Wiley - Fundamentals Of Physics

Standards of Length, Mass, and

Time

1.2 The Building Blocks of Matter

1.3 Density

1.4 Dimensional Analysis

1.5 Conversion of Units

1.6 Estimates and Order-of-Magnitude

Calculations

1.7 Significant Figures

C h a p t e r O u t l i n e

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3

ike all other sciences, physics is based on experimental observations and quantitative

measurements. The main objective of physics is to find the limited number

of fundamental laws that govern natural phenomena and to use them to

develop theories that can predict the results of future experiments. The fundamental

laws used in developing theories are expressed in the language of mathematics,

the tool that provides a bridge between theory and experiment.

When a discrepancy between theory and experiment arises, new theories must

be formulated to remove the discrepancy. Many times a theory is satisfactory only

under limited conditions; a more general theory might be satisfactory without

such limitations. For example, the laws of motion discovered by Isaac Newton

(1642–1727) in the 17th century accurately describe the motion of bodies at normal

speeds but do not apply to objects moving at speeds comparable with the

speed of light. In contrast, the special theory of relativity developed by Albert Einstein

(1879–1955) in the early 1900s gives the same results as Newton’s laws at low

speeds but also correctly describes motion at speeds approaching the speed of

light. Hence, Einstein’s is a more general theory of motion.

Classical physics, which means all of the physics developed before 1900, includes

the theories, concepts, laws, and experiments in classical mechanics, thermodynamics,

and electromagnetism.

Important contributions to classical physics were provided by Newton, who developed

classical mechanics as a systematic theory and was one of the originators

of calculus as a mathematical tool. Major developments in mechanics continued in

the 18th century, but the fields of thermodynamics and electricity and magnetism

were not developed until the latter part of the 19th century, principally because

before that time the apparatus for controlled experiments was either too crude or

unavailable.

A new era in physics, usually referred to as modern physics, began near the end

of the 19th century. Modern physics developed mainly because of the discovery

that many physical phenomena could not be explained by classical physics. The

two most important developments in modern physics were the theories of relativity

and quantum mechanics. Einstein’s theory of relativity revolutionized the traditional

concepts of space, time, and energy; quantum mechanics, which applies to

both the microscopic and macroscopic worlds, was originally formulated by a number

of distinguished scientists to provide descriptions of physical phenomena at

the atomic level.

Scientists constantly work at improving our understanding of phenomena and

fundamental laws, and new discoveries are made every day. In many research

areas, a great deal of overlap exists between physics, chemistry, geology, and

biology, as well as engineering. Some of the most notable developments are

(1) numerous space missions and the landing of astronauts on the Moon,

(2) microcircuitry and high-speed computers, and (3) sophisticated imaging techniques

used in scientific research and medicine. The impact such developments

and discoveries have had on our society has indeed been great, and it is very likely

that future discoveries and developments will be just as exciting and challenging

and of great benefit to humanity.

STANDARDS OF LENGTH, MASS, AND TIME

The laws of physics are expressed in terms of basic quantities that require a clear definition.

In mechanics, the three basic quantities are length (L), mass (M), and time

(T). All other quantities in mechanics can be expressed in terms of these three.

1.1

L

4 CHAPTER 1 Physics and Measurements

If we are to report the results of a measurement to someone who wishes to reproduce

this measurement, a standard must be defined. It would be meaningless if

a visitor from another planet were to talk to us about a length of 8 “glitches” if we

do not know the meaning of the unit glitch. On the other hand, if someone familiar

with our system of measurement reports that a wall is 2 meters high and our

unit of length is defined to be 1 meter, we know that the height of the wall is twice

our basic length unit. Likewise, if we are told that a person has a mass of 75 kilograms

and our unit of mass is defined to be 1 kilogram, then that person is 75

times as massive as our basic unit.1 Whatever is chosen as a standard must be readily

accessible and possess some property that can be measured reliably—measurements

taken by different people in different places must yield the same result.

In 1960, an international committee established a set of standards for length,

mass, and other basic quantities. The system established is an adaptation of the

metric system, and it is called the SI system of units. (The abbreviation SI comes

from the system’s French name “Système International.”) In this system, the units

of length, mass, and time are the meter, kilogram, and second, respectively. Other

SI standards established by the committee are those for temperature (the kelvin),

electric current (the ampere), luminous intensity (the candela), and the amount of

substance (the mole). In our study of mechanics we shall be concerned only with

the units of length, mass, and time.

Length

In A.D. 1120 the king of England decreed that the standard of length in his country

would be named the yard and would be precisely equal to the distance from the

tip of his nose to the end of his outstretched arm. Similarly, the original standard

for the foot adopted by the French was the length of the royal foot of King Louis

XIV. This standard prevailed until 1799, when the legal standard of length in

France became the meter, defined as one ten-millionth the distance from the equator

to the North Pole along one particular longitudinal line that passes through

Paris.

Many other systems for measuring length have been developed over the years,

but the advantages of the French system have caused it to prevail in almost all

countries and in scientific circles everywhere. As recently as 1960, the length of the

meter was defined as the distance between two lines on a specific platinum–

iridium bar stored under controlled conditions in France. This standard was abandoned

for several reasons, a principal one being that the limited accuracy with

which the separation between the lines on the bar can be determined does not

meet the current requirements of science and technology. In the 1960s and 1970s,

the meter was defined as 1 650 763.73 wavelengths of orange-red light emitted

from a krypton-86 lamp. However, in October 1983, the meter (m) was redefined

as the distance traveled by light in vacuum during a time of 1/299 792 458

second. In effect, this latest definition establishes that the speed of light in vacuum

is precisely 299 792 458 m per second.

Table 1.1 lists approximate values of some measured lengths.

1 The need for assigning numerical values to various measured physical quantities was expressed by

Lord Kelvin (William Thomson) as follows: “I often say that when you can measure what you are speaking

about, and express it in numbers, you should know something about it, but when you cannot express

it in numbers, your knowledge is of a meagre and unsatisfactory kind. It may be the beginning of

knowledge but you have scarcely in your thoughts advanced to the state of science.”

1.1 Standards of Length, Mass, and Time 5

Mass

The basic SI unit of mass, the kilogram (kg), is defined as the mass of a specific

platinum–iridium alloy cylinder kept at the International Bureau of

Weights and Measures at Sèvres, France. This mass standard was established in

1887 and has not been changed since that time because platinum–iridium is an

unusually stable alloy (Fig. 1.1a). A duplicate of the Sèvres cylinder is kept at the

National Institute of Standards and Technology (NIST) in Gaithersburg, Maryland.

Table 1.2 lists approximate values of the masses of various objects.

Time

Before 1960, the standard of time was defined in terms of the mean solar day for the

year 1900.2 The mean solar second was originally defined as of a mean

solar day. The rotation of the Earth is now known to vary slightly with time, however,

and therefore this motion is not a good one to use for defining a standard.

In 1967, consequently, the second was redefined to take advantage of the high

precision obtainable in a device known as an atomic clock (Fig. 1.1b). In this device,

the frequencies associated with certain atomic transitions can be measured to a

precision of one part in 1012. This is equivalent

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