight of a body is the force exerted on it by gravity. In a fixed gravitational field, weight is directly proportional to mass, and the distinction between mass and weight can be easily overlooked. However, if a body is moved to a different gravitational field, for example, that of the moon, its weight alters, but its mass remains unchanged. Because the gravitational field on earth varies from place to place by only a small amount, and because weight is proportional to mass, it is practical to use the weight of unit mass as a unit of force, and this procedure is adopted in both the English and older metric systems of measurement. In common usage, they are given the same names, and we say that a mass of 1 pound has a weight of 1 pound. In the former case the pound is being used as a unit of mass, and in the latter case, as a unit of force. This procedure is convenient in some branches of engineer- ing, but leads to confusion in others.
Copyright 2020, Industrial Press, Inc.
ebooks.industrialpress.com
Made with FlippingBook - Share PDF online