Physics For Scientists And Engineers 6E - part 2

latest definition establishes that the speed of light in vacuum is precisely 299 792 458
meters per second.

Table 1.1 lists approximate values of some measured lengths. You should study this

table as well as the next two tables and begin to generate an intuition for what is meant
by a length of 20 centimeters, for example, or a mass of 100 kilograms or a time inter-
val of 3.2 ! 10

seconds.

Mass

The 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 al-
loy. A duplicate of the Sèvres cylinder is kept at the National Institute of Standards and
Technology (NIST) in Gaithersburg, Maryland (Fig. 1.1a).

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. (A solar day is the time interval between successive appearances of the Sun
at the highest point it reaches in the sky each day.) The second was 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 time standard.

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

in a device known as an atomic clock (Fig. 1.1b), which uses the characteristic frequency
of the cesium-133 atom as the “reference clock.”

The second (s) is now defined as

9 192 631 770 times the period of vibration of radiation from the cesium atom.

S E C T I O N 1 . 1 • Standards of Length, Mass, and Time

Period is defined as the time interval needed for one complete vibration.

Length (m)

Distance from the Earth to the most remote known quasar

1.4 ! 10

Distance from the Earth to the most remote normal galaxies

9 ! 10

Distance from the Earth to the nearest large galaxy

2 ! 10

(M 31, the Andromeda galaxy)
Distance from the Sun to the nearest star (Proxima Centauri)

4 ! 10

One lightyear

9.46 ! 10

Mean orbit radius of the Earth about the Sun

1.50 ! 10

Mean distance from the Earth to the Moon

3.84 ! 10

Distance from the equator to the North Pole

1.00 ! 10

Mean radius of the Earth

6.37 ! 10

Typical altitude (above the surface) of a

2 ! 10

satellite orbiting the Earth

Length of a football field

9.1 ! 10

Length of a housefly

5 ! 10

Size of smallest dust particles

# 10

Size of cells of most living organisms

# 10

Diameter of a hydrogen atom

# 10

Diameter of an atomic nucleus

# 10

Diameter of a proton

# 10

Approximate Values of Some Measured Lengths

Table 1.1

▲

PITFALL PREVENTION

1.2 Reasonable Values

Generating  intuition  about  typi-
cal  values  of  quantities  is  impor-
tant  because  when  solving  prob-
lems  you  must  think  about  your
end  result  and  determine  if  it
seems  reasonable.  If  you  are  cal-
culating  the  mass  of  a  housefly
and  arrive  at  a  value  of  100 kg,
this  is  unreasonable—there  is  an
error somewhere.

▲

PITFALL PREVENTION

1.1 No Commas in

Numbers with Many
Digits

We will use the standard scientific
notation  for  numbers  with  more
than  three  digits,  in  which
groups  of  three  digits  are  sepa-
rated  by  spaces  rather  than
commas.  Thus,  10 000  is  the
same  as  the  common  American
notation  of  10,000.  Similarly,
# $

3.14159265 is written as

3.141 592 65.

Mass (kg)

Observable

# 10

Universe

Milky Way

# 10

galaxy

Sun

1.99 ! 10

Earth

5.98 ! 10

Moon

7.36 ! 10

Shark

# 10

Human

# 10

Frog

# 10

Mosquito

# 10

Bacterium

# 1 ! 10

Hydrogen

1.67 ! 10

atom

Electron

9.11 ! 10

Table 1.2

Masses of Various Objects
(Approximate Values)

To keep these atomic clocks—and therefore all common clocks and watches that are
set to them—synchronized, it has sometimes been necessary to add leap seconds to our
clocks.

Since Einstein’s discovery of the linkage between space and time, precise measure-

ment of time intervals requires that we know both the state of motion of the clock used
to measure the interval and, in some cases, the location of the clock as well. Otherwise,
for example, global positioning system satellites might be unable to pinpoint your loca-
tion with sufficient accuracy, should you need to be rescued.

Approximate values of time intervals are presented in Table 1.3.

C H A P T E R 1 • Physics and Measurement

(a)

(b)

Figure 1.1 (a) The National Standard Kilogram No. 20, an accurate copy of the
International Standard Kilogram kept at Sèvres, France, is housed under a double bell jar in
a vault at the National Institute of Standards and Technology. (b) The nation’s primary time
standard is a cesium fountain atomic clock developed at the National Institute of Standards
and Technology laboratories in Boulder, Colorado. The clock will neither gain nor lose a
second in 20 million years.

(Courtesy of National Institute of Standards and T

echnology

, U.S. Department of Commerce)

Time

Interval (s)

Age of the Universe

5 ! 10

Age of the Earth

1.3 ! 10

Average age of a college student

6.3 ! 10

One year

3.2 ! 10

One day (time interval for one revolution of the Earth about its axis)

8.6 ! 10

One class period

3.0 ! 10

Time interval between normal heartbeats

8 ! 10

Period of audible sound waves

# 10

Period of typical radio waves

# 10

Period of vibration of an atom in a solid

# 10

Period of visible light waves

# 10

Duration of a nuclear collision

# 10

Time interval for light to cross a proton

# 10

Approximate Values of Some Time Intervals

Table 1.3

In addition to SI, another system of units, the U.S. customary system, is still used in the

United States despite acceptance of SI by the rest of the world. In this system, the units of
length, mass, and time are the foot (ft), slug, and second, respectively. In this text we shall
use SI units because they are almost universally accepted in science and industry. We shall
make some limited use of U.S. customary units in the study of classical mechanics.

In addition to the basic SI units of meter, kilogram, and second, we can also use

other units, such as millimeters and nanoseconds, where the prefixes milli- and nano-
denote multipliers of the basic units based on various powers of ten. Prefixes for the
various powers of ten and their abbreviations are listed in Table 1.4. For example,
10

m is equivalent to 1 millimeter (mm), and 10

m corresponds to 1 kilometer

(km). Likewise, 1 kilogram (kg) is 10

grams (g), and 1 megavolt (MV) is 10

volts (V).

1.2 Matter and Model Building

If physicists cannot interact with some phenomenon directly, they often imagine a
model for  a  physical  system  that  is  related  to  the  phenomenon.  In  this  context,  a
model is a system of physical components, such as electrons and protons in an atom.
Once  we  have  identified  the  physical  components,  we  make  predictions  about  the
behavior of the system, based on the interactions among the components of the sys-
tem  and/or  the  interaction  between  the  system  and  the  environment  outside  the
system.

As an example, consider the behavior of matter. A 1-kg cube of solid gold, such as

that at the left of Figure 1.2, has a length of 3.73 cm on a side. Is this cube nothing but
wall-to-wall gold, with no empty space? If the cube is cut in half, the two pieces still re-
tain their chemical identity as solid gold. But what if the pieces are cut again and
again, indefinitely? Will the smaller and smaller pieces always be gold? Questions such
as these can be traced back to early Greek philosophers. Two of them—Leucippus and
his student Democritus—could not accept the idea that such cuttings could go on for-
ever. They speculated that the process ultimately must end when it produces a particle

S E C T I O N 1 . 2 • Matter and Model Building

Power

Prefix

Abbreviation

yocto

zepto

atto

femto

pico

nano

micro

milli

centi

deci

kilo

mega

giga

tera

peta

exa

zetta

yotta

Prefixes for Powers of Ten

Table 1.4

that can no longer be cut. In Greek, atomos means “not sliceable.” From this comes our
English word atom.

Let us review briefly a number of historical models of the structure of matter.

The Greek model of the structure of matter was that all ordinary matter consists of
atoms, as suggested to the lower right of the cube in Figure 1.2. Beyond that, no ad-
ditional structure was specified in the model— atoms acted as small particles that in-
teracted with each other, but internal structure of the atom was not a part of the
model.

In 1897, J. J. Thomson identified the electron as a charged particle and as a con-

stituent of the atom. This led to the first model of the atom that contained internal
structure. We shall discuss this model in Chapter 42.

Following the discovery of the nucleus in 1911, a model was developed in which

each atom is made up of electrons surrounding a central nucleus. A nucleus is shown
in Figure 1.2. This model leads, however, to a new question—does the nucleus have
structure? That is, is the nucleus a single particle or a collection of particles? The exact
composition of the nucleus is not known completely even today, but by the early 1930s
a model evolved that helped us understand how the nucleus behaves. Specifically, sci-
entists determined that occupying the nucleus are two basic entities, protons and neu-
trons. The proton carries a positive electric charge, and a specific chemical element is
identified by the number of protons in its nucleus. This number is called the

atomic

number of the element. For instance, the nucleus of a hydrogen atom contains one
proton (and so the atomic number of hydrogen is 1), the nucleus of a helium atom
contains two protons (atomic number 2), and the nucleus of a uranium atom contains
92 protons (atomic number 92). In addition to atomic number, there is a second num-
ber characterizing atoms—

mass number, defined as the number of protons plus neu-

trons in a nucleus. The atomic number of an element never varies (i.e., the number of
protons does not vary) but the mass number can vary (i.e., the number of neutrons
varies).

The existence of neutrons was verified conclusively in 1932. A neutron has no

charge and a mass that is about equal to that of a proton. One of its primary purposes

C H A P T E R 1 • Physics and Measurement

Gold atoms

Nucleus

Quark composition of a proton

Gold cube

Gold

nucleus

Proton

Neutron

Figure 1.2 Levels of organization in matter. Ordinary matter consists of atoms, and at the
center of each atom is a compact nucleus consisting of protons and neutrons. Protons and
neutrons are composed of quarks. The quark composition of a proton is shown.

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