Matter, Energy, and Basic Properties

5-1

Physics for Aviation

Chapter 5 Physical science, which is most often called physics, is a very interesting and exciting topic. For an individual who likes technical things and is a hands-on type of person, physics is an invaluable tool. Physics allows us to explain how engines work, both piston and gas turbine; how airplanes and helicopters fly; and countless other things related to the field of aviation and aerospace. In addition to allowing us to explain the operation of the things around us, it also allows us to quantify them. For example, through the use of physics we can explain what the concept of thrust means for a jet engine, and then follow it up by mathematically calculating the pounds of thrust being created.

Physics is the term applied to an area of knowledge regarding the basic and fundamental nature of matter and energy. It does not attempt to determine why matter and energy behave as they do in their relation to physical phenomena, but rather how they behave. The people who maintain and repair aircraft should have knowledge of basic physics, which is sometimes called the science of matter and energy.

Matter

Matter is the foundation, or the building blocks, for any discussion of physics. According to the dictionary, matter is what all things are made of; whatever occupies space, has mass, and is perceptible to the senses in some way. According to the Law of Conservation, matter cannot be created or destroyed, although it is possible to change its physical state. When liquid gasoline vaporizes and mixes with air, and then burns, it might seem that this piece of matter has disappeared and no longer exists. Although it no longer exists in the state of liquid gasoline, the matter still exists in the form of the gases given off by the burning fuel.

Characteristics of Matter Mass & Weight Mass is a measure of the quantity of matter in an object. In other words, how many molecules are in the object, how many atoms are in the object, or to be more specific, how many protons, neutrons, and electrons are in the object. The mass of an object does not change regardless of where you take it in the universe, or with a change of state. The only way to change the mass of an object is to add or take away atoms. Mathematically, mass can be stated as follows: Mass = Weight ÷ Acceleration due to gravity The acceleration due to gravity here on earth is 32.2 feet per second per second (32.2 fps/s). An object weighing 32.2 pounds (lb) here on earth is said to have a mass of 1 slug.

A slug is a quantity of mass that will accelerate at a rate of 1 ft. /s2 when a force of 1 pound is applied. In other words, under standard atmospheric condition, which is that gravity is equal to 32.2 fps/s, a mass of one slug would be equal to 32.2 lb. Weight is a measure of the pull from gravity acting on the mass of an object. The more mass an object has, the more it will weigh under the earth’s force of gravity. The only way for an object to be weightless is for gravity to go away, because it is not possible for the mass of an object to disappear. When we view astronauts on the space shuttle, it appears that they are weightless. Even though the shuttle is far from the surface of the earth, the force of gravity has not completely gone away, and the astronauts are not weightless. The astronauts and the space shuttle are actually in a state of free fall, so relative to the shuttle the astronauts appear to be weightless.

Mathematically, weight can be stated as follows: Weight = Mass × Gravity Attraction Attraction is mutual force acting between particles of matter, which tends to draw them together. Sir Isaac Newton called this the “Law of Universal Gravitation.” Newton showed how each particle of matter attracts every other particle, how people are bound to the earth, and how the planets are attracted in the solar system. Porosity Porosity means having pores or spaces where smaller particles may fit when a mixture takes place. This is sometimes referred to as granular—consisting or appearing to consist of small grains or granules.

Impenetrability Impenetrability means that no two objects can occupy the same place at the same time. Thus, two portions of matter cannot at the same time occupy the same space. 5-2 Density The density of a substance is its weight per unit volume. The unit volume selected for use in the English system of measurement is 1 cubic foot (ft 3). In the metric system, it is 1 cubic centimeter (cm3). Therefore, density is expressed in pounds per cubic foot (lb⁄ft 3) or in grams per cubic centimeter (g⁄cm 3). To find the density of a substance, its weight and volume must be known. Its weight is then divided by its volume to find the weight per unit volume. For example, the liquid which fills a certain container weighs 1,497.6 lb. The container is 4 ft long, 3 ft wide and 2 ft deep. Its volume is 24 ft 3 (4 ft. × 3 ft. × 2 ft.). If 24 ft3 of liquid weighs 1,497.6 lb, then 1 ft3 weighs 1,497.6 ÷ 24, or 62.4 lb. Therefore, the density of the liquid is 62.4 lb/ft3. This is the density of water at 4 °C (Centigrade) and is usually used as the standard for comparing densities of other substances. In the metric system, the density of water is 1 g⁄cm3. The standard temperature of 4 °C is used when measuring the density of liquids and solids. Changes in temperature will not change the weight of a substance, but will change the volume of the substance by expansion or contraction, thus changing its weight per unit volume.

The procedure for finding density applies to all substances; however, it is necessary to consider the pressure when finding the density of gases. Pressure is more critical when measuring the density of gases than it is for other substances. The density of a gas increases in direct proportion to the pressure exerted on it. Standard conditions for the measurement of the densities of gases have been established at 0 °C for temperature and a pressure of 76 cm of mercury (Hg), which is the average pressure of the atmosphere at sea level. Density is computed based on these conditions for all gases. Specific Gravity It is often necessary to compare the density of one substance with another substance. For this purpose, a standard is needed. Water is the standard that physicists have chosen to use when comparing the densities of all liquids and solids.

For gases, air is most commonly used, but hydrogen is also sometimes used as a standard for gases. In physics, the word “specific” implies a ratio. Thus, specific gravity is calculated by comparing the weight of a definite volume of the given substance with the weight of an equal volume of water. The terms “specific weight” or “specific density” are sometimes used to express this ratio. The following formulas are used to find the specific gravity of liquids and solids. Specific Gravity = Weight of an equal volume of water Weight of the substance or Specific Gravity = Density of water Density of the substance The same formulas are used to find the density of gases by substituting air or hydrogen for water.

Specific gravity is not expressed in units, but as pure numbers. For example, if a certain hydraulic fluid has a specific gravity of 0.8, 1 ft3 of the liquid weighs 0.8 times as much as 1 ft 3 of water: 62.4 times 0.8, or 49.92 lb. Specific gravity and density are independent of the size of the sample under consideration and depend only upon the substance of which it is made. See Figure 5-1 for typical values of specific gravity for various substances. A device called a hydrometer is used for measuring specific gravity of liquids. This device consists of a tubular glass float contained in a larger glass tube. [Figure 5-2] The larger glass tube provides the container for the liquid. A rubber suction bulb draws the liquid up into the container. There must be enough liquid raising the float to prevent it from touching the bottom. The float is weighted and has a vertically graduated scale. To determine specific gravity, the scale is read at the surface of the liquid in which the float is immersed. An indication of 1000 is read when the float is immersed in pure water. When immersed in a liquid of greater density, the float rises, indicating a greater specific gravity. For liquids of lesser density, the float sinks, indicating a lower specific gravity.

An example of the use of the hydrometer is to determine the specific gravity of the electrolyte (battery liquid) in an aircraft battery. When a battery is discharged, the calibrated float immersed in the electrolyte will indicate approximately 1150. The indication of a charged battery is between 1275 and 1310. The values 1150, 1275, and 1310 represent 1.150, 1.275, and 1.310. The electrolyte in a discharged battery is 1.15 times denser than water, and in a charged battery 1.275 to 1.31 times denser than water.

Energy

Energy is typically defined as something that gives us the capacity to perform work. As individuals, saying that we feel full of energy is an indicator that we can perform a lot of work. Energy can be classified as one of two types: either as potential energy or kinetic energy. Potential Energy Potential energy is defined as being energy at rest, or energy that is stored. Potential energy may be classified into three groups: (1) energy due to position, (2) energy due to distortion of an elastic body, and (3) energy which produces work 5-3 Liquid Specific Gravity Specific GravitySolid Specific GravityGas Gasoline Jet Fuel Jp-4 Ethyl Alcohol Jet Fuel Jp-5 Kerosene Lube Oil Synthetic Oil Water Sulfuric Acid Mercury Ice Aluminum Titanium Zinc Iron Brass Copper Lead Gold Platinum Hydrogen Helium Acetylene Nitrogen Air Oxygen Carbon Dioxide 0.917 2.7 4.4 7.1 7.9 8.4 8.9 11.4 19.3 21.5 0.0695 0.138 0.898 0.967 1.000 1.105 1.528 0.72 0.785 0.789 0.82 0.89 0.928 1.000 1.84 13.6 1100 1150 1200 1250 1300 1100 1150 1200 1250 1300 1,150 Discharged 1,275 Charged through chemical action. Examples of the first group are water in an elevated reservoir or an airplane raised off the ground with jacks; a stretched bungee cord on a Piper Tri- Pacer or compressed spring are examples of the second group; and energy in aviation gasoline, food, or storage batteries are examples of the third group.

To calculate the potential energy of an object due to its position, as in height, the following formula is used: Potential Energy = Weight × Height A calculation based on this formula will produce an answer that has units of foot-pounds (ft-lb) or inch-pounds (in-lb), which are the same units that apply to work. Work, which is covered later in this chapter, is described as a force being applied over a measured distance, with the force being pounds and the distance being feet or inches. Potential energy and work have a lot in common. Example: A Boeing 747 weighing 450,000 pounds needs to be raised 4 feet in the air so maintenance can be done on the landing gear. How much potential energy does the airplane possess because of this raised position?

Potential Ener gy = Weight × Height PE = 450,000 lb × 4 ft PE = 1,800,000 ft-lb As previously mentioned, aviation gasoline possesses potential energy because of its chemical nature. Gasoline has the potential to release heat energy, based on its British thermal unit (BTU) content. One pound of aviation gas contains 18,900 BTU of heat energy, and each BTU is capable of 778 ft-lb of work. So, when we multiply 778 by 18,900, we find that one pound of aviation gas is capable of 14,704,200 ft-lb of work. Imagine the potential energy in the completely serviced fuel tanks of an airplane. Kinetic Energy Kinetic energy is defined as being energy that is in motion.

An airplane rolling down the runway or a rotating flywheel on an engine are both examples of kinetic energy. Kinetic energy has the same units as potential energy, namely foot- pounds or inch-pounds. To calculate the kinetic energy for something in motion, the following formula is used: Kinetic Energy = 1⁄2 Mass × Velocity2 To use the formula, we will show the mass as weight divided by gravity and the velocity of the object will be in feet per second. This is necessary to end up with units in foot-pounds. 5-4 Example: An Airbus A380 weighing 600,000 lb is moving down the runway on its takeoff roll with a velocity of 200 fps.

How many foot-pounds of kinetic energy does the airplane possess? [Figure 5-3] Kinetic Energy = 1⁄2 Mass × Velocity2 Kinetic Energy = 1⁄2 × 600,000 ÷ 32.2 × 2002 KE = 372,670,000 ft-lb

Force, Work, Power, & Torque

Force Before the concept of work, power, or torque can be discussed, we need to understand what force means. According to the dictionary, force is the intensity of an impetus, or the intensity of an input. For example, if we apply a force to an object, the tendency will be for the object to move. Another way to look at it is that for work, power, or torque to exist, there must be a force that initiates the process. The unit for force in the English system of measurement is pounds, and in the metric system it is newtons. One pound of force is equal to 4.448 newtons. When we calculate the thrust of a turbine engine, we use the formula “Force = Mass × Acceleration,” and the thrust of the engine is expressed in pounds. The GE90-115 turbofan engine (power plant for the Boeing 777-300), for example, has 115,000 pounds of thrust.

Work The study of machines, both simple and complex, can be seen as a study of the energy of mechanical work. This is true because all machines transfer input energy, or the work done on the machine, to output energy, or the work done by the machine. Work, in the mechanical sense of the term, is done when a resistance is overcome by force acting through a measurable distance. Two factors are involved: (1) force and (2) movement through a distance. As an example, suppose a small aircraft is stuck in the snow. Two men push against it for a period of time, but the aircraft does not move. According to the technical definition, no work had been done when the men were pushing against the aircraft. By definition, work is accomplished only when an object is displaced some distance against a resistive force. To calculate work, the following formula is used: Work = Force (F) × distance (d) In the English system, the force will be identified in pounds and the distance either in feet or inches, so the units will be foot-pounds or inch-pounds. Notice these are the same units that were used for potential and kinetic energy.

In the metric system, the force is identified in newtons (N) and the distance in meters, with the resultant units being joules. One pound of force is equal to 4.448 N and one meter is equal to 3.28 feet. One joule is equal to 0.74 ft-lb. Example: How much work is accomplished by jacking a 150,000-lb Airbus A-320 airplane a vertical height of 4 ft? [Figure 5-4] Work = Force × Distance = 150,000 lb × 4 ft = 600,000 ft-lb Example: How much work is accomplished when a tow tractor is hooked up to a tow bar and a Boeing 737-800 airplane weighing 130,000 lb is pushed 80 ft. into the hangar? The force on the tow bar is 5,000 lb.

Work = Force × Distance = 5,000 lb × 80 ft = 400,000 ft-lb In this last example, notice the force does not equal the weight of the airplane. This is because the airplane is being moved horizontally and not lifted vertically. In almost all cases, it takes less work to move something horizontally than it does to lift it vertically. Most people can push their car a short distance if it runs out of gas, but they cannot get under their car and lift it off the ground. Friction & Work In calculating work done, the actual resistance overcome is measured. This is not necessarily the weight of the object being moved. [Figure 5-5] A 900-lb load is being pulled a distance of 200 ft. This does not mean that the work done (force × distance) is 180,000 ft-lb (900 lb × 200 ft). This is 5-5 because the person pulling the load is not working against the total weight of the load, but rather against the rolling friction of the cart, which may be no more than 90 lb.

Friction is an important aspect of work. Without friction, it would be impossible to walk. One would have to shove oneself from place to place, and would have to bump against some obstacle to stop at a destination. Yet friction is a liability as well as an asset, and requires consideration when dealing with any moving mechanism. In experiments relating to friction, measurement of the applied forces reveals that there are three kinds of friction. One force is required to start a body moving, while another is required to keep the body moving at constant speed. Also, after a body is in motion, a definitely larger force is required to keep it sliding than to keep it rolling.

Thus, the three kinds of friction may be classified as: (1) starting or 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 which is 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 following formula: 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 lb block would be 3 lb; a 40-lb block, 12 lb.

Starting friction for objects equipped with wheels and roller bearings is much smaller than that for sliding objects. For example, 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 starting the train, the engineer 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. However, once the cars are in motion, the 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 been set in 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 using the following formula: F = mN In the formula above, “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 surface over which it slides; and “m” (mu) is the coefficient of sliding friction. On a horizontal surface, N is equal to the weight of the object in pounds. The area of the sliding object exposed to the sliding surface has no effect on the results. A block of wood, for 5-6 Gravity 200 ft Force 90 lb Resistance Work = force x distance = 90 lb x 200 ft = 18,000 ft-lb example, will not slide any easier on one of the broad sides than it will on a narrow side, assuming all sides have the same smoothness. Therefore, area does not enter into the equation above.

Rolling Friction Resistance to motion is greatly reduced if an object is mounted on wheels or rollers. The force of friction for objects mounted on wheels or rollers is called rolling friction. This force may be computed by the same equation used in computing sliding friction, but the values of “m” will be much smaller. For example, the value of “m” for rubber tires on concrete or macadam is about 0.02. The value of “m” for roller bearings is very small, usually ranging from 0.001 to 0.003 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 = mN = 0.02 mu × 79,600 lb = 1,592 lb Power The concept of power involves the previously discussed topic of work, which was a force being applied over a measured distance, but adds one more consideration—time. In other words, how long it takes to accomplish the work. If someone asked the average person if they could lift one million pounds 5 feet off the ground, the answer most assuredly would be no. This person would probably assume that they are to lift it all at once. What if they are given 365 days to lift it, and could lift small amounts of weight at a time? The work involved would be the same, regardless of how long it took to lift the weight, but the power required is different. If the weight is to be lifted in a shorter period of time, it will take more power. The formula for power is as follows: Power = Force × distance ÷ time The units for power will be foot-pounds per minute, foot- pounds per second, inch-pounds per minute or second, and possibly mile-pounds per hour. The units depend on how distance and time are measured.

Many years ago, there was a desire to compare the power of the newly evolving steam engine to that of horses. People wanted to know how many horses the steam engine was equivalent to. The value we know currently as one horsepower (hp) was developed, and it is equal to 550 foot- pounds per second (ft-lb/s) because of this. It was found that the average horse could lift a weight of 550 lb, one foot off the ground, in one second. The values we use today, in order to convert power to horsepower, are as follows: 1 hp = 550 ft-lb/s 1 hp = 33,000 ft-lb/min. 1 hp = 375 mile pounds per hour (mi-lb/hr.) 1 hp = 746 watts (electricity conversion) To convert power to horsepower, divide the power by the appropriate conversion based on the units being used.

Example: What power would be needed, and also horsepower, to raise the GE-90 turbofan engine into position to install it on a Boeing 777-300 airplane? The engine weighs 19,000 lb, and it must be lifted 4 ft in 2 minutes. Power = Force × distance ÷ time = 19,000 lb × 4 ft ÷ 2 min. = 38,000 ft-lb/min. Hp = 38,000 ft-lb/min. ÷ 33,000 ft-lb/min. Hp = 1.15 The hoist that will be used to raise this engine into position will need to be powered by an electric motor because the average person will not be able to generate 1.15 hp in their arms for the necessary 2 minutes. Torque Torque is a very interesting concept and occurrence, and it is definitely something that needs to be discussed in conjunction with work and power. Whereas work is described as force acting through a distance, torque is described as force acting along a distance. Torque is something that creates twisting