25
The kilogram
The 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 by measuring our planetís
gravitational attraction for the object being weighed, but using that type of
scale to define mass operationally would be undesirable because gravity
varies in strength from place to place on the earth.
Thereís a surprising amount of disagreement among physics textbooks
about how mass should be defined, but hereís how itís actually handled by
the few working physicists who specialize in ultra-high-precision measure-
ments. They maintain a physical object in Paris, which is the standard
kilogram, a cylinder made of platinum-iridium alloy. Duplicates are
checked against this mother of all kilograms by putting the original and the
copy on the two opposite pans of a balance. Although this method of
comparison depends on gravity, the problems associated with differences in
gravity in different geographical locations are bypassed, because the two
objects are being compared in the same place. The duplicates can then be
removed from the Parisian kilogram shrine and transported elsewhere in the
world.
Combinations of metric units
Just about anything you want to measure can be measured with some
combination of meters, kilograms, and seconds. Speed can be measured in
m/s, volume in m
3
, and density in kg/m
3
. Part of what makes the SI great is
this basic simplicity. No more funny units like a cord of wood, a bolt of
cloth, or a jigger of whiskey. No more liquid and dry measure. Just a simple,
consistent set of units. The SI measures put together from meters, kilo-
grams, and seconds make up the mks system. For example, the mks unit of
speed is m/s, not km/hr.
Discussion question
Isaac Newton wrote, ď...the natural days are truly unequal, though they are
commonly considered as equal, and used for a measure of time... It may be
that there is no such thing as an equable motion, whereby time may be
accurately measured. All motions may be accelerated or retarded...Ē Newton
was right. Even the modern definition of the second in terms of light emitted by
cesium atoms is subject to variation. For instance, magnetic fields could cause
the cesium atoms to emit light with a slightly different rate of vibration. What
makes us think, though, that a pendulum clock is more accurate than a
sundial, or that a cesium atom is a more accurate timekeeper than a pendulum
clock. That is, how can one test experimentally how the accuracies of different
time standards compare.
0.6The Newton, the Metric Unit of Force
A force is a push or a pull, or more generally anything that can change
an objectís speed or direction of motion. A force is required to start a car
moving, to slow down a baseball player sliding in to home base, or to make
an airplane turn. (Forces may fail to change an objectís motion if they are
canceled by other forces, e.g. the force of gravity pulling you down right
now is being canceled by the force of the chair pushing up on you.) The
metric unit of force is the Newton, defined as the force which, if applied for
one second, will cause a 1-kilogram object starting from rest to reach a
Section 0.6The Newton, the Metric Unit of Force
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