Chapter 7-PRINCIPLES OF MEASUREMENT 



object or body, is completely independent of the 

 force of gravity, so the mass of any given ob- 

 ject is always the same, no matter where it is 

 located on the surface of the earth; indeed, the 

 body would have the same mass even if it were 

 located at the center of the earth, on the moon, 

 in outer space, or anywhere else. Weight , on 

 the other hand, is a measure of the force of 

 attraction between the mass of the earth and 

 the mass of another body or object. Since the 

 force of attraction between the earth and another 

 body is not identical in all places, the weight of 

 a body depends upon the location of the body 

 with respect to the earth. 



The relationship between mass and weight 

 can be understood from the equation 



w 



ms 



where 



w = weight 



m= mass 



g = acceleration due to gravity 



The value for acceleration due to gravity 

 (normally represented by the letter g) is almost 

 constant for bodies at or near the surface of the 

 earth. This value is approximately 32 feet per 

 second per second in British systems of meas- 

 urement, 9.8 meters per second per second in 

 one metric system, and 980 centimeters per 

 second per second in another metric system. 

 More precise values of g, including variations 

 that occur with changes in latitude and changes 

 in elevation, may be obtained from physics and 

 engineering textbooks and handbooks. 



BASIC MECHANICAL UNITS 



Table 7-1 shows the basic mechanical quan- 

 tities of length, mass or force, and time, to- 

 gether with a number of derived units, used in 

 several systems of measurement. By examin- 

 ing some of the units, we may see how force 

 is defined and thus see why each system is 

 called "absolute" or "gravitational," as the 

 case may be. 



In the metric absolute meter-kilogram- 

 second (MKS) system of measurement, the unit 

 of mass is the kilogram, the unit of length is 

 the meter, the unit of time is the second, and 

 the unit of acceleration is meters per second 

 per second. (This is sometimes written as 

 m/sec2.) The unit of force is called a Newton. 



By definition, 1 newton is the force required to 

 accelerate a mass of 1 kilogram at the rate of 1 

 meter per second per second. In other words, 

 the unit of force is defined in such a way that 

 unit force gives unit acceleration to unit mass. 



^The same thing holds true in the other metric 

 absolute system shown in table 7-1. In the 

 metric absolute centimeter-gram-second (CGS) 

 system of measurement, the gram is the unit 

 of mass, the centimeter is the unit of length, 

 the second is the unit of time, and centimeters 

 per second (cm/sec^) is the unit of accelera- 

 tion. In this system, the unit of force is called 

 a dyne. By definition, 1 dyne is the force re- 

 quired^ to accelerate a mass of 1 gram at the 

 rate of 1 centimeter per second per second. 

 Again, force is defined in such a way that unit 

 force gives unit acceleration to unit mass. 



The same applies to the British absolute 

 foot-pound-second (FPS) system of measure- 

 ment, where the pound is the unit of mass, the 

 foot is the unit of length, the second is the unit 

 of time, and feet per second per second is the 

 unit of acceleration. In this system, the unit of 

 force is called a poundal. By definition, 1 

 poundal is the amount of force required to give 

 a mass of 1 pound an acceleration of 1 foot per 

 second per second. Again, force is defined in 

 such a way that unit force gives unit accelera- 

 tion to unit mass. 



Now let's look at a British gravitational 

 system— the foot-pound-second (FPS) gravita- 

 tional system that we use in the United States 

 for most everyday measurements. The foot is 

 the unit of length, the pound is the unit of mass, 

 the second is the unit of time, and feet per 

 second per second is the unit of acceleration. 

 In this system, the unit of force is called the 

 pound. (Actually, it should be called the pound- 

 force; but this usage is rarely followed.) in 

 this system, a force of 1 pound acting upon a 

 mass of 1 pound produces an acceleration of 32 

 feet per second per second. Note that unit 

 force does not produce unit acceleration when 

 acting on unit mass; rather, unit force produces 

 unit acceleration when acting on unit weight. 

 Since force is defined in gravitational terms, 

 rather than in absolute terms, we say that this 

 is a gravitational system of measurement. 



The gravitational system that is usually 

 called the British Engineering System also uses 

 the pound (or, more precisely, the pound-force) 

 as the unit of force. But this system has its 

 own unit of mass: the slug . By definition, 1 

 slug is the quantity of mass that is accelerated 



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