Principles of naval engineering - Historic Naval Ships Association

Chapter 7-PRINCIPLES OF MEASUREMENTobject or body, is completely independent of theforce of gravity, so the mass of any given objectis always the same, no matter where it islocated on the surface of the earth; indeed, thebody would have the same mass even if it werelocated at the center of the earth, on the moon,in outer space, or anywhere else. Weight,onthe other hand, is a measure of the force ofattraction between the mass of the earth andthe mass of another body or object. Since theforce of attraction between the earth and anotherbody is not identical in all places, the weight ofa body depends upon the location of the bodywith respect to the earth.The relationship between mass and weightcan be understood from the equationwherewmsw = weightm= massg = acceleration due to gravityThe value for acceleration due to gravity(normally represented by the letter g) is almostconstant for bodies at or near the surface of theearth. This value is approximately 32 feet persecond per second in British systems of measurement,9.8 meters per second per second inone metric system, and 980 centimeters persecond per second in another metric system.More precise values of g, including variationsthat occur with changes in latitude and changesin elevation, may be obtained from physics andengineering textbooks and handbooks.BASIC MECHANICAL UNITSTable 7-1 shows the basic mechanical quantitiesof length, mass or force, and time, togetherwith a number of derived units, used inseveral systems of measurement. By examiningsome of the units, we may see how forceis defined and thus see why each system iscalled "absolute" or "gravitational," as thecase may be.In the metric absolute meter-kilogramsecond(MKS) system of measurement, the unitof mass is the kilogram, the unit of length isthe meter, the unit of time is the second, andthe unit of acceleration is meters per secondper second. (This is sometimes written asm/sec2.) The unit of force is called a Newton.By definition, 1 newton is the force required toaccelerate a mass of 1 kilogram at the rate of 1meter per second per second. In other words,the unit of force is defined in such a way thatunit force gives unit acceleration to unit mass.^The same thing holds true in the other metricabsolute system shown in table 7-1. In themetric absolute centimeter-gram-second (CGS)system of measurement, the gram is the unitof mass, the centimeter is the unit of length,the second is the unit of time, and centimetersper second (cm/sec^) is the unit of acceleration.In this system, the unit of force is calleda dyne. By definition, 1 dyne is the force required^to accelerate a mass of 1 gram at therate of 1 centimeter per second per second.Again, force is defined in such a way that unitforce gives unit acceleration to unit mass.The same applies to the British absolutefoot-pound-second (FPS) system of measurement,where the pound is the unit of mass, thefoot is the unit of length, the second is the unitof time, and feet per second per second is theunit of acceleration. In this system, the unit offorce is called a poundal. By definition, 1poundal is the amount of force required to givea mass of 1 pound an acceleration of 1 foot persecond per second. Again, force is defined insuch a way that unit force gives unit accelerationto unit mass.Now let's look at a British gravitationalsystem— the foot-pound-second (FPS) gravitationalsystem that we use in the United Statesfor most everyday measurements. The foot isthe unit of length, the pound is the unit of mass,the second is the unit of time, and feet persecond per second is the unit of acceleration.In this system, the unit of force is called thepound. (Actually, it should be called the poundforce;but this usage is rarely followed.) inthis system, a force of 1 pound acting upon amass of 1 pound produces an acceleration of 32feet per second per second. Note that unitforce does not produce unit acceleration whenacting on unit mass; rather, unit force producesunit acceleration when acting on unit weight.Since force is defined in gravitational terms,rather than in absolute terms, we say that thisis a gravitational system of measurement.The gravitational system that is usuallycalled the British Engineering System also usesthe pound (or, more precisely, the pound-force)as the unit of force. But this system has itsown unit of mass: the slug . By definition, 1slug is the quantity of mass that is accelerated121