Each form of matter has its own specific properties, some of which are obvious and some of which are not. This chapter discusses the elementary physical properties of matter.
The atoms could further be combined to form "molecules". For example, if the element oxygen is burned with the element hydrogen, each oxygen atom forms "chemical bonds" with two hydrogen atoms to form water molecules. Large numbers of atoms can combine into a single molecule, particularly in the case of the complex carbon-based "biomolecules" that make up living organisms. Of course, different assemblies of atoms and molecules can also be mixed together.
By the first decades of the end of the 19th century, physicists had come to realize that atoms themselves were not indivisible and had an internal structure. They realized that an atom had a heavy central "nucleus" that had positive electric charge, surrounded by light orbiting "electrons" that had a negative electric charge.
Electrons could be stripped from atoms to be sent through wires as electrical "currents". If an atom lost its normal complement of electrons, it became a positively charged "ion". Atoms could also acquire an excess of electrons, becoming negatively charged ions. Such charge imbalances were one mechanism that contributed to the bonding of atoms into molecules, though subtler processes were involved as well.
Physicists soon found that the interior of the atom was a complicated place where things happened that seemed, and in fact were, impossible at a larger scale, and this simple model of a "classical atom" had to be revised. However, it still provides a useful basis for the discussion of the fundamental properties of matter.
At a high level, chunks of matter have certain properties that can be characterized, for example color; density, or ratio of mass to volume; and various measures of strength, or the ability of that chunk of matter to retain its structure or "integrity" when subjected to various forces. Obviously these things are much easier to characterize for, say, a diamond than for a block of compacted trash.
Solid matter also has certain properties of "scale" that are independent of what the matter is made up of. For example, let's take a set of cubes of matter without regard to what the matter is. Suppose one cube is a centimeter on a side. Now let's stack up the cubes to make a bigger cube that is two centimeters on a side.
We have doubled the linear dimensions of the cube. The surface area of the cube has expanded by a factor of four, while the volume and mass of the cube has expanded by a factor of eight. In more formal terms, doubling the linear dimensions of an object squares its surface area and cubes its volume and mass. This means that as an object grows bigger, its volume and mass increase much more rapidly than its surface area.
1950s horror movies such as THEM envisioned monster ants, but in fact such scaling effects prevent insects from becoming very large. For one thing, they don't have lungs, and have to acquire oxygen through pores in their chitinous skins. Doubling their size would increase their volume and mass twice as fast as it would increase their surface area, halving their ability to obtain oxygen for that mass, and at a certain size a giant insect would simply suffocate.
A more important scaling issue that rules out giant insects is the issue of "compressive strength", or the ability of a structural support to bear weight placed on top of it. The compressive strength of a structural support, such as a column that holds up a building, is proportional to the cross-sectional area of a slice through the column. A cross section is just one face of the surface of an object, and so like surface area increases with the square of a linear increase in size. However, the mass of the building increases with the cube of a linear increase in size.
Double the linear dimensions of a building and the ability of a column to support the building's weight is increased by four, while the mass and the load on the column is increased by eight. The column now has to proportionately bear twice as much load as it did at the smaller scale. This means that more, or disproportionately large, columns must be used to support a larger building.
Insects generally have spindly bodies and legs, while an elephant has great massive legs. If an insect was scaled up to large size, it would simply collapse of its own weight. However, horror movie fans can still take comfort that deadly venomous or parasitic insects are not ruled out by the laws of physics.
Forces can be applied to structures in a number of ways. Along with the compression force described in the previous section, a structural element can be subjected to:
A metal beam will respond to such forces in different ways as the force is increased:
Not all materials respond to forces in such a nice graded way. They may not deform at all up to the level of force where they snap. Such materials are known as "brittle". Glass is a good example, since any practical experience shows how difficult it is to bend glass without breaking it.
Not all materials respond to different forces in the same way. Although metals are strong in both compression and tension, stone is very strong in compression but is weak in tension. Wood can be split easily by shear forces applied along the line of its grain, but will resist larger shear forces applied at a right angle to its grain.
Forces acting consistently on a structural element over a long period of time may cause a slow deformation, or "creep", that can lead to failure even if the elastic limit is never exceeded. Similarly, a cycle of changing stresses repeated over and over may cause "fatigue" that that will eventually lead to the failure of a structural element.
Engineers formally refer to the forces applied to a structural element as "stress". The deformation of a structural element under stress is referred to as "strain". The ratio of strain of a material to the stress on the material is known as the "elastic modulus".
The stresses are set up by what engineers refer to as "loads". Some of the loads on a structure are obvious: the "dead load" set up by the weight of the structure, and the "live load" set up by the people, furnishings, and equipment contained in the structure. These are known as "static loads" because they don't change, or don't change much, over time.
Others loads are not quite so obvious. There are the "hidden" loads, with stresses set up by the expansion or contraction of structural elements due to changes in temperature, or by unequal settling of the building's foundations. Structures may also be subjected to rapidly changing "dynamic" loads, such as those caused by winds and earthquakes.
Dynamic loads can be particularly treacherous as they are somewhat unpredictable. In one famous example, the designer of the Citicorp skyscraper in New York City received a letter from a student who was curious about the building's stability in winds. The designer replied that the building's design had been analyzed to ensure that it would stand up to winds and that it was safe.
However, after sending his reply, the designer realized that the analysis had been performed with the assumption that the winds would be perpendicular to the faces of the building. He re-did his analysis to see what would happen if the winds were at an angle, and to his shock found out that a severe windstorm would generate torsion forces that would bring the skyscraper down in the middle of Manhattan. The Citicorp building's steel framework was hastily reinforced.
One of the simplest examples of a compression structure is a brick wall, with the bricks piled on top of each other. One of the simplest examples of a tensile structure is a circus tent, with the canvas "big top" held up by ropes hung from a central post. Of course, in practice most structures feature both compressive and tensile elements.
The first really big structures were compression structures, since it was difficult to build durable large structures of wood, and stone doesn't lend itself to tensile structures. The major problem with stone compressive structures is that stone is very heavy, or in other terms has a low "strength to weight" ratio.
This means that the weight of such a structure grows very quickly as it the structure grows bigger, and walls have to be made thicker and thicker at the base so the structure doesn't collapse. This approach approach ultimately leads to the simplest of all large stone structures, the pyramid, built not only in Egypt but in China and in the Pre-Columbian New World as well.
The earliest wooden bridges no doubt consisted just of two beams covered with planks set up across a stream. The major problem with this is that such a bridge is limited in length. It is supported at the ends but not in the middle, and as it gets longer so does the "lever arm" of the half-spans of the bridge, meaning that a person stepping on the middle of the bridge inflicts proportionately greater stress on it.
If the bridge was over the top of a shallow stream this could be corrected by driving pilings in the middle of the stream and fastening the middle of the span to them, but if the stream wasn't shallow or if the bridge were over the top of deep canyon, such a measure wasn't possible.
There were two possible solutions. The first was the rope "suspension bridge", a tension-based design. Wooden or stone towers could be constructed on both sides of the canyon, with heavy ropes slung across their tops and anchored to the ground. A wooden walkway could then be suspended from the ropes.
This type of bridge has been around for millennia, and is thoroughly familiar from B-grade adventure movies as they are excellent sites for dramatic action scenes. They always seem to be in a dangerously bad state of repair.
We'll return to suspension bridges in a bit. For the moment, the second option is more interesting. Suppose Dexter has a wooden bridge and wants to brace up the middle of the span from each end. He can do this by fitting a beam from the bank to the midspan at an angle. This allows the forces directed downward at midspan to be shunted towards the banks. Since this sets up a sideways force on the two support beams that tends to splay them apart, it is also useful to link them together at the bottom with a third beam, forming a triangular support structure known as a "truss".
The truss is a basic structural form, and is composed of various triangular structural subunits linked together. The triangular shape is very useful as it will stand up to stresses imposed in different directions, and it is also employed in the "cross-bracing" of structures used to keep them from falling over in heavy winds and the like. The truss is of course in as wide use as it ever was, commonly seen in the prefabricated roof trusses used to build houses.
The arch did imply the provision of supports to deal with the sideways loads it set up. This was generally simple with bridges, as they might be built between stony riverbanks or, if such weren't available, heavy footings could be constructed on each bank.
This could be a tricky matter for other structures. The Gothic cathedrals of Europe, with their high arched or "vaulted" ceilings, were built with "flying buttresses", structures attached to the outside of the building to provide the necessary lateral support. The "dome" was an extension of the arch, rotated around in a full circle. Like the arch, the dome required lateral support to handle the horizontal stresses.
Although complete spheres are not ordinarily used in buildings, they are an extension of the notion of an arch or dome, in which compression is distributed around the sphere. An egg can be surprisingly hard to crack if subjected to balanced compression forces, though this is a somewhat foolish experiment to actually try, and spheres are often used in the crew-carrying elements of deep-ocean submersibles, as they can withstand extreme pressures.
Classical construction forms, such as trusses and arches, could be built with such metal beams. The beams were generally in the form of "I-beams", which consist of a length of metal with a long flat horizontal plate on the bottom, a similar long flat horizontal plate on top, and a vertical plate connecting the two horizontal plates. A beam is subjected to compression on top and tension on the bottom, and the I-beam is designed to provide the maximum cross-sectional area on bottom and top to resist these stresses.
Such techniques could be used to build new sorts of structures, such as the modern skyscraper. The poor strength-to-weight ratio of stone made very tall buildings impossible, but metal structural elements allowed buildings to be made much taller.
A skyscraper consists of a "cage" of steel girders that supports the floors and the walls. The spectacular explosive demolition of such structures, which usually makes TV news, is based on the sequential detonation of charges that cut critical structural supports in a particular order, causing the building to cave in on itself in a heap if the event has been properly planned.
Metal building elements also allowed the development of large truss bridges, with a latticework of metal beams to allow distribution of stresses, and most impressively with modern suspension bridges, in which the roadbed is hung from huge cables slung over high towers and anchored to heavy concrete "anchors" at each end.
Concrete has been around since at least Roman times, but modern building techniques make it much more useful. Using steel reinforcing rods, it is commonly used for foundations, walls, and other structural elements under compressive loads.
However, "prestressed" concrete elements can also be used to handle tension loads that would cause ordinary reinforced concrete to crack. A prestressed concrete structural element is cast in a frame that supports steel cables under tension and laced through the concrete. When the concrete hardens or "cures", the frame is removed, and the tension of the cables within the concrete matrix prevents it from cracking under tension loads.
Another obvious characteristic of liquids is that a body of liquid will seek a common level. A pond undisturbed by wind may be "smooth as glass", as the saying goes, and it will be perfectly level, at least if it's small relative to the curvature of the Earth. From this observation, it is also apparent after a moment's thought that if multiple pipes of different diameter are stuck into the top of a sealed vessel and the vessel is overfilled with water, that water will be at the same level no matter the diameter of any individual pipe.
Yet another obvious property of liquids is that not only can they flow through pipes, objects can flow through or over them. This leads to the concept of "buoyancy", the tendency of objects to float or sink in a liquid. This is unsurprisingly due to the density of the object relative to the liquid. A block of wood is less dense than water and floats on water, a rock is more dense than water and sinks.
The sunken rock will displace a volume of water equal to the volume of the rock. The floating block of wood has a slightly subtler behavior. It will sink into the water under the influence of gravity until it displaces a volume of water equal to its own weight. At that point, it will reach an equilibrium of forces and sink no further. This is known as "Archimedes' Principle".
Similarly, if a more dense liquid is poured into a less dense liquid, as long as the two liquids don't have a tendency to mix, the two will separate, with the less dense liquid on top and the more dense liquid on bottom. The classic example of this is oil and water.
Once underwater, a submarine needs to maintain a density comparable to that of water so that it will not tend to either rise or sink. It can then maneuver freely by essentially "flying" underwater, using the "diving planes" that are mounted on nose or the "sail" (what was once called the "conning tower") of the submarine, along with the tailfins, which are generally arranged in a cross or an "X" pattern.
However, there is an added complication for a submarine moving underwater. It is not firmly supported, and so if its center of gravity shifts from the middle of the vessel, it will tend to tip down or up, making it difficult to control. This issue, known as "trim", was a particular problem for early submarines. It was solved by adding an additional set of "trim" tanks, in addition to the ballast tanks. There is a trim tank in the forward section of the submarine, a trim tank in the rear section of the submarine, and trim is maintained by adjusting the relative amounts of water in these tanks.
However, there is a limit to how deep a submarine can go, which is imposed by "fluid pressure", or the weight of the water above the submarine, which increases linearly with depth. Double the depth, you double the pressure. Pressure, incidentally, is measured in terms of force per unit area. The formal metric unit of pressure is the "pascal (Pa)", which is a newton per square meter. As a pascal is a somewhat small unit, it is often expressed in terms of "kilopascals (kPa)", or thousands of pascals.
There's nothing particularly tricky about this idea. Suppose Dexter has a set of identical concrete blocks, and proceed to stack them up one by one on top of each other. Of course, the force per unit area on the bottom of the stack grows linearly with each block that is added.
What is not quite so intuitive is that the fluid pressure is the same in all directions. Suppose Dexter applies pressure to the top of a tank of water. Then, ignoring the increment of pressure added by the water in the tank as it gets deeper, the pressure of the water against the sides and bottom of the tank is exactly the same as the pressure on the water on top of the tank. This is known as "Pascal's principle".
In other words, this arrangement gives Dexter a mechanical advantage of 10:1. As with levers and pulleys and so on, of course he doesn't get something for nothing. A simple consideration of the relative volume of fluid moved from the small tube to the big big tube in this example shows that the piston in the big tube only moves a tenth of the distance upward that he shoves the piston in the small tube down.
Another aspect of Pascal's principle is that it accounts for the buoyancy of a floating object, as discussed in the previous section. It is the force of pressure, exerted upward against the floating object, that prevents it from sinking further. Once the volume of water displace equals the weight of the object, the force of fluid pressure will then support that object.
For water of any real depth, the increment of pressure caused by the accumulated weight of water as the depth increases is of course not negligible. Water has a mass of a tonne (1,000 kilograms) per cubic meter, and so on Earth, where the gravitational acceleration is 9.81 meters per second, a cubic tank of water a meter on a side exerts a force of 1,000 * 9.81 = 9,810 newtons on the square-meter base, or 9.81 kilopascals.
If Dexter keeps the sides of the base the same size, but doubles the height to two meters, the pressure grows linearly to 19.6 kilopascals. If he goes up to three meters, the pressure goes up to 29.4 kilopascals. The fluid pressure on the sides of the tank increases linearly from zero at the top to the same as the bottom when it reaches the bottom.
However ... let's suppose Dexter has a tank of water that's a meter high and has a base two meters on a side. This tank has a volume of four cubic meters. Is the bottom then under 39.2 kilopascals of pressure?
No, of course not. Pressure is force per unit area. He's increased the volume by a factor of four, but he's also increased the area of the base by a factor of four, and so the pressure remains the same as it was for the one-cubic-meter tank. The pressure is due to the weight of water pressing down only in the vertical direction.
This means that it doesn't matter what size the base of the tank is. As long as the water in it is a meter deep, the pressure on the bottom in 9.8 kilopascals. This is more or less intuitive.
What is not so intuitive is that Pascal's principle dictates that fluid pressure is exerted in all directions. What this means is that a dam has to be just as strong to hold back a body of water that extends, say, only 10 meters behind the dam, as it must be to hold back a body of water of equal depth that extends 100 kilometers behind the dam. The depth is the only real determinant of pressure.
There are two basic forms of dams: "gravity" dams, which simply use great mass to hold back the water, and "arch" dams, which are built in narrow rocky canyons in the form of a horizontal arch, which transfers the massive load of the water to the canyon walls.
This should not be surprising. A solid mass held at a height has potential energy due to its elevated position in a gravitational field, and the only difference between that and a liquid is that the liquid is in effect a continuous series of masses held at a continuous range of heights. This makes calculation of the precise value of potential energy of the liquid in a tank a bit tricky to figure out. We won't do that here, but the important thing is to realize that fluid pressure is equivalent to potential energy.
Now let's suppose Dexter decides to tap this potential energy by opening the valve on the bottom of the tank. Water floods out in a stream. As the water is now moving, it has kinetic energy. Now conservation of energy says that he can't get something for nothing, and so this increase in kinetic energy must be obtained by a decrease in potential energy. As fluid pressure is equivalent to the potential energy of a fluid, this means that the pressure must decrease as well.
In other words, the faster a fluid moves, the more its pressure decreases. The following illustration demonstrates this principle, which is known as the "Bernoulli effect".
Similarly, the adhesion of water to, say, glass surfaces will cause it to crawl up into glass tubes stuck into the surface of the water. This sort of "capillary action" is greater for tubes with very small diameters than it is for tubes with very large diameters. Again, this is due to a scaling effect, since doubling the diameter of a tube only doubles its circumference and the area of its glass walls, while the cross-sectional area and the amount of water that is to be lifted increases by four times.
Gases also are subject to considerations of pressure like to those of a liquid. For example, the weight of the atmosphere presses down on those who live at the bottom of it, and this atmospheric pressure drops off as we go to higher ground or fly up into the sky. I live in a region where the ground elevation is a mile (1.6 kilometers) above sea level, and as a result if I buy food products such as potato chips that are sealed in airtight bags, the bags are puffed out like pillows here.
The atmospheric pressure of the Earth at sea level makes a convenient reference point for discussions of pressure, and one older measure of pressure is the "atmosphere", or 101,325 pascals. This is a somewhat arbitrary measure of pressure, however, and not convenient to work with using metric units, but the value of 100,000 pascals, known as a "bar", can be used as a reasonable approximation, all the more so because the pressure of air at sea level actually varies with changes in humidity, temperature, and wind conditions.
A "barometer" is used to measure atmospheric pressure. A traditional scheme for building a barometer involves a U-shaped tube partially filled with mercury. One end of the tube is sealed and the other is open to the atmosphere. Mercury is squirted into the sealed end of the tube while it's upside down, and when the tube is turned over, the mercury falls down to the bend in the tube, leaving behind a vacuum in the sealed side.
Air pressure will push the mercury up into the vacuum, and the height of mercury on the sealed side will provide an indication of atmospheric pressure. The mercury will be 76 centimeters higher in the sealed side of the tube than the open side of the tube at a standard atmosphere of pressure. Of course, since pressure is force per unit area, it doesn't matter how wide the tube is.
A more modern scheme is to use a metal bellows that has been evacuated. The bellows is connected to an indicator needle through some mechanical arrangement that amplifies any minor motion in the bellows, and as the bellows flexes under changes in pressure, the needle moves to give the pressure value on the indicator scale. This device is known as an "anaeroid barometer". If the indicator scale is calibrated to give altitude instead of air pressure, the device is called an "altimeter".
An aircraft has "flight control surfaces" that modify the airflow to control the machine's direction. There are moving panels at the trailing edge of each wing known as "ailerons" that are pivoted in an alternating fashion -- on one side up, on the other down -- to allow the aircraft to "roll". There are "elevators" at the trailing edge of the horizontal tailplane that are pivoted together to cause the aircraft to "pitch" up and down. And there is a "rudder" at the trailing edge of the vertical tailplane that can be pivoted to cause the aircraft to "yaw" back and forth.
These are the "basic" control surfaces, but there are many variations. For example, many tailless aircraft, usually delta-winged machines, have "elevons" that can be pivoted in an alternating direction to provide roll control or in the same direction to provide pitch control.
There may also be a number of auxiliary control surfaces. "Flaps" can be extended below the wings to increase the curvature and the lift for take-off or low-speed flight, and similarly a "slat" can be extended from the leading edge of the wing to increase curvature for the same purpose. Control surfaces named "spoilers" can be attached to the top of the wing to disrupt airflow and destroy lift, helping the aircraft to land.
Like a submarine, an aircraft has to maintain trim. This is obvious in the case of cargoes, which clearly can't be loaded onto a cargo plane in an unbalanced fashion, but less obvious in the important case of fuel management. An aircraft may have several fuel tanks, and care often must be taken to empty the tanks in a specific order, or the aircraft may become unbalanced. This was done manually by the pilot in the past, but now sophisticated aircraft have automatic systems to ensure the proper sequencing.
As an aircraft will always have slight imbalances, rather than have the pilot try to compensate for imperfections in trim by keeping the control surfaces slightly activated at all times, which would be very tiring, traditionally aircraft have featured small control surfaces called "trim tabs" that can be set to a fixed position to keep the machine flying level.
Osborne devised an apparatus in which he could observe the flow of dye in water pumped through an tube. He observed that the dye would flow straight for a distance, what was called "laminar" flow, and then break up into a tangle of eddies, what was called "turbulent" flow. The drag of the flow doubled when the flow changed from laminar to turbulent.
What Reynolds discovered was that whether flow through the tube was laminar
or turbulent depended on the speed of the flow, and the density and viscosity
of the fluid. He gave the relationship between these three elements in the
Reynolds equation:
fluid_velocity * length_of_fluid_flow * fluid_density / fluid_viscosity
If the RN exceeds a certain critical value, the flow will change from laminar to turbulent, and the fluid drag will increase greatly. Fluid flows with similar RNs behave in much the same way, no matter if the fluid is air or water or whatever. A sailboat moving at low speed in a dense medium like water has much the same behavior in terms of fluid dynamics as an aircraft moving much faster in a thin medium like air.
This has a major, though not obvious, implication for issues of scaling in aircraft design. The smaller an aircraft gets, the greater the effective viscosity of the air. To a gnat, the air feels as viscous as oil, and flying is more like swimming. Researchers working on tiny robot aircraft have finding out that conventional aircraft designs are not very workable at such small scale, and they have gravitated towards unusual designs, such as circular flying wings, or even "ornithopters" that flap their wings to fly.
Although this document has mentioned temperature effects in a casual fashion, to go much further requires a more detailed discussion. Similarly, although matter can often be converted between solid, liquid, and gaseous forms through changes in temperature, that also requires a more detailed look. These issues will be discussed in the next chapter.
From Vectorsite.net.
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