Machinery's Handbook, 31st Edition
Mechanics 157 Acceleration is the time-rate of change of velocity and is expressed as velocity divided by time or as distance divided by time squared, that is, in feet per second per second or feet per second squared (ft/sec 2 ); inches per second per second or inches per second squared (in/sec 2 ); centimeters per second per second or centimeters per second squared (cm/sec 2 ); etc. The metric SI unit is the meter per second squared (m/sec 2 ). Unit Abbreviations.— Standard abbreviations for the units of physical quantities are used throughout the Handbook. Comprehensive tables of unit abbreviations are found starting on page 2827 for US units, and on page 2832 for metric units. Unit Systems.— In mechanics calculations, both absolute and gravitational systems of units are employed. The fundamental quantities in absolute systems are length , time , and mass , and from these the dimension of force is derived. Two absolute systems that have been in use for many years are the CGS (centimeter-gram-second) and the MKS (meter- kilogram-second) systems. They are named for the fundamental units of length, mass and time, respectively. Another system known as MKSA (meter-kilogram-second-ampere) links the MKS system of units of mechanics with electromagnetic units. The General Conference of Weights and Measures (CGPM), which is the body responsible for all international matters concerning the metric system, adopted in 1954 a rationalized and coherent system of units based on the four MKSA units, including the kelvin as the unit of temperature and the candela as the unit of lumi nous intensity. In 1960, the CGPM formally named this system the “Système Inter national d’Unités,” for which the abbreviation is SI in all languages. In 1971, the 14th CGPM adopted a seventh base unit, the mole, which is the unit of quantity (“amount of substance”). Further details of the SI are given in the section MEASURING UNITS starting on page 2831 , and its application in mechanics calculations, contrasted with the use of the English system, is considered below. The fundamental quantities in gravitational systems are length , time , and force , and from these units, the dimension of mass is derived. In the gravitational system most widely used in English measure countries, the units of length, time, and force are, respec- tively, the foot (ft), the second (s or sec), and the pound (lb). The corresponding unit of mass, commonly called the slug , is equal to 1 lb-s 2 /ft and is derived from the formula, M = W/g in which M = mass in slugs, W = weight in pounds, and g = acceleration due to gravity, commonly taken as 32.16 ft/s 2 . A body that weighs 32.16 lbs on the surface of the earth has, therefore, a mass of 1 slug. Many engineering calculations utilize a system of units consisting of the inch,the sec ond, and the pound. The corresponding units of mass are pounds second squared per inch (lb-s 2 /in) and the value of g is taken as 386 in/s 2 . In a gravitational system that has been widely used in metric countries, the units of length, time, and force are, respectively, the meter, the second, and the kilogram-force (1 kgf = 9.80665 N). The corresponding units of mass are kgf-s 2 /m and the value of g is taken as 9.81 m/s 2 . Acceleration of Gravity g Used in Mechanics Formulas.— The acceleration of a freely falling body varies according to location on the earth’s surface as well as the height from which the body falls. Its value measured at sea level at the equator is 32.09 ft/sec 2 while at the poles is 32.26 ft/sec 2 . In the United States it is customary to regard 32.16 as satisfactory for most practical purposes in engineering calculations. Standard Pound Force: For use in defining the magnitude of a standard unit of force, known as the pound force , a fixed value of 32.1740 ft/sec 2 , designated by the symbol g 0 , has been adopted by international agreement. As a result of this agreement, whenever the term mass, M , appears in a mechanics formula and the substitution M = W / g is made, use of the standard value g 0 = 32.1740 ft/sec 2 is implied, although as stated previously, it is customary to use approximate values for g except where extreme accuracy is required.
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