Force cos angle e Resistance FIGURE 7-37. Working against friction.
Thus, the three kinds of friction may be classified as: (1) Starting (static) friction, (2) sliding friction, and (3) rolling friction.
Static Friction When an attempt is made to slide a heavy object along a surface, the object must first be broken loose or started. Once in motion, it slides more easily. The "breaking loose" force is, of course, proportional to the weight of the body.
The force necessary to start the body moving slowly is designated "F," and "F" is the normal force pressing the body against the surface (usually its weight). Since the nature of the surfaces rubbing against each other is important, they must be considered. The nature of the surfaces is indicated by the coefficient of starting friction which is designated by the letter "k" This coefficient can be established for various materials and is often published in tabular form. Thus, when the load (weight of the object) is known, starting friction can be calculated by using the equation, F = kF'.
For example, if the coefficient of sliding friction of a smooth iron block on a smooth, horizontal surface is 0.3, the force required to start a 10- pound block would be 3 pounds; a 40-pound block, 12 pounds.
Starting friction for objects equipped with wheels and roller bearings is much smaller than that for sliding objects. Nevertheless, a locomotive would have difficulty getting a long train of cars in motion all at one time. Therefore, the couples between the cars are purposely made to have a few inches of play. When the engineer is about to start the train, he backs the engine until all the cars are pushed together. Then, with a quick start forward the first car is set in motion.
This technique is employed to overcome the static friction of each wheel (as well as the inertia of each car). It would be impossible for the engine to start all of the cars at the same instant, for static friction, which is the resistance of being set in motion, would be greater than the force exerted by the engine. Once the cars are in motion, however, static friction is greatly reduced and a smaller force is required to keep the train in motion than was required to start it.
Sliding Friction Sliding friction is the resistance to motion offered by an object sliding over a surface. It pertains to friction produced after the object has once been set into motion, and is always less than starting friction. The amount of sliding resistance is dependent on the nature of the surface of the object, the surface over which it slides, and the normal force between the object and the surface.
This resistive force may be computed by the formula, F = uN where: "F" is the resistive force due to friction expressed in pounds; "N" is the force exerted on or by the object perpendicular (normal) to the 251
surface over which it slides; and "" (mu) is the given in minutes. If time in minutes is used in coefficient of sliding friction. (On a horizontal this equation, then power will be expressed in ft.- surface, N is equal to the weight of the object Ibs./min.
in pounds.) The area of the sliding object exposed to the sliding surface has no effect on the results. Power = pounds x feet -_ =ft.-Ibs./ sec.
A block of wood, for example, will not slide any seconds easier on one of the broad sides than it will on a or, smoothness). Therefore, area does not enter into narrow side, (assuming all sides have the same Power = pounds x feet minutes - = ft.-Ibs./min.
the equation above. Example:
An aircraft engine weighing 3,500 pounds was hoisted a vertical height of 7 feet in order to install Rolling Friction it on an aircraft. The hoist was hand-powered and Resistance to motion is greatly reduced if an How much power was developed by the man crankobject is mounted on wheels or rollers. The force ing the hoist? (Neglect friction in the hoist.)
of friction for objects mounted on wheels or rollers is called rolling friction. This force may be Power = fa computed by the same equation used in computing sliding friction, but the values of u will be much = 3,500 pounds x 7 feet smaller. For example, u for rubber tires on con- 3 minutes crete or macadam is about .02. The value of u for =8,167 ft.-lbs./min.
roller bearings is very small, usually ranging from .001 to .003 and is often disregarded.
Example:
An aircraft with a gross weight of 79,600 lb. is towed over a concrete ramp. What force must be exerted by the towing vehicle to keep the airplane rolling after once set in motion?
F = uN Power is often expressed in units of horsepower.
One horsepower is equal to 550 ft.-lbs./sec. or 33,000 ft.-lbs./min.
Example:
In the hoist example above, calculate the horsepower developed by the man.
= .02 × 79,600 = 1,592 lb.
Power Horsepower = Power in ft. lbs./min.
Power is a badly abused term. In speaking of 33,000 power-driven equipment, people often confuse the Fd term 'power" with the ability to move heavy loads.
This is not the meaning of power. A sewing ma- hp. = 33,000 chine motor is powerful enough to rotate an air- craft engine propeller providing it is connected to = 33,000 8167 =0.247, or about ¼ hp the crankshaft through a suitable mechanism. It could not rotate the propeller at 2,000 r.p.m., however, for it is not powerful enough to move a large Power is rate of doing work:
load at a high speed. Power, thus, means rate of doing work. It is measured in terms of work ac- P= complished per unit of time. In equation form, Fower = . Force x Distance watt, where In the metric system the unit of power is the time 1 watt= 1 joule/sec.
0x, P= FD The watt is the metric unit of power, thus a motor with a power output of 5,000 watts is capable If force is expressed in pounds, distance in feet, of doing 5,000 joules of work per second.
and time in seconds, then power is given in ft.-lbs./ A kilowatt (kw) is equal to 1,000 watts. Hence sec. (foot-pounds per second). Time may also be the above motor has a power output of 5 kw.
How much time does the elevator cab of the previous example need to ascend 30 meters if it is being lifted by a 5-kw motor? We rewrite P=W/t in the form W *= P and then substitute w=1.47 x 10s joules and p=5.103 watts to find that ‡= P 1.47 x 105 joules 5 x 103 watts = 29.4 sec.
Energy In many cases when work is done on an object, something is given to the object which it retains and which later enables it to do work. When a weight is lifted to a certain height such as in the case of a trip-hammer, or when a clock spring is wound, the object acquires, through having work done on it, the ability to do work itself. In storage batteries and gasoline, energy is stored which can be used later to do work. Energy stored in coal or food can be used to do work. This storage gives such objects the ability to do work;
thus, energy is defined as the ability to do work In general, a change in energy is equal to the work done; the loss in energy of a body may be measured by the work it does, or the gain in energy of a body may be measured by the amount of work done on it. For convenience, energy which bodies possess is classified into two categories:
(1) Potential and (2) kinetic.
Potential energy may be classified into three groups: (1) That due to position, (2) that due to distortion of an elastic body, and (3) that which produces work through chemical action. Water in an elevated reservoir, and the lifted weight of a pile-driver are examples of the first group; a stretched rubber band or compressed spring are examples of the second group; and energy in coal, food, and storage batteries are examples of the third group.
Bodies in motion required work to put them in motion. Thus, they possess energy of motion.
Energy due to motion is known as kinetic energy.
A moving vehicle, a rotating flywheel, and a hammer in motion are examples of kinetic energy.
Energy is expressed in the same units as those used to express work. The quantity of potential energy possessed by an elevated weight may be computed by the equation, Potential Energy = Weight X Height.
If weight is given in pounds and height in feet, the final unit of energy will be ft.-lbs. (footpounds).
Example: An aircraft with a gross weight of 110,000 pounds is flying at an altitude of 15,000 feet above the surface of the earth. How much potential energy does the airplane possess with respect to the earth?
Potential Energy = Weight X Height PE = 110,000 × 15,000 = 1,650,000,000 ft.-lbs.
Forms of Energy The most common forms of energy are heat, mechanical, electrical, and chemical. The various forms of energy can be changed, or transformed, into another form in many different ways. For example, in the case of mechanical energy, the energy of work done against friction is always converted into heat energy, and the mechanical energy that turns an electric generator develops electrical energy at the output of the generator.
MOTION OF BODIES General The study of the relationship between the motion of bodies or objects and the forces acting on them is often called the study of "force and motion." In a more specific sense, the relationship between velocity, acceleration, and distance is known as kinematics.
Uniform Motion Motion may be defined as a continuing change of position or place, or as the process in which a body undergoes displacement. When an object is at different points in space at different times, that object is said to be in motion, and if the distance the object moves remains the same for a given period of time, the motion may be described as uniform. Thus, an object in uniform motion always has a constant speed.
Speed and Velocity In everyday usage, speed and velocity often mean the same thing. In physics they have definite 253
and distinct meanings. Speed refers to how fast an object is moving, or how far the object will travel in a specific time. The speed of an object tells nothing about the direction an object is moving. For example, if the information is supplied that an airplane leaves New York City and travels 8 hours at a speed of 150 m.p.h., this information tells nothing about the direction in which the airplane is moving. At the end of 8 hours, it might be in Kansas City, or if it traveled in a circular route, it could be back in New York City.
Velocity is that quantity in physics which denotes both the speed of an object and the direction in which the object moves. Velocity can be defined as the rate of motion in a particular direction.
The average velocity of an object can be calculated using the formula, Va= where:
Va = the average velocity.
= the rate of motion or average speed.
t = the elapsed time.
Acceleration Acceleration is defined by the physicist as the rate of change of velocity. If the velocity of an object is increased from 20 m.p.h. to 30 m.p.h., the object has been accelerated. If the increase in velocity is 10 m.p.h. in 5 seconds, the rate of change in velocity is 10 m.p.h. in 5 seconds, or 2 m.p.h.
-. Expressed as an equation, sec.
1 = V- Vi where:
A = acceleration.
V; = the final velocity (30 m.p.h.).
V; = the initial velocity (20 m.p.h.).
t = the elapsed time.
The example used can be expressed as follows:
A = 30 m.p.h. - 20 m.p.h.
5 sec.
4 = 2 m.p.h.
sec.
If the object accelerated to 22 m.p.h. in the first second, 24 m.p.h. in the next second, and 26 m.p.h. in the third second, the change in velocity each second is 2 m.p.h. The acceleration is said to be constant, and the motion is described as uniformly accelerated motion.
If a body has a velocity of 3 m.p.h. at the end of the first second of its motion, 5 m.p.h. at the end of the next second, and 8 m.p.h. at the end of the third second, its motion is described as acceleration, but it is variable accelerated motion.
Newton's Law of Motion When a magician snatches a tablecloth from a table and leaves a full setting of dishes undisturbed, he is not displaying a mystic art; he is demonstrating the principle of inertia.
Inertia is responsible for the discomfort felt when an airplane is brought to a sudden halt in the parking area and the passengers are thrown forward in their seats. Inertia is a property of matter.
This property of matter is described by Newton's first law of motion, which states:
Objects at rest tend to remain at rest; objects in motion tend to remain in motion at the same speed and in the same direction.
Bodies in motion have the property called momentum. A body that has great momentum has a strong tendency to remain in motion and is therefore hard to stop. For example, a train moving at even low velocity is difficult to stop because of its large mass. Newton's second law applies to this property. It states:
When a force acts upon a body, the momentum of that body is changed. The rate of change of momentum is proportional to the applied force.
The momentum of a body is defined as the product of its mass and its velocity. Thus, Momentum = mass x velocity or, M=mV Now if a force is applied, the momentum changes at a rate equal to the force or:
F=rate of change of momentum = Substituting mV for M:
miVe-m;Vi F= 254
Since the mass does not usually change, mf=mi= Newton's third law of motion is often called the
m. Then law of action and reaction. It states that for every mVe-mVi action there is an equal and opposite reaction.
F= This means that if a force is applied to an object, From the previous section the second term is recognized as acceleration. Then the second law becomes:
F=ma the object will supply a resistive force exactly equally to and in the opposite direction of the force applied. It is easy to see how this might apply to objects at rest. For example, as a man stands on the floor, the floor exerts a force against his feet exactly equal to his weight. But this law is also applicable when a force is applied to an object in On earth, gravity exerts a force on each body causing an acceleration of 32 ft./sec.? which is usually designated as 4g". The force is commonly called weight, W. Using the formula above:
W=mg and;
W m= m Then on earth the second law becomes:
F= ma When a force applied to an object is more than sufficient to produce and sustain uniform motion, inertia of the object will cause such a resistive force that the force opposing the motion of the object equals the force producing the motion.
sistance to change in velocity due to inertia is usually referred to as internal force. When several forces act upon an object to produce accelerated motion, the sums of the external forces are in a state of unbalance; however, the sums of the external and the internal forces are always in a state W of balance, whether motion is being either sustained
(a) or produced.
formula. The following examples illustrate the use of this force" means the force one body exerts on a second Forces always occur in pairs. The term acting body, and reacting force means the force the second Example: body exerts on the first.
A train weighs 32,000 lbs. and is traveling at 10 ft./sec. What force is required to bring it to rest in 10 seconds? air backward with a force of 500 pounds, the air When an aircraft propeller pushes a stream of pushes the blades forward with a force of 500 F = g W - (a) move forward. In like manner, the discharge of pounds. This forward force causes the aircraft to W (Ve-V;) exhaust gases from the tailpipe of a turbine engine = is the action which causes the aircraft to move 32,000 (0- 10) The three laws of motion which have been dis- 32 10 cussed here are closely related. In many cases, all 32,000 × (- 10) three laws may be operating on a body at the 32 x 10 = - 1,000 lbs.
The negative sign means that the force must be applied against the train's motion.
Example:
An aircraft weighs 6,400 pounds. How much force is needed to give it an acceleration of 6 ft./sec.2?
Circular Motion Circular motion is the motion of an object along a curved path that has a constant radius. For example, if one end of a string is tied to an object and the other end is held in the hand, the object can be swung in a circle. The object is constantly deflected from a straight (linear) path by the pull exerted on the string, as shown in figure 7-38.
As an object in figure 7-38 travels along the F= W (a) the string deflects it from Y toward Z. This pull circumference from X to Y, the pull or force on = 6400 × 6 = 1,200 Ib. is called centripetal force, which deflects an object from a straight path and forces it to travel in a 32 curved path. Thus, the string exerts a centripetal 255
FIGURE 7-38. Circular motion.
force on the object, and the object exerts an equal but opposite force on the string, obeying Newton's The difference between rotary and circular motion is that, in the case of rotary motion, the body or object spins, while in circular motion the whole object moves along a curved path.
When an object spins at a constant speed about a fixed axis, it has uniform rotary motion. When its direction or rate of spin changes, it has variable rotary motion.
Momentum Momentum is defined as the product of an object's mass and its velocity. The force required to accelerate an object is proportional to an object's mass and the acceleration given it. Acceleration has been defined as the rate of change of an object's velocity. This is expressed as a The force that is equal to centripetal force, but acting in an opposite direction, is called centrifugal force. In the example of figure 7-38, it is the force exerted by the object on the string. Without a centripetal force, there is no centrifugal force.
Centripetal force is always directly proportional to the mass of the object in circular motion. Thus, if the mass of the object in figure 7-38 is doubled, the pull on the string must be doubled to keep the object in its circular path, provided the speed of the object remains constant.
Centripetal force is inversely proportional to the radius of the circle in which an object travels. If the string in figure 7-38 is shortened and the speed remains constant, the pull on the string must be increased since the radius is decreased, and the string must pull the object from its linear path more rapidly.
Using the same reasoning, the pull on the string must be increased if the object is swung more rapidly in its orbit. Centripetal force is thus directly proportional to the square of the velocity of the object. The formula for centripetal force is:
C.P.= MV: R where:
M =the mass of the object.
V=velocity.
R= radius of the object's path.
Rotary Motion The motion of a body turning about an axis is called rotary motion. This is the familiar motion that occurs as the crankshaft of an engine turns.
Vs- Vi A = where:
A = acceleration.
V¿ = final velocity.
V; = initial velocity.
t = elapsed time.
Newton's second law of motion, F = MA, involves acceleration. If the original expression for acceleration is substituted in Newton's second law, it becomes:
F = MV, - MV;
This formula can be further resolved to illustrate momentum by multiplying both sides by t:
Ft = MV; - MV i.
This formula illustrates that an object's momentum is a product of its mass and its velocity.
HEAT Heat is a form of energy. It is produced only by the conversion of one of the other forms of energy.
Heat may also be defined as the total kinetic energy of the molecules of any substance.
Some forms of energy which can be converted into heat energy are as follows:
(1) Mechanical Energy. This includes all methods of producing increased motion of molecules such as friction, impact of bodies, or compression of gases.
(2) Electrical Energy. Electrical energy is converted to heat energy when an electric current flows through any form of resistance. This might be an electric iron, electric light, or an electric blanket.
(3) Chemical Energy. Most forms of chemical reaction convert stored potential energy into heat. Some examples are the explosive effects of gunpowder, the burning of oil or wood, and the combining of oxygen
(4) Radiant Energy. Electromagnetic waves of certain frequencies produce heat when they are absorbed by the bodies they strike. Included are X-rays, light rays,
(5) Nuclear Energy. Energy stored in the nucleus of atoms is released during the process of nuclear fission in a nuclear
(6) The Sun. All heat energy can be directly or indirectly traced to the nuclear re- Mechanical Equivalent of Heat When a gas is compressed, work is done and the gas becomes warm or hot. Conversely, when a gas under high pressure is allowed to expand, the expanding gas becomes cool. In the first case, work was converted into energy in the form of heat; in the second case heat energy was expended. Since heat is given off or absorbed, there must be a relationship between heat energy and work. Also, when two surfaces are rubbed together, the friction develops heat. However, work was required to cause the heat, and by experimentation, it has been shown that the work required and the amount of heat produced by friction are proportional. Thus, heat can be regarded as a form of energy.
According to this theory of heat as a form of energy, the molecules, atoms, and electrons in all bodies are in a continual state of motion. In a hot body, these small particles possess relatively large amounts of kinetic energy, but in cooler bodies they have less. Because the small particles are given motion, and hence kinetic energy, work must be done to slide one body over the other.
Mechanical energy apparently is transformed, and what we know as heat is really kinetic energy of the small molecular subdivisions of matter.
Two different units are used to express quantities of heat energy. They are the calorie and the British thermal unit. One calorie is equal to the amount of heat required to change the temperature of 1 gram of water 1 degree centigrade.
1 This term "calorie" (spelled with a small e) is 1,000 of the Calorie (spelled with a capital C) used in the measurement of heat-producing or energyproducing value in foods. One B.t.u. (British thermal unit) is defined as the amount of heat required to change the temperature of 1 pound of water 1 degree Fahrenheit. The calorie and the gram are seldom used in discussing aviation maintenance. The B.t.u., however, is commonly referred to in discussions of engine thermal efficiencies and the heat content of aviation fuel.
A device known as the calorimeter is used to measure quantities of heat energy. For example, it may be used to determine the quantity of heat energy available in 1 pound of aviation gasoline.
A given weight of the fuel is burned in the calorimeter, and the heat energy is absorbed by a large quantity of water. From the weight of the water and the increase in its temperature, it is possible to compute the heat yield of the fuel.
A definite relationship exists between heat and mechanical energy. This relationship has been established and verified by many experiments which show that:
One B.t.u. = 778 ft.-lbs.
Thus, if the l-pound sample of the fuel mentioned above were found to yield 20,000 B.t.u., it would be the equivalent of 20,000 B.t.u. X 778 ft.- Ibs./B.t.u. or 15,560,000 ft.-lbs. of mechanical energy.
Unfortunately no heat engine is capable of transforming all of the available heat energy in the fuel it burns into mechanical energy. A large portion of this energy is wasted through heat losses and operational friction.
Methods of Heat Transfer There are three methods by which heat is trans.
ferred from one location to another or from one substance to another. These three methods are conduction, convection, and radiation.
Conduction Everyone knows from experience that the metal handle of a heated pan can burn the hand. A 257
Wax rings along by actual contact, gases are poor con- Aluminum Nickel ductors.
2009 At the point of application of the heat source the molecules become violently agitated. These molecules strike adjacent molecules causing them to become agitated. This process continues until 020 the heat energy is distributed evenly throughout Copper Iron the substance. Because molecules are farther apart in gases than in solids, the gases are much poorer conductors of heat.
Materials that are poor conductors are used to prevent the transfer of heat and are called heat insulators. A wooden handle on a pot or a soldering iron serves as a heat insulator. Certain materials such as finely spun glass or asbestos are particularly poor heat conductors. These materials are therefore used for many types of insulation.
FIGURE 7-39. Various metals conduct heat at different rates.
plastic or wood handle, however, remains relatively cool even though it is in direct contact with the pan. The metal transmits the heat more easily than the wood because it is a better conductor of heat. Different materials conduct heat at different rates. Some metals are much better conductors of heat than others. Aluminum and copper are used in pots and pans because they conduct heat very rapidly. Woods and plastics are used for handles because they conduct heat very slowly.
Figure 7-39 illustrates the different rates of conduction of various metals. Four rods of different metals have several wax rings handing on them. One flame is used to heat one end of each rod simultaneously. The rings melt and drop off the copper rod first, then from the aluminum rod, then from the nickel rod, and last from the iron rod. This example shows that among the four metals used, copper is the best conductor of heat and iron is the poorest.
Liquids are poorer conductors of heat than metals. Notice that the ice in the test tube shown in figure 7-40 is not melting rapidly even though the water at the top is boiling. The water conducts heat so poorly that not enough heat reaches the ice to melt it.
Gases are even poorer conductors of heat than liquids. It is possible to stand quite close to a stove without being burned because air is such a poor conductor. Since conduction is a process whereby the increase in molecular energy is passed Convection Convection is the process by which heat is transferred by movement of a heated fluid (gas or liquid). For example, an electronic tube will, when heated, become increasingly hotter until the air surrounding it begins to move. The motion of the air is upward. This upward motion of the heated air carries the heat away from the hot tube by convection. Transfer of heat by convection may be hastened by using a ventilating fan to move the air surrounding a hot object. The rate of cooling of a hot vacuum tube can be increased if it is provided with copper fins that conduct heat Steam Boiling water Water Ice Metal ring to keep ice Burner from rising FIGURE 7-40. Water is a poor conductor of heat.
Cooling pipes Transformer windings FIGURE 7-41. Oil convection currents cool a transformer.
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. Figure 7-41 shows 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 are 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.
Radiation Conduction and convection cannot wholly account for some of the phenomena associated with heat transfer. For example, the heat one feels when sitting in front of an open fire cannot be transferred by convection because the air currents are moving toward the fire. It cannot be transferred through conduction because the conductivity of the air is very small, and the cooler currents of air moving toward the fire would more than overcome the transfer of heat outward.
Therefore, there must be some way for heat to travel across space other than by 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 some medium, such as a gas or a liquid, heat from the sun must reach the earth by another method, since space is an almost perfect vacuum. Radiation is the name given to this third method of heat transference.
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, radio waves, or X-rays, which are all alike except for a difference in wave lengths. These waves travel at the velocity of light and are transmitted through a vacuum more easily than through air because air absorbs some of them. Most forms of energy can be traced back to the energy of sunlight. Sunlight is a form of radiant heat energy which travels through space to reach the earth. These electromagnetic heat waves are absorbed when they come in contact with nontransparent bodies. The 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 between conduction, convection, and radiation may now be considered. First, although conduction and convection are extremely slow, radiation takes place with the speed of light.
This fact is evident at the time of an eclipse of the sun when the shutting off of the heat from the sun takes place at the same time as the shutting off of the light. Second, 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. Third, 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.
Material Specific heat Mercury- 0.033 Copper- 0.095 Iron and steel.. 0.113 Glass _ 0.200 Alcohol. 0.500 Water_ 1.000 FIGURE 7-42. Specific heat values for some common materials.
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 which 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 season.
A practical example of the control of loss of heat is the thermos bottle. The flask itself is made of two walls of glass separated by a vacuum.
The vacuum prevents the loss of heat by conduction and convection, and a silver coating on the walls prevents the loss of heat by radiation.
Specific Heat One important way in which substances differ is in the requirement of different quantities of heat to produce the same temperature change in a given mass of the substance. Each substance requires a quantity of heat, called its specific heat capacity, to increase the temperature of a unit of its mass 1° C. The specific heat of a substance is the ratio of its specific heat capacity to the specific heat capacity of water. 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.
It is fortunate that water has a high specific heat capacity. The larger bodies of water on the earth keep the air and solid matter on or near 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 falls below that of such bodies of water, they give off large quantities of heat. This process keeps the atmospheric temperature at the surface of the earth from changing rapidly.
The specific heat values of some common materials are listed in figure 7-42.
Thermal Expansion Thermal expansion takes place in solids, liquids, and gases when they are heated. With few exceptions, solids will expand when heated and contract when cooled. Because the molecules of solids are much closer together and are more strongly attracted to each other, the expansion of solids when heated is very ślight in comparison to the expansion in liquids and gases. The expansion of fluids has been discussed in the study of Boyle's law. Thermal expansion in solids must be explained in some detail because of its close relationship to aircraft metals and materials.
Expansion in Solids Solid materials expand in length, width, and thickness when they are heated. An example of the expansion and contraction of substances is the ball and ring, illustrated in figure 7-43. The ball and ring are made of iron. When both are at the same temperature, the ball will barely slip through the ring. When the ball is heated or the ring is cooled, however, the ball cannot slip through the ring.
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 FIGURE 7-43. Ball and ring.
to expand nearly twice as much as a piece of glass of the same size and shape. For this reason, Coefficient of the lead wires into an electronic tube cannot be Substance linear expansion made of copper but must be made of a metal that (per degree C.)
expands at the same rate as glass. If the metal does not expand at the same rate as the glass, Aluminum_. 24 × 10-6 the vacuum in the tube is broken by air leaking Brass_ - 19 × 10- past the wires in the glass stem. Copper 17 × 10- Because some substances expand more than Glass _ _ 4 to 9 X 10-8 others, it is necessary to measure experimentally Quartz_. 0.4 X 10-5 the exact rate of expansion of each one. The Steel__ 11 × 10 amount that a unit length of any substance ex- Zinc_ 26 × 10-6 pands for a one-degree rise in temperature is known as the coefficient of linear expansion for that substance. FIGURE 7-44. Expansion coefficients of some common materials.
Coefficients of Expansion To estimate the expansion of any object, such as a steel rail, it is necessary to know three things about it; namely, its length, the rise in temperature to which it is subjected, and its coefficient of expansion. This relationship is expressed by the equation:
Expansion = (coefficient) X (length) X (rise in temperature) e = kL (12 - tị).
In this equation, the letter "k" represents the coefficient of expansion for the particular substance. In some instances, the Greek letter "a" (alpha) is used to indicate the coefficient of linear expansion.
If a steel rod measures exactly 9 feet at 21° C., what is its length at 55° C? The value of "k" for steel is 10 X 10-6. If the equation e = kL (te - t1) is used, then: e = (10 × 10-) × 9 × (55 - 21) e = 0.000010 X 9 X 34 e = 0.00306.
A practical application which uses the difference in the coefficients of linear expansion of metals is the thermostat. This instrument consists of an arrangement of two bars of dissimilar metal fastened together. When the temperature changes, a bending takes place because of the unequal expansion of the metals. Figure 7-45 shows such an instrument, made with a wooden handle for laboratory demonstrations. Thermostats are used in overload relays in motors, in temperaturesensitive switches, and in heating systems.
SOUND Sound has been defined as a series of disturbances in matter that the human ear can detect.
This definition can also be applied to disturbances which are beyond the range of human hearing.
There are three elements which are necessary for the transmission and reception of sound. These are the source, a medium for carrying the sound, Brass This amount, when added to the original length of the rod, makes the rod 9.00306 feet long.
The increase in the length of the rod is relatively Before heating Iron small; but if the rod were placed where it could not expand freely, there would be a tremendous Brass force exerted due to thermal expansion. Thus, thermal expansion must be taken into consider- After heating ation when designing airframes, powerplants, or related equipment. Iron Figure 7-44 contains a list of the coefficients of linear expansion for some common substances. FIGURE 7-45. Compound bar.
-Wave Length - FIGURE 7-46. A transverse wave.
and the detector. Anything which moves back and forth (vibrates) and disturbs the medium around it may be considered a sound source.
An example of the production and transmission of sound is the ring of a bell. When the bell is struck and begins to vibrate, the particles of the medium (the surrounding air) in contact with the bell also vibrate. The vibrational disturbance is transmitted from one particle of the medium to the next, and the vibrations travel in a "wave" through the medium until they reach the ear.
The eardrum, acting as detector, is set in motion by the vibrating particles of air, and the brain interprets the eardrum's vibrations as the characteristic sound associated with a bell.
Wave Motion Since sound is a wave motion in matter, it can best be understood by first considering water waves. When a stone is thrown into a pool, a series of circular waves travel away from the disturbance. In figure 7-46 such waves are diagramed as though seen in cross section, from the side. Notice that water waves are a succession of crests and troughs. The wavelength is the distance from the crest of one wave to the crest of the next. Water waves are known as transverse waves because the motion of the water molecules is up and down, or at right angles to the direction in which the waves are traveling. This can be seen by observing a cork on the water, bobbing up and down as the waves pass by; the corks moves very little from side to side.
Sound traveles through matter in the form of longitudinal wave motions. These waves are called longitudinal waves because the particles of the medium vibrate back and forth longitudinally in the direction of propagation, as shown in figure
7-47.
When the tine of a tuning fork (figure 7-47) moves in an outward direction, the air immediately in front of the tine is compressed so that its momentary pressure is raised above that at other points in the sorrounding medium. Because air is elastic, this disturbance is transmitted progressively in an outward direction from the tine in the form of a compression wave.
When the tine returns and moves in an inward direction, the air in front of the tine is rarefied so that its momentary pressure is reduced below that at other points in the surrounding medium.
This disturbance is transmitted in the form of a rarefaction (expansion) wave and follows the compression wave through the medium.
The progress of any wave involves two distinct motions: (1) The wave itself moves forward with constant speed, and (2) simultaneously, the particles of the medium that convey the wave vibrate harmonically. (Examples of harmonic motion are the motion of a clock pendulum, the balance wheel in a watch, and the piston in a reciprocating The period of a vibrating particle is the time "¿" (in seconds) required for the particle to complete one vibration.
The frequency "f" is the number of vibrations completed per second and may be expressed in
c.p.s. When expressed in this unit, the word "cycles" means vibrations. The period is the reciprocal of the frequency:
t = 1/f.
The velocity of a wave is equal to the wavelength › (lambda) divided by the period. Since the period is the reciprocal of the frequency, the velocity is, where:
v = velocity in ft./ sec.
f = frequency in c.p.s.
› = wavelength in ft.
The amplitude of vibration is the maximum displacement of the particle from its equilibrium Two particles are in phase when they are vibrating with the same frequency, and continually pass through corresponding points of their paths at the same time. For any other condition the particles are out of phase. The two particles are in phase opposition when they reach their maximum displacement in opposite directions at the same time.
The wavelength is the distance measured along the direction of propagation between two corre- 262