Simple Nature - Light and Matter

The kilogramThe third base unit of the SI is the kilogram, a unit of mass.Mass is intended to be a measure of the amount of a substance,but that is not an operational definition. Bathroom scales work bymeasuring our planet’s gravitational attraction for the object beingweighed, but using that type of scale to define mass operationallywould be undesirable because gravity varies in strength from placeto place on the earth.There’s a surprising amount of disagreement among physics textbooksabout how mass should be defined, but here’s how it’s actuallyhandled by the few working physicists who specialize in ultra-highprecisionmeasurements. They maintain a physical object in Paris,which is the standard kilogram, a cylinder made of platinum-iridiumalloy. Duplicates are checked against this mother of all kilogramsby putting the original and the copy on the two opposite pans of abalance. Although this method of comparison depends on gravity,the problems associated with differences in gravity in different geographicallocations are bypassed, because the two objects are beingcompared in the same place. The duplicates can then be removedfrom the Parisian kilogram shrine and transported elsewhere in theworld. It would be desirable to replace this at some point with auniversally accessible atomic standard rather than one based on aspecific artifact, but as of 2010 the technology for automated countingof large numbers of atoms has not gotten good enough to makethat work with the desired precision.Combinations of metric unitsJust about anything you want to measure can be measured withsome combination of meters, kilograms, and seconds. Speed can bemeasured in m/s, volume in m 3 , and density in kg/m 3 . Part of whatmakes the SI great is this basic simplicity. No more funny units likea cord of wood, a bolt of cloth, or a jigger of whiskey. No moreliquid and dry measure. Just a simple, consistent set of units. TheSI measures put together from meters, kilograms, and seconds makeup the mks system. For example, the mks unit of speed is m/s, notkm/hr.f / A duplicate of the Pariskilogram, maintained at the DanishNational Metrology Institute.Checking unitsA useful technique for finding mistakes in one’s algebra is toanalyze the units associated with the variables.Checking units example 2⊲ Jae starts from the formula V = 1 3Ah for the volume of a cone,where A is the area of its base, and h is its height. He wants tofind an equation that will tell him how tall a conical tent has to bein order to have a certain volume, given its radius. His algebra26 Chapter 0 Introduction and Review