Accurate physical laws can permit new standard units: The two laws F=ma and the proportionality of weight to mass
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2014 American Association of Physics Teachers. Three common approaches to F =ma are: (1) as an exactly true definition of force F in terms of measured inertial mass m and measured acceleration a; (2) as an exactly true axiom relating measured values of a, F and m; and (3) as an imperfect but accurately true physical law relating measured a to measured F, with m an experimentally determined, matter-dependent constant, in the spirit of the resistance R in Ohm's law. In the third case, the natural units are those of a and F, where a is normally specified using distance and time as standard units, and F from a spring scale as a standard unit; thus mass units are derived from force, distance, and time units such as newtons, meters, and seconds. The present work develops the third approach when one includes a second physical law (again, imperfect but accurate)-that balance-scale weight W is proportional to m-and the fact that balance-scale measurements of relative weight are more accurate than those of absolute force. When distance and time also are more accurately measurable than absolute force, this second physical law permits a shift to standards of mass, distance, and time units, such as kilograms, meters, and seconds, with the unit of force-the newton-a derived unit. However, were force and distance more accurately measurable than time (e.g., time measured with an hourglass), this second physical law would permit a shift to standards of force, mass, and distance units such as newtons, kilograms, and meters, with the unit of time-the second-a derived unit. Therefore, the choice of the most accurate standard units depends both on what is most accurately measurable and on the accuracy of physical law.
American Journal of Physics
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