Acceleration,
change in the velocity of a body with respect to time. Since velocity is a
vector quantity, involving both magnitude and direction, acceleration is
also a vector. In order to produce an acceleration, a force must be
applied to the body. The magnitude of the force F must be directly
proportional to both the mass of the body m and the desired
acceleration a, according to Newton's second law of motion, F=ma.
The exact nature of the acceleration produced depends on the relative
directions of the original velocity and the force. A force acting in the
same direction as the velocity changes only the
speed of the body. An appropriate force acting
always at right angles to the velocity changes the direction of the
velocity but not the speed. An example of such an accelerating force is
the gravitational force exerted by a planet on a satellite moving in a
circular orbit. A force may also act in the opposite direction from the
original velocity. In this case the speed of the body is decreased. Such
an acceleration is often referred to as a deceleration.
Ampere
Pronounced As: ampr
, abbr. amp or A, basic unit of electric current. It is the fundamental
electrical unit used with the mks system of units of the metric system.
The ampere is officially defined as the current in a pair of equally long,
parallel, straight wires 1 meter apart that produces a force of 0.0000002
newton (2 × 10−7 N) between the wires for each meter of their
length. Current meters such as ammeters and galvanometers are calibrated
in reference to a current balance that actually measures the force between
two wires.
Archimedes' principle,
principle that states that a body immersed in a fluid is buoyed up by a
force equal to the weight of the displaced fluid. The principle applies to
both floating and submerged bodies and to all fluids, i.e., liquids and
gases. It explains not only the buoyancy of ships and other vessels in
water but also the rise of a balloon in the air and the apparent loss of
weight of objects underwater. In determining whether a given body will
float in a given fluid, both weight and volume must be considered; that
is, the relative density, or weight per unit of volume, of the body
compared to the fluid determines the buoyant force. If the body is less
dense than the fluid, it will float or, in the case of a balloon, it will
rise. If the body is denser than the fluid, it will sink. Relative density
also determines the proportion of a floating body that will be submerged
in a fluid. If the body is two thirds as dense as the fluid, then two
thirds of its volume will be submerged, displacing in the process a volume
of fluid whose weight is equal to the entire weight of the body. In the
case of a submerged body, the apparent weight of the body is equal to its
weight in air less the weight of an equal volume of fluid. The fluid most
often encountered in applications of Archimedes' principle is water, and
the specific gravity of a substance is a convenient measure of its
relative density compared to water. In calculating the buoyant force on a
body, however, one must also take into account the shape and position of
the body. A steel rowboat placed on end into the water will sink because
the density of steel is much greater than that of water. However, in its
normal, keel-down position, the effective volume of the boat includes all
the air inside it, so that its average density is then less than that of
water, and as a result it will float.
Associative law,
in mathematics, law holding that for a given operation combining three
quantities, two at a time, the initial pairing is arbitrary; e.g., using
the operation of addition, the numbers 2, 3, and 4 may be combined
(2+3)+4=5+4=9 or 2+(3+4)=2+7=9. More generally, in addition, for any three
numbers a, b, and c the associative law is expressed as (a+b)+c=a+(b+c).
Multiplication of numbers is also associative, i.e., (a×b)×c=a×(b×c).
In general, any binary operation, symbolized by, joining mathematical
entities A, B, and C obeys the associative law if (AB)C=A(BC)
for all possible choices of A, B, and C. Not all operations
are associative. For example, ordinary division is not, since
(60÷12)÷3=5÷3=5/3, while 60÷(12÷3)=60÷4=15. When an operation is
associative, the parentheses indicating which quantities are first to be
combined may be omitted, e.g., (2+3)+4=2+(3+4)=2+3+4.
Axiom,
in mathematics and logic, general statement accepted without proof as the
basis for logically deducing other statements (theorems). Examples of
axioms used widely in mathematics are those related to equality (e.g.,
"Two things equal to the same thing are equal to each other; "If equals
are added to equals, the sums are equal) and those related to operations
(e.g., the associative law and the commutative law). A postulate, like an
axiom, is a statement that is accepted without proof; however, it deals
with specific subject matter (e.g., properties of geometrical figures) and
thus is not so general as an axiom. It is sometimes said that an axiom or
postulate is a "self-evident statement, but the truth of the statement
need not be evident and may in some cases even seem to contradict common
sense. Moreover, a statement may be an axiom or postulate in one deductive
system and may instead be derived from other statements in another system.
A set of axioms on which a system is based is often wished to be
independent; i.e., no one of its members can be deduced from any
combination of the others. (Historically, the development of non-Euclidean
geometry grew out of attempts to prove or disprove the independence of the
parallel postulate of Euclid.) The axioms should also be consistent; i.e.,
it should not be possible to deduce contradictory statements from them.
Completeness is another property sometimes mentioned in connection with a
set of axioms; if the set is complete, then any true statement within the
system described by the axioms may be deduced from them.
Axiomatic Approach to
Geometry
Euclid's Elements
organized the geometry then known into a systematic presentation that is
still used in many texts. Euclid first defined his basic terms, such as
point and line, then stated without proof certain axioms and postulates
about them that seemed to be self-evident or obvious truths, and finally
derived a number of statements (theorems) from the postulates by means of
deductive logic. This axiomatic method has since been adopted not only
throughout mathematics but in many other fields as well. The close
examination of the axioms and postulates of Euclidean geometry during the
19th cent. resulted in the realization that the logical basis of geometry
was not as firm as had previously been supposed. New axiom and postulate
systems were developed by various mathematicians, notably David Hilbert
(1899).
Blow molding
In a processes similar
to glass blowing, thermoplastics can be blown up and then sealed in a
mold. Typical examples include liter soft drink bottles.
Buoyancy
Pronounced As: boins, booyn-
, upward force exerted by a fluid on any body immersed in it. Buoyant
force can be explained in terms of Archimedes' principle.
Calculus,
branch of mathematics that studies continuously changing quantities. The
calculus is characterized by the use of infinite processes, involving
passage to a limit-the notion of tending toward, or approaching, an
ultimate value. The English physicist Isaac Newton and the German
mathematician G. W. Leibniz, working independently, developed the calculus
during the 17th cent. The calculus and its basic tools of differentiation
and integration serve as the foundation for the larger branch of
mathematics known as analysis. The methods of calculus are essential to
modern physics and to most other branches of modern science and
engineering.
Cartesian coordinates
Pronounced As: kärtzhn
[for René Descartes], system for representing the relative positions of
points in a plane or in space. In a plane, the point P is specified
by the pair of numbers (x,y) representing the distances of the
point from two intersecting straight lines, referred to as the x-axis
and the y-axis. The point of intersection of these axes, which are
called the coordinate axes, is known as the origin. In rectangular
coordinates, the type most often used, the axes are taken to be
perpendicular, with the x-axis horizontal and the y-axis
vertical, so that the x-coordinate, or abscissa, of P is
measured along the horizontal perpendicular from P to the y-axis
(i.e., parallel to the x-axis) and the y-coordinate, or
ordinate, is measured along the vertical perpendicular from P to
the x-axis (parallel to the y-axis). In oblique coordinates
the axes are not perpendicular; the abscissa of P is measured along
a parallel to the x-axis, and the ordinate is measured along a
parallel to the y-axis, but neither of these parallels is
perpendicular to the other coordinate axis as in rectangular coordinates.
Similarly, a point in space may be specified by the triple of numbers (x,y,z)
representing the distances from three planes determined by three
intersecting straight lines not all in the same plane; i.e., the x-coordinate
represents the distance from the yz-plane measured along a parallel
to the x-axis, the y-coordinate represents the distance from
the xz-plane measured along a parallel to the y-axis, and
the z-coordinate represents the distance from the xy-plane
measured along a parallel to the z-axis (the axes are usually taken
to be mutually perpendicular). Analogous systems may be defined for
describing points in abstract spaces of four or more dimensions. Many of
the curves studied in classical geometry can be described as the set of
points (x,y) that satisfy some equation f(x,y)=0. In this
way certain questions in geometry can be transformed into questions about
numbers and resolved by means of analytic geometry.
Center of mass,
the point at which all the mass of a body may be considered to be
concentrated in analyzing its motion. The center of mass of a sphere of
uniform density coincides with the center of the sphere. The center of
mass of a body need not be within the body itself; the center of mass of a
ring or a hollow cylinder is located in the enclosed space, not in the
object itself. Under the action of a constant force of gravity, a body
suspended or balanced at its center of mass will be stable; there will be
no net moment acting on it. Sometimes a problem may be analyzed from the
point of view of the center of mass of an entire system of objects, such
as several colliding elementary particles or a multiple-star system. For
example, the complex motions of the earth and moon about the sun become
somewhat simpler when viewed from the common center of mass of the
earth-moon system, located about 1,000 mi (1,600 km) below the earth's
surface. It is this point that is moving in an elliptical orbit around the
sun rather than the center of mass of the earth alone.
Cgs system,
system of units of measurement based on the metric system and having the
centimeter of length, the gram of mass, and the second of time as its
fundamental units. Other cgs units are the dyne of force and the erg of
work or energy. The units of the cgs system are generally much smaller
than the comparable units of the mks system.
Chemical engineering
deals with the design, construction, and operation of plants and machinery
for making such products as acids, dyes, drugs, plastics, and synthetic
rubber by adapting the chemical reactions discovered by the laboratory
chemist to large-scale production. The chemical engineer must be familiar
with both chemistry and mechanical engineering.
Civil engineering
includes the planning, designing, construction, and maintenance of
structures and altering geography to suit human needs. Some of the
numerous subdivisions are transportation (e.g., railroad facilities and
highways); hydraulics (e.g., river control, irrigation, swamp draining,
water supply, and sewage disposal); and structures (e.g., buildings,
bridges, and tunnels).
Compression
molding
A mold is filled with
pieces of thermoset plastic as well as various fillers such as wood fiber,
cotton and pigments. Heat and pressure is applied to the mold cavity to
force the material to melt and fill the mold.
Commutative law,
in mathematics, law holding that for a given binary operation (combining
two quantities) the order of the quantities is arbitrary; e.g., in
addition, the numbers 2 and 5 can be combined as 2+5=7 or as 5+2=7. More
generally, in addition, for any two numbers a and b the
commutative law is expressed as a+b=b+a.
Multiplication of numbers is also commutative, i.e., a×b=b×a.
In general, any binary operation, symbolized by , joining mathematical
entities A and B obeys the commutative law if AB=BA
for all possible choices of A and B. Not all operations are
commutative; e.g., subtraction is not since 2−5≠5−2, and division is not
since 2/5≠5/2.
Decimal system
[Lat.,=of tenths], numeration system based on powers of 10. A number is
written as a row of digits, with each position in the row corresponding to
a certain power of 10. A decimal point in the row divides it into those
powers of 10 equal to or greater than 0 and those less than 0, i.e.,
negative powers of 10. Positions farther to the left of the decimal point
correspond to increasing positive powers of 10 and those farther to the
right to increasing negative powers, i.e., to division by higher positive
powers of 10. For example, 4,309=(4×103)+(3x102)+(0×101)+(9×100)=4,000+300+0+9,
and 4.309=(4×100)+(3×10−1)+(0×10−2)+(9×10−3)=4+3/10+0/100+9/1000.
It is believed that the decimal system is based on 10 because humans have
10 fingers and so became used to counting by 10s early in the course of
civilization. The decimal system was introduced into Europe c.1300. It
greatly simplified arithmetic and was a much-needed improvement over the
Roman numerals, which did not use a positional system. A number written in
the decimal system is called a decimal, although sometimes this term is
used to refer only to a proper fraction written in this system and not to
a mixed number. Decimals are added and subtracted in the same way as are
integers (whole numbers) except that when these operations are written in
columnar form the decimal points in the column entries and in the answer
must all be placed one under another. In multiplying two decimals the
operation is the same as for integers except that the number of decimal
places in the product, i.e., digits to the right of the decimal point, is
equal to the sum of the decimal places in the factors; e.g., the factor
7.24 to two decimal places and the factor 6.3 to one decimal place have
the product 45.612 to three decimal places. In division, e.g., 4.32 12.8
where there is a decimal point in the divisor (4.32), the point is shifted
to the extreme right (i.e., to 432.) and the decimal point in the dividend
(12.8) is shifted the same number of places to the right (to 1280), with
one or more zeros added before the decimal to make this possible. The
decimal point in the quotient is then placed above that in the dividend,
i.e., 432 1280.0 zeros are added to the right of the decimal point in the
dividend as needed, and the division proceeds the same as for integers.
The decimal system is widely used in various systems employing numbers.
The metric system of weights and measures, used in most of the world, is
based on the decimal system, as are most systems of national currency.
Density,
ratio of the mass of a substance to its volume, expressed, for example, in
units of grams per cubic centimeter or pounds per cubic foot. The density
of a pure substance varies little from sample to sample and is often
considered a characteristic property of the substance. Most substances
undergo expansion when heated and therefore have lower densities at higher
temperatures. Many substances, especially gases, can be compressed into a
smaller volume by increasing the pressure acting on them. For these
reasons, the temperature and pressure at which the density of a substance
is measured are usually specified. The density of a gas is often converted
mathematically to what it would be at a standard temperature and pressure
(see STP). Water is unusual in that it expands, and thus decreases in
density, as it is cooled below 3.98°C (its temperature of maximum
density). Density often is taken as an indication of how "heavy a
substance is. Iron is denser than cork, since a given volume of iron is
more massive (and weighs more) than the same volume of cork. It is often
said that iron is "heavier than cork, although a large volume of cork
obviously can be more massive and thus be heavier (i.e., weigh more) than
a small volume of iron.
Descriptive geometry,
branch of geometry concerned with the two-dimensional representation of
three-dimensional objects; it was introduced in 1795 by Gaspard Monge. By
means of such representations, geometrical problems in three dimensions
may be solved in the plane. (Such problems arise in all branches of
engineering.) Modern mechanical drawing and architectural drawing are
based on the principles of descriptive geometry.
Dynamics,
branch of mechanics that deals with the motion of objects; it may be
further divided into kinematics, the study of motion without regard to the
forces producing it, and kinetics, the study of the forces that produce or
change motion. Motion is caused by an unbalanced force acting on a body.
Such a force will produce either a change in the body's speed or a change
in the direction of its motion. The motion may be either translational
(straight-line) or rotational. With the principles of dynamics one can
solve problems involving work and energy and explain the pressure and
expansion of gases, the motion of planets, and the behavior of flowing
liquids and gases. Solids are rigid, having a definite shape, but fluids
(liquids and gases) are not, and special branches of dynamics have been
developed that treat the particular effects of forces and motions in
fluids. These include fluid mechanics, the study of liquids in motion, and
aerodynamics, the study of gases in motion. The applications of liquids
both at rest and in motion are studied under hydraulics, a branch of
engineering closely related to dynamics. The principles of dynamics may
also be combined with the study of other phenomena, as in electrodynamics,
the study of charges in motion.
Dyne
Pronounced As: din
, unit of force in the cgs system of units, which is based on the metric
system; an acceleration of 1 centimeter per second per second is produced
when a force of 1 dyne is exerted on a mass of 1 gram. In terms of the
newton, the force unit in the mks system, 1 dyne equals 0.00001 newtons.
Elasticity,
the ability of a body to resist a distorting influence or stress and to
return to its original size and shape when the stress is removed. All
solids are elastic for small enough deformations or strains, but if the
stress exceeds a certain amount known as the elastic limit, a permanent
deformation is produced. Both the resistance to stress and the elastic
limit depend on the composition of the solid. Some different kinds of
stresses are tension, compression, torsion, and shearing. For each kind of
stress and the corresponding strain there is a modulus, i.e., the ratio of
the stress to the strain; the ratio of tensile stress to strain for a
given material is called its Young's modulus. Hooke's law [for
Robert Hooke] states that, within the elastic limit, strain is
proportional to stress.
Electrical engineering
encompasses all aspects of electricity from power engineering, the
development of the devices for the generation and transmission of
electrical power, to electronics. Electronics is a branch of electrical
engineering that deals with devices that use electricity for control of
processes. Subspecialties of electronics include computer engineering,
microwave engineering, communications, and digital signal processing. It
is the engineering specialty that has grown the most in recent decades.
Electromagnetic
radiation,
energy radiated in the form of a wave as a result of the motion of
electric charges. A moving charge gives rise to a magnetic field, and if
the motion is changing (accelerated), then the magnetic field varies and
in turn produces an electric field. These interacting electric and
magnetic fields are at right angles to one another and also to the
direction of propagation of the energy. Thus, an electromagnetic wave is a
transverse wave. If the direction of the electric field is constant, the
wave is said to be polarized. Electromagnetic radiation does not require a
material medium and can travel through a vacuum. The theory of
electromagnetic radiation was developed by James Clerk Maxwell and
published in 1865. He showed that the speed of propagation of
electromagnetic radiation should be identical with that of light, about
186,000 mi (300,000 km) per sec. Subsequent experiments by Heinrich Hertz
verified Maxwell's prediction through the discovery of radio waves, also
known as hertzian waves. Light is a type of electromagnetic radiation,
occupying only a small portion of the possible spectrum of this energy.
The various types of electromagnetic radiation differ only in wavelength
and frequency; they are alike in all other respects. The possible sources
of electromagnetic radiation are directly related to wavelength: long
radio waves are produced by large antennas such as those used by
broadcasting stations; much shorter visible light waves are produced by
the motions of charges within atoms; the shortest waves, those of gamma
radiation, result from changes within the nucleus of the atom. In order of
decreasing wavelength and increasing frequency, various types of
electromagnetic radiation include: electric waves, radio waves (including
AM, FM, TV, and shortwaves), microwaves, infrared radiation, visible
light, ultraviolet radiation, X rays, and gamma radiation. According to
the quantum theory, light and other forms of electromagnetic radiation may
at times exhibit properties like those of particles in their interaction
with matter. (Conversely, particles sometimes exhibit wavelike
properties.) The individual quantum of electromagnetic radiation is known
as the photon and is symbolized by the Greek letter gamma. Quantum effects
are most pronounced for the higher frequencies, such as gamma rays, and
are usually negligible for radio waves at the long-wavelength,
low-frequency end of the spectrum.
Engineering,
profession devoted to designing, constructing, and operating the
structures, machines, and other devices of industry and everyday life.
English units of
measurement,
principal system of weights and measures used in a few nations, the only
major industrial one being the United States. It actually consists of two
related systems-the U.S. Customary System of units, used in the United
States and dependencies, and the British Imperial System. The names of the
units and the relationships between them are generally the same in both
systems, but the sizes of the units differ, sometimes considerably.
Epoxy resins,
group of synthetic resins used to make plastics and adhesives. These
materials are noted for their versatility, but their relatively high cost
has limited their use. High resistance to chemicals and outstanding
adhesion, durability, and toughness have made them valuable as coatings.
Because of their high electrical resistance, durability at high and low
temperatures, and the ease with which they can be poured or cast without
forming bubbles, epoxy resin plastics are especially useful for
encapsulating electrical and electronic components. Epoxy resin adhesives
can be used on metals, construction materials, and most other synthetic
resins. They are strong enough to be used in place of rivets and welds in
certain industrial applications.
Equilibrium,
state of balance. When a body or a system is in equilibrium, there is no
net tendency to change. In mechanics, equilibrium has to do with the
forces acting on a body. When no force is acting to make a body move in a
line, the body is in translational equilibrium; when no force is acting to
make the body turn, the body is in rotational equilibrium. A body in
equilibrium at rest is said to be in static equilibrium. However, a state
of equilibrium does not mean that no forces act on the body, but only that
the forces are balanced. For example, when a lever is being used to hold
up a raised object, forces are being exerted downward on each end of the
lever and upward on its fulcrum, but the upward and downward forces
balance to maintain translational equilibrium, and the clockwise and
counterclockwise moments of the forces on either end balance to maintain
rotational equilibrium. The stability of a body is a measure of its
ability to return to a position of equilibrium after being disturbed. It
depends on the shape of the body and the location of its center of
gravity. A body with a large flat base and a low center of gravity will be
very stable, returning quickly to its position of equilibrium after being
tipped. However, a body with a small base and high center of gravity will
tend to topple if tipped and is thus less stable than the first body. A
body balanced precariously on a point is in unstable equilibrium. Some
bodies, such as a ball or a cone lying on its side, do not return to their
original position of equilibrium when pushed, assuming instead a new
position of equilibrium; these are said to be in neutral equilibrium. In
thermodynamics, two bodies placed in contact with each other are said to
be in thermal equilibrium when, after a sufficient length of time, their
temperatures are equal. Chemical equilibrium refers to reversible chemical
reactions in which the reactions involved are occurring in opposite
directions at equal rates, so that no net change is observed.
Erg
Pronounced As: ûrg
, unit of work or energy in the cgs system of units, which is based on the
metric system; it is the work done or energy expended by a force of 1 dyne
acting through a distance of 1 centimeter. In terms of the joule, the unit
of work or energy in the mks system, 1 erg equals 0.0000001 joule.
Extrusion
molding
Extrusion is typically
reserved for thermoplastics. The material is carried by a screw to a
heating chamber, and then forced through a heated die (much like
toothpaste through a tube). The extruded material then rests on a conveyor
and is cooled by air or water. The extruded lengths may be cut to length
(as in plastic channel) or coiled in a tube (as with pipe).
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