Skill-trade professionals work with complex machines and equipment. They are expected to understand, operate, service, and maintain these machines and equipment; and to instruct new personnel so they can also perform these functions. No matter how complex a machine or item of equipment is, its performance can be explained as an application of a few basic principles of physics. The tradesman who understands physics is better equipped to meet the demands of the job. The study of physics is devoted to finding and defining problems, as well as to search for their solutions.

Physics not only teaches a person to be curious about the physical world, but it also provides a means of satisfying that curiosity. The distinction between physics and other sciences cannot be well defined because the principles of physics also pertain to the other sciences. Physics is a basic branch of science and deals with matter, motion, force, and energy. It deals with the phenomena that arise because matter moves, exerts force, and possesses energy. It is the foundation for the laws governing these phenomena, as expressed in the study of mechanics, hydraulics, magnetism, electricity, heat, light, sound, and nuclear physics. It is closely associated with chemistry and depends heavily upon mathematics for many of its theories and explanations.

When you have completed this chapter, you will be able to do the following:

1. Recognize the relationship between metric and English units of measurement.
2. State the relationship between volume, mass, weight, force, temperature, and various derived units, such as speed, velocity, work, energy and power.
3. Identify and convert Celsius and Fahrenheit temperatures.
4. Recognize the structure of matter including elements, compounds, and mixtures, the various states in which it can exist, and its relationship to energy.
5. Describe the relationship between force, mass, and motion; between work, power and energy; and between mechanics and revolving bodies.
6. Recognize the nature of heat and the various means of transferring and measuring heat, and identify principles of thermal expansion and changes in heat states.
7. Define the characteristics of light and identify colors in the frequency spectrum.
 Contents 1.0 MEASUREMENTS2.0 DERIVED UNITS 3.0 TEMPERATURE 4.0 SOUND 5.0 STRUCTURE OF MATTER 6.0 COMPOUNDS AND MIXTURES 7.0 STATES OF MATTER 8.0 MECHANICS 9.0 HEAT 10.0 LIGHT REVIEW QUESTIONS

## 1.0 MEASUREMENTS

In any study of physics, specific words and terms have specific meanings that must be mastered. If you do not know the exact meaning of a term, you won’t understand the principles involved in the use of that term. Once you understand the term, however, a discussion of principles illustrates and/or emphasizes a particular point. The first part of this chapter defines some physical terms and briefly discusses a few principles.

To evaluate results, you must often ask the questions "how much, how far, how many, how often, or in what direction." As scientific investigations become more complex, measurements must become more accurate and new methods must be developed to measure new things. Measurements are classified into three broad categories; magnitude, direction, and time. These categories are broken down into several types, each with its own standard units. Measurements of direction and time are standardized and have comparatively few subdivisions. Magnitude, on the other hand, is an extremely complex category with many classes and subdivisions.

The unit of measurement is just as important as the number that precedes it, and both are necessary to give an accurate description. There are two widely used sets of fundamental units of measurement; the metric and English units. The metric unit is normally used to express scientific observations. When using metrics, the basic unit for measuring distance is the meter; for measuring mass, the kilogram is used; and for measuring time, the second. This is called the meter-kilogram-second (mks) system. The English system uses the foot for distance, the pound for mass, and the second for time; thus, it is called the foot-pound-second (fps). See Table 1 for other frequently used units.

Table 1 — Frequently Used Units of Measurement

 English System Metric System General acre bar (metrology) ELECTRICAL Btu (British thermal unit) calorie ampere bushel gram coulomb dram hectare decibel foot hertz farad gallon hour henry hertz joule ohm horsepower liter volt hour meter watt inch metric ton (1,000 kilogram) knot micrometer LIGHT mil minute candela mile newton lumen minute quintal ounce second peck stere pint pound quart second slug ton (short 2,000 pounds, long 2,240 pounds) yard

### Distance

You should be familiar with both the metric and English systems of measurement, since personnel in the AE rating will use both systems in measuring distance and length.

#### Metric Units of Length

Metric units of length are based on the standard meter, first measured as one ten-millionth part of the distance between the earth's equator and one of the poles. In 1960,the International Bureau of Weights and Measures defined the meter as 1,650,763.73 wavelengths of the  2p10 - 5d5 spectral emission of the krypton isotope, Kr86 .

Kilometers are used to measure large distances;

1 kilometer (km) = 1,000 meters (m)

For smaller measurements, the meter and its subdivisions are used.

1 meter equals 100 centimeters (1m = 100 cm)

1 centimeter equals 10 millimeters (1cm = 10 mm)

1 meter equals 1,000 millimeters (1 m = 1,000 mm)

The micrometer is even smaller. It is the unit often used to state the wavelength of light, or to refer to the size of a particle of foreign matter that may pass through a certain screen or filter in the liquid cooling system of electronic equipment.

1 micrometer is one-millionth of 1 meter (1mm = 10-6m)

1 nanometer is one-billionth of 1 meter (1nm = 10-9m)

#### English Units of Length

The common units of the English system of distance measurement are inches, feet, yards, and miles; where 1 foot equals 12 inches, 1 yard equals 3 feet, and 1 mile equals 1,760 yards. Whereas a standard mile is 5,270 feet, a nautical mile is equal to 6,076.115 feet. A mil is equal to 1/1000 inch.

In 1866 the United States, by an act of Congress, defined the yard to be 3600/3937 part of a standard meter, or in decimal form, 0.9144 meter. Thus, other conversions between the systems may be found by proper multiplication or division. Some approximate conversions are listed in Table 2.

Table 2 — Conversion Factors for Units of Length

 km m cm mm in. ft yd mile 1 km = 1 1,000 100,000 1 X 106 39,370 3,280.83 1,093.61 0.621369 1m= 0.001 1 100 1,000 39.37 3.28083 1.09361 6.214 x 10-4 1 cm= 1 X 10-5 0.01 1 10 0.3937 0.032808 1.094 x 10-2 6.214 x 10-6 1 mm = 1 x 10-6 1 x 10-3 0.1 1 0.03937 3.28 x 10-3 1.094 x 10-3 6.214 x 10-7 1 in.= 2.54 X l0-5 2.54 x 10-2 2.54 25.4 1 0.08333 0.02777 1.58 X 10-5 1 ft = 3.048 x 10-4 0.3048 30.48 304.8 12 1 0.33333 1.89 x 10- 4 1 yd = 9.144 x 10-4 0.9144 91.44 914.4 36 3 1 5.68 x 10- 4 1 mile = 1.60934 1,609.34 160,934 1,609,344 63,360 5,280 1,760 1
 NoteWhen a number is multiplied by a power of ten, the decimal point is moved the number of places represented by the power. A negative power moves the decimal point to the left. A positive power moves it to the right. Thus: 84 x 10- 2 = .84, and 84 x 102 = 8,400 Simply stated, a power of ten merely moves the decimal point left or right.

### Volume

Volume is the amount of space enclosed within the bounding surfaces of a body. To determine the volume of a regularly shaped body, you will need three measurements; length, width, and height (depth).

Volume = Length x Width x Depth (Height)

or

V = LWH

Figure 1 — Volume measurement.

Volume measurement (Figure  1) is expressed as dimensions of length cubed because it is the product of three length measurements. The unit of volume is a cube having edges of unit length.

A great deal of ingenuity is often needed to measure the volume of irregularly shaped bodies. Sometimes it is practical to divide a body into a series of regularly shaped parts and then apply the rule that the total volume is equal to the sum of the volumes of all individual parts. Figure 2 shows another way to measure the volume of small irregular bodies. The volume of water displaced by a body submerged in water is equal to the volume of the body. Measuring the volume of floating bodies can be done in a similar way. A floating body displaces its own weight of liquid. This may be proved by filling a container to the brim with liquid, then lowering the body to the surface of the liquid. Next, the liquid that flows over the brim is collected. By weighing the displaced liquid and the original body, the statement, “A floating body displaces its own weight of liquid,” can be proven.

Figure 2 — Measuring the volume of an irregular object.

### Mass, Weight, and Force

The measure of the quantity of matter that a body contains is called mass. The mass of a body does not change. It may be compressed or expanded, but the quantity or mass of matter remains the same.

For practical purposes, the metric unit of mass is based on the gram (g), which is equal to the mass of 1 cubic centimeter of pure water at a temperature of 4° Celsius. The standard pound (lb.) is the mass equal to 453.6 grams.

The mass of a body is constant no matter where the body is located. However, its weight (the force with which it is attracted toward the earth) is not constant. Its weight is slightly higher at the poles than at the equator, and it becomes less as the body moves away from the earth's surface.

In addition to using grams (and pounds) as units of mass, these units are used to describe the weight of a body by comparing the body's weight to the weight of a standard mass unit. Unless otherwise specified, when an object is described as having a weight of 1 pound, it means the object has the same pull of gravity that a mass of 1 pound would have when located near sea level.

 NoteAlthough the pound is not mass unit (it is a force unit), it is often used as such.

To avoid confusion, the slug is used as the unit of mass. It weighs 32 pounds at sea level in the English system. In the metric system, the term newton, the force that causes 1 kilogram mass to be accelerated , is used.

Conversion between the weight units of the metric system is simple. It is only a matter of moving the decimal point. For example:

• 1,000 milligrams (mg) = 1 g
• 1,000 g = 1 kg
• 1,000 kg = 1 metric ton

Conversion between units of the English system requires more effort, since the pound is divided into 16 ounces and the ounce into 16 drams. The short ton is 2,000 pounds, while the long ton is 2,240 pounds. The metric ton is fairly close to the long ton, converting to 2,205 pounds.

## 2.0 DERIVED UNITS

Units based on combinations of two or three fundamental units are expressed as some combination of these units. The watt (unit of power) is written as a joule (unit of work) per second. The joule, in turn, could be expressed as newtons (force) times meters (distance), and the watt then becomes newton-meters per second. Likewise, the unit of horsepower is expressed in foot-pounds per second. Although there are conversion factors between derived units of the English system and the metric system, fundamental units of the two systems are not combined. For instance, if force is given in pounds and distance in meters, one or the other must be changed before combining them to get work units.

### Speed and Velocity

One example of a derived unit is the knot, a unit of speed. This unit combines the nautical mile as the unit of distance and the hour as the unit of time. The knot is derived by dividing the distance traveled by the time required. Thus, if a ship traveled at a constant rate for 15 minutes (0.25 hr) and moved a distance of 6 nautical miles, its speed would be 6 divided by 0.25 or 24 knots. The rate of travel (speed) is also used to solve for distance traveled when time is known. If the above ship were to travel for 3 hours at 24 knots, it would move 72 nautical miles. Likewise, the time required to move a certain distance may be determined when the speed is known. A movement of 36 nautical miles by a ship traveling at 24 knots would require 36/24 = 1.5 hours, or 1 hour 30 minutes. Often, speed is expressed with two fundamental units, such as miles per hour, kilometers per hour, or feet, inches, meters, or centimeters per minute or per second. Conversion is a matter of replacement of one unit by its equivalent in another unit. For example, a speed of 60 miles per hour (60 mph) is converted to feet per second by replacing the mile with 5,280 feet and the hour with 3,600 seconds. Thus, a speed of 60 mph = 60 (5,280 ft/3,600 s) = 88 feet per second. Table 3 gives the conversion factors between meters per second, feet per second, kilometers per hour, miles per hour, and knots.

Table 3 — Conversion Factors for Speed and Velocity

 Speed m/s ft/s km/hr mi/hr knots 1 m/s = 1 3.281 3.6 2.24 1.94 1 ft/s = 0.3048 1 1.0973 0.6818 0.5921 1km/hr = 0.27778 0.9113 1 0.6214 0.5396 1 mi/hr = 0.44704 1.4667 1.6093 1 0.8684 1 knot = 0.5148 1.689 1.853 1.152 1

The terms speed and velocity are sometimes used as if they had the same meaning. However, velocity is a vector quantity; that is, it is speed in a given direction. Thus, a car may move around a circular path with a constant speed while its velocity is continuously changing. When a body moves with constant speed along a straight line whose direction is specified, it is customary to speak of its velocity (which is numerically equal to its speed). When a body moves along a curved path or along a straight path with no reference being made to direction, it is proper to speak of its speed.

### Work and Energy

Units of work and energy are derived units. They are the product of the units of force and distance. The joule is the unit of work in the mks system, where 1 newton acts through a distance of 1 meter.

In the English system, the unit foot-pound is defined as the work done in lifting 1 pound a distance of 1 foot against the force of gravity. Thus, the work done in lifting a mass of 5 pounds vertically 4 feet (5 lb x 4 ft = 20 foot-pounds) is 20 foot-pounds. Do not confuse the term foot-pound with the term used to measure torque. Since 1 pound force equals 4.448 newtons, and 1 foot equals 0.3048 meter, then 1 foot-pound is approximately 1.356 joules.

The British thermal unit (Btu) is the heat energy required to raise the temperature of 1 pound of water 1 degree Fahrenheit. It is equivalent to 252 calories and, incidentally, to 777.8 foot-pounds of mechanical energy.

### Power

All units of power include measurements of force, distance, and time because power equals work, which is force times distance divided by time. The watt is the unit of power frequently used with electrical units, and it is also the rate of doing 1 joule of work in 1 second. Thus, if a force of 5 newtons acts through a distance of 12 meters in 3 seconds, the power required is

 P = 5 x 12 =  20 watts 3

If the same work is to be done in 2 seconds, 30 watts will be required. Horsepower is a larger unit of power. It is equal to 550 foot-pounds per second, or 746 watts; therefore, 1 foot-pound per second is 746/550 watts, or about 1.356 watts.

## 3.0 TEMPERATURE

If an object is hot to the touch, it is said to have a high temperature; if it is cold to the touch, it is said to have a low temperature. In other words, temperature is used as a measure of the hotness or coldness of an object being described. Hotness and coldness are only relative. For example, on a cold day, metals seem colder to the touch than nonmetals because they conduct heat away from the body more rapidly. Also, upon leaving a warm room, the outside air seems cooler than the actual air temperature. Coming from the cold outside into a warm room, the room seems warmer than is the actual room temperature. In other words, the temperature a person feels depends upon the state of their body.

### Temperature Conversion

There are many systems of temperature measurement, and you will often need to convert from one to the other. The four most common scales (Figure 3) in use today are the Fahrenheit (F), Celsius (C), Kelvin (K), and Rankine (R) scales.

FAHRENHEIT SCALE – The most familiar scale to most Americans is the Fahrenheit scale, which was established so that its zero point approximates the temperature produced by mixing equal quantities by weight of snow and common salt. Under standard atmospheric pressure, the boiling point of water is 212 degrees above zero, and the freezing point is 32 degrees above zero. Each degree represents an equal division, and there are 180 such divisions between freezing and boiling.

CELSIUS SCALE – This scale uses the freezing point and boiling point of water under standard atmospheric pressure as fixed points of 0 and 100, respectively, with 100 equal divisions between them.

Figure 3 — Comparison of the four common temperature scales.

The 100 divisions represent the same difference in temperature as the 180 divisions of the Fahrenheit scale. This creates a ratio of 100/180, which reduces to 5/9. This means that a change of 1°F is equal to a change of 5/9°C. A change of 5 degrees on the Celsius scale, therefore, is equal to a change of 9 degrees on the Fahrenheit scale. Because 0 degrees on the Celsius scale corresponds to 32 degrees on the Fahrenheit scale, a difference in reference points exists between the two scales. (See Figure 3.)

To convert from the Fahrenheit scale to the Celsius scale, subtract the 32 degree difference and multiply the result by 5/9. Try converting 68°F to Celsius.

 5 (68 - 32) = 9 x 36 = 20°C 9 5

To convert Celsius to Fahrenheit, reverse the procedure. First multiply the reading on the Celsius thermometer by 9/5 and then add 32 to the result.

 9 (20) x 32 = 36 + 32 = 68°F 5

One way to remember when to use 9/5 and when to use 5/9 is to keep in mind that the Fahrenheit scale has smaller divisions than the Celsius scale. In going from Celsius to Fahrenheit, multiply by the ratio that is larger; in going from Fahrenheit to Celsius, use the smaller ratio.

Another method of temperature conversion that uses these same ratios is based on the fact that the Fahrenheit and Celsius scales both register the same temperature at -40 degrees; that is, -40°F equals -40°C. This method of conversion, sometimes called the 40 rule, is calculated by adding 40 to the temperature to be converted, whether it is Fahrenheit or Celsius. Then, multiply the number by 9/5 when changing from Celsius to Fahrenheit or by 5/9 when changing from Fahrenheit to Celsius. Finally, subtract 40 from the previous number. This is the answer. For example, to convert 100 degrees to the equivalent Fahrenheit temperature using the 40 rule, complete the following steps:

1. 100 + 40 = 140
2. 140 x 9/5 = 252
3. 252- 40 = 212

Therefore, 100°C = 212 °F

Remember that the multiplying ratio for converting Fahrenheit to Celsius is 5/9, and the multiplying ratio for converting Celsius to Fahrenheit is 9/5. Also, remember to ADD 40 first, multiply, and then subtract 40, regardless of the direction of the conversion.

It is important for you to be able to read thermometers and convert from one scale to the other. In some types of electronic equipment, thermometers are provided as a check on operating temperatures. Thermometers are also used to check the temperature of a charging battery.

KELVIN SCALE – Also known as the absolute scale, the Kelvin scale has as its zero point the temperature at which all molecular motion ceases and no additional heat can be extracted from the substance. Theoretically, this is referred to as absolute zero temperature. This point is -273.16°C, but -273°C is used for most calculations (Figure  3). The spacing between points on the Kelvin scale is the same as the spacing between degrees on the Celsius scale; conversion from Celsius to Kelvin is made by adding 273 to the Celsius temperature.

RANKINE SCALE – This scale has the same spacing between degrees as the Fahrenheit scale, but has its zero corresponding to 0.01 Kelvin (absolute zero). This is calculated to be -459.67°F; however, -460°F is usually used. To convert from the Fahrenheit scale to the Rankine scale, add 460 degrees to the Fahrenheit temperature. Since the Rankine and Kelvin scales both have the same zero point, conversion between the two scales requires no addition or subtraction. Rankine temperature is equal to 9/5 the Kelvin temperature, and Kelvin temperature is equal to 5/9 the Rankine temperature.

### Thermometers

The measurement of temperature is known as thermometry. Many modern thermometers use liquids in sealed containers. Water was the first liquid used, but because it freezes at 0°C, it could not measure temperatures below that point. After much experimentation, scientists decided that the best liquids to use in the construction of thermometers are alcohol and mercury because of the low freezing points of these liquids.

LIQUID THERMOMETERS – The construction of the common laboratory thermometer gives some of the meaning to a change of 1 degree in temperature. A bulb is blown at one end of a piece of glass tubing that has a small bore. The tube and bulb are filled with a liquid. The temperature of both the liquid and the tube during this process are kept at a point higher than the thermometer will reach in normal usage. The glass tube is then sealed and the thermometer cooled. During the cooling process, the liquid falls away from the top of the tube and creates a vacuum within the thermometer.

Next, the thermometer is marked. The thermometer is placed in melting ice, and the height of the liquid column is marked as the 0°C point. Next, the thermometer is placed in steam at a pressure of 101,325 Pascals (Pa), and a mark is made at the point to which the liquid inside rises. That point is the boiling point or the 100°C mark. The space between these two marks is then divided into 100 equal parts. These spacing are known as degrees. This is the Celsius thermometer, which is used in laboratory work and in testing electrical equipment.

SOLID THERMOMETERS – Because the range of liquid thermometers is limited, other methods of thermometry are necessary. Most liquids freeze at temperatures between  0°C and -200°C. At the upper end of the temperature range where high heat levels are encountered, the use of liquid thermometers is limited by the high vapor pressures of those liquids. Among the most widely used types of thermometers, other than the standard liquid thermometers, are the resistance thermometer and the thermocouple.

The resistance thermometer makes use of the fact that the electrical resistance of metals change as the temperature changes. Resistance thermometers are usually made of platinum wire wound on a mica form and enclosed in a thin- walled, silver tube. It is extremely accurate from the lowest temperature to the melting point of the unit.

The thermocouple (Figure 4) is an electric circuit. Its operation is based on the principle that when two unlike metals are joined and the junction is at a different temperature from the remainder of the circuit, an electromotive force is produced. This electromotive force can be measured with great accuracy by a galvanometer. Thermocouples can be located wherever measuring temperature is important and wires run to a galvanometer located at any convenient point. By using a rotary selector switch, one galvanometer can be used to read the temperatures of thermocouples at any number of widely separated points.

Figure 4 — Thermocouple.

The principle used in compound bar thermometers (Figure 5) is the Coefficient of linear expansion which deals with Thermal Expansion in different types of metals (Temperature Differential). The bar may be in the shape of a spiral or a helix. Through the use of these shapes in a given enclosure, a greater length of the compound bar may be used; the movement of the free end per degree of temperature change is increased. Also, the indicating pointer may be joined to the moving end of the compound bar by a distance multiplying linkage to make the thermometer easier to read. Often this linkage is arranged to give the pointer a circular movement.

Figure 5 — Compound bar.

## 4.0 SOUND

The range of sound that the human ear can detect varies with the individual. The normal range extends from about 20 to 20,000 vibrations per second. In the faintest audible speech sounds, the intensity at the ear is about about 10-16 watts/cm2 at the threshold of feeling, the maximum intensity that the ear perceives as sound is about 10-4 watts/cm2.

If the ear is tested with tones of any one frequency, the threshold of audibility is, reached when intensity is reduced to such a low level that auditory sensation ceases. On the other hand, the threshold of feeling is reached when intensity is increased to such a high level that the sound produces the sensation of feeling and becomes painful. If this procedure is performed over a wide frequency range, the data can be used to plot two curves, one for the lower limit of audibility and the other for the upper limit (Figure  6).

Figure 6 — Field of audibility.

Below the lower curve, the sound is too faint for you to hear. Above the upper curve, the sensation is one of feeling rather than of hearing; that is, the sensation of sound is masked by pain. The area between the two curves shows the pressure ranges for auditory response at various frequencies.

### Sound Units

The loudness of sound is not measured by the same type of scale used to measure length. Units of sound measurement vary logarithmically with the amplitude of the sound variations. These units are the bel and decibel, which refer to the difference between sounds of unequal intensity or sound levels. The decibel (one-tenth of a bel) is the minimum change of sound level that human ear perceives. Hence, the decibel merely describes the ratio of two sound levels. A sound for which the power is 10 times as great as that of another sound level differs in power level by 1 bel, or 10 decibels. For example, 5 decibels may represent almost any volume of sound, depending on the intensity of the reference level on which the ratio is based. In sound system engineering, decibels are used to express the ratio between electrical powers or between acoustical powers.

### Intensity Level

An arbitrary zero reference level is used to describe the loudness of various sounds. This zero reference level is the sound produced by 10-16 watts per square centimeter of surface area facing the source. This level approximates the least sound perceptible to the ear, and it is usually called the threshold of audibility. Therefore, the sensation experienced by the ear when subjected to a noise of 40 decibels above reference level would be 10,000 times as great as when subjected to a sound that is barely perceptible.

## 5.0 STRUCTURE OF MATTER

All matter is composed of atoms, which are composed of smaller subatomic particles. The subatomic particles of major interest in basic physics are the electron, the proton, and the neutron. They are electrical in nature, with the proton representing a positive charge, the electron representing a negative charge, and the neutron being neutral (neither positive nor negative). Although the composition of matter follows a consistent pattern for all atoms, the detailed arrangement of subatomic particles is different for each distinct substance. It is the combination and arrangement of the subatomic particles that gives a substance its distinguishing chemical and physical characteristics.

The protons and the neutrons of an atom are closely packed together in a nucleus (core), with the electrons revolving around the nucleus (Figure 7.) Normally, atoms are electrically neutral; that is, they contain an equal number of electrons and protons. However, atoms are not electrically neutral under all conditions. Atoms that contain an equal number of electrons and protons are known as balanced atoms; those with an excess (too many electrons) or a deficiency (too few electrons) of electrons are known as ions.

Figure 7 — An atom.

The proton and the neutron have approximately the same mass (1,836 times that of an electron). In any atom, nearly all the mass is contained in the nucleus. Under normal conditions, if there were a change in the composition of the atom, there would be a change in the number or arrangement of the electrons.

 NoteBecause of their smaller mass, electrons are more easily repositioned than protons.

### Elements

The word element identifies more than a hundred substances that comprise the basic substance of all matter. Two or more elements combine chemically to form a compound; and any combination that does not result in a chemical reaction between the different elements is known as a mixture. The atom is the smallest unit that exhibits the distinguishing characteristics of an element. An atom of one element differs from an atom of any other element in the number of protons in the nucleus. All atoms of a given element contain the same number of protons. Therefore, the number of protons in the nucleus determines the type of matter. Elements are tabulated according to the number of protons they contain. The number of protons in the nucleus of the atom is referred to as the atomic number of the element.

### Nucleus

The study of the nucleus of the atom is known as nucleonic or nuclear physics. Experiments dealing with nuclei (plural of nucleus) usually involve the bombardment of the nucleus of an atom by various types of nuclear particles. By doing this, the composition of the nuclei is changed, and usually results in the release of energy. The change to the nuclei may occur as an increase or a decrease in the number of protons and/ or neutrons.

If the number of protons is changed, the atom has become an atom of a different element. Changing one element into another is known as transmutation (attempted by alchemists during the Middle Ages through chemical means, giving an impetus to the development of chemistry).

If the number of neutrons in the nucleus of an atom is changed, the atom remains an atom of the same element. All atoms of a particular element have the same number of protons (atomic number). Atoms of certain elements may contain various numbers of neutrons; for example, hydrogen, which is the sole exception to the rule that all atoms are composed of three kinds of subatomic particles. Normally, a hydrogen atom contains a single proton, a single electron, and no neutrons. If the hydrogen atom contains a neutron, it is known as deuterium. Such an atom (although still a hydrogen atom) is also known as heavy hydrogen. (This atom is termed heavy because the addition of the neutron has nearly doubled the weight of the atom.) The atomic weight of an atom is an indication of the total number of protons and neutrons in the nucleus.

Atoms of the same element having different atomic weights are known as isotopes. Nearly all elements have several isotopes; some are common, and some are rare. A few isotopes occur naturally; but most are produced by nuclear bombardment, and are radioactive or have unstable nuclei. These unstable isotopes undergo a spontaneous nuclear bombardment that eventually results in either a new element or a different isotope of the same element. The rate of spontaneous radioactive decay is measured by half-life, which is the time required for one-half the atoms of a sample of radioactive material to change (by spontaneous radioactive decay) into a different substance. For example, uranium, after a few billion years and several substance changes, becomes lead.

### Electron Shells

The physical and chemical characteristics of an element are determined by the number and distribution of electrons in the atoms of that element. The electrons are arranged in successive groups of electron shells that rotate around the nucleus. Each shell can contain no more than a specific number of electrons. An inert element (a gas element that does not combine chemically with any other element) is a substance in which the outer electron shell of each atom is completely filled. In all other elements, there are one or more electrons missing from the outer shell.

An atom with only one or two electrons in its outer shell can give up those electrons. Conversely, an atom whose outer shell needs only one or two electrons to be completely filled can accept electrons from another element that has one or two extras. The concept of needed or extra electrons arises from the basic fact that all atoms have a tendency toward completing (filling) the outer shell. For example, if an atom’s outer shell has only two electrons, it needs to collect six additional electrons (no easy task, from an energy standpoint) to have the eight required for that shell to be full. A much easier way to achieve the same objective is to give up the two electrons in the outer shell and let the full shell next to it serve as the new outer shell. In chemical terminology, this concept is termed a valence, which is the determining factor in predicting chemical combinations.

## 6.0 COMPOUNDS AND MIXTURES

Under certain conditions, two or more elements can be brought together so that they unite chemically to form a compound. The resulting substance may differ widely from any of its component elements. For example, ordinary drinking water is formed by the chemical union of two gases; hydrogen and oxygen. When a compound is produced, two or more atoms of the combining elements join chemically to form the molecule that is typical of the new compound. The molecule is the smallest unit that exhibits the distinguishing characteristics of a compound.

The combination of sodium and chlorine to form the chemical compound sodium chloride (common table salt) is a typical example of the formation of molecules. Sodium is a highly caustic, poisonous metal whose atom contains 11 electrons. Its outer shell has a single electron, which may be considered extra (a valence of +1). Chlorine, a highly poisonous gas whose atom contains 17 electrons, needs a single electron to fill its outer shell (has a valence of -1). When the atom of sodium gives up its extra electron, it becomes a positively charged ion. (It has lost a unit of negative charge.) The chlorine, having taken on this extra unit of negative charge (electron) to fill its outer shell, becomes a negative ion. Since opposite electric charges attract, the ions stick together to form a molecule of the compound sodium chloride.

The attracting force that holds the ions together in the molecular form is known as the valence bond. You will see this term when learning about transistors.

Remember, in the chemical combination, there is no change in the nucleus of either atom; the only change has occurred in the distribution of electrons between the outer shells of the atoms. Also, the total number of electrons has not changed, although they have been redistributed. Therefore, the molecule is electrically neutral, and has no resultant electrical charge.

Not all chemical combinations of atoms are on a one-for-one basis. In the case of drinking water, two atoms of hydrogen (valence of +1) are required to combine with a single atom of oxygen (valence of -2) to form a single molecule of water. Some of the more complex chemical compounds consist of many elements having various numbers of each atom. All molecules, like all atoms, are normally considered electrically neutral. One exception to this rule is the chemical activity in batteries.

Elements or compounds may be physically combined without undergoing any chemical change. Grains of finely powdered iron and sulfur stirred and shaken together retain their own identity as iron or sulfur. Salt dissolved in water is not a compound; it is merely salt dissolved in water. Each chemical substance retains its chemical identity, even though it may undergo a physical change. This is the typical characteristic of a mixture.

## 7.0 STATES OF MATTER

In their natural condition, forms of matter are classified and grouped in many different ways. One way to classify matter is according to its natural state; solid, liquid, or gas. This classification is important because of the common characteristics possessed by substances in one group distinguish them from substances in the other groups. However, you should remember that most substances can be made to assume any of the three forms.

In all matter, molecules are in constant motion, and it is the extent of this motion that determines the state of that matter. The moving molecular particles in all matter possess kinetic energy of motion. The total of this kinetic energy is the equivalent of the quantity of heat in a sample of the substance. When heat is added, the energy level is increased, and molecular agitation (motion) is increased. When heat is removed, the energy level decreases, and molecular motion diminishes.

In solids, the motion of the molecules is greatly restricted by the rigidity of the crystalline structure of the material. In liquids, the molecular motion is somewhat less restricted, and the substance is permitted to flow. In gases, molecular motion is almost entirely random; the molecules are free to move in any direction and are almost constantly in collision both among themselves and with the surfaces of a container.

### Solids

The outstanding characteristic of a solid is its tendency to retain its size and shape. Any change in these values requires the exchange of energy. The common properties of a solid are cohesion, adhesion, tensile strength, ductility, malleability, hardness, brittleness, and elasticity. Ductility is a measure of the ease with which the material can be drawn into a wire. Malleability is the ability of some materials to assume a new shape when pounded. Hardness and brittleness are self-explanatory terms. The remaining properties are discussed in the following paragraphs.

COHESION AND ADHESION – Cohesion is the molecular attraction between like particles throughout a body, or the force that holds any substance or body together. Adhesion is the molecular attraction existing between surfaces of bodies in contact, or the force that causes unlike materials to stick together. Cohesion and adhesion are possessed by different materials to widely varying degrees. Generally, solid bodies are highly cohesive but only slightly adhesive. Conversely, fluids (liquids and gases) are usually highly adhesive but only slightly cohesive. Generally, a material having one of these properties to a high degree possesses the other property to a relatively low degree.

TENSILE STRENGTH – The cohesion between the molecules of a solid explains the property known as tensile strength. Tensile strength is a measure of the resistance of a solid to being pulled apart. Steel possesses this property to a high degree; therefore, it is very useful in structural work. When a break does occur, the pieces of the solid cannot be stuck back together because merely pressing them together does not bring the molecules into close enough contact to restore the molecular force of cohesion. However, melting the edges of the break (welding) allow the molecules on both sides of the break to flow together, bringing them into the close contact required for cohesion.

ELASTICITY – If a substance will spring back to its original form after being deformed, it has the property of elasticity. This property is useful in materials used as springs. Steel and bronze are examples of materials that exhibit this property. Elasticity of compression is exhibited to some degree by all solids, liquids, and gases. The closeness of the molecules in solids and liquids makes them hard to compress, but gases are easily compressed because the molecules are farther apart.

### Liquids

Liquids tend to retain their own volume while assuming the shape of their container. Therefore, liquids are considered almost completely flexible and highly fluid.

Liquids are practically incompressible; applied pressure is transmitted through them instantaneously, equally, and undiminished to all points on the enclosing surfaces. Hydraulic apparatus can increase or decrease input forces, and provides an action similar to mechanical advantage in mechanical systems. Because of the properties of liquids, hydraulic servomechanisms have advantages and limitations when compared with other systems.

ADVANTAGES – The fluidity of hydraulic liquids permits the component parts of a system to be placed at widely separated points when necessary. Hydraulic power units transmit energy around corners and bends without using complicated gears and levers. 1-17 They operate with a minimum of slack and friction, which are often excessive in mechanical linkages. Uniform action is obtained without vibration, and the operation of the system remains largely unaffected by variations in the load. The accumulator (a component that provides the necessary pressurization of the system to furnish practically instantaneous response) can be pressurized during periods of non-action, eliminating the buildup time characteristic of electric servos.

DISADVANTAGES – Hydraulic hoses used to transmit fluid from unit to unit are bulky and heavy when compared to electric wiring. Many of the hydraulic fluids are messy and are safety hazards, such as contributing to the danger of slipping. Also, hydraulic fluids cause deterioration of electric wiring insulation and they conduct electricity, increasing the hazards of short circuits. Some hydraulic fluids are flammable.

### Gases

The most notable characteristics of a gas are its tendency to assume the shape and volume of its containers and the definite relationship that exists between the volume, pressure, and temperature of a confined gas. The ability of a gas to assume the shape and volume of its container is the result of its extremely active molecular particles, which are free to move in any direction. There is little cohesion between the molecules so they tend to separate and distribute themselves uniformly throughout the volume of the container. In an unpressurized container of liquid, pressure is exerted on the bottom and the sides of the container up to the level of the liquid. In a like container of gas, however, the pressure is also exerted against the top surface, and the pressure is equal at all points on the enclosing surfaces.

The relationship of volume, pressure, and temperature of confined gas are explained by Boyle's law, Charles' law, and the general gas law. Many laboratory experiments based on these laws make use of the ideas of standard pressure and standard temperature. These are not natural standards, but are standard values selected for convenience in laboratory usage. Standard values are used at the beginning of an experiment, or when a temperature or a pressure is to be held constant. Standard temperature is 0°C, the temperature at which pure ice melts. Standard pressure is a pressure of 101,325 Pa. In many practical uses, these standards must be changed to other systems of measurement.

All calculations based on the laws of gases make use of absolute temperature and pressure. These topics require a somewhat more detailed explanation.

GAS PRESSURE – Gas pressure is indicated in either of two ways absolute pressure or gauge pressure. Since the pressure of an absolute vacuum is zero, any pressure measured with respect to this reference is referred to as absolute pressure. In this section, absolute pressure represents the actual pressure exerted by the confined gas.

At sea level, the average atmospheric pressure is about 14.7 pounds per square inch (PSI). In a mercury barometer, this pressure would support a column of mercury 760 millimeters in height and be equal to 101,325 Pa. However, the actual pressure at sea level varies considerably and the pressure at any given altitude may differ from that at sea level. Therefore, the actual atmospheric pressure must be considered when converting absolute pressure to gauge pressure (or vice versa).

When a pressure is expressed as the difference between its absolute value and that of the local atmospheric pressure, the measurement is termed gauge pressure and is usually expressed in pounds-per-square-inch gauge (PSIG). You can convert gauge pressure to absolute pressure by adding the local atmospheric pressure to the gauge pressure.

ABSOLUTE ZERO – Absolute zero, one of the fundamental constants of physics, is usually expressed in terms of the Celsius scale. It is used in the study of the kinetic theory of gases. According to the kinetic theory of gases, if the heat energy of a given gas sample could be progressively reduced, some temperature should be reached at which the motion of the molecules would cease entirely. If accurately determined, this temperature could then be taken as a natural reference, or a true absolute zero value.

Experiments with hydrogen indicate that if a gas were cooled to -273.15°C (-273°C is used for most calculations), all molecular motion would cease and no additional heat could be extracted from the substance. In theory, at this point both the volume and the pressure of gas would shrink to zero. When temperatures are measured with respect to the absolute zero reference, they are expressed in the absolute or Kelvin scale; absolute zero may be expressed either as 0 K or as -273°C.

BOYLE’S LAW – The English scientist, Robert Boyle, was among the first to study what he called the springiness of air. By direct measurement, he discovered that when the temperature of an enclosed sample of gas was kept constant and the pressure doubled, the volume was reduced to half the former value; as the applied pressure was decreased, the resulting volume increased. From these observations, he concluded that for a constant temperature, the product of the volume and pressure of an enclosed gas remains constant.

CHARLES’ LAW – The French scientist, Jacques Charles, provided the foundation for the modern kinetic theory of gases. He found that all gases expand and contract in direct proportion to the change in the absolute temperature, provided the pressure is held constant.

Since any change in the temperature of a gas causes a corresponding change in volume, it is reasonable to expect that if a given sample of a gas were heated while confined within a given volume, the pressure should increase. By actual experiment, it was found that the increase in pressure was approximately 1/273 of 0°C pressure for each 1°C increase. Because of this fact, it is normal practice to state this relationship in terms of absolute temperature.

Figure 8 below shows Boyle's law in view A, while the effects of temperature changes on pressure and volume (Charles' law) are shown in views B and C.

 NoteThe capital P and T in the figure below represent absolute pressure and temperature, respectively.

Figure 8 — Boyle’s, Charles’, and general gas laws.

By combining Boyle's and Charles’ laws, a single expression can be derived that states all the information contained in both. This expression is called the general gas equation (Figure 8, view D).

You can see in Figure 8, views A, B, and C, the three equations are applications of the general equation. Thus, if the temperature remains constant, equals , and both can be eliminated from the general formula, which then reduces to the form shown in view A. When the volume remains constant, equals thereby reducing the general equation to the form shown in view B. Similarly, is equal to for constant pressure, and the equation is that shown in view C.

The general gas law (Figure 8, view D) applies only when one of the three measurements remains constant. When a gas is compressed, the work of compression is done to the gas. Work energy is converted to heat energy in the gas, so dynamic heating takes place. For example, when air at 0°C is compressed in a non-conducting cylinder to half its original volume, its temperature will rise to 90°C. When compressed to one tenth its original volume, its temperature rises to 429°C.

The general gas law (Figure 8, view D) applies with exactness only to ideal gases in which the molecules are assumed to be perfectly elastic. However, it describes the behavior of actual gases with enough accuracy for most practical purposes.

## 7.0 MATTER AND ENERGY

Matter is defined as anything that occupies space and has weight or mass. It exists naturally in three states; solid, liquid, or gas. Matter may be changed or combined by physical, chemical, or nuclear means. Matter has many properties; properties possessed by all forms of matter are called general properties, while those properties possessed only by certain classes of matter are referred to as special properties.

Energy is defined as the capacity for doing work, and it is classified in many ways. In this discussion, however, energy is classified as mechanical, chemical, radiant, heat, light, sound, electrical, or magnetic. Energy is constantly being exchanged from one object to another and from one form to another.

### Law of Conservation

Matter may be converted from one form to another with no change in the total amount of matter. Energy may also be changed in form with no resultant change in the total quantity of energy. In addition, a third statement has been added within the past half century, "Although the total amount of matter and energy remains constant, matter can be converted into energy or energy into matter.'' This statement is known as the law of conservation for energy and matter. The basic mathematical equation that shows the relationship between matter and energy is:

E = mc2

where:

E represents the amount of energy
m represents the amount of matter (mass)
c represents the velocity of light

This equation mathematically states that ''the destruction of matter creates energy, and that the creation of matter requires an expenditure of energy.'' From this observation, it may be inferred that a given quantity of matter is the equivalent of some amount of energy. In common usage, it is usually stated that ''matter possesses energy.''

### General Properties of Matter

All forms of matter possess certain properties. In the basic definition of matter, it is stated that "matter occupies space and has mass." Those two ideas contain most, if not all, of the general properties of matter.

Space – The amount of space occupied by, or enclosed within, the bounding surfaces of a body is termed volume. In the study of physics, this concept is modified to be completely accurate. As stated previously, matter may appear as a solid, as a liquid, or as a gas, each having special properties. For a specific substance, the volume may vary with changes in circumstances, and liquids and solids tend to retain their volume when physically moved from one container to another, and gases tend to assume the volume of the container.

To clarify the concept of occupying space, minute particles of matter must be dealt with. These are composed of still smaller particles separated from each other by empty space (which contains no matter). This idea is used to explain two general properties of matter, impenetrability and porosity.

Impenetrability of Matter – Two objects cannot occupy the same space at the same time. This statement defines the concept known as the impenetrability of matter. The actual space occupied by the individual subatomic particles cannot be occupied by any other matter. The impenetrability of matter may, at first glance, seem invalid when a cup of salt is poured into a cup of water. The result is considerably less than two cups of salt water. However, matter has an additional general property called porosity.

Porosity – Porosity explains this apparent loss of volume; the water simply occupies space between particles of salt. Porosity is present in all material, but some material is more porous than other material. Generally, gases are extremely porous, liquids only slightly porous, and the porosity of solids varies from that of the sponge to the steel ball.

Inertia – Every object tends to maintain a uniform state of motion. A body at rest never starts to move by itself; a body in motion will maintain its speed and direction unless it is caused to change. To cause a body to deviate from its condition of uniform motion, a push or pull must be exerted on it. This requirement is due to the general property of all matter known as inertia. The greater the tendency of a body to maintain uniform motion, the greater its inertia. The quantitative measure of inertia is the mass of the body.

Acceleration – Any change in the state of motion of a body is known as acceleration. In other words, acceleration is the rate of change in the motion of a body and acceleration may represent either an increase or a decrease in speed and/or change in direction of motion.

The amount of acceleration is stated as, ''the change of velocity divided by the time required to make the change." For example, if a car traveling 15 mph increased its speed to 45 mph in 4 seconds, the 30 mph increase divided by 4 seconds gives 7.5 miles per hour per second as its acceleration. By converting the 30 mph speed to 44 feet per second, the acceleration could be expressed as 11 feet per second per second, or as 11 .

Force – Force is the action or effect on a body that tends to change the state of motion of the body acted upon. A force tends to move a body at rest. It tends to increase or decrease the speed of a moving body, or it tends to change the body's direction of motion. The application of a force to a body does not necessarily result in a change in the state of motion; it may only tend to cause such a change.

A force is any push or pull, which acts on a body. Water in a can exerts a force on the sides and bottom of the can. A tug exerts a push or a pull (force) on a barge. A person leaning against a bulkhead exerts a force on the bulkhead.

In the above examples, a physical object is exerting the force and is in direct contact with the body upon which the force is being exerted. Forces of this type are called contact forces. There are other forces, which act through empty space without contact; in some cases without even seeming to have any mass associated with them. The force of gravity exerted on a body by the earth (known as the weight of the body) is an example of a force that acts on a body through empty space and without contact. Such a force is known as an action-at-a-distance force. Electric and magnetic forces are other examples of these action-at-a-distance forces. The space through which these action-at-a-distance forces are effective is called a force field.

Force is a vector quantity; that is, it has both direction and magnitude. A force is completely described when its magnitude, direction, and point of application are given. In a force vector diagram, the starting point of the line represents the point of application of the force.

Any given body, at any given time, is subjected to many forces. In many cases, all these forces may be combined into a single resultant force, which is then used to determine the total effect on the body.

Each body of matter in the universe attracts every other body with a force that is directly proportional to the mass of the bodies and inversely proportional to the square of the distance between them. This force is called the universal force of gravitational attraction. When considering the forces acting on a single body and since everybody exerts this force on every other body, it is an almost universal practice to resolve all gravitational forces into a single resultant. At or near the surface of the earth, this becomes a fairly simple process. Because of its extremely large mass, the earth exerts so large a gravitational attraction that it is entirely practical to ignore all other such attractions and merely use the earth's gravitational attraction as the resultant.

Although gravitational attraction is exerted by each body on the other, it’s often more convenient to consider the force as being exerted by the larger mass on the smaller mass. Usually, this happens when there is a great difference in the mass of two bodies. Therefore, it is commonly stated that the earth exerts a gravitational force of attraction on a body. The gravitational attraction exerted by the earth on a body is known as gravity.

The gravitational force exerted by the earth on a body is called the weight of that body, and is expressed in force units. In the English system, force is expressed in pounds. If a body is attracted by a gravitational force of 160 pounds, the body is said to weigh 160 pounds. The gravitational force between two bodies decreases as the distance between them increases; therefore, a body weighs less a mile above the surface of the ocean than it weighs at sea level; it weighs more a mile below sea level.

### Density and Specific Gravity

The density of a substance is its weight per unit volume. A cubic foot of water weighs 62.4 pounds; the density of water is 62.4 pounds per cubic foot. (In the metric system the density of water is 1 gram per cubic centimeter.)

The specific gravity (sp gr) of a substance is the ratio of the density of the substance to the density of water, or:

 sp gr = Weight of the substance Weight of equal volume of water

Specific gravity is not expressed in units but as a pure number. For example, if a substance has a specific gravity of 4, 1 cubic foot of the substance weighs 4 times as much as a cubic foot of water: 62.4 x 4 = 249.6 pounds. In metric units, 1 cubic centimeter of a substance with a specific gravity of 4 weighs 1 times 4 or 4 grams.

 NoteIn the metric system, the specific gravity of a substance has the same numerical value as its density.

Specific gravity and density are independent of the size of the sample. They depend only upon the substance of which the sample is made. Look at Table 4 below. It contains some typical values of the specific gravity for various substances.

Table 4 — Typical Values of Specific Gravity

 Substance Specific Gravity Aluminum 2.7 Brass 8.6 Copper 8.9 Gold 19.3 Ice 0.92 Iron 7.8 Lead 11.3 Platinum 21.3 Silver 10.5 Steel 7.8 Mercury 13.6 Ethyl alcohol 0.81 Water 1.00

### Pressure and Total Force

Pressure and force, while closely related, are not identical. A weight of 10 pounds resting on a table exerts a force of 10 pounds. However, the shape of the weight determines the effect of the weight. If the weight consists of a thin sheet of steel resting on a flat surface, the effect is quite different than if the same sheet of steel were resting on a sharp corner.

Pressure is concerned with the distribution of a force with respect to the area over which that force is distributed. Pressure is defined as the force per unit of area, or P= F/A.

A flat pan of water with a bottom area of 24 square inches and a total weight of 72 pounds exerts a total force of 72 pounds, or a pressure of 72/24 or 3 pounds per square inch on the flat table. If the pan is balanced on a block with a surface area of 1 square inch, the pressure is 72/1 or 72 pounds per square inch. An aluminum pan with a thin bottom is suitable for use on a flat surface, but may be damaged if placed on the small block.

The concept of pressure and force explains why a sharp knife cuts more easily than a dull one. The smaller area concentrates the applied force (increases the pressure) and penetrates more easily. For hydraulic applications, the relationship between pressure and force is a basic operating principle. In enclosed liquids under pressure, the pressure is equal at every point on the surfaces of the enclosing container; therefore, the force on a given surface is dependent on the area.

### Kinetic Energy

Moving bodies possess energy because they are capable of doing work. The energy of mass in motion is called kinetic energy, which is expressed by the equation:

Kinetic Energy = ½mv2

where:

m represents the mass of the body,
v is the velocity of its motion

When the moving body is stopped, it loses its kinetic energy. The energy is not destroyed, but is merely converted into other forms of energy such as heat and potential energy. Remember, bodies at rest also possess energy by virtue of their position.

## 8.0 MECHANICS

Mechanics is the branch of physics that deals with force, mass, and motion. Normally considered the fundamental branch of physics, it deals with matter. Many of its principles and ideas may be seen, measured, and tested. Since all other branches of physics are also concerned (to some extent at least) with force, mass, and motion, understanding this section will help you understand other branches of physics.

### Force, Mass, and Motion

Each particle in a body is acted upon by gravitational force. In every body, there is one point at which a single force, equal to the gravitational force and directed upward, would sustain the body in a condition of rest. This point is known as the center of gravity (cg), and it represents the point at which the entire mass of the body appears to be concentrated (Figure 9). The gravitational effect is measured from the center of gravity. In symmetrical objects of uniform mass, this is the geometrical center. In the case of the earth, the center of gravity is near the center of the earth.

When discussing the motion of a body, it usually describes the path followed by the center of gravity. The natural tendency of a moving body is to move in a manner so that the center of gravity travels in a straight line. Movement of this type is called linear motion.

Some moving bodies, however, do not move in a straight line, but describe an arc or a circular path. Circular motion falls into two general classes; rotation and revolution.

Figure 9 — Center of gravity in various bodies.

Objects come in many different shapes, and to discuss rotary and revolutionary motion, it is necessary to consider the location of the center of gravity with respect to the body. While reading this discussion, refer to Figure 9.

In view A, the center of gravity of a ball coincides with the physical center of the ball. However, in the flat washer (view B), the center of gravity does not coincide with any part of the object, but is located at the center of the hollow space inside the ring. In irregularly shaped bodies (view C); the center of gravity may be difficult to locate exactly.

If the body is completely free to rotate, the center of rotation coincides with the center of gravity. But, a body may be restricted so its rotation is about some point other than the center of gravity. Here, the center of gravity revolves around the center of rotation. These conditions are illustrated in Figure 10.

Generally, the gyro rotor (view A) is said to rotate about its axis, and the ball (view B) is said to revolve about a point at the center of its path.

Figure 10 — Center of gravity and center of rotation.

#### Masses in Motion

Motion is defined as the act or process of changing place or position. The state of motion refers to the amount and the type of motion possessed by a body at some definite instant (or during some interval) of time. A body at rest is not changing in place or position; it has zero motion, or is motionless.

The natural tendency of any body at rest is to remain at rest; a moving body tends to continue moving in a straight line with no change in speed or direction. A body that obeys this natural tendency is in uniform motion.

Any change in the speed or direction of motion of a body is known as acceleration and requires the application of some force. The acceleration of a body is directly proportional to the force causing that acceleration; acceleration also depends upon the mass of the body. For example, the greater mass of a lead ball makes it harder to move than a wood ball of the same diameter. The wood ball moves farther with the same push.

These observations point to a connection between force, mass, and acceleration. They indicate that the acceleration of a body is directly proportional to the force exerted on that body and inversely proportional to the mass of that body. In mathematical form, this relationship may be expressed as:

 a = F m

Or, as it is more commonly stated, "Force is equal to mass times acceleration":

F = ma

#### Acceleration Due to Gravity

The small letter g used in formulas for solving weight when mass is known (W = mg) represents the acceleration of a body in free fall, neglecting any friction. This can happen only in a vacuum. At sea level near the equator, g has the approximate values of 32 ft/s2 in the fps system, and 9.8 m/s2 in the mks system. Transposing the formula W = mg to solve for m, the absolute units of mass of a body may be determined when its weight is known.

If the accelerating force is applied to the center of gravity in such a manner as to accelerate the body with no rotation, it is called a translational force. A force applied in such a manner as to cause the body to rotate about a point is called a torque force.

#### Laws of Motion

Among the most important discoveries in theoretical physics are Newton’s three fundamental laws of motion. These laws have been used in explanations of various topics earlier in this chapter. At this point, they clarify and summarize much of the discussion about mechanical physics.

• Every body tends to maintain a state of uniform motion unless a force is applied to change the speed or direction of motion.
• The acceleration of a body is directly proportional to the magnitude of the applied force and inversely proportional to the mass of the body; acceleration is in the direction of the applied force.
• For every force applied to a body, the body exerts an equal force in the opposite direction.

#### Momentum

Every moving body tends to maintain uniform motion. Quantitative measurement of this tendency is proportional to the mass and velocity of the body:

momentum = mass x velocity

The concept of momentum explains why heavy objects in motion at a given speed are harder to stop than lighter objects, and also why it’s easier to stop a given body moving at low speed than it is to stop the same body moving at high speed.

### Work, Power, and Energy

You learned earlier that energy is the capacity for doing work. In mechanical physics, work involves the idea of a mass in motion; it is usually thought of as the product of the applied force and the distance through which the mass is moved:

work = force x distance

For example, if a man raises a weight of 100 pounds to a height of 10 feet, he accomplishes 1,000 foot-pounds of work. The amount of work accomplished is the same regardless of the time involved. However, the rate of doing the work varies greatly.

The rate of doing work, known as power, is defined as the work accomplished per unit of time:

 power  = work time

Refer to the previous example about the man raising a weight of 100 pounds. If the work is accomplished in 10 seconds, power is being expended at the rate of 100 foot-pounds per second; if it takes 5 minutes (300 seconds), power is being expended at the rate of approximately 3.3 foot-pounds per second. Therefore, measurements of power include force, distance, and time.

In the English system of measurements, the unit of mechanical power is known as horsepower, and it is the equivalent of 33,000 foot-pounds per minute or 550 foot-pounds per second. Energy is readily convertible from one form to another; therefore, the work and power measurements based on the conversion of energy must be readily convertible. For example, the electrical unit of power is the watt. Electrical energy can be converted into mechanical energy; therefore, electrical power must be converted into mechanical power. One horsepower is the mechanical equivalent of 746 watts of electrical power, and 1 horsepower is capable of doing the same amount of work as 746 watts in the same time.

The accomplishment of work always involves a change in the type of energy, but does not change the total quantity of energy. Thus, energy applied to an object may produce work, changing the composition of the energy possessed by the object.

#### Potential Energy

A body has potential energy if, by virtue of its position or its state, it can do work. A wound clock spring and a cylinder of compressed gas both possess potential energy since they can do work in returning to their uncompressed condition. Also, a weight raised above the earth has potential energy since it can do work in returning to the ground. Thus, potential energy results when work has been done against a restoring force. The water in a reservoir above a hydroelectric plant has potential energy regardless of whether the water was placed there by work applied via a pump or by the work done by the sun to lift it from the sea and place it in the reservoir in the form of rain.

#### Kinetic Energy

The ability of a body to do work by virtue of its motion is called its kinetic energy. A rotating wheel on a machine has kinetic energy of rotation. A car moving along the highway has kinetic energy of translation.

For a given mass (m) moving in a straight line with a velocity (v), the kinetic energy is determined by:

kinetic energy = ½mv2

where m is expressed in slugs, v in feet per second, and kinetic energy in foot-pounds

For example, the kinetic energy of a 3,200 pound car that is traveling at 30 miles per hour can be found by expressing the 3,200 pounds as 100 slugs and the 30 mph as 44 feet per second. Inserting these values into the formula makes; kinetic energy = x 100 x 44 x 44 = 96,800 foot-pounds of energy.

This amount of kinetic energy is the result of 96,800 foot-pounds of work (plus that to overcome friction) having been applied to the car to get it traveling at the rate of 44 feet per second. The same amount of energy could do the work of lifting the 3,200 pounds vertically to a distance of 30.25 feet. Also, it would have the potential energy to move the car if it were at rest on an incline and then allowed to coast to a point that is vertically 30.25 feet below its starting point (again neglecting friction).

#### Efficiency

Provided there is no change in the quantity of matter, energy is convertible with no gain or loss. However, the energy that results from a given action may not be in the desired form; it may not even be usable in its resultant form. In all branches of physics, this concept is known as efficiency.

The energy expended is always greater than the energy recovered. An automobile in motion possesses a quantity of kinetic energy that depends on its mass and velocity. To stop the car, energy must be converted into potential energy. When the car comes to rest, its potential energy is considerably less than the kinetic energy it possessed while in motion. The difference, or the energy lost, is converted into heat by the brakes. The heat serves no useful purpose, so the recovered energy is less than the expended energy. The system is less than 100 percent efficient in converting kinetic to potential energy.

The term efficiency, normally used in connection with work and power, means the ratio of the input to the output work, power, or energy. It is always expressed as a decimal or as a percentage less than one.

#### Friction

In mechanical physics, the most common cause for the loss of efficiency is friction. Whenever one object slides or rolls over another, irregularities in the contacting surfaces interlock and cause an opposition to the force being exerted. Even rubbing two smooth pieces of ice together produces friction. Friction also exists in the contact of air with all exposed parts of an aircraft in flight.

When a nail is struck with a hammer, the energy of the hammer is transferred to the nail, and the nail is driven into a board. The depth of penetration depends on the momentum of the hammer, the size and shape of the nail, and the hardness of the wood. The larger or duller the nail and the harder the wood, the greater the friction; therefore, there is lower efficiency and less depth of penetration, but greater heating of the nail.

Friction is always present in moving machinery, which means that the useful work accomplished by the machine is never as great as the energy applied. Work accomplished to overcome friction is usually not recoverable. Friction can be minimized by decreasing the number of contacting points, by making the contacting areas as small and as smooth as possible, by the use of bearings, or by the use of lubricants.

There are two kinds of friction; sliding and rolling. Rolling friction is usually of lower magnitude, so most machines are built so rolling friction is present rather than sliding friction. The ball bearing and the roller bearing are used to convert sliding friction to rolling friction. A third type of bearing, the common (or friction) bearing requires application of a lubricant to surfaces that have been made as smooth as possible. Many new types of machines use self-lubricating bearings to minimize friction and maximize efficiency.

The concept of mechanical advantage has proved to be one of the great discoveries of science. Mechanical advantage is the basic principle involved in levers, block and tackle systems, screws, hydraulic mechanisms, and other work saving devices. However, in the true sense, these devices do not save work; they merely enable humans to accomplish tasks that they could not otherwise do. For example, a normal human could not lift the rear end of a truck to change a tire; but with a jack, a block and tackle, or a lever, a human can do the job.

Mechanical advantage is usually considered with respect to work. Work represents the application of a force through a distance to move an object through a distance. Thus, it may be seen that there are two forces involved, each with an appropriate distance. These forces are shown by the simple lever in Figure 11. Refer to this figure as you read this section.

Assuming perfect efficiency, the work input (F1 D1) is equal to the work output (F2 D2).

Assuming equal distances D1 and D2, a force of 10 pounds must be applied at the source to counteract a weight of 10 pounds at the load.

If the fulcrum is moved nearer the load, less force is required to balance the same load. This is an example of the mechanical advantage of force. If force is applied to raise the load 1 foot, the source must be moved through a distance greater than 1 foot. Thus, mechanical advantage of force represents a mechanical disadvantage of distance. By moving the fulcrum nearer the source, these conditions are reversed.

Ideally, the input work equals the output work (assuming no losses), and the mechanical advantage may be stated as a ratio of the force or of the distances. In actual situations, friction results in energy loss and decreased efficiency, thereby requiring an even greater input to accomplish the same work.

### Revolving Bodies

Revolving bodies represent masses in motion; therefore, they possess all the characteristics and obey all the laws associated with moving bodies. In addition, since they possess a specific type of motion, they have special properties. Revolving bodies travel in a constantly changing direction, and they are constantly subjected to an accelerating force. Momentum tends to produce linear motion, but this is prevented by application of a force that restrains the object. This restraining force that prevents the object from continuing in a straight line is known as centripetal force. Remember Newton's third law of motion that states “for every force applied to a body, the body exerts an equal force in the opposite direction”; therefore, the centripetal force exerted on a revolving body must be opposed by an equal force that tends to produce linear motion. This second force is known as centrifugal force. The two forces, their relationships, and their effects are shown in Figure 12.

Figure 12 — Forces on revolving bodies.

The various forces involved in revolving bodies may be shown by using a ball and string. A slip knot is tied in the center of a 10 foot length of string to shorten the line to 5 feet; a rubber ball is attached to one end of the string. Holding the other end of the line, whirl the ball slowly in a circle. Note that the ball exerts a force against the hand (through the string); and to restrain the ball in its circular path, the hand must exert a force (through the string) on the ball. Now, make the ball revolve at a higher speed. Note that as the forces increase, the ball continues in a circular path.

At some rotational speed, the forces involved become great enough to overcome inertial friction and the knot slips. At this time, allow the velocity of the rotation to stabilize (keep whirling the ball at the same speed) so you can analyze the existing conditions. When the knot slips, the ball is temporarily unrestrained and is free to assume linear motion in the direction of travel at that instant (tangent to the circle at the instantaneous position). The ball travels in a straight line until the string reaches its full length; during this time, no force is exerted on or by the hand. As soon as all the slack is taken up, there is a sharp jerk. An accelerating force is exerted to change the direction of motion from its linear path into a circular rotation. The ball again assumes rotational motion, but with an increase in radius.

The ball does not make as many revolutions in the same time (rotational velocity is decreased), but it does maintain its former linear velocity. (The kinetic energy and the momentum of the ball have not changed.) Since the change in direction is less abrupt with a large radius than with a small one, less accelerating force is required, and the hand will feel less force. If you accelerate the ball to the same rotational velocity as you were doing just before the knot slipped, the linear velocity of the ball becomes much greater than before, as do the centripetal and centrifugal forces.

In this example, the hand is fixed at a point that represents the center of rotation. This assumption is not actually accurate but it doesn't affect the general conclusions. For practical purposes, the two forces are equal at all points along the string at any given time, and the magnitude of each force is equal at all points along the string.

In revolving or rotating bodies, all particles of the matter that are not on the axis of rotation are subjected to the forces just described. The statement is true whether the motion is through a complete circle or merely around a curve: An aircraft tends to skid when changing course; an automobile tends to take curves on two wheels. The sharper the curve (smaller radius), or the higher the velocity, the greater the tendency to skid.

## 9.0 HEAT

Heat represents a form of energy. Therefore, it must be readily exchangeable with, or convertible into, other forms of energy. When a piece of lead is struck a sharp blow with a hammer, part of the kinetic energy of the hammer is converted into heat. In the core of a transformer, electrical and magnetic energy are exchanged; but due to hysteresis and eddy currents, some of the energy is lost as heat. These are some examples of the unwanted conversions, but many times the production of heat is desirable. Many devices are used to produce heat.

Regardless of how or why heat is produced, it possesses certain characteristics that make it important to the technician. Knowledge of the nature and behavior of heat may help you understand the operation of some types of electronic equipment or to determine why equipment doesn't operate or operates incorrectly.

### Nature of Heat

There are several theories regarding the nature of heat, none of which explain all the characteristics and properties exhibited by heat. The two theories most commonly included in discussions regarding the nature of heat are the kinetic theory and the radiant energy theory.

In the kinetic theory, it is assumed that the quantity of heat contained by a body is represented by the total kinetic energy possessed by the molecules of the body.

The radiation theory treats radio waves, heat, and light as the same general form of energy, differing primarily in frequency. Heat is considered as a form of electromagnetic energy involving a specific band of frequencies falling between the radio spectrum and light.

A common method used to produce heat energy is the burning process. Burning is a chemical process in which the fuel unites with oxygen and a flame is usually produced. The amount of heat liberated per unit mass or per unit volume during complete burning is known as the heat of combustion of a substance. Through experimentation, scientists have found that each fuel produces a given amount of heat per unit quantity burned.

### Transfer of Heat

There are three methods of heat transfer; conduction, convection, and radiation. In addition to these, a phenomenon called absorption is related to the radiation method of heat transfer.

#### Conduction

The metal handle of a hot pot may burn the hand; a plastic or wooden handle, however, remains relatively cool even though it is in direct contact with the pot. This phenomenon is due to a property of matter known as thermal conductivity. All materials conduct heat, some very readily, some to an almost negligible extent.

When heat is applied to a body, the molecules at the point of application become violently agitated, strike the molecules next to them, and cause increased agitation. The process continues until the heat energy is distributed evenly throughout the material. Aluminum and copper are used for cooking pots because they conduct heat very readily to the food being cooked. Wood and plastic are used as handles because they are very poor conductors of heat. As a general rule metals are the best conductors of heat, although some metals are considerably better than others.

Among solids, there is an extremely wide range of thermal conductivity. In the original example, the metal handle transmits heat from the pot to the hand, with the possibility of burns. The wooden or plastic handle does not conduct heat very well, so the hand is given some protection. Materials that are extremely poor conductors are called insulators and are used to reduce heat transfer. Some examples are the wood handle of soldering irons, the finely spun glass or rock wool insulation in houses, or the wrapping used on steam pipes.

Figure 13 — Water is a poor conductor of heat.

Liquids are generally poorer conductors than metals. Look at Figure 13. The ice in the bottom of the test tube has not yet melted, although the water at the top is boiling. Water is such a poor conductor that the rate of heating of the water at the top of the tube is not sufficient to cause rapid melting of the ice at the bottom. Since thermal conduction is a process by which molecular energy is passed on by actual contact, gases are generally even poorer conductors than liquids because the molecules are farther apart and molecular contact is not so pronounced. A double pane window with airspace between the panes is a fair insulator.

#### Convection

Convection is the process by which heat is transferred by movement of a hot fluid. For example, an electron tube gets hotter and hotter until the air surrounding it begins to move. The motion of the air is upward because heated air expands in volume and is forced upward by the denser cool air surrounding it. The upward motion of the heated air carries the heat away from the hot tube by convection. Transfer of heat by convection is sped by using a ventilating fan to move the air surrounding a hot object. The rate of cooling of a hot vacuum tube can also be increased by providing copper fins to conduct heat away from the hot tube. The fins provide large surfaces against which cool air can be blown.

A convection process may take place in a liquid as well as in a gas. One example is a transformer in an oil bath. The hot oil is less dense (has less weight per unit volume) and rises; while the cool oil falls, is heated, and rises in turn.

When the circulation of gas or liquid is not rapid enough to remove sufficient heat, fans or pumps may be used to accelerate the motion of the cooling material. In some installations, pumps are used to circulate water or oil to help cool large equipment. In airborne installations, electric fans and blowers are used to aid convection.

Conduction and convection cannot wholly account for some of the phenomena associated with heat transfer. For example, heating through convection cannot occur in front of an open fire because the air currents are moving toward the fire. It cannot occur through conduction because the conductivity of the air is very low, and the cooler currents of air moving toward the fire would more than overcome the transfer of heat outward. Therefore, heat must travel across space by some means other than conduction and convection.

The existence of another process of heat transfer is still more evident when the heat from the sun is considered. Since conduction and convection take place only through molecular contact within some medium, heat from the sun must reach the earth by some other method. (Outer space is an almost perfect vacuum.) Radiation is the name given to this third method by which heat travels from one place to another.

The term radiation refers to the continual emission of energy from the surface of all bodies. This energy is known as radiant energy. It is in the form of electromagnetic waves and is identical in nature with light waves, radio waves, and x-rays, except for a difference in wavelength. Sunlight is a form of radiant heat energy that has traveled a great distance to reach the earth. These electromagnetic heat waves are absorbed when they come in contact with nontransparent bodies. The net result is that the motion of the molecules in the body is increased, as indicated by an increase in the temperature of the body.

The differences in conduction, convection, and radiation are described as follows:

• Although conduction and convection are extremely slow, radiation takes place with the speed of light. For example, an eclipse of the sun shuts off the heat from the sun at the same time as the light is shut off.
• Radiant heat may pass through a medium without heating it. For example, the air inside a greenhouse may be much warmer than the glass through which the sun’s rays pass.
• Although conducted or convected heat may travel in roundabout routes, radiant heat always travels in a straight line. For example, radiation can be cut off with a screen placed between the source of heat and the body to be protected.

#### Absorption

The sun, a fire, and an electric light bulb all radiate energy, but a body need not glow to give off heat. A kettle of hot water or a hot soldering iron radiates heat. If the surface is polished or light in color, less heat is radiated. Bodies that do not reflect are good radiators and good absorbers, and bodies that reflect are poor radiators and poor absorbers. For this reason, white clothing is worn in the summer. A practical example of the control of heat is the thermos bottle. The flask itself is made of two walls of silvered glass with a vacuum between them. The vacuum prevents the loss of heat by conduction and convection, and the silver coating reduces the loss of heat by radiation. The most effective color for heat transfer is dull black; dull black is the ideal absorber and also the best radiator.

#### Thermal Expansion

Nearly all substances expand or increase in size when their temperature increases. Railroad tracks are laid with small gaps between the sections to prevent buckling when the temperature increases in summer. Concrete pavement has strips of soft material inserted at intervals to prevent buckling when the sun heats the roadway. A steel building or bridge is put together with red hot rivets so that when the rivets cool they shrink, and the separate pieces are pulled tightly together.

As a substance is expanded by heat, the weight per unit volume decreases because the weight of the substance remains the same, while the volume is increased by the application of heat. Density decreases with an increase in temperature.

Experiments show that for a given change in temperature, the change in length or volume is different for each substance. For example, a given change in temperature causes a piece of copper to expand nearly twice as much as a piece of glass of the same size and shape. For this reason, the connecting wires into an electronic tube are not made of copper but of a metal that expands at the same rate as glass. If the metal does not expand at the same rate as the glass, the vacuum in the tube is broken by air leaking past the wires in the glass stem. The metal usually used for this purpose is an alloy called Kovar.

The amount that a unit length of any substance expands for a 1 degree rise in temperature is known as the coefficient of linear expansion for that substance. To estimate the expansion of any object, such as a steel rail, you need to know three things about the object; its length, the rise in temperature to which it is subjected, and its rate of coefficient of linear expansion. You can use the following equation to find the amount of expansion.

Expansion = coefficient x length x rise in temperature

or

e = kl (t2 - t1)

where:

k is the coefficient of expansion for the substance (In some instances, the Greek letter alpha (α) is used to indicate the coefficient of linear expansion.).

l represents the length,

t2 - t1 is the difference of the two temperatures

Use the equation shown above to solve the following problem:

If a steel rod measures exactly 9 feet at 21°C, what is its length at 55°C?

The coefficient of linear expansion for steel is 11 x 10-6. If the equation e = kl (t2 - t1)  is used, then;

e = (11 x 10-6 ) x 9 x (55 – 21)

e = 0.000011 x 9 x 34

e = 0.003366

This amount, when added to the original length of the rod, makes the rod 9.003366 feet long. (Since the temperature has increased, the rod is longer by the amount of e. If the temperature had been lowered, the rod would have become shorter by a corresponding amount.) The increase in the length of the rod is relatively small; but, if the rod were placed where it could not expand freely, there would be a tremendous force exerted due to thermal expansion. You can see that thermal expansion is a consideration when designing ships, buildings, and all forms of machinery. Table 5 is a list of the coefficients of approximate linear expansion of some substances per degree Celsius.

Table 5 — Linear Expansion Coefficients

 Substance Coefficients of Approximate Linear Expansion Aluminum 24 x 10-6 Brass 19 x 10-6 Copper 17 x 10-6 Glass 4 to 9 x 10-6 Kovar 4 to 9 x 10-6 Lead 28 x 10-6 Iron, Steel 11 x 10-6 Quartz 0.4 x 10-6 Zinc 26 x

You can see the practical application for the differences in the coefficients of linear expansion in the thermostat (Figure 14).

Figure 14 — Thermostat.

This instrument is made from two strips of dissimilar metal (compound bar) fastened together. When the temperature changes, the bar bends because of the unequal expansion of the metals. Thermostats are used in overload relays for motors, in temperature sensitive switches, and in electric ovens. The coefficient of surface or area expansion is approximately twice the coefficient of linear expansion. The coefficient of volume expansion is approximately three times the coefficient of linear expansion. It is interesting that if a plate contains a hole, the area of the hole expands at the same rate as the surrounding material. When a volume is enclosed by a thin solid wall, the volume expands at the same rate as the solid body containing the volume of material.

### Tabulation of Heat

A unit of heat must be defined as the heat necessary to produce some agreed upon standard of change. The internationally accepted unit in common use is the Btu. One Btu is the quantity of heat necessary to raise the temperature of 1 pound of water 1°F. The terms quantity of heat and temperature are commonly misused. The distinction between them should be understood clearly. For example, place two identical pans containing different amounts of water of the same temperature, over identical gas burner flames for the same length of time. At the end of that time, the smaller amount of water will have reached a higher temperature. Equal amounts of heat have been supplied, but the increases in temperatures are not equal. In another example, if the water in both pans is the same temperature, say 80°F, and both are to be heated to the boiling point, more heat must be supplied to the larger amount of water. The temperature rises are the same for both pans, but the quantities of heat necessary are different.

### Mechanical Equivalent

Mechanical energy is usually expressed in joules, or foot-pounds. Energy in the form of heat is expressed in calories or in Btu. In a precise experiment in which electric energy is converted into heat in a resistance wire immersed in water, the results show that 4.184 joules equals 1 thermochemical calorie, or that 778 foot-pounds equals 1 Btu. The following equation is used when converting from the English system to the metric system: 1 Btu = 252 calories.

### Specific Heat

One way that one substance differs from another is that they require different quantities of heat to produce the same temperature change in a given mass of substance. The thermal capacity of a substance is the quantity, measured in calories, of heat needed per gram mass to increase the temperature 1°C. The specific heat of a substance is the ratio of its thermal capacity to the thermal capacity of water at 15°C. Specific heat is expressed as a number, which, because it is a ratio, has no units and applies to both the English and the metric systems.

Water has a high thermal heat capacity. Large bodies of water on the earth keep the air and the surface of the earth at a fairly constant temperature. A great quantity of heat is required to change the temperature of a large lake or river. Therefore, when the temperature of the air falls below that of such bodies of water, they give off large quantities of heat to the air. This process keeps the atmospheric temperature at the surface of the earth from changing very rapidly.

To find the heat required to raise the temperature of a substance, multiply its mass by the rise in temperature times its specific heat. For example, it takes 1,000 Btu to raise the temperature of 100 pounds of water 10°F, but only 31 Btu to raise 100 pounds of lead 10°F. Table 6 gives the specific heats of several common substances listed in descending order.

Table 6 — Specific Heats of Some Common Substances

 Hydrogen (at constant pressure) 3.409 Water at 4°C 1.0049 Water at 15°C 1 Water at 30°C 0.9971 Ice at 0°C 0.502 Steam at 100°C 0.421 Air (at constant pressure) 0.237 Aluminum 0.217 Glass 0.16 Iron 0.114 Copper 0.093 Brass, Zinc 0.092 Silver 0.057 Tin 0.056 Mercury 0.033 Gold, Lead 0.031

### Change of State

A thermometer placed in melting snow behaves in a strange manner. The temperature of the snow rises slowly until it reaches 0°C. Provided that the mixture is stirred constantly, it remains at the point until all the snow has changed to water. When all the snow has melted, the temperature again begins to rise. A definite amount of heat is required to change the snow to water at the same temperature. This heat is required to change the water from crystal form to liquid form.

### Heat of Fusion

Heat of Fusion is the amount of heat required to convert a unit mass of a solid at its melting point into a liquid without an increase in temperature. Eighty gram calories of heat are required to change 1 gram of ice at 0°C to water at 0°C. In English units, the heat required to change 1 pound of ice at 32°F to water at 32°F is 144 Btu. These values (80 gram-calories and 144 Btu) are called the heat of fusion of water. The heat used while the ice is melting represents the work done to produce the change of state. Since 80 calories are required to change a gram of ice to water at 0°C, when a gram of water is frozen, it gives up 80 calories.

Many substances behave very much like water. At a given pressure, they have a definite heat of fusion and an exact melting point. Many materials, however, do not change from a liquid to a solid state at one temperature. Molasses, for example, gets thicker and thicker as the temperature decreases; but there is no exact temperature at which the change of state occurs. Wax, celluloid, and glass are other substances that do not change from a liquid to a solid state at any particular temperature. In fact, measurements of the glass thickness at the bottom of windows in ancient cathedrals tend to indicate that the glass is still flowing at an extremely slow rate. Most types of solder used in electronics maintenance also tend to become malleable before melting.

### Heat of Vaporization

Damp clothing dries more rapidly under a hot, flat iron than under a cold one. A pool of water evaporates more rapidly in the sun than in the shade. It may be concluded that heat has something to do with evaporation. The process of changing a liquid to a vapor is like the process that occurs when a solid melts.

Heat of Vaporization is the amount of heat required to convert a unit mass of a liquid at its boiling point into vapor without an increase in temperature. If a given quantity of water is heated until it evaporates, a much greater amount of heat is used than that necessary to raise the same amount of water to the boiling point. For example, 540 calories are required to change 1 gram of water to vapor at a temperature of 100°C. It takes 972 Btu to change 1 pound of water at 212°F to water vapor (steam) at 212°F. The amount of heat necessary for this change is called the heat of vaporization of water. Over five times as much heat is required to change a given amount of water to vapor than to raise the same amount of water from the freezing to the boiling point.

The change from water to vapor occurs as follows. As the water molecules take up more and more energy from the heating source, their kinetic energy increases. The motion resulting from the high kinetic energy of the water molecules causes a pressure known as the vapor pressure. As the velocity of the molecules increases, the vapor pressure increases. The boiling point of a liquid is that temperature at which the vapor pressure equals the external or atmospheric pressure. At normal atmospheric pressure at sea level, the boiling point of water is 100°C or 212°F.

While the water is below the boiling point, a number of molecules acquire enough kinetic energy to break away from the liquid state into a vapor. For this reason some evaporation takes place below the boiling point. At or above the boiling point, large numbers of molecules have enough energy to change from liquid to vapor, and evaporation rapidly occurs.

If the molecules of water are changing to water vapor in an open space, the air currents carry them away quickly. In a closed container, they rapidly become crowded and some of them bounce back into the liquid as a result of collisions. When as many molecules are returning to the liquid state as are leaving it, the vapor is said to be saturated. Experiments have shown that saturated vapor in a closed container exerts a pressure and has a given density at every temperature.

## 10.0 LIGHT

The exact nature of light is not fully understood, although we have been studying the subject for many centuries. Some experiments seem to show that light is composed of tiny particles, and some indicate that it is made up of waves.

First, one theory, and then the other, attracted the approval and acceptance of the physicists. Today, there are scientific phenomena that are explained only by the wave theory and another large group of occurrences that are explained only by the particle or corpuscular theory. Physicists, constantly searching for some new discovery that would bring these contradictory theories into agreement, gradually have come to accept a theory concerning light that is a combination of these two views.

According to the view now generally accepted, light is a form of electromagnetic radiation; that is, light and similar forms of radiation are made up of moving electric and magnetic forces.

### Characteristics

Light waves travel in straight lines. When they encounter any substance, they are transmitted, reflected, or absorbed. Those substances that permit clear vision through them, and that transmit almost all the light falling upon them, are said to be transparent. Those substances that allow the passage of part of the light, but appear clouded and impair vision substantially, are called translucent. Those substances that transmit no light are called opaque.

Objects that are not light sources are visible only because they reflect part of the light reaching them from some luminous source. If light is neither transmitted nor reflected, it is absorbed or taken up by the medium. When light strikes a substance, some absorption and reflection always take place. No substance completely transmits, reflects, or absorbs all the light that reaches its surface.

#### Luminous Intensity and Intensity of Illumination

Though these two terms may sound like the description of the same property, they really aren't. Luminous intensity refers to the total light produced by a source, while intensity of illumination describes the amount of light received per unit area at a distance from the source. Some of the terms used to describe luminous intensity and intensity of illumination are defined in the following paragraphs.

Candela – A unit of luminous intensity, in a given direction, of a source that emits monochromatic radiation.

Footcandle – The intensity of illumination of a surface (illuminance) is directly proportional to the luminous intensity of the light source and is inversely proportional to the square of the distance between the light source and the surface.

Look at Figure 15, which shows the inverse square law of light.

Figure 15 — Inverse square law of light.

If a card is placed 1 foot from a light source, the light striking the card is of certain intensity. If the card is moved 2 feet away, the intensity of light decreases with the square of the distance (2 x 2 or 4 times) and is 1/4 as bright. If the card is moved to 3 feet away from the light source, the intensity decreases the square of the distance (3 x 3 or 9 times), and the light is 1/9 the intensity it was at 1 foot. If the card is moved to 4 feet away, the light is 1/16 as intense as it was at 1 foot.

The footcandle is one unit of measuring the intensity of incident light, and it can be computed by using the following formula:

 Illumination in footcandles  = candlepower of source (distance in feet)2

A surface 1 foot from a 1 candlepower source would have an illumination of 1 footcandle, but if it was moved to a distance of 4 feet, a 16-candlepower source would be required for the same illumination.

The inverse square law of light holds true for undirected light only; that is, light emissions not controlled by a reflector or lens. For light that is directed, the rate at which its intensity diminishes is dependent upon the rate or divergence of the beam.

Lumen – is the amount of light flowing through a solid angle of 1 steradian (sr) from a standard candle. A light source of 1 candlepower, placed in the center of a sphere that has a radius of 1 foot, will illuminate every point on the surface of the sphere at an intensity of 1 footcandle. Then every square foot of the surface receives 1 lumen of light.

The output of light bulbs may be given either in candlepower or in lumens, but since light bulbs do not distribute light equally in all directions, the lumen is most frequently used. It is customary for light bulb manufacturers to measure the light output in all directions and specify its total output in lumens. The common, gas filled, tungsten-filament light bulbs are usually more efficient in the larger sizes. For example, a 25-watt light bulb produces about 260 lumens (10.4 lumens per watt), while a 200-watt bulb produces 3,640 lumens (18.2 lumens per watt).

Lux – is the illumination given to a surface 1 meter away from a 1 candlepower source and is sometimes called a meter-candle.

Luminance – whether a body is self-luminous or just a reflector of the light that falls upon it luminance (or brightness) refers to the light a surface gives off in the direction of the observer.

### Reflection

Light waves obey the law of reflection. Optical devices incorporated specifically for the purpose of reflecting light are generally classed as mirrors. They may be of a polished opaque surface, or they may be a specially coated glass. In the case of the glass mirror, there is some refraction as well as reflection; however, if the glass is of good quality and not excessively thick, the refraction will cause no trouble. The following discussion is based on a polished surface mirror.

Several classes of mirrors are shown in Figure 16, views A, B, and C. All the devices work on the basis of the law of reflection. The applications of the law are briefly summarized here. Basically, the reflector is used to change the direction of a light beam (view A), to focus a beam of light (view B), or to intensify the illumination of an area (view C).

Figure 16 — Reflectors of light.

In Figure 16, view A, the angle of the reflected light may be changed to some degree by changing the angle at which the incident light impinges upon the mirror. In Figure 16, view B, the focusing action of a concave mirror is indicated. The point of focus may be made any convenient distance from the reflector by proper selection of the arc of curvature of the mirror. The sharper the curvature, the shorter the focal length. In Figure 16, view C, the principle of intensification of illumination for a specific area is shown. The flashlight is an example of this application. In the system shown, the light source (bulb) is located approximately at the principal focus point, and that all rays reflected from the surface are parallel. Also, the reflector alone does not concentrate all the rays; some are transmitted without being reflected and are not included in the principal beam.

### Refraction

As light passes through a transparent substance, it travels in a straight line. However, as it passes into or out of that substance, it is refracted in the same manner as other waves. Refraction of light waves results from the fact that light travels at slightly different velocity in different transparent media (Figure 17). To simplify the problem of understanding the action of light refraction and to make it possible to predict the outcome of specific applications, many transparent substances have been tested for refractive effectiveness. The ratio of the speed of light in air to its speed in each transparent substance is called the index of refraction for that substance. For example, light travels about 1.5 times as fast in air as it does in glass, so the index of refraction of glass is about 1.5. When using the law of refraction in connection with light, a "denser" medium refers to a medium with a higher index of refraction.

Figure 17 — The law of refraction.

Refraction through a piece of plate glass is shown in Figure 17. The ray of light strikes the glass plate at an oblique angle along path AB. If it were to continue in a straight line, it would emerge from the plate at point N; but obeying the law of refraction, it is bent toward the normal (RS) and emerges from the glass at point C. Upon entering the air, the ray does not continue on its path but is bent away from the normal (XY) and along the path CD in the air. If the two surfaces of the glass are parallel, the ray leaving the glass is parallel to the ray entering the glass. The displacement depends upon the thickness of the glass plate, the angle of entry into it, and the index of refraction for the glass.

All rays striking the glass at any angle other than perpendicular are refracted in the same manner. In the case of a perpendicular ray, no refraction takes place, and the ray continues through the glass and into the air in a straight line.

PRISMS – When a ray of light passes through a flat sheet of glass, it emerges parallel to the incident ray. This holds true only when the two surfaces of the glass are parallel. When the two surfaces are not parallel, as in a prism, the ray is refracted differently at each surface of the glass and does not emerge parallel to the incident ray.

Figure 18 — Passage of light through a prism.

Figure 18, view A, shows that both refractions are in the same direction, and that the ray coming out of the prism is not parallel to the ray going into it. The law of refraction explains what has happened. When the ray entered the prism, it was bent toward the normal; and when it emerged, it was bent away from the normal. Notice that the deviation is the result of the two normals not being parallel.

If two triangular prisms are placed base to base (Figure 18, view B), parallel incident rays passing through them are refracted and caused to intersect. The rays passing different parts of the prisms, however, do not intersect at the same point. In the case of two prisms, there are only four refracting surfaces. The light rays from different points on the same plane are not refracted to a point on the same plane behind the prism. They emerge from the prisms and intersect at different points along an extended common baseline, as shown in Figure 18, view B, points A, B, and C.

Parallel incident light rays falling upon two prisms that have been joined apex to apex (Figure 18, view C) are spread apart. The upper prism refracts light rays toward its base; and the lower prism refracts light rays toward its base, causing the two sets of rays to diverge.

POSITIVE LENSES – A positive (convergent) lens acts like two base-to-base prisms with their surfaces rounded off into a curve. Rays that strike the upper half of the lens bend downward, and rays that strike the lower half bend upward. A good lens causes all wavelengths within each ray to cross at the same point behind the lens (Figure 19, view A).

When the incident ray of light enters the denser medium (the lens), it bends toward the normal. When it passes through into the less dense medium (the air), it bends away from the normal. Look at Figure 19, view B. It shows the refraction of only one ray of light, but all rays passing through a positive lens are affected in the same way. All incident light rays, either parallel or slightly diverging, will converge to a point after passing through a positive lens.

Figure 19 — Positive lenses.

The only ray of light that can pass through a lens without bending is the ray that strikes the first surface of the lens at a right angle, perpendicular or normal to the surface. It passes through that surface without bending and strikes the second surface at the same angle. It leaves the lens without bending. This ray is shown in Figure 19, view B.

Positive lens and convergent lens are synonymous terms, since either of them may be used to describe the action of a lens that focuses (brings to a point of convergence) all light rays passing through it. All simple positive lenses are easy to identify since they are thicker in the center than at the edges. The three most common types of simple positive lenses are shown in Figure 19, view C.

Figure 20 — Negative lenses.

NEGATIVE LENSES – Figure  18, view C, shows the refraction of light rays by two prisms apex to apex. If the prism surfaces are rounded, the result is a negative (divergent) lens. A negative lens is called a divergent lens since it does not focus the rays of light passing through it. Light rays passing through a negative lens diverge or spread apart, as shown in Figure 20, view A.

Figure 20, view B, applies the law of refraction to one ray of light passing through a negative lens. Just as in a positive lens, a ray of light passing through the center of a negative lens is not affected by refraction and passes through without bending.

Three simple negative lenses are shown in Figure 20, view C. They are often referred to as concave lenses and are readily identified by their concave surfaces. The simple negative lenses are thicker at the edges than at the center. They are generally used in conjunction with simple positive lenses where their primary use is to help form a sharper image by eliminating or subduing various defects present in an uncorrected simple positive lens.

### Frequencies and Color

The electromagnetic waves that produce the sensation of light are very high in frequency, which means that they have very short wavelengths. These wavelengths are measured in nanometers (millionths of millimeters). Figure 21 indicates that light with a wavelength of 700 nanometers is red, and that a light with a wavelength of 500 nanometers is blue-green.

The color scale in Figure 21 is based on the wavelengths in air. All color component wavelengths of the visible spectrum are present in equal amounts in white light. Variations in composition of the component wavelengths result in other characteristic colors. If a beam of white light is passed through a prism, as shown in Figure 21, it is refracted and dispersed into its component wavelengths. Each of these wavelengths react differently on the eye, which then sees the colors making up the visible spectrum.

Figure 21 — Electromagnetic wavelengths and the refraction of light.

The visible spectrum is a mixture of red, orange, yellow, green, blue, indigo, and violet. When the primaries (red, green, and blue) are mixed together in overlapping beams of light, white light results.

 NoteThese are not the primaries used in mixing pigments.

Furthermore, the complementary or secondary colors (magenta, yellow, and cyan) are shown by mixing any two of the primary colors in overlapping beams of light. If red and green light is mixed in equal intensities, it will make yellow light; mixing green and blue light produces blue-green light (cyan); and mixing blue and red light correctly produces magenta (a purplish red color).

## Review Questions

1. What are the three broad categories of measurement?

A. English, Metrics, and Mass
B. Magnitude, Direction, and Time
C. Meter, Kilogram, and Second
D. Foot, Pound, and Btu

2. What unit of measurement is normally used to express scientific measurements?

A. English
C. Metric
D. Lumen

3. What element is being measured when using the term kilogram?

A. Distance
B. Mass
C. Time
D. Heat

4. What is the difference between the mass of a body and the weight of a body?

A. The mass of a body changes in form but the weight of the body remains constant.
B. The mass of a body and weight are constant at all times.
C. Mass of a body does not change but the weight of a body changes when in a solid form.
D. The mass of a body is constant no matter where the body is located; however its weight is not constant.

5. What is meant when a person is described as weighing 195 pounds?

A. That person has the pull of gravity of 195 grams.
B. The mass of the body is equivalent to the volume of 195.
C. That person has the same pull of gravity a mass of 195 would have located near sea level.
D. That person has the same pull of gravity when in constant motion.

6. What term is defined as the work done in lifting 1 pound a distance of 1 foot against the force of gravity?

A. Foot-pound
B. Inch-pound
C. Force
D. Energy

7. List the measurements included in the units of power?

A. Joule and Horsepower
B. Force, Distance, and Time
C. Watt, Foot-pound, and Newtons
D. Velocity and Mass

8. What are the four types of temperature scales?

A. Celsius, Fahrenheit, Kelvin, and Rankine
B. Hot, Cold, Fahrenheit, and Celsius
C. Atmospheric, Liquid, Solid, and Gas
D. Freezing, Boiling, Steam, and Vapor

9. What procedure is used to convert from the Fahrenheit scale to the Celsius scale?

A. Subtract the 32 degree difference and multiply the result by 5/9.
B. First multiply the reading on the thermometer by 5/9 and then add 32 to the result.
C. Add 32 degrees and multiply the result by 5/9.
D. Add 40 to the temperature then multiply by 9/5.

10. What type of thermometer is usually used in the laboratory?

A. Liquid
B. Solid
C. Gas
D. Resistant

11. What principle is used in compound bar thermometers?

A. Pascals
B. Resistance
C. Coefficient of linear expansion
D. Thermocouple

12. What terms are used to describe sound?

A. Frequency and change
B. Loudness and frequency
C. Watts and audibility
D. Bel and Decibel

13. What gives a substance its distinguishing chemical and physical characteristics?

A. The atom’s negative charge
B. The arraignment of the atom’s neutral particle and the density of the hydrogen atom
C. The combination and arrangement of the atom’s subatomic particles’
D. The physical characteristics of the atom

14. What is a balanced atom?

A. An atom that has more protons than electrons
B. An atom that contains an equal number of protons and electrons
C. An atom that contains more electrons than neutron
D. An atom that has neither positive nor negative charge

15. How is the atomic number of an element determined?

A. By the number of electrons
B. By the chemical reaction with the different elements
C. By the amount of mixture
D. By the number of protons in its nucleus

16. The outer electron shell of an element is completely filled. What type of element is this?

A. Electron
B. Proton
C. Inert
D. Neutral

17. What is the smallest unit that forms a compound?

A. Molecule
B. Element
C. Neutron
D. Hydrogen

18. What are the states of matter?

A. Liquid, Mass, and Hardness
B. Solid, Liquid, and Gas
C. Solid and Liquid
D. Gas, Vapor, and Solid

19. Which is a common property of solids?

A. Resistant to heat
C. Material compound
D. Mixture of properties

20. What is one of the main uses of absolute zero?

A. A natural source reference
B. It’s a fundamental constant of physics
C. Change in temperature changes volume
D. To study kinetic gases

21. What are the absolute zero points on the Kelvin and Celsius scales?

A. 0 Kelvin and -100° Celsius
B. 0 Kelvin and -273° Celsius
C. 10 Kelvin and -300° Celsius
D. 15 Kelvin and -373° Celsius

22. What does Charles' law state?

A. Temperature of an enclosed sample of gas was kept constant and the pressure doubled; the volume was reduced to half the former value.
B. When temperature changes, the pressure changes.
C. Constant temperature and volume of an enclosed gas remains constant.
D. All gases expand and contract in direct proportion to the change in the absolute temperature, provided the pressure is held constant.

23. What is mathematically stated by the formula E = mc2?

A. The destruction of matter creates energy, and that the creation of matter requires an expenditure of energy.
B. Anything that can occupy space and has weight or mass.
C. Energy can be changed in form with no resultant change in the total quantity of energy.
D. Matter can be converted from one form to another.

24. Why is force considered a vector quantity?

A. Force has a direction.
B. Force has both direction and magnitude.
C. The direction of force is constant.
D. The mass remains constant and the amount of force is variable.

25. In the English system of measurement, what force is expressed in pounds?

A. The momentum of a moving object in a given direction
B. When the mass of an object remains constant if movement remains constant
C. Gravitational force exerted by the earth on the body, known as weight of that body, expressed in force units
D. The gravitational force it takes to keep an object in one location

26. How is the density of a substance described?

A. Its mass and shape
B. By the form of the substance when in its solid state
C. Its total weight
D. Its weight per unit volume

27. What term describes the energy of mass in motion?

A. Density
B. Universal force
C. Kinetic energy
D. Volume

28. What branch of physics deals with force, mass, and motion?

A. Hydraulics
B. Mechanics
C. Kinetics
D. Specific gravity

29. What point of an object is its center of gravity?

A. The point where the gravitational force is at its greatest
B. The point that is farthest away from the largest mass area of an object
C. The point where a single force is less than the gravitational direction of an object
D. The point where a single force equal to the gravitational force and directed up, and sustains the body at rest

30. Generally, a gyro rotor ________ about its axis.

A. revolves
B. is stationary
C. rotates
D. exceeds gravity

31. What type of force is an accelerating force applied to the center of gravity of a body so that the body is accelerated with no rotation?

A. Translational
C. Momentum
D. Torque

32. What is the most common reason for efficiency loss in mechanical physics?

A. Motion
B. Force
C. Time
D. Friction

33. What is the principle that allows man to accomplish work that he normally could not do?

A. Efficiency
C. Kinetic energy
D. Potential energy

34. What force prevents an object from continuing along a straight line?

A. Momentum
B. Linear
C. Centripetal
D. Centrifugal

35. In the radiation theory, heat is generally treated the same as which form of energy?

B. Absorption
C. Kinetic theory
D. Insulators

36. What are the three methods of heat transfer?

B. Contact, thermal, and air space
C. Conductivity, absorption, and air

37. In what state is matter the poorest conductor of heat?

A. Solid
B. Liquid
C. Gas
D. Mass

38. What principle is involved in temperature-sensitive switches?

A. Refraction of thermal energy
B. Coefficient of linear expansion
C. Change of state
D. Heat of vaporization

39. What effect does the heat of fusion have on solder?

A. It causes it to become malleable before it melts; that is, it flows at a very slow rate.
B. It causes the solder to become brittle as the temperature increases.
C. It causes the solder to have an exact melting point.
D. It causes the solder to be thicker at the bottom.

40. What is meant by the term luminous intensity?

A. The constant color level of the light source
B. The maximum angle in degree of reflected light without loss of brightness
C. The total light produced by a source
D. The reflected light without loss of color

41. What term is usually used to describe the output of a light bulb?

A. Lumen
B. Watt
C. Joule
D. Vector

42. What are the principle uses of reflectors?

A. To focus in one area
B. Focus in two directions simultaneously without loss of directional light
C. To intensify the illumination of an area only
D. Focus a beam of light, change direction of a light beam, or intensify the illumination of an area

43. Which are the primary colors of light frequencies?

A. Magenta, yellow, and cyan
B. Green, blue, and yellow
C. Red, orange, and yellow
D. Red, green, and blue

44. What is the result if you mix the primary colors together?

A. Yellow light
B. Blue-green light
C. White light
D. Purple light