knowledge, science, and the universe chapter 1 - Physical Science ...

SECTION 2–5 The Second Law of Motion 23
STANDARDS OF MEASUREMENT
As we have already noted in this chapter, mass is the property of objects that determines
how much they accelerate in response to a force. To be useful, the concept of mass must
be made quantitative. To shop for dinner we need to know, for example, whether a sack of
potatoes has a mass of one kilogram or two kilograms. Quantities of mass are defined by
comparison to a standard. The standard measurement of one kilogram has been decreed
to be the mass of a specific piece of platinum- iridium which is kept under the watchful care
of the Bureau Internationals des Poids et Measures at Sevres, near Paris, France. To know if
you have one kilogram of potatoes, you must directly or indirectly compare the mass of your
potatoes with the mass of this piece of metal.
Obviously, neither you nor your grocer are going to take that sack of potatoes to France
to make sure you’re getting exactly one kilogram of spuds. To make weighing objects against
standards both exact and practical, copies of the standard kilogram are supplied to
government bureaus of standards around the world. Those bureaus, in turn, make exactweight
copies—some of which are split in halves, quarters, etc.—to distribute to manufacturers
who make and sell commercial copies. You may have seen a box of “weights” in a chemistry
laboratory that is the result of this process.
One way to find the mass of your potatoes is to balance them against known weights.
Put your potatoes on one side of a scale and add standard masses to the other until both
sides balance. The sum of the standard masses used equals the mass of the potatoes. You
have made your comparison accurately but indirectly with the standard kilogram secured
in a bell jar near Paris.
Length and time must also be given quantitative meaning by comparison to standards.
For many years the standard meter was the official measurement of a long bar of metal kept
with the standard kilogram in France. Improved technology now allows us to define it as how
far light travels in a vacuum in 1/299,792,458 seconds.
Standard kilogram
The unit of mass, the kilogram (kg),
remains the only base unit in the
International System of Units that is
still defined in terms of a physical
artifact. The standard was manufactured
in 1879. It is stored in an
evacuated chamber near Paris.
The ancient measure of time was the sun’s position in the sky. The invention of clocks allowed greater accuracy, and was
soon followed by the “invention” of the “second,” defined as 1/84,600th of a day. Today we have more precise standards of
time based atomic vibrations. One second is defined as 9,192,631,770 vibrations of a Cesium 133 atom.
Newton summarized these various features
about force, mass, and acceleration in a simple
equation, termed Newton’s Second Law of
Motion:
Force = mass ¥ acceleration
or just
F = ma
Alternatively, we may write it as
a = F/m
The second way of writing the Second Law
more clearly shows that the acceleration of an
object is directly proportional to the (net) force
on it and inversely proportional to its mass. If
you double the force on an object without
changing its mass, the acceleration doubles. It
you have two objects, the first of which has
twice the mass of the second, and the same
force is applied to both of them, the first will
accelerate at half the rate of the second. Can
you see how this is described by the Second
Law
Suppose an object has a mass of 100 kilograms.
If it is pushed by a force that causes it
to accelerate at a rate of 5 meters per second
every second, then the Second Law tells us that
the force is 100 ¥ 5 = 500 newtons. If the
object was originally at rest, and this force was
in effect for 10 seconds, the object will emerge
with a velocity of 50 meters per second.
We note that the First Law is a special case
of the Second Law. It is the case in which no
forces act on the object, allowing it to remain
in uniform motion. The First Law may also be
considered as a qualitative statement about
motion and the presence or absence of force.
The Second Law is quantitative. It says exactly
how much the motion of an object of mass “m”
changes when acted on by a force of magnitude
“F.”
The significance of the Second Law cannot
be overstated. It was the first universal principle
discovered that enabled changes observed
in our physical world to be described in mathematical
terms.