1.
Mass
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In physics, mass is a property of a physical body. It is the measure of a resistance to acceleration when a net force is applied. It also determines the strength of its gravitational attraction to other bodies. The basic SI unit of mass is the kilogram, Mass is not the same as weight, even though mass is often determined by measuring the objects weight using a spring scale, rather than comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity and this is because weight is a force, while mass is the property that determines the strength of this force. In Newtonian physics, mass can be generalized as the amount of matter in an object, however, at very high speeds, special relativity postulates that energy is an additional source of mass. Thus, any body having mass has an equivalent amount of energy. In addition, matter is a defined term in science. There are several distinct phenomena which can be used to measure mass, active gravitational mass measures the gravitational force exerted by an object. Passive gravitational mass measures the force exerted on an object in a known gravitational field. The mass of an object determines its acceleration in the presence of an applied force, according to Newtons second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A bodys mass also determines the degree to which it generates or is affected by a gravitational field and this is sometimes referred to as gravitational mass. The standard International System of Units unit of mass is the kilogram, the kilogram is 1000 grams, first defined in 1795 as one cubic decimeter of water at the melting point of ice. Then in 1889, the kilogram was redefined as the mass of the prototype kilogram. As of January 2013, there are proposals for redefining the kilogram yet again. In this context, the mass has units of eV/c2, the electronvolt and its multiples, such as the MeV, are commonly used in particle physics. The atomic mass unit is 1/12 of the mass of a carbon-12 atom, the atomic mass unit is convenient for expressing the masses of atoms and molecules. Outside the SI system, other units of mass include, the slug is an Imperial unit of mass, the pound is a unit of both mass and force, used mainly in the United States
2.
Spring scale
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A spring scale or spring balance or newton meter is a type of weighing scale. It consists of spring fixed at one end with a hook to attach an object at the other and it works by Hookes Law, which states that the force needed to extend a spring is proportional to the distance that spring is extended from its rest position. Therefore, the markings on the spring balance are equally spaced. A spring scale can not measure mass, only weight, also, the spring in the scale can permanently stretch with repeated use. A spring scale will only read correctly in a frame of reference where the acceleration in the axis is constant. This can be shown by taking a spring scale into an elevator, if two or more spring balances are hung one below the other in series, each of the scales will read approximately the same, the full weight of the body hung on the lower scale. The scale on top would read slightly heavier due to supporting the weight of the lower scale itself. Spring balances come in different sizes, generally, small scales that measure newtons will have a less firm spring than larger ones that measure tens, hundreds or thousands of newtons or even more depending on the scale of newtons used. The largest spring scale ranged in measurement from 5000-8000 newtons, a spring balance may be labeled in both units of force and mass. Strictly speaking, only the values are correctly labeled. Main uses of spring balances are industrial, especially related to weighing heavy loads such as trucks, storage silos and they are also common in science education as basic accelerators. They are used when the accuracy afforded by other types of scales can be sacrificed for simplicity, cheapness, a spring balance measures the weight of an object by opposing the force of gravity acting with the force of an extended spring. The first spring balance in Britain was made around 1770 by Richard Salter of Bilston and he and his nephews John & George founded the firm of George Salter & Co. still notable makers of scales and balances, who in 1838 patented the spring balance. They also applied the same spring balance principle to steam locomotive safety valves, weighing scale Media related to spring balance at Wikimedia Commons Media related to spring scales at Wikimedia Commons
3.
International System of Units
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The International System of Units is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, the system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as the result of an initiative began in 1948. It is based on the system of units rather than any variant of the centimetre-gram-second system. The motivation for the development of the SI was the diversity of units that had sprung up within the CGS systems, the International System of Units has been adopted by most developed countries, however, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the metre and kilogram as standards of length, in the 1830s Carl Friedrich Gauss laid the foundations for a coherent system based on length, mass, and time. In the 1860s a group working under the auspices of the British Association for the Advancement of Science formulated the requirement for a coherent system of units with base units and derived units. Meanwhile, in 1875, the Treaty of the Metre passed responsibility for verification of the kilogram, in 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, kilogram, second, ampere, kelvin, in 1971, a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. On 11 July 1792, the proposed the names metre, are, litre and grave for the units of length, area, capacity. The committee also proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as centi for a hundredth, on 10 December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the magnetic field had only been described in relative terms. The technique used by Gauss was to equate the torque induced on a magnet of known mass by the earth’s magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length, a French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention. Initially the convention only covered standards for the metre and the kilogram, one of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mètre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the prototypes to serve as the national prototype for that country. Initially its prime purpose was a periodic recalibration of national prototype metres. The official language of the Metre Convention is French and the version of all official documents published by or on behalf of the CGPM is the French-language version
4.
Newton (unit)
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The newton is the International System of Units derived unit of force. It is named after Isaac Newton in recognition of his work on classical mechanics, see below for the conversion factors. One newton is the force needed to one kilogram of mass at the rate of one metre per second squared in direction of the applied force. In 1948, the 9th CGPM resolution 7 adopted the name newton for this force, the MKS system then became the blueprint for todays SI system of units. The newton thus became the unit of force in le Système International dUnités. This SI unit is named after Isaac Newton, as with every International System of Units unit named for a person, the first letter of its symbol is upper case. Note that degree Celsius conforms to this rule because the d is lowercase. — Based on The International System of Units, section 5.2. Newtons second law of motion states that F = ma, where F is the applied, m is the mass of the object receiving the force. The newton is therefore, where the symbols are used for the units, N for newton, kg for kilogram, m for metre. In dimensional analysis, F = M L T2 where F is force, M is mass, L is length, at average gravity on earth, a kilogram mass exerts a force of about 9.8 newtons. An average-sized apple exerts about one newton of force, which we measure as the apples weight, for example, the tractive effort of a Class Y steam train and the thrust of an F100 fighter jet engine are both around 130 kN. One kilonewton,1 kN, is 102.0 kgf,1 kN =102 kg ×9.81 m/s2 So for example, a platform rated at 321 kilonewtons will safely support a 32,100 kilograms load. Specifications in kilonewtons are common in safety specifications for, the values of fasteners, Earth anchors. Working loads in tension and in shear, thrust of rocket engines and launch vehicles clamping forces of the various moulds in injection moulding machines used to manufacture plastic parts
5.
SI base unit
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The International System of Units defines seven units of measure as a basic set from which all other SI units can be derived. The SI base units form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science, thus, the kelvin, named after Lord Kelvin, has the symbol K and the ampere, named after André-Marie Ampère, has the symbol A. Many other units, such as the litre, are not part of the SI. The definitions of the units have been modified several times since the Metre Convention in 1875. Since the redefinition of the metre in 1960, the kilogram is the unit that is directly defined in terms of a physical artifact. However, the mole, the ampere, and the candela are linked through their definitions to the mass of the platinum–iridium cylinder stored in a vault near Paris. It has long been an objective in metrology to define the kilogram in terms of a fundamental constant, two possibilities have attracted particular attention, the Planck constant and the Avogadro constant. The 23rd CGPM decided to postpone any formal change until the next General Conference in 2011
6.
Intensive and extensive properties
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Physical properties of materials and systems can often be categorized as being either intensive or extensive quantities, according to how the property changes when the size of the system changes. According to IUPAC, a property is one whose magnitude is independent of the size of the system. An extensive property is one whose magnitude is additive for subsystems, an intensive property is a bulk property, meaning that it is a physical property of a system that does not depend on the system size or the amount of material in the system. Examples of intensive properties include temperature, T, refractive index, n, density, ρ, when a diamond is cut, the pieces maintain their intrinsic hardness, so hardness is independent of the size of the system. By contrast, a property is additive for subsystems. For example, both the mass, m, and the volume, V, of a diamond are directly proportional to the amount that is left after cutting it from the raw mineral, mass and volume are extensive properties, but hardness is intensive. The ratio of two properties of the same object or system is an intensive property. For example, the ratio of a mass and volume. The terms intensive and extensive quantities were introduced by Richard C, an intensive property is a physical quantity whose value does not depend on the amount of the substance for which it is measured. For example, the temperature of a system in equilibrium is the same as the temperature of any part of it. If the system is divided the temperature of each subsystem is identical, the same applies to the density of a homogeneous system, if the system is divided in half, the mass and the volume change in the identical ratio and the density remains unchanged. Additionally, the point of a substance is another example of an intensive property. For example, the point of water is 100 °C at a pressure of one atmosphere. The distinction between intensive and extensive properties has some theoretical uses, other intensive properties are derived from those two variables. Examples of intensive properties include, The IUPAC Gold Book defines an extensive property as a physical quantity whose magnitude is additive for subsystems. The value of such a property is proportional to the size of the system it describes. For example, the amount of required to melt ice at constant temperature and pressure is an extensive property. The amount of required to melt one ice cube would be much less than the amount of heat required to melt an iceberg
7.
Dimensional analysis
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Converting from one dimensional unit to another is often somewhat complex. Dimensional analysis, or more specifically the method, also known as the unit-factor method, is a widely used technique for such conversions using the rules of algebra. The concept of physical dimension was introduced by Joseph Fourier in 1822, Physical quantities that are measurable have the same dimension and can be directly compared to each other, even if they are originally expressed in differing units of measure. If physical quantities have different dimensions, they cannot be compared by similar units, hence, it is meaningless to ask whether a kilogram is greater than, equal to, or less than an hour. Any physically meaningful equation will have the dimensions on their left and right sides. Checking for dimensional homogeneity is an application of dimensional analysis. Dimensional analysis is routinely used as a check of the plausibility of derived equations and computations. It is generally used to categorize types of quantities and units based on their relationship to or dependence on other units. Many parameters and measurements in the sciences and engineering are expressed as a concrete number – a numerical quantity. Often a quantity is expressed in terms of other quantities, for example, speed is a combination of length and time. Compound relations with per are expressed with division, e. g.60 mi/1 h, other relations can involve multiplication, powers, or combinations thereof. A base unit is a unit that cannot be expressed as a combination of other units, for example, units for length and time are normally chosen as base units. Units for volume, however, can be factored into the units of length. Sometimes the names of units obscure that they are derived units, for example, an ampere is a unit of electric current, which is equivalent to electric charge per unit time and is measured in coulombs per second, so 1 A =1 C/s. Similarly, one newton is 1 kg⋅m/s2, percentages are dimensionless quantities, since they are ratios of two quantities with the same dimensions. In other words, the % sign can be read as 1/100, derivatives with respect to a quantity add the dimensions of the variable one is differentiating with respect to on the denominator. Thus, position has the dimension L, derivative of position with respect to time has dimension LT−1 – length from position, time from the derivative, the second derivative has dimension LT−2. In economics, one distinguishes between stocks and flows, a stock has units of units, while a flow is a derivative of a stock, in some contexts, dimensional quantities are expressed as dimensionless quantities or percentages by omitting some dimensions
8.
Science
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Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. The formal sciences are often excluded as they do not depend on empirical observations, disciplines which use science, like engineering and medicine, may also be considered to be applied sciences. However, during the Islamic Golden Age foundations for the method were laid by Ibn al-Haytham in his Book of Optics. In the 17th and 18th centuries, scientists increasingly sought to formulate knowledge in terms of physical laws, over the course of the 19th century, the word science became increasingly associated with the scientific method itself as a disciplined way to study the natural world. It was during this time that scientific disciplines such as biology, chemistry, Science in a broad sense existed before the modern era and in many historical civilizations. Modern science is distinct in its approach and successful in its results, Science in its original sense was a word for a type of knowledge rather than a specialized word for the pursuit of such knowledge. In particular, it was the type of knowledge which people can communicate to each other, for example, knowledge about the working of natural things was gathered long before recorded history and led to the development of complex abstract thought. This is shown by the construction of calendars, techniques for making poisonous plants edible. For this reason, it is claimed these men were the first philosophers in the strict sense and they were mainly speculators or theorists, particularly interested in astronomy. In contrast, trying to use knowledge of nature to imitate nature was seen by scientists as a more appropriate interest for lower class artisans. A clear-cut distinction between formal and empirical science was made by the pre-Socratic philosopher Parmenides, although his work Peri Physeos is a poem, it may be viewed as an epistemological essay on method in natural science. Parmenides ἐὸν may refer to a system or calculus which can describe nature more precisely than natural languages. Physis may be identical to ἐὸν and he criticized the older type of study of physics as too purely speculative and lacking in self-criticism. He was particularly concerned that some of the early physicists treated nature as if it could be assumed that it had no intelligent order, explaining things merely in terms of motion and matter. The study of things had been the realm of mythology and tradition, however. Aristotle later created a less controversial systematic programme of Socratic philosophy which was teleological and he rejected many of the conclusions of earlier scientists. For example, in his physics, the sun goes around the earth, each thing has a formal cause and final cause and a role in the rational cosmic order. Motion and change is described as the actualization of potentials already in things, while the Socratics insisted that philosophy should be used to consider the practical question of the best way to live for a human being, they did not argue for any other types of applied science
9.
Engineering
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The term Engineering is derived from the Latin ingenium, meaning cleverness and ingeniare, meaning to contrive, devise. Engineering has existed since ancient times as humans devised fundamental inventions such as the wedge, lever, wheel, each of these inventions is essentially consistent with the modern definition of engineering. The term engineering is derived from the engineer, which itself dates back to 1390 when an engineer originally referred to a constructor of military engines. In this context, now obsolete, a referred to a military machine. Notable examples of the obsolete usage which have survived to the present day are military engineering corps, the word engine itself is of even older origin, ultimately deriving from the Latin ingenium, meaning innate quality, especially mental power, hence a clever invention. The earliest civil engineer known by name is Imhotep, as one of the officials of the Pharaoh, Djosèr, he probably designed and supervised the construction of the Pyramid of Djoser at Saqqara in Egypt around 2630–2611 BC. Ancient Greece developed machines in both civilian and military domains, the Antikythera mechanism, the first known mechanical computer, and the mechanical inventions of Archimedes are examples of early mechanical engineering. In the Middle Ages, the trebuchet was developed, the first steam engine was built in 1698 by Thomas Savery. The development of this gave rise to the Industrial Revolution in the coming decades. With the rise of engineering as a profession in the 18th century, similarly, in addition to military and civil engineering, the fields then known as the mechanic arts became incorporated into engineering. The inventions of Thomas Newcomen and the Scottish engineer James Watt gave rise to mechanical engineering. The development of specialized machines and machine tools during the revolution led to the rapid growth of mechanical engineering both in its birthplace Britain and abroad. John Smeaton was the first self-proclaimed civil engineer and is regarded as the father of civil engineering. He was an English civil engineer responsible for the design of bridges, canals, harbours and he was also a capable mechanical engineer and an eminent physicist. Smeaton designed the third Eddystone Lighthouse where he pioneered the use of hydraulic lime and his lighthouse remained in use until 1877 and was dismantled and partially rebuilt at Plymouth Hoe where it is known as Smeatons Tower. The United States census of 1850 listed the occupation of engineer for the first time with a count of 2,000, there were fewer than 50 engineering graduates in the U. S. before 1865. In 1870 there were a dozen U. S. mechanical engineering graduates, in 1890 there were 6,000 engineers in civil, mining, mechanical and electrical. There was no chair of applied mechanism and applied mechanics established at Cambridge until 1875, the theoretical work of James Maxwell and Heinrich Hertz in the late 19th century gave rise to the field of electronics
10.
Force
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In physics, a force is any interaction that, when unopposed, will change the motion of an object. In other words, a force can cause an object with mass to change its velocity, force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity and it is measured in the SI unit of newtons and represented by the symbol F. The original form of Newtons second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. In an extended body, each part usually applies forces on the adjacent parts, such internal mechanical stresses cause no accelation of that body as the forces balance one another. Pressure, the distribution of small forces applied over an area of a body, is a simple type of stress that if unbalanced can cause the body to accelerate. Stress usually causes deformation of materials, or flow in fluids. In part this was due to an understanding of the sometimes non-obvious force of friction. A fundamental error was the belief that a force is required to maintain motion, most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Sir Isaac Newton formulated laws of motion that were not improved-on for nearly three hundred years, the Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known, in order of decreasing strength, they are, strong, electromagnetic, weak, high-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction. Since antiquity the concept of force has been recognized as integral to the functioning of each of the simple machines. The mechanical advantage given by a machine allowed for less force to be used in exchange for that force acting over a greater distance for the same amount of work. Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was famous for formulating a treatment of buoyant forces inherent in fluids. Aristotle provided a discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotles view, the sphere contained four elements that come to rest at different natural places therein. Aristotle believed that objects on Earth, those composed mostly of the elements earth and water, to be in their natural place on the ground. He distinguished between the tendency of objects to find their natural place, which led to natural motion, and unnatural or forced motion
11.
Gravity
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Gravity, or gravitation, is a natural phenomenon by which all things with mass are brought toward one another, including planets, stars and galaxies. Since energy and mass are equivalent, all forms of energy, including light, on Earth, gravity gives weight to physical objects and causes the ocean tides. Gravity has a range, although its effects become increasingly weaker on farther objects. The most extreme example of this curvature of spacetime is a hole, from which nothing can escape once past its event horizon. More gravity results in time dilation, where time lapses more slowly at a lower gravitational potential. Gravity is the weakest of the four fundamental interactions of nature, the gravitational attraction is approximately 1038 times weaker than the strong force,1036 times weaker than the electromagnetic force and 1029 times weaker than the weak force. As a consequence, gravity has an influence on the behavior of subatomic particles. On the other hand, gravity is the dominant interaction at the macroscopic scale, for this reason, in part, pursuit of a theory of everything, the merging of the general theory of relativity and quantum mechanics into quantum gravity, has become an area of research. While the modern European thinkers are credited with development of gravitational theory, some of the earliest descriptions came from early mathematician-astronomers, such as Aryabhata, who had identified the force of gravity to explain why objects do not fall out when the Earth rotates. Later, the works of Brahmagupta referred to the presence of force, described it as an attractive force. Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th and this was a major departure from Aristotles belief that heavier objects have a higher gravitational acceleration. Galileo postulated air resistance as the reason that objects with less mass may fall slower in an atmosphere, galileos work set the stage for the formulation of Newtons theory of gravity. In 1687, English mathematician Sir Isaac Newton published Principia, which hypothesizes the inverse-square law of universal gravitation. Newtons theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted for by the actions of the other planets. Calculations by both John Couch Adams and Urbain Le Verrier predicted the position of the planet. A discrepancy in Mercurys orbit pointed out flaws in Newtons theory, the issue was resolved in 1915 by Albert Einsteins new theory of general relativity, which accounted for the small discrepancy in Mercurys orbit. The simplest way to test the equivalence principle is to drop two objects of different masses or compositions in a vacuum and see whether they hit the ground at the same time. Such experiments demonstrate that all objects fall at the rate when other forces are negligible
12.
Euclidean vector
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In mathematics, physics, and engineering, a Euclidean vector is a geometric object that has magnitude and direction. Vectors can be added to other vectors according to vector algebra, a Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B, and denoted by A B →. A vector is what is needed to carry the point A to the point B and it was first used by 18th century astronomers investigating planet rotation around the Sun. The magnitude of the vector is the distance between the two points and the direction refers to the direction of displacement from A to B. These operations and associated laws qualify Euclidean vectors as an example of the more generalized concept of vectors defined simply as elements of a vector space. Vectors play an important role in physics, the velocity and acceleration of a moving object, many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances, their magnitude and direction can still be represented by the length, the mathematical representation of a physical vector depends on the coordinate system used to describe it. Other vector-like objects that describe physical quantities and transform in a similar way under changes of the system include pseudovectors and tensors. The concept of vector, as we know it today, evolved gradually over a period of more than 200 years, about a dozen people made significant contributions. Giusto Bellavitis abstracted the basic idea in 1835 when he established the concept of equipollence, working in a Euclidean plane, he made equipollent any pair of line segments of the same length and orientation. Essentially he realized an equivalence relation on the pairs of points in the plane, the term vector was introduced by William Rowan Hamilton as part of a quaternion, which is a sum q = s + v of a Real number s and a 3-dimensional vector. Like Bellavitis, Hamilton viewed vectors as representative of classes of equipollent directed segments, grassmanns work was largely neglected until the 1870s. Peter Guthrie Tait carried the standard after Hamilton. His 1867 Elementary Treatise of Quaternions included extensive treatment of the nabla or del operator ∇, in 1878 Elements of Dynamic was published by William Kingdon Clifford. Clifford simplified the quaternion study by isolating the dot product and cross product of two vectors from the complete quaternion product and this approach made vector calculations available to engineers and others working in three dimensions and skeptical of the fourth. Josiah Willard Gibbs, who was exposed to quaternions through James Clerk Maxwells Treatise on Electricity and Magnetism, the first half of Gibbss Elements of Vector Analysis, published in 1881, presents what is essentially the modern system of vector analysis. In 1901 Edwin Bidwell Wilson published Vector Analysis, adapted from Gibbs lectures, in physics and engineering, a vector is typically regarded as a geometric entity characterized by a magnitude and a direction. It is formally defined as a line segment, or arrow
13.
Free fall
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In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of relativity, where gravitation is reduced to a space-time curvature. The present article only concerns itself with free fall in the Newtonian domain, an object in the technical sense of free fall may not necessarily be falling down in the usual sense of the term. An object moving upwards would not normally be considered to be falling, the moon is thus in free fall. The term free fall is used more loosely than in the strict sense defined above. Thus, falling through an atmosphere without a parachute, or lifting device, is also often referred to as free fall. The ancient Greek philosopher Aristotle discussed falling objects in Physics which was perhaps the first book on mechanics, the Italian scientist Galileo Galilei subjected the Aristotelian theories to experimentation and careful observation. He then combined the results of experiments with mathematical analysis in an unprecedented way. According to a tale that may be apocryphal, in 1589–92 Galileo dropped two objects of mass from the Leaning Tower of Pisa. Given the speed at such a fall would occur, it is doubtful that Galileo could have extracted much information from this experiment. Most of his observations of falling bodies were really of bodies rolling down ramps and this slowed things down enough to the point where he was able to measure the time intervals with water clocks and his own pulse. This he repeated a full hundred times until he had achieved an accuracy such that the deviation between two observations never exceeded one-tenth of a pulse beat, in 1589–92, Galileo wrote De Motu Antiquiora, an unpublished manuscript on the motion of falling bodies. Examples of objects in free fall include, A spacecraft with propulsion off, an object dropped at the top of a drop tube. An object thrown upward or a jumping off the ground at low speed. Technically, an object is in free fall even when moving upwards or instantaneously at rest at the top of its motion, if gravity is the only influence acting, then the acceleration is always downward and has the same magnitude for all bodies, commonly denoted g. Since all objects fall at the rate in the absence of other forces, objects. Examples of objects not in free fall, Flying in an aircraft, standing on the ground, the gravitational force is counteracted by the normal force from the ground. Descending to the Earth using a parachute, which balances the force of gravity with a drag force
14.
Drag (physics)
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In fluid dynamics, drag is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two layers or a fluid and a solid surface. Unlike other resistive forces, such as dry friction, which are independent of velocity. Drag force is proportional to the velocity for a laminar flow, even though the ultimate cause of a drag is viscous friction, the turbulent drag is independent of viscosity. Drag forces always decrease fluid velocity relative to the object in the fluids path. In the case of viscous drag of fluid in a pipe, in physics of sports, the drag force is necessary to explain the performance of runners, particularly of sprinters. Types of drag are generally divided into the categories, parasitic drag, consisting of form drag, skin friction, interference drag, lift-induced drag. The phrase parasitic drag is used in aerodynamics, since for lifting wings drag it is in general small compared to lift. For flow around bluff bodies, form and interference drags often dominate, further, lift-induced drag is only relevant when wings or a lifting body are present, and is therefore usually discussed either in aviation or in the design of semi-planing or planing hulls. Wave drag occurs either when an object is moving through a fluid at or near the speed of sound or when a solid object is moving along a fluid boundary. Drag depends on the properties of the fluid and on the size, shape, at low R e, C D is asymptotically proportional to R e −1, which means that the drag is linearly proportional to the speed. At high R e, C D is more or less constant, the graph to the right shows how C D varies with R e for the case of a sphere. As mentioned, the equation with a constant drag coefficient gives the force experienced by an object moving through a fluid at relatively large velocity. This is also called quadratic drag, the equation is attributed to Lord Rayleigh, who originally used L2 in place of A. Sometimes a body is a composite of different parts, each with a different reference areas, in the case of a wing the reference areas are the same and the drag force is in the same ratio to the lift force as the ratio of drag coefficient to lift coefficient. Therefore, the reference for a wing is often the area rather than the frontal area. For an object with a surface, and non-fixed separation points—like a sphere or circular cylinder—the drag coefficient may vary with Reynolds number Re. For an object with well-defined fixed separation points, like a disk with its plane normal to the flow direction
15.
Isaac Newton
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His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations of classical mechanics. Newton also made contributions to optics, and he shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus. Newtons Principia formulated the laws of motion and universal gravitation that dominated scientists view of the universe for the next three centuries. Newtons work on light was collected in his influential book Opticks. He also formulated a law of cooling, made the first theoretical calculation of the speed of sound. Newton was a fellow of Trinity College and the second Lucasian Professor of Mathematics at the University of Cambridge, politically and personally tied to the Whig party, Newton served two brief terms as Member of Parliament for the University of Cambridge, in 1689–90 and 1701–02. He was knighted by Queen Anne in 1705 and he spent the last three decades of his life in London, serving as Warden and Master of the Royal Mint and his father, also named Isaac Newton, had died three months before. Born prematurely, he was a child, his mother Hannah Ayscough reportedly said that he could have fit inside a quart mug. When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabas Smith, leaving her son in the care of his maternal grandmother, Newtons mother had three children from her second marriage. From the age of twelve until he was seventeen, Newton was educated at The Kings School, Grantham which taught Latin and Greek. He was removed from school, and by October 1659, he was to be found at Woolsthorpe-by-Colsterworth, Henry Stokes, master at the Kings School, persuaded his mother to send him back to school so that he might complete his education. Motivated partly by a desire for revenge against a bully, he became the top-ranked student. In June 1661, he was admitted to Trinity College, Cambridge and he started as a subsizar—paying his way by performing valets duties—until he was awarded a scholarship in 1664, which guaranteed him four more years until he would get his M. A. He set down in his notebook a series of Quaestiones about mechanical philosophy as he found it, in 1665, he discovered the generalised binomial theorem and began to develop a mathematical theory that later became calculus. Soon after Newton had obtained his B. A. degree in August 1665, in April 1667, he returned to Cambridge and in October was elected as a fellow of Trinity. Fellows were required to become ordained priests, although this was not enforced in the restoration years, however, by 1675 the issue could not be avoided and by then his unconventional views stood in the way. Nevertheless, Newton managed to avoid it by means of a special permission from Charles II. A and he was elected a Fellow of the Royal Society in 1672. Newtons work has been said to distinctly advance every branch of mathematics then studied and his work on the subject usually referred to as fluxions or calculus, seen in a manuscript of October 1666, is now published among Newtons mathematical papers
16.
Units of measurement
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A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same quantity. Any other value of quantity can be expressed as a simple multiple of the unit of measurement. For example, length is a physical quantity, the metre is a unit of length that represents a definite predetermined length. When we say 10 metres, we actually mean 10 times the definite predetermined length called metre, the definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. Different systems of units used to be very common, now there is a global standard, the International System of Units, the modern form of the metric system. In trade, weights and measures is often a subject of regulation, to ensure fairness. The International Bureau of Weights and Measures is tasked with ensuring worldwide uniformity of measurements, metrology is the science for developing nationally and internationally accepted units of weights and measures. In physics and metrology, units are standards for measurement of quantities that need clear definitions to be useful. Reproducibility of experimental results is central to the scientific method, a standard system of units facilitates this. Scientific systems of units are a refinement of the concept of weights, science, medicine, and engineering often use larger and smaller units of measurement than those used in everyday life and indicate them more precisely. The judicious selection of the units of measurement can aid researchers in problem solving, in the social sciences, there are no standard units of measurement and the theory and practice of measurement is studied in psychometrics and the theory of conjoint measurement. A unit of measurement is a quantity of a physical property. Units of measurement were among the earliest tools invented by humans, primitive societies needed rudimentary measures for many tasks, constructing dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials. Weights and measures are mentioned in the Bible and it is a commandment to be honest and have fair measures. As of the 21st Century, multiple unit systems are used all over the world such as the United States Customary System, the British Customary System, however, the United States is the only industrialized country that has not yet completely converted to the Metric System. The systematic effort to develop an acceptable system of units dates back to 1790 when the French National Assembly charged the French Academy of Sciences to come up such a unit system. After this treaty was signed, a General Conference of Weights, the CGPM produced the current SI system which was adopted in 1954 at the 10th conference of weights and measures. Currently, the United States is a society which uses both the SI system and the US Customary system
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Moon
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The Moon is an astronomical body that orbits planet Earth, being Earths only permanent natural satellite. It is the fifth-largest natural satellite in the Solar System, following Jupiters satellite Io, the Moon is second-densest satellite among those whose densities are known. The average distance of the Moon from the Earth is 384,400 km, the Moon is thought to have formed about 4.51 billion years ago, not long after Earth. It is the second-brightest regularly visible celestial object in Earths sky, after the Sun and its surface is actually dark, although compared to the night sky it appears very bright, with a reflectance just slightly higher than that of worn asphalt. Its prominence in the sky and its cycle of phases have made the Moon an important cultural influence since ancient times on language, calendars, art. The Moons gravitational influence produces the ocean tides, body tides, and this matching of apparent visual size will not continue in the far future. The Moons linear distance from Earth is currently increasing at a rate of 3.82 ±0.07 centimetres per year, since the Apollo 17 mission in 1972, the Moon has been visited only by uncrewed spacecraft. The usual English proper name for Earths natural satellite is the Moon, the noun moon is derived from moone, which developed from mone, which is derived from Old English mōna, which ultimately stems from Proto-Germanic *mǣnōn, like all Germanic language cognates. Occasionally, the name Luna is used, in literature, especially science fiction, Luna is used to distinguish it from other moons, while in poetry, the name has been used to denote personification of our moon. The principal modern English adjective pertaining to the Moon is lunar, a less common adjective is selenic, derived from the Ancient Greek Selene, from which is derived the prefix seleno-. Both the Greek Selene and the Roman goddess Diana were alternatively called Cynthia, the names Luna, Cynthia, and Selene are reflected in terminology for lunar orbits in words such as apolune, pericynthion, and selenocentric. The name Diana is connected to dies meaning day, several mechanisms have been proposed for the Moons formation 4.51 billion years ago, and some 60 million years after the origin of the Solar System. These hypotheses also cannot account for the angular momentum of the Earth–Moon system. This hypothesis, although not perfect, perhaps best explains the evidence, eighteen months prior to an October 1984 conference on lunar origins, Bill Hartmann, Roger Phillips, and Jeff Taylor challenged fellow lunar scientists, You have eighteen months. Go back to your Apollo data, go back to computer, do whatever you have to. Dont come to our conference unless you have something to say about the Moons birth, at the 1984 conference at Kona, Hawaii, the giant impact hypothesis emerged as the most popular. Afterward there were only two groups, the giant impact camp and the agnostics. Giant impacts are thought to have been common in the early Solar System, computer simulations of a giant impact have produced results that are consistent with the mass of the lunar core and the present angular momentum of the Earth–Moon system
18.
Theory of relativity
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The theory of relativity usually encompasses two interrelated theories by Albert Einstein, special relativity and general relativity. Special relativity applies to particles and their interactions, describing all their physical phenomena except gravity. General relativity explains the law of gravitation and its relation to other forces of nature and it applies to the cosmological and astrophysical realm, including astronomy. The theory transformed theoretical physics and astronomy during the 20th century and it introduced concepts including spacetime as a unified entity of space and time, relativity of simultaneity, kinematic and gravitational time dilation, and length contraction. In the field of physics, relativity improved the science of elementary particles and their fundamental interactions, with relativity, cosmology and astrophysics predicted extraordinary astronomical phenomena such as neutron stars, black holes, and gravitational waves. Max Planck, Hermann Minkowski and others did subsequent work, Einstein developed general relativity between 1907 and 1915, with contributions by many others after 1915. The final form of general relativity was published in 1916, the term theory of relativity was based on the expression relative theory used in 1906 by Planck, who emphasized how the theory uses the principle of relativity. In the discussion section of the paper, Alfred Bucherer used for the first time the expression theory of relativity. By the 1920s, the community understood and accepted special relativity. It rapidly became a significant and necessary tool for theorists and experimentalists in the new fields of physics, nuclear physics. By comparison, general relativity did not appear to be as useful and it seemed to offer little potential for experimental test, as most of its assertions were on an astronomical scale. Its mathematics of general relativity seemed difficult and fully understandable only by a number of people. Around 1960, general relativity became central to physics and astronomy, new mathematical techniques to apply to general relativity streamlined calculations and made its concepts more easily visualized. Special relativity is a theory of the structure of spacetime and it was introduced in Einsteins 1905 paper On the Electrodynamics of Moving Bodies. Special relativity is based on two postulates which are contradictory in classical mechanics, The laws of physics are the same for all observers in motion relative to one another. The speed of light in a vacuum is the same for all observers, the resultant theory copes with experiment better than classical mechanics. For instance, postulate 2 explains the results of the Michelson–Morley experiment, moreover, the theory has many surprising and counterintuitive consequences. Some of these are, Relativity of simultaneity, Two events, simultaneous for one observer, time dilation, Moving clocks are measured to tick more slowly than an observers stationary clock
19.
Curvature
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In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry. This article deals primarily with extrinsic curvature and its canonical example is that of a circle, which has a curvature equal to the reciprocal of its radius everywhere. Smaller circles bend more sharply, and hence have higher curvature, the curvature of a smooth curve is defined as the curvature of its osculating circle at each point. Curvature is normally a scalar quantity, but one may define a curvature vector that takes into account the direction of the bend in addition to its magnitude. The curvature of more objects is described by more complex objects from linear algebra. This article sketches the mathematical framework which describes the curvature of a curve embedded in a plane, the curvature of C at a point is a measure of how sensitive its tangent line is to moving the point to other nearby points. There are a number of equivalent ways that this idea can be made precise and it is natural to define the curvature of a straight line to be constantly zero. The curvature of a circle of radius R should be large if R is small and small if R is large, thus the curvature of a circle is defined to be the reciprocal of the radius, κ =1 R. Given any curve C and a point P on it, there is a circle or line which most closely approximates the curve near P. The curvature of C at P is then defined to be the curvature of that circle or line, the radius of curvature is defined as the reciprocal of the curvature. Another way to understand the curvature is physical, suppose that a particle moves along the curve with unit speed. Taking the time s as the parameter for C, this provides a natural parametrization for the curve, the unit tangent vector T also depends on time. The curvature is then the magnitude of the rate of change of T. Symbolically and this is the magnitude of the acceleration of the particle and the vector dT/ds is the acceleration vector. Geometrically, the curvature κ measures how fast the unit tangent vector to the curve rotates. If a curve close to the same direction, the unit tangent vector changes very little and the curvature is small, where the curve undergoes a tight turn. These two approaches to the curvature are related geometrically by the following observation, in the first definition, the curvature of a circle is equal to the ratio of the angle of an arc to its length. e. For such a curve, there exists a reparametrization with respect to arc length s. This is a parametrization of C such that ∥ γ ′ ∥2 = x ′2 + y ′2 =1, the velocity vector T is the unit tangent vector
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Spacetime
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In physics, spacetime is any mathematical model that combines space and time into a single interwoven continuum. Until the turn of the 20th century, the assumption had been that the 3D geometry of the universe was distinct from time, Einsteins theory was framed in terms of kinematics, and showed how measurements of space and time varied for observers in different reference frames. His theory was an advance over Lorentzs 1904 theory of electromagnetic phenomena. A key feature of this interpretation is the definition of an interval that combines distance. Although measurements of distance and time between events differ among observers, the interval is independent of the inertial frame of reference in which they are recorded. The resultant spacetime came to be known as Minkowski space, non-relativistic classical mechanics treats time as a universal quantity of measurement which is uniform throughout space and which is separate from space. Classical mechanics assumes that time has a constant rate of passage that is independent of the state of motion of an observer, furthermore, it assumes that space is Euclidean, which is to say, it assumes that space follows the geometry of common sense. General relativity, in addition, provides an explanation of how gravitational fields can slow the passage of time for an object as seen by an observer outside the field. Mathematically, spacetime is a manifold, which is to say, by analogy, at small enough scales, a globe appears flat. An extremely large scale factor, c relates distances measured in space with distances measured in time, waves implied the existence of a medium which waved, but attempts to measure the properties of the hypothetical luminiferous aether implied by these experiments provided contradictory results. For example, the Fizeau experiment of 1851 demonstrated that the speed of light in flowing water was less than the speed of light in air plus the speed of the flowing water, the partial aether-dragging implied by this result was in conflict with measurements of stellar aberration. By 1904, Lorentz had expanded his theory such that he had arrived at equations formally identical with those that Einstein were to derive later, but with a fundamentally different interpretation. As a theory of dynamics, his theory assumed actual physical deformations of the constituents of matter. For example, most physicists believed that Lorentz contraction would be detectable by such experiments as the Trouton–Noble experiment or the Experiments of Rayleigh and Brace. However, these negative results, and in his 1904 theory of the electron. Einstein performed his analyses in terms of kinematics rather than dynamics and it would appear that he did not at first think geometrically about spacetime. It was Einsteins former mathematics professor, Hermann Minkowski, who was to provide an interpretation of special relativity. Einstein was initially dismissive of the interpretation of special relativity
21.
Ancient Greece
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Ancient Greece was a civilization belonging to a period of Greek history from the Greek Dark Ages of the 12th-9th centuries BC to the end of antiquity. Immediately following this period was the beginning of the Early Middle Ages and this was followed by the period of Classical Greece, an era that began with the Greco-Persian Wars, lasting from the 5th to 4th centuries BC. Due to the conquests by Alexander the Great of Macedonia, Hellenistic civilization flourished from Central Asia to the end of the Mediterranean Sea. Classical Greek culture, especially philosophy, had a influence on ancient Rome. For this reason Classical Greece is generally considered to be the culture which provided the foundation of modern Western culture and is considered the cradle of Western civilization. Classical Antiquity in the Mediterranean region is considered to have begun in the 8th century BC. Classical Antiquity in Greece is preceded by the Greek Dark Ages and this period is succeeded, around the 8th century BC, by the Orientalizing Period during which a strong influence of Syro-Hittite, Jewish, Assyrian, Phoenician and Egyptian cultures becomes apparent. The end of the Dark Ages is also dated to 776 BC. The Archaic period gives way to the Classical period around 500 BC, Ancient Periods Astronomical year numbering Dates are approximate, consult particular article for details The history of Greece during Classical Antiquity may be subdivided into five major periods. The earliest of these is the Archaic period, in which artists made larger free-standing sculptures in stiff, the Archaic period is often taken to end with the overthrow of the last tyrant of Athens and the start of Athenian Democracy in 508 BC. It was followed by the Classical period, characterized by a style which was considered by observers to be exemplary, i. e. classical, as shown in the Parthenon. This period saw the Greco-Persian Wars and the Rise of Macedon, following the Classical period was the Hellenistic period, during which Greek culture and power expanded into the Near and Middle East. This period begins with the death of Alexander and ends with the Roman conquest, Herodotus is widely known as the father of history, his Histories are eponymous of the entire field. Herodotus was succeeded by authors such as Thucydides, Xenophon, Demosthenes, Plato, most of these authors were either Athenian or pro-Athenian, which is why far more is known about the history and politics of Athens than those of many other cities. Their scope is limited by a focus on political, military and diplomatic history, ignoring economic. In the 8th century BC, Greece began to emerge from the Dark Ages which followed the fall of the Mycenaean civilization, literacy had been lost and Mycenaean script forgotten, but the Greeks adopted the Phoenician alphabet, modifying it to create the Greek alphabet. The Lelantine War is the earliest documented war of the ancient Greek period and it was fought between the important poleis of Chalcis and Eretria over the fertile Lelantine plain of Euboea. Both cities seem to have suffered a decline as result of the long war, a mercantile class arose in the first half of the 7th century BC, shown by the introduction of coinage in about 680 BC
22.
Stoa of Attalos
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The Stoa of Attalos was a stoa in the Agora of Athens, Greece. It was built by and named after King Attalos II of Pergamon, the current building was reconstructed from 1952–1956 by American architects. Typical of the Hellenistic age, the stoa was more elaborate, the stoas dimensions are 115 by 20 metres and it is made of Pentelic marble and limestone. The building skillfully makes use of different architectural orders, the Doric order was used for the exterior colonnade on the ground floor with Ionic for the interior colonnade. This combination had been used in stoas since the Classical period and was by Hellenistic times quite common, on the first floor of the building, the exterior colonnade was Ionic and the interior Pergamene. Each story had two aisles and twenty-one rooms lining the western wall, the rooms of both stories were lighted and vented through doorways and small windows located on the back wall. There were stairways leading up to the story at each end of the stoa. The building is similar in its design to the Stoa that Attalos brother. The main difference is that Attalos stoa had a row of rooms at the rear on the floor that have been interpreted as shops. The stoa is identified as a gift to the city of Athens for the education that Attalos received there, a dedicatory inscription on the architrave is engraved as built by Attalos II, ruler of Pergamon from 159 BC to 138 BC. The stoa was in frequent use until it was destroyed by the Heruli in 267, the ruins became part of a fortification wall, which made it easily seen in modern times. The Stoa of Attalos houses the Museum of the Ancient Agora and its exhibits are mostly connected with the Athenian democracy. Fotopedia. com, Selected photos of the Stoa of Attalus Ministry of Culture, The Museum The Museum Stoa of Attalos photos
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Ancient Greek philosophy
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Ancient Greek philosophy arose in the 6th century BC and continued throughout the Hellenistic period and the period in which Ancient Greece was part of the Roman Empire. Philosophy was used to sense out of the world in a non-religious way. It dealt with a variety of subjects, including political philosophy, ethics, metaphysics, ontology, logic, biology, rhetoric. Many philosophers around the world agree that Greek philosophy has influenced much of Western culture since its inception, alfred North Whitehead once noted, The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato. Clear, unbroken lines of lead from ancient Greek and Hellenistic philosophers to Early Islamic philosophy, the European Renaissance. Some claim that Greek philosophy, in turn, was influenced by the wisdom literature. But they taught themselves to reason, Philosophy as we understand it is a Greek creation. Subsequent philosophic tradition was so influenced by Socrates as presented by Plato that it is conventional to refer to philosophy developed prior to Socrates as pre-Socratic philosophy. The periods following this, up to and after the wars of Alexander the Great, are those of classical Greek, the pre-Socratics were primarily concerned with cosmology, ontology and mathematics. They were distinguished from non-philosophers insofar as they rejected mythological explanations in favor of reasoned discourse, Thales of Miletus, regarded by Aristotle as the first philosopher, held that all things arise from water. It is not because he gave a cosmogony that John Burnet calls him the first man of science, according to tradition, Thales was able to predict an eclipse and taught the Egyptians how to measure the height of the pyramids. He began from the observation that the world seems to consist of opposites, therefore, they cannot truly be opposites but rather must both be manifestations of some underlying unity that is neither. This underlying unity could not be any of the classical elements, for example, water is wet, the opposite of dry, while fire is dry, the opposite of wet. Anaximenes in turn held that the arche was air, although John Burnet argues that by this he meant that it was a transparent mist, the aether. Xenophanes was born in Ionia, where the Milesian school was at its most powerful, Burnet says that Xenophanes was not, however, a scientific man, with many of his naturalistic explanations having no further support than that they render the Homeric gods superfluous or foolish. He has been claimed as an influence on Eleatic philosophy, although that is disputed, and a precursor to Epicurus, a representative of a total break between science and religion. Pythagoras lived at roughly the time that Xenophanes did and, in contrast to the latter. Parmenides of Elea cast his philosophy against those who held it is and is not the same, and all travel in opposite directions, —presumably referring to Heraclitus
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Plato
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Plato was a philosopher in Classical Greece and the founder of the Academy in Athens, the first institution of higher learning in the Western world. He is widely considered the most pivotal figure in the development of philosophy, unlike nearly all of his philosophical contemporaries, Platos entire work is believed to have survived intact for over 2,400 years. Along with his teacher, Socrates, and his most famous student, Aristotle, Plato laid the foundations of Western philosophy. Alfred North Whitehead once noted, the safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato. In addition to being a figure for Western science, philosophy. Friedrich Nietzsche, amongst other scholars, called Christianity, Platonism for the people, Plato was the innovator of the written dialogue and dialectic forms in philosophy, which originate with him. He was not the first thinker or writer to whom the word “philosopher” should be applied, few other authors in the history of Western philosophy approximate him in depth and range, perhaps only Aristotle, Aquinas and Kant would be generally agreed to be of the same rank. Due to a lack of surviving accounts, little is known about Platos early life, the philosopher came from one of the wealthiest and most politically active families in Athens. Ancient sources describe him as a bright though modest boy who excelled in his studies, the exact time and place of Platos birth are unknown, but it is certain that he belonged to an aristocratic and influential family. Based on ancient sources, most modern scholars believe that he was born in Athens or Aegina between 429 and 423 BCE. According to a tradition, reported by Diogenes Laertius, Ariston traced his descent from the king of Athens, Codrus. Platos mother was Perictione, whose family boasted of a relationship with the famous Athenian lawmaker, besides Plato himself, Ariston and Perictione had three other children, these were two sons, Adeimantus and Glaucon, and a daughter Potone, the mother of Speusippus. The brothers Adeimantus and Glaucon are mentioned in the Republic as sons of Ariston, and presumably brothers of Plato, but in a scenario in the Memorabilia, Xenophon confused the issue by presenting a Glaucon much younger than Plato. Then, at twenty-eight, Hermodorus says, went to Euclides in Megara, as Debra Nails argues, The text itself gives no reason to infer that Plato left immediately for Megara and implies the very opposite. Thus, Nails dates Platos birth to 424/423, another legend related that, when Plato was an infant, bees settled on his lips while he was sleeping, an augury of the sweetness of style in which he would discourse about philosophy. Ariston appears to have died in Platos childhood, although the dating of his death is difficult. Perictione then married Pyrilampes, her mothers brother, who had served many times as an ambassador to the Persian court and was a friend of Pericles, Pyrilampes had a son from a previous marriage, Demus, who was famous for his beauty. Perictione gave birth to Pyrilampes second son, Antiphon, the half-brother of Plato and these and other references suggest a considerable amount of family pride and enable us to reconstruct Platos family tree
25.
Aristotle
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Aristotle was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidice, on the northern periphery of Classical Greece. His father, Nicomachus, died when Aristotle was a child, at seventeen or eighteen years of age, he joined Platos Academy in Athens and remained there until the age of thirty-seven. Shortly after Plato died, Aristotle left Athens and, at the request of Philip II of Macedon, teaching Alexander the Great gave Aristotle many opportunities and an abundance of supplies. He established a library in the Lyceum which aided in the production of many of his hundreds of books and he believed all peoples concepts and all of their knowledge was ultimately based on perception. Aristotles views on natural sciences represent the groundwork underlying many of his works, Aristotles views on physical science profoundly shaped medieval scholarship. Their influence extended from Late Antiquity and the Early Middle Ages into the Renaissance, some of Aristotles zoological observations, such as on the hectocotyl arm of the octopus, were not confirmed or refuted until the 19th century. His works contain the earliest known study of logic, which was incorporated in the late 19th century into modern formal logic. Aristotle was well known among medieval Muslim intellectuals and revered as The First Teacher and his ethics, though always influential, gained renewed interest with the modern advent of virtue ethics. All aspects of Aristotles philosophy continue to be the object of academic study today. Though Aristotle wrote many elegant treatises and dialogues – Cicero described his style as a river of gold – it is thought that only around a third of his original output has survived. Aristotle, whose means the best purpose, was born in 384 BC in Stagira, Chalcidice. His father Nicomachus was the physician to King Amyntas of Macedon. Aristotle was orphaned at a young age, although there is little information on Aristotles childhood, he probably spent some time within the Macedonian palace, making his first connections with the Macedonian monarchy. At the age of seventeen or eighteen, Aristotle moved to Athens to continue his education at Platos Academy and he remained there for nearly twenty years before leaving Athens in 348/47 BC. Aristotle then accompanied Xenocrates to the court of his friend Hermias of Atarneus in Asia Minor, there, he traveled with Theophrastus to the island of Lesbos, where together they researched the botany and zoology of the island. Aristotle married Pythias, either Hermiass adoptive daughter or niece and she bore him a daughter, whom they also named Pythias. Soon after Hermias death, Aristotle was invited by Philip II of Macedon to become the tutor to his son Alexander in 343 BC, Aristotle was appointed as the head of the royal academy of Macedon. During that time he gave not only to Alexander
26.
Archimedes
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Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the scientists in classical antiquity. He was also one of the first to apply mathematics to physical phenomena, founding hydrostatics and statics and he is credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion. Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere and a cylinder, unlike his inventions, the mathematical writings of Archimedes were little known in antiquity. Archimedes was born c.287 BC in the city of Syracuse, Sicily, at that time a self-governing colony in Magna Graecia. The date of birth is based on a statement by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years, in The Sand Reckoner, Archimedes gives his fathers name as Phidias, an astronomer about whom nothing is known. Plutarch wrote in his Parallel Lives that Archimedes was related to King Hiero II, a biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he married or had children. During his youth, Archimedes may have studied in Alexandria, Egypt and he referred to Conon of Samos as his friend, while two of his works have introductions addressed to Eratosthenes. Archimedes died c.212 BC during the Second Punic War, according to the popular account given by Plutarch, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet General Marcellus but he declined, the soldier was enraged by this, and killed Archimedes with his sword. Plutarch also gives an account of the death of Archimedes which suggests that he may have been killed while attempting to surrender to a Roman soldier. According to this story, Archimedes was carrying mathematical instruments, and was killed because the thought that they were valuable items. General Marcellus was reportedly angered by the death of Archimedes, as he considered him a valuable asset and had ordered that he not be harmed. Marcellus called Archimedes a geometrical Briareus, the last words attributed to Archimedes are Do not disturb my circles, a reference to the circles in the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier. This quote is given in Latin as Noli turbare circulos meos. The phrase is given in Katharevousa Greek as μὴ μου τοὺς κύκλους τάραττε
27.
Buoyancy
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In science, buoyancy or upthrust, is an upward force exerted by a fluid that opposes the weight of an immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid, thus the pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object and this pressure difference results in a net upwards force on the object. For this reason, an object whose density is greater than that of the fluid in which it is submerged tends to sink, If the object is either less dense than the liquid or is shaped appropriately, the force can keep the object afloat. This can occur only in a reference frame, which either has a gravitational field or is accelerating due to a force other than gravity defining a downward direction. In a situation of fluid statics, the net upward force is equal to the magnitude of the weight of fluid displaced by the body. The center of buoyancy of an object is the centroid of the volume of fluid. Archimedes principle is named after Archimedes of Syracuse, who first discovered this law in 212 B. C, more tersely, Buoyancy = weight of displaced fluid. The weight of the fluid is directly proportional to the volume of the displaced fluid. Thus, among completely submerged objects with equal masses, objects with greater volume have greater buoyancy and this is also known as upthrust. Suppose a rocks weight is measured as 10 newtons when suspended by a string in a vacuum with gravity acting upon it, suppose that when the rock is lowered into water, it displaces water of weight 3 newtons. The force it exerts on the string from which it hangs would be 10 newtons minus the 3 newtons of buoyancy force,10 −3 =7 newtons. Buoyancy reduces the apparent weight of objects that have sunk completely to the sea floor and it is generally easier to lift an object up through the water than it is to pull it out of the water. The density of the object relative to the density of the fluid can easily be calculated without measuring any volumes. Density of object density of fluid = weight weight − apparent immersed weight Example, If you drop wood into water, Example, A helium balloon in a moving car. During a period of increasing speed, the air mass inside the car moves in the direction opposite to the cars acceleration, the balloon is also pulled this way. However, because the balloon is buoyant relative to the air, it ends up being pushed out of the way, If the car slows down, the same balloon will begin to drift backward. For the same reason, as the car goes round a curve and this is the equation to calculate the pressure inside a fluid in equilibrium
28.
Euclid
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Euclid, sometimes called Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the father of geometry. He was active in Alexandria during the reign of Ptolemy I, in the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, Euclid is the anglicized version of the Greek name Εὐκλείδης, which means renowned, glorious. Very few original references to Euclid survive, so little is known about his life, the date, place and circumstances of both his birth and death are unknown and may only be estimated roughly relative to other people mentioned with him. He is rarely mentioned by name by other Greek mathematicians from Archimedes onward, the few historical references to Euclid were written centuries after he lived by Proclus c.450 AD and Pappus of Alexandria c.320 AD. Proclus introduces Euclid only briefly in his Commentary on the Elements, Proclus later retells a story that, when Ptolemy I asked if there was a shorter path to learning geometry than Euclids Elements, Euclid replied there is no royal road to geometry. This anecdote is questionable since it is similar to a story told about Menaechmus, a detailed biography of Euclid is given by Arabian authors, mentioning, for example, a birth town of Tyre. This biography is generally believed to be completely fictitious, however, this hypothesis is not well accepted by scholars and there is little evidence in its favor. The only reference that historians rely on of Euclid having written the Elements was from Proclus, although best known for its geometric results, the Elements also includes number theory. The geometrical system described in the Elements was long known simply as geometry, today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century. In addition to the Elements, at least five works of Euclid have survived to the present day and they follow the same logical structure as Elements, with definitions and proved propositions. Data deals with the nature and implications of information in geometrical problems. On Divisions of Figures, which only partially in Arabic translation. It is similar to a first-century AD work by Heron of Alexandria, catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution is held to be anachronistic however by J J OConnor, phaenomena, a treatise on spherical astronomy, survives in Greek, it is quite similar to On the Moving Sphere by Autolycus of Pitane, who flourished around 310 BC. Optics is the earliest surviving Greek treatise on perspective, in its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth, Things seen under a greater angle appear greater, proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal. Other works are attributed to Euclid, but have been lost
29.
Jean Buridan
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Jean Buridan was a French priest who sowed the seeds of the Copernican revolution in Europe. He developed the concept of impetus, the first step toward the concept of inertia. His name is most familiar through the thought experiment known as Buridans ass, born, most probably, in Béthune, France, Buridan studied and later taught at the University of Paris. Unusually, he spent his life in the faculty of arts. He further maintained his independence by remaining a secular cleric. By 1340, his confidence had grown sufficiently for him to launch an attack on his predecessor, Buridan also wrote on solutions to paradoxes such as the liar paradox. An ordinance of Louis XI of France in 1473, directed against the nominalists, the bishop Albert of Saxony, himself renowned as a logician, was among the most notable of his students. The concept of inertia was alien to the physics of Aristotle, Aristotle, and his peripatetic followers held that a body was only maintained in motion by the action of a continuous external force. Thus, in the Aristotelian view, a projectile moving through the air would owe its continuing motion to eddies or vibrations in the surrounding medium, in the absence of a proximate force, the body would come to rest almost immediately. Jean Buridan, following in the footsteps of John Philoponus and Avicenna, proposed that motion was maintained by some property of the body, Buridan named the motion-maintaining property impetus. Moreover, he rejected the view that the impetus dissipated spontaneously, asserting that a body would be arrested by the forces of air resistance and gravity which might be opposing its impetus. Buridan further held that the impetus of a body increased with the speed with which it was set in motion, clearly, Buridans impetus is closely related to the modern concept of momentum. Buridan saw impetus as causing the motion of the object, Buridan anticipated Isaac Newton when he wrote. The theory of impetus was also adapted to explain phenomena in terms of circular impetus. Apocryphal stories abound about his amorous affairs and adventures which are enough to show that he enjoyed a reputation as a glamorous and mysterious figure in Paris life. In particular, a rumour held that he was sentenced to be thrown in a sack into the River Seine, françois Villon alludes to this in his famous poem Ballade des Dames du Temps Jadis. Buridan also seems to have had a facility for attracting academic funding which suggests that he was indeed a charismatic figure. Hughes, G. E. John Buridan on Self-Reference, Chapter Eight of Buridans Sophismata, an edition and translation with an introduction, and philosophical commentary
30.
Momentum
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In classical mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass and velocity of an object, quantified in kilogram-meters per second. It is dimensionally equivalent to impulse, the product of force and time, Newtons second law of motion states that the change in linear momentum of a body is equal to the net impulse acting on it. If the truck were lighter, or moving slowly, then it would have less momentum. Linear momentum is also a quantity, meaning that if a closed system is not affected by external forces. In classical mechanics, conservation of momentum is implied by Newtons laws. It also holds in special relativity and, with definitions, a linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory. It is ultimately an expression of one of the symmetries of space and time. Linear momentum depends on frame of reference, observers in different frames would find different values of linear momentum of a system. But each would observe that the value of linear momentum does not change with time, momentum has a direction as well as magnitude. Quantities that have both a magnitude and a direction are known as vector quantities, because momentum has a direction, it can be used to predict the resulting direction of objects after they collide, as well as their speeds. Below, the properties of momentum are described in one dimension. The vector equations are almost identical to the scalar equations, the momentum of a particle is traditionally represented by the letter p. It is the product of two quantities, the mass and velocity, p = m v, the units of momentum are the product of the units of mass and velocity. In SI units, if the mass is in kilograms and the velocity in meters per second then the momentum is in kilogram meters/second, in cgs units, if the mass is in grams and the velocity in centimeters per second, then the momentum is in gram centimeters/second. Being a vector, momentum has magnitude and direction, for example, a 1 kg model airplane, traveling due north at 1 m/s in straight and level flight, has a momentum of 1 kg m/s due north measured from the ground. The momentum of a system of particles is the sum of their momenta, if two particles have masses m1 and m2, and velocities v1 and v2, the total momentum is p = p 1 + p 2 = m 1 v 1 + m 2 v 2. If all the particles are moving, the center of mass will generally be moving as well, if the center of mass is moving at velocity vcm, the momentum is, p = m v cm. This is known as Eulers first law, if a force F is applied to a particle for a time interval Δt, the momentum of the particle changes by an amount Δ p = F Δ t
31.
Copernican heliocentrism
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Copernican heliocentrism is the name given to the astronomical model developed by Nicolaus Copernicus and published in 1543. It positioned the Sun near the center of the Universe, motionless, with Earth, Philolaus was one of the first to hypothesize movement of the Earth, probably inspired by Pythagoras theories about a spherical, moving globe. Aristarchus of Samos in the 3rd century BCE had developed theories of Heraclides Ponticus to propose what was, so far as is known. Though his original text has been lost, a reference in Archimedes book The Sand Reckoner describes a work by Aristarchus in which he advanced the heliocentric model and this is the common account as you have heard from astronomers. It is an idea that the heliocentric view was rejected by the contemporaries of Aristarchus. This is due to Gilles Ménages translation of a passage from Plutarchs On the Apparent Face in the Orb of the Moon. Plutarch reported that Cleanthes as a worshipper of the Sun and opponent to the model, was jokingly told by Aristarchus that he should be charged with impiety. Gilles Ménage, shortly after the trials of Galileo and Giordano Bruno, amended an accusative with a nominative, the resulting misconception of an isolated and persecuted Aristarchus is still transmitted today. Several Islamic astronomers questioned the Earths apparent immobility, and centrality within the universe, some accepted that the earth rotates around its axis, such as Abu Said al-Sijzi. Who invented an astrolabe based on a held by some of his contemporaries that the motion we see is due to the Earths movement. In the 12th century, Nur ad-Din al-Bitruji proposed an alternative to the Ptolemaic system. He declared the Ptolemaic system as a model, successful at predicting planetary positions. Al-Btirujis alternative system spread through most of Europe during the 13th century, for reasons unknown, he did not include this passage in the publication of his book. Inspiration came to Copernicus not from observation of the planets, in Cicero he found an account of the theory of Hicetas. Plutarch provided an account of the Pythagoreans Heraclides Ponticus, Philolaus and these authors had proposed a moving Earth, which did not, however, revolve around a central sun. When Copernicus book was published, it contained a preface by the Lutheran theologian Andreas Osiander. This cleric stated that Copernicus wrote his account of the Earths movement as a mere mathematical hypothesis. Since Copernicus hypothesis was believed to contradict the Old Testament account of the Suns movement around the Earth, however, there is no evidence that Copernicus himself considered the heliocentric model as merely mathematically convenient, separate from reality
32.
Galileo Galilei
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Galileo Galilei was an Italian polymath, astronomer, physicist, engineer, philosopher, and mathematician. He played a role in the scientific revolution of the seventeenth century. Galileo also worked in applied science and technology, inventing an improved military compass, Galileos championing of heliocentrism and Copernicanism was controversial during his lifetime, when most subscribed to either geocentrism or the Tychonic system. He met with opposition from astronomers, who doubted heliocentrism because of the absence of a stellar parallax. He was tried by the Inquisition, found vehemently suspect of heresy and he spent the rest of his life under house arrest. He has been called the father of observational astronomy, the father of modern physics, the father of scientific method, and the father of science. Galileo was born in Pisa, Italy, on 15 February 1564, the first of six children of Vincenzo Galilei, a famous lutenist, composer, and music theorist, and Giulia, three of Galileos five siblings survived infancy. The youngest, Michelangelo, also became a noted lutenist and composer although he contributed to financial burdens during Galileos young adulthood, Michelangelo was unable to contribute his fair share of their fathers promised dowries to their brothers-in-law, who would later attempt to seek legal remedies for payments due. Michelangelo would also occasionally have to borrow funds from Galileo to support his musical endeavours and these financial burdens may have contributed to Galileos early fire to develop inventions that would bring him additional income. When Galileo Galilei was eight, his family moved to Florence and he then was educated in the Vallombrosa Abbey, about 30 km southeast of Florence. Galileo Bonaiuti was buried in the church, the Basilica of Santa Croce in Florence. It was common for mid-sixteenth century Tuscan families to name the eldest son after the parents surname, hence, Galileo Galilei was not necessarily named after his ancestor Galileo Bonaiuti. The Italian male given name Galileo derives from the Latin Galilaeus, meaning of Galilee, the biblical roots of Galileos name and surname were to become the subject of a famous pun. In 1614, during the Galileo affair, one of Galileos opponents, in it he made a point of quoting Acts 1,11, Ye men of Galilee, why stand ye gazing up into heaven. Despite being a genuinely pious Roman Catholic, Galileo fathered three children out of wedlock with Marina Gamba and they had two daughters, Virginia and Livia, and a son, Vincenzo. Their only worthy alternative was the religious life, both girls were accepted by the convent of San Matteo in Arcetri and remained there for the rest of their lives. Virginia took the name Maria Celeste upon entering the convent and she died on 2 April 1634, and is buried with Galileo at the Basilica of Santa Croce, Florence. Livia took the name Sister Arcangela and was ill for most of her life, Vincenzo was later legitimised as the legal heir of Galileo and married Sestilia Bocchineri
33.
Newton's laws of motion
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Newtons laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. More precisely, the first law defines the force qualitatively, the second law offers a measure of the force. These three laws have been expressed in different ways, over nearly three centuries, and can be summarised as follows. The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica, Newton used them to explain and investigate the motion of many physical objects and systems. For example, in the volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation. Newtons laws are applied to objects which are idealised as single point masses, in the sense that the size and this can be done when the object is small compared to the distances involved in its analysis, or the deformation and rotation of the body are of no importance. In this way, even a planet can be idealised as a particle for analysis of its orbital motion around a star, in their original form, Newtons laws of motion are not adequate to characterise the motion of rigid bodies and deformable bodies. Leonhard Euler in 1750 introduced a generalisation of Newtons laws of motion for rigid bodies called Eulers laws of motion, if a body is represented as an assemblage of discrete particles, each governed by Newtons laws of motion, then Eulers laws can be derived from Newtons laws. Eulers laws can, however, be taken as axioms describing the laws of motion for extended bodies, Newtons laws hold only with respect to a certain set of frames of reference called Newtonian or inertial reference frames. Other authors do treat the first law as a corollary of the second, the explicit concept of an inertial frame of reference was not developed until long after Newtons death. In the given mass, acceleration, momentum, and force are assumed to be externally defined quantities. This is the most common, but not the interpretation of the way one can consider the laws to be a definition of these quantities. Newtonian mechanics has been superseded by special relativity, but it is useful as an approximation when the speeds involved are much slower than the speed of light. The first law states that if the net force is zero, the first law can be stated mathematically when the mass is a non-zero constant, as, ∑ F =0 ⇔ d v d t =0. Consequently, An object that is at rest will stay at rest unless a force acts upon it, an object that is in motion will not change its velocity unless a force acts upon it. This is known as uniform motion, an object continues to do whatever it happens to be doing unless a force is exerted upon it. If it is at rest, it continues in a state of rest, if an object is moving, it continues to move without turning or changing its speed
34.
Newton's law of universal gravitation
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This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning. It is a part of classical mechanics and was formulated in Newtons work Philosophiæ Naturalis Principia Mathematica, in modern language, the law states, Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them, the first test of Newtons theory of gravitation between masses in the laboratory was the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798. It took place 111 years after the publication of Newtons Principia, Newtons law of gravitation resembles Coulombs law of electrical forces, which is used to calculate the magnitude of the electrical force arising between two charged bodies. Both are inverse-square laws, where force is proportional to the square of the distance between the bodies. Coulombs law has the product of two charges in place of the product of the masses, and the constant in place of the gravitational constant. Newtons law has since been superseded by Albert Einsteins theory of general relativity, at the same time Hooke agreed that the Demonstration of the Curves generated thereby was wholly Newtons. In this way, the question arose as to what, if anything and this is a subject extensively discussed since that time and on which some points, outlined below, continue to excite controversy. And that these powers are so much the more powerful in operating. Thus Hooke clearly postulated mutual attractions between the Sun and planets, in a way that increased with nearness to the attracting body, Hookes statements up to 1674 made no mention, however, that an inverse square law applies or might apply to these attractions. Hookes gravitation was also not yet universal, though it approached universality more closely than previous hypotheses and he also did not provide accompanying evidence or mathematical demonstration. It was later on, in writing on 6 January 1679|80 to Newton, Newton, faced in May 1686 with Hookes claim on the inverse square law, denied that Hooke was to be credited as author of the idea. Among the reasons, Newton recalled that the idea had been discussed with Sir Christopher Wren previous to Hookes 1679 letter, Newton also pointed out and acknowledged prior work of others, including Bullialdus, and Borelli. D T Whiteside has described the contribution to Newtons thinking that came from Borellis book, a copy of which was in Newtons library at his death. Newton further defended his work by saying that had he first heard of the inverse square proportion from Hooke, Hooke, without evidence in favor of the supposition, could only guess that the inverse square law was approximately valid at great distances from the center. Thus Newton gave a justification, otherwise lacking, for applying the inverse square law to large spherical planetary masses as if they were tiny particles, after his 1679-1680 correspondence with Hooke, Newton adopted the language of inward or centripetal force. They also involved the combination of tangential and radial displacements, which Newton was making in the 1660s, the lesson offered by Hooke to Newton here, although significant, was one of perspective and did not change the analysis. This background shows there was basis for Newton to deny deriving the inverse square law from Hooke, on the other hand, Newton did accept and acknowledge, in all editions of the Principia, that Hooke had separately appreciated the inverse square law in the solar system
35.
Inertia
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Inertia is the resistance of any physical object to any change in its state of motion, this includes changes to its speed, direction, or state of rest. It is the tendency of objects to keep moving in a line at constant velocity. The principle of inertia is one of the principles of classical physics that are used to describe the motion of objects. Inertia comes from the Latin word, iners, meaning idle, Inertia is one of the primary manifestations of mass, which is a quantitative property of physical systems. In common usage, the inertia may refer to an objects amount of resistance to change in velocity, or sometimes to its momentum. Thus, an object will continue moving at its current velocity until some force causes its speed or direction to change. On the surface of the Earth, inertia is often masked by the effects of friction and air resistance, both of which tend to decrease the speed of moving objects, and gravity. Aristotle explained the continued motion of projectiles, which are separated from their projector, by the action of the surrounding medium, Aristotle concluded that such violent motion in a void was impossible. Despite its general acceptance, Aristotles concept of motion was disputed on several occasions by notable philosophers over nearly two millennia, for example, Lucretius stated that the default state of matter was motion, not stasis. Philoponus proposed that motion was not maintained by the action of a surrounding medium, although this was not the modern concept of inertia, for there was still the need for a power to keep a body in motion, it proved a fundamental step in that direction. This view was opposed by Averroes and by many scholastic philosophers who supported Aristotle. However, this view did not go unchallenged in the Islamic world, in the 14th century, Jean Buridan rejected the notion that a motion-generating property, which he named impetus, dissipated spontaneously. Buridans position was that an object would be arrested by the resistance of the air. Buridan also maintained that impetus increased with speed, thus, his idea of impetus was similar in many ways to the modern concept of momentum. Buridan also believed that impetus could be not only linear, but also circular in nature, buridans thought was followed up by his pupil Albert of Saxony and the Oxford Calculators, who performed various experiments that further undermined the classical, Aristotelian view. Their work in turn was elaborated by Nicole Oresme who pioneered the practice of demonstrating laws of motion in the form of graphs, benedetti cites the motion of a rock in a sling as an example of the inherent linear motion of objects, forced into circular motion. The law of inertia states that it is the tendency of an object to resist a change in motion. According to Newton, an object will stay at rest or stay in motion unless acted on by a net force, whether it results from gravity, friction, contact
36.
Principle of equivalence
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Kepler, using Galileos discoveries, showed knowledge of the equivalence principle by accurately describing what would occur if the moon were stopped in its orbit and dropped towards Earth. This can be deduced without knowing if or in what manner gravity decreases with distance, the 1/54 ratio is Keplers estimate of the Moon–Earth mass ratio, based on their diameters. The accuracy of his statement can be deduced by using Newtons inertia law F=ma, setting these accelerations equal for a mass is the equivalence principle. Einstein stated it thus, we assume the physical equivalence of a gravitational field. That is, being on the surface of the Earth is equivalent to being inside a spaceship that is being accelerated by its engines, from this principle, Einstein deduced that free-fall is inertial motion. Objects in free-fall do not experience being accelerated downward but rather weightlessness, in an inertial frame of reference bodies obey Newtons first law, moving at constant velocity in straight lines. Analogously, in a curved spacetime the world line of a particle or pulse of light is as straight as possible. Such a world line is called a geodesic and from the point of view of the frame is a straight line. This is why an accelerometer in free-fall doesnt register any acceleration, as an example, an inertial body moving along a geodesic through space can be trapped into an orbit around a large gravitational mass without ever experiencing acceleration. This is possible because spacetime is curved in close vicinity to a large gravitational mass. In such a situation the geodesic lines bend inward around the center of the mass, an accelerometer on-board would never record any acceleration. By contrast, in Newtonian mechanics, gravity is assumed to be a force and this force draws objects having mass towards the center of any massive body. At the Earths surface, the force of gravity is counteracted by the resistance of the Earths surface. So in Newtonian physics, a person at rest on the surface of an object is in an inertial frame of reference. Einstein also referred to two frames, K and K. This observation was the start of a process that culminated in general relativity, by assuming this to be so, we arrive at a principle which, if it is really true, has great heuristic importance. So the original equivalence principle, as described by Einstein, concluded that free-fall and this form of the equivalence principle can be stated as follows. An observer in a windowless room cannot distinguish between being on the surface of the Earth, and being in a spaceship in deep space accelerating at 1g
37.
Top Fuel
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Because of the speeds, this class almost exclusively races to only a 1,000 foot distance, and not the traditional 1⁄4 mile. The shortening of the distance was used in the FIA at some tracks, a top fuel dragster accelerates from a standstill to 100 miles per hour in as little as 0.8 seconds and can exceed 450 km/h in just 200 metres. This subjects the driver to an acceleration of about 39 m/s2 over the duration of the race. Before their run, racers often perform a burnout in order to clean, additionally, the burnout applies a layer of fresh rubber to the track surface, which greatly improves traction during launch. At maximum throttle and RPM, the exhaust gases escaping from a dragsters open headers produce about 4. 0–4.9 kilonewtons of downforce. The massive airfoil over and behind the rear wheels produces much more, the engine of a Top Fuel dragster generates around 150 dB of sound at full throttle, enough to cause physical pain or even permanent damage. Before a run, race announcers usually advise spectators to cover or plug their ears, ear plugs and even earmuffs are often handed out to fans at the entrance of a Top Fuel event. Dragsters are limited to a wheelbase of 760 centimetres. The first female driver in the Top Fuel category is also the most associated female in the racing world, Shirley Muldowney. NHRA regulations limit the composition of the fuel to a maximum of 90% nitromethane, however, this mixture is not mandatory, and less nitromethane may be used if desired. While nitromethane has a lower energy density than either gasoline or methanol. This means that an engine can burn 8.7 times more nitromethane than gasoline, nitromethane also has a high latent heat of vaporization, meaning that it will absorb substantial engine heat as it vaporizes, providing an invaluable cooling mechanism. The laminar flame speed and combustion temperature are higher than gasoline at 0.5 m/s and 2400 °C respectively, power output can be increased by using very rich air fuel mixtures. This is also something that helps prevent pre-ignition, something that is usually a problem when using nitromethane, in a typical run the engine can consume between 12 US gallons and 22.75 US gallons of fuel during warmup, burnout, staging, and the quarter-mile run. In some regards, teams are forced to use technologies that may be decades old, NHRA competition rules limit the engine displacement to 8,190 cubic centimetres. A 106-millimetre bore with a 114-millimetre stroke are customary dimensions, larger bores have been shown to weaken the cylinder block. Compression ratio is about 6.5,1, as is common on engines with overdriven Roots-type superchargers, the engine used to power a Top Fuel drag racing car follows the basic layout found in the second generation Chrysler 426 Hemi Elephant Engine made from 1964-71. Although the Top Fuel engine is built exclusively of specialist parts, the engine has hemispherical combustion chambers, a 90 degree V-angle,120 millimetres bore pitch
38.
Pythagorean theorem
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In mathematics, the Pythagorean theorem, also known as Pythagorass theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the two sides. There is some evidence that Babylonian mathematicians understood the formula, although little of it indicates an application within a mathematical framework, Mesopotamian, Indian and Chinese mathematicians all discovered the theorem independently and, in some cases, provided proofs for special cases. The theorem has been given numerous proofs – possibly the most for any mathematical theorem and they are very diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The Pythagorean theorem was known long before Pythagoras, but he may well have been the first to prove it, in any event, the proof attributed to him is very simple, and is called a proof by rearrangement. The two large squares shown in the figure each contain four triangles, and the only difference between the two large squares is that the triangles are arranged differently. Therefore, the space within each of the two large squares must have equal area. Equating the area of the white space yields the Pythagorean theorem and that Pythagoras originated this very simple proof is sometimes inferred from the writings of the later Greek philosopher and mathematician Proclus. Several other proofs of this theorem are described below, but this is known as the Pythagorean one, If the length of both a and b are known, then c can be calculated as c = a 2 + b 2. If the length of the c and of one side are known. The Pythagorean equation relates the sides of a triangle in a simple way. Another corollary of the theorem is that in any triangle, the hypotenuse is greater than any one of the other sides. A generalization of this theorem is the law of cosines, which allows the computation of the length of any side of any triangle, If the angle between the other sides is a right angle, the law of cosines reduces to the Pythagorean equation. This theorem may have more known proofs than any other, the book The Pythagorean Proposition contains 370 proofs, Let ABC represent a right triangle, with the right angle located at C, as shown on the figure. Draw the altitude from point C, and call H its intersection with the side AB, point H divides the length of the hypotenuse c into parts d and e. By a similar reasoning, the triangle CBH is also similar to ABC, the proof of similarity of the triangles requires the triangle postulate, the sum of the angles in a triangle is two right angles, and is equivalent to the parallel postulate. Similarity of the leads to the equality of ratios of corresponding sides. The first result equates the cosines of the angles θ, whereas the second result equates their sines, the role of this proof in history is the subject of much speculation
39.
Weighing scale
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Weighing scales are devices to measure weight or calculate mass. Scales and balances are used in commerce, as many products are sold. Very accurate balances, called analytical balances, are used in fields such as chemistry. Although records dating to the 1700s refer to spring scales for measuring weight, the earliest design for such a device dates to 1770 and credits Richard Salter, an early scale-maker. Postal workers could work quickly with spring scales than balance scales because they could be read instantaneously. By the 1940s various electronic devices were being attached to these designs to make more accurate. A spring scale measures weight by reporting the distance that a spring deflects under a load and this contrasts to a balance, which compares the torque on the arm due to a sample weight to the torque on the arm due to a standard reference weight using a horizontal lever. Spring scales measure force, which is the force of constraint acting on an object. They are usually calibrated so that measured force translates to mass at earths gravity, the object to be weighed can be simply hung from the spring or set on a pivot and bearing platform. In a spring scale, the spring either stretches or compresses, by Hookes law, every spring has a proportionality constant that relates how hard it is pulled to how far it stretches. Rack and pinion mechanisms are used to convert the linear spring motion to a dial reading. With proper manufacturing and setup, however, spring scales can be rated as legal for commerce, to remove the temperature error, a commerce-legal spring scale must either have temperature-compensated springs or be used at a fairly constant temperature. To eliminate the effect of gravity variations, a spring scale must be calibrated where it is used. It is also common in high-capacity applications such as crane scales to use force to sense weight. The test force is applied to a piston or diaphragm and transmitted through hydraulic lines to an indicator based on a Bourdon tube or electronic sensor. A digital bathroom scale is a type of electronic weighing machine, the digital bathroom scale is a smart scale which has many functions like smartphone integration, cloud storage, fitness tracking, etc. In electronic versions of spring scales, the deflection of a beam supporting the weight is measured using a strain gauge. The capacity of such devices is only limited by the resistance of the beam to deflection and these scales are used in the modern bakery, grocery, delicatessen, seafood, meat, produce and other perishable goods departments
40.
Weightlessness
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Counterintuitively, a uniform gravitational field does not by itself cause stress or strain, and a body in free fall in such an environment experiences no g-force acceleration and feels weightless. This is also termed zero-g where the term is more understood as meaning zero g-force. In such cases, a sensation of weight, in the sense of a state of stress can occur, in such cases, g-forces are felt, and bodies are not weightless. When the gravitational field is non-uniform, a body in free fall suffers tidal effects and is not stress-free, near a black hole, such tidal effects can be very strong. In the case of the Earth, the effects are minor, especially on objects of relatively small dimension and this condition is known as microgravity and it prevails in orbiting spacecraft. In October 2015, the NASA Office of Inspector General issued a health hazards related to human spaceflight. In Newtonian mechanics the term weight is two distinct interpretations by engineers. Weight1, Under this interpretation, the weight of a body is the force exerted on the body. Near the surface of the earth, a body mass is 1 kg has a weight of approximately 9.81 N, independent of its state of motion, free fall. Weightlessness in this sense can be achieved by removing the body far away from the source of gravity and it can also be attained by placing the body at a neutral point between two gravitating masses. Weight2, Weight can also be interpreted as that quantity which is measured when one uses scales, what is being measured there is the force exerted by the body on the scales. In a standard weighing operation, the body being weighed is in a state of equilibrium as a result of a force exerted on it by the weighing machine cancelling the gravitational field. By Newtons 3rd law, there is an equal and opposite force exerted by the body on the machine, typically, it is a contact force and not uniform across the mass of the body. If the body is placed on the scales in a lift in free fall in pure uniform gravity, the scale would read zero, and this describes the condition in which the body is stress free and undeformed. This is the weightlessness in free fall in a gravitational field. To sum up, we have two notions of weight of which weight1 is dominant, yet weightlessness is typically exemplified not by absence of weight1 but by the absence of stress associated with weight2. This is the sense of weightlessness in what follows below. A body is free, exerts zero weight2, when the only force acting on it is weight1 as when in free fall in a uniform gravitational field
41.
Balloon
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A balloon is a flexible bag that can be inflated with a gas, such as helium, hydrogen, nitrous oxide, oxygen, or air. Modern day balloons are made from such as rubber, latex, polychloroprene, or a nylon fabric. Some early balloons were made of dried animal bladders, such as the pig bladder, some balloons are used for decorative purposes or entertaining purposes, while others are used for practical purposes such as meteorology, medical treatment, military defense, or transportation. A balloons properties, including its low density and low cost, have led to a range of applications. The rubber balloon was invented by Michael Faraday in 1824, during experiments with various gases, Balloon Decorating Balloons are used for decorating birthday parties, weddings, corporate functions, school events, and for other festive gatherings. The artists who use the round balloons to build are called stackers, the most common types of balloon decor include arches, columns, centerpieces, balloon drops, sculptures, and balloon bouquets. Party balloons are made of a natural latex tapped from rubber trees. The rubbers elasticity makes the volume adjustable, often the term Party Balloon will refer to a twisting balloon or pencil balloon. These balloons are manipulated to create shapes and figures for parties and events, filling the balloon with air can be done with the mouth, a manual or electric inflater, or with a source of compressed gas. When rubber or plastic balloons are filled with helium so that they float, they retain their buoyancy for only a day or so. The enclosed helium atoms escape through pores in the latex which are larger than the helium atoms. Balloons filled with air usually hold their size and shape much longer, even a perfect rubber balloon eventually loses gas to the outside. The process by which a substance or solute migrates from a region of high concentration, through a barrier or membrane, to a region of lower concentration is called diffusion. The inside of balloons can be treated with a gel which coats the inside of the balloon to reduce the helium leakage. Beginning in the late 1970s, some more expensive foil balloons made of thin, unstretchable and these balloons have attractive shiny reflective surfaces and are often printed with color pictures and patterns for gifts and parties. The most important attribute of metallised nylon for balloons is its lightweight, increasing buoyancy, foil balloons have been criticized for interfering with power lines. Balloon artists are entertainers who twist and tie inflated tubular balloons into sculptures, the balloons used for sculpture are made of extra-stretchy rubber so that they can be twisted and tied without bursting. Since the pressure required to inflate a balloon is inversely proportional to the diameter of the balloon, a pump is usually used to inflate these balloons
42.
International Organization for Standardization
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The International Organization for Standardization is an international standard-setting body composed of representatives from various national standards organizations. Founded on 23 February 1947, the organization promotes worldwide proprietary and it is headquartered in Geneva, Switzerland, and as of March 2017 works in 162 countries. It was one of the first organizations granted general consultative status with the United Nations Economic, ISO, the International Organization for Standardization, is an independent, non-governmental organization, the members of which are the standards organizations of the 162 member countries. It is the worlds largest developer of international standards and facilitates world trade by providing common standards between nations. Nearly twenty thousand standards have been set covering everything from manufactured products and technology to food safety, use of the standards aids in the creation of products and services that are safe, reliable and of good quality. The standards help businesses increase productivity while minimizing errors and waste, by enabling products from different markets to be directly compared, they facilitate companies in entering new markets and assist in the development of global trade on a fair basis. The standards also serve to safeguard consumers and the end-users of products and services, the three official languages of the ISO are English, French, and Russian. The name of the organization in French is Organisation internationale de normalisation, according to the ISO, as its name in different languages would have different abbreviations, the organization adopted ISO as its abbreviated name in reference to the Greek word isos. However, during the meetings of the new organization, this Greek word was not invoked. Both the name ISO and the logo are registered trademarks, the organization today known as ISO began in 1926 as the International Federation of the National Standardizing Associations. ISO is an organization whose members are recognized authorities on standards. Members meet annually at a General Assembly to discuss ISOs strategic objectives, the organization is coordinated by a Central Secretariat based in Geneva. A Council with a membership of 20 member bodies provides guidance and governance. The Technical Management Board is responsible for over 250 technical committees, ISO has formed joint committees with the International Electrotechnical Commission to develop standards and terminology in the areas of electrical and electronic related technologies. Information technology ISO/IEC Joint Technical Committee 1 was created in 1987 to evelop, maintain, ISO has three membership categories, Member bodies are national bodies considered the most representative standards body in each country. These are the members of ISO that have voting rights. Correspondent members are countries that do not have their own standards organization and these members are informed about ISOs work, but do not participate in standards promulgation. Subscriber members are countries with small economies and they pay reduced membership fees, but can follow the development of standards
