1.
Bouncy ball
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A bouncy ball, power ball or super ball is a small polybutadiene rubber bouncing ball which rebounds proportionally to the amount of force used when thrown at a hard surface. Bouncy balls can bounce over three stories high when thrown at the ground, the first such ball was the proprietary Super Ball, and another was the larger, helium-filled Skyball. The bouncy ball was patented in 1966 by a California chemist named Norman Stingley, in 1965, Stingley spent his spare time experimenting with rubber. He compressed various scraps of synthetic rubber together under about 3500 pounds per inch of pressure. The result was a rubber ball with an extreme resilience. In some countries, for example the United States and Denmark, frauenfelder, Mark, Sinclair, Carla, Branwyn, Gareth, eds. Garwin, Richard L. Kinematics of an Ultraelastic Rough Ball
2.
Ping-Pong virus
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The Ping-Pong virus is a boot sector virus discovered on March 1,1988 at the Politecnico di Torino Turin Polytechnic University in Italy. It was likely the most common and best known boot sector virus until outnumbered by the Stoned virus, computers could be contaminated by an infected diskette, showing up as a 1 KB bad cluster to most disk checking programs. Due to being labelled as bad cluster, MS-DOS will avoid overwriting it and it infects disks on every active drive and will even infect non-bootable partitions on the hard disk. Upon infection, the virus becomes memory resident, the virus would become active if a disk access is made exactly on the half-hour and start to show a small ball bouncing around the screen in both text mode and graphical mode. No serious damage is incurred by the virus except on 286 machines, the cause of this crash is the MOV CS, AX instruction, which only exists on 88 and 86 processors. For this reason, users of machines at risk were advised to save their work and reboot, the original Ping Pong virus only infects floppy disks. Later variants of this such as Ping-Pong. B and Ping-Pong. C also infect the hard disk boot sector as well. While the virus is active, one cannot replace the boot sector—it either prevents writing to it or it immediately re-infects it, Ping-Pong. A is extinct but the hard-disk variants can still appear
3.
Parabola
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A parabola is a two-dimensional, mirror-symmetrical curve, which is approximately U-shaped when oriented as shown in the diagram below, but which can be in any orientation in its plane. It fits any of several different mathematical descriptions which can all be proved to define curves of exactly the same shape. One description of a parabola involves a point and a line, the focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus, a parabola is a graph of a quadratic function, y = x2, for example. The line perpendicular to the directrix and passing through the focus is called the axis of symmetry, the point on the parabola that intersects the axis of symmetry is called the vertex, and is the point where the parabola is most sharply curved. The distance between the vertex and the focus, measured along the axis of symmetry, is the focal length, the latus rectum is the chord of the parabola which is parallel to the directrix and passes through the focus. Parabolas can open up, down, left, right, or in some arbitrary direction. Any parabola can be repositioned and rescaled to fit exactly on any other parabola — that is, conversely, light that originates from a point source at the focus is reflected into a parallel beam, leaving the parabola parallel to the axis of symmetry. The same effects occur with sound and other forms of energy and this reflective property is the basis of many practical uses of parabolas. The parabola has many important applications, from an antenna or parabolic microphone to automobile headlight reflectors to the design of ballistic missiles. They are frequently used in physics, engineering, and many other areas, the earliest known work on conic sections was by Menaechmus in the fourth century BC. He discovered a way to solve the problem of doubling the cube using parabolas, the name parabola is due to Apollonius who discovered many properties of conic sections. It means application, referring to application of concept, that has a connection with this curve. The focus–directrix property of the parabola and other conics is due to Pappus, Galileo showed that the path of a projectile follows a parabola, a consequence of uniform acceleration due to gravity. The idea that a reflector could produce an image was already well known before the invention of the reflecting telescope. Designs were proposed in the early to mid seventeenth century by many mathematicians including René Descartes, Marin Mersenne, when Isaac Newton built the first reflecting telescope in 1668, he skipped using a parabolic mirror because of the difficulty of fabrication, opting for a spherical mirror. Parabolic mirrors are used in most modern reflecting telescopes and in satellite dishes, solving for y yields y =14 f x 2. The length of the chord through the focus is called latus rectum, one half of it semi latus rectum
4.
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
5.
Deflection (physics)
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Deflection, in physics, refers to the change in an objects acceleration as a consequence of contact with a surface or the influence of a field. An objects deflective efficiency can never equal or surpass 100%, for example, a mirror will never reflect exactly the same amount of light cast upon it. Also, on hitting the ground, a previously in free-fall will never bounce back up to the place where it first started to descend
6.
Ball
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A ball is a round object with various uses. It is used in games, where the play of the game follows the state of the ball as it is hit. Balls can also be used for activities, such as catch, marbles. Balls made from hard-wearing materials are used in engineering applications to very low friction bearings. Black-powder weapons use stone and metal balls as projectiles, although many types of balls are today made from rubber, this form was unknown outside the Americas until after the voyages of Columbus. The Spanish were the first Europeans to see bouncing rubber balls which were employed most notably in the Mesoamerican ballgame, balls used in various sports in other parts of the world prior to Columbus were made from other materials such as animal bladders or skins, stuffed with various materials. As balls are one of the most familiar spherical objects to humans, no Old English representative of any of these is known. If ball- was native in Germanic, it may have been a cognate with the Latin foll-is in sense of a blown up or inflated. In the later Middle English spelling balle the word coincided graphically with the French balle ball, French balle is assumed to be of Germanic origin, itself, however. In Ancient Greek the word πάλλα for ball is attested besides the word σφαίρα, a ball, as the essential feature in many forms of gameplay requiring physical exertion, must date from the very earliest times. A rolling object appeals not only to a baby but to a kitten. Some form of game with a ball is found portrayed on Egyptian monuments, in Homer, Nausicaa was playing at ball with her maidens when Odysseus first saw her in the land of the Phaeacians. And Halios and Laodamas performed before Alcinous and Odysseus with ball play, of regular rules for the playing of ball games, little trace remains, if there were any such. Pollux mentions a game called episkyros, which has often been looked on as the origin of football and it seems to have been played by two sides, arranged in lines, how far there was any form of goal seems uncertain. Among the Romans, ball games were looked upon as an adjunct to the bath, and were graduated to the age and health of the bathers and this was struck from player to player, who wore a kind of gauntlet on the arm. These games are known to us through the Romans, though the names are Greek, the various modern games played with a ball or balls and subject to rules are treated under their various names, such as polo, cricket, football, etc. Several sports use a ball in the shape of a prolate spheroid, Ball Buckminster Fullerene Football Kickball Marbles Penny floater Prisoner Ball Shuttlecock Super Ball
7.
Motion (physics)
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In physics, motion is a change in position of an object over time. Motion is described in terms of displacement, distance, velocity, acceleration, time, motion of a body is observed by attaching a frame of reference to an observer and measuring the change in position of the body relative to that frame. If the position of a body is not changing with respect to a frame of reference. An objects motion cannot change unless it is acted upon by a force, momentum is a quantity which is used for measuring motion of an object. As there is no frame of reference, absolute motion cannot be determined. Thus, everything in the universe can be considered to be moving, more generally, motion is a concept that applies to objects, bodies, and matter particles, to radiation, radiation fields and radiation particles, and to space, its curvature and space-time. One can also speak of motion of shapes and boundaries, so, the term motion in general signifies a continuous change in the configuration of a physical system. For example, one can talk about motion of a wave or about motion of a quantum particle, in physics, motion is described through two sets of apparently contradictory laws of mechanics. Motions of all large scale and familiar objects in the universe are described by classical mechanics, whereas the motion of very small atomic and sub-atomic objects is described by quantum mechanics. It produces very accurate results within these domains, and is one of the oldest and largest in science, engineering, classical mechanics is fundamentally based on Newtons laws of motion. These laws describe the relationship between the acting on a body and the motion of that body. They were first compiled by Sir Isaac Newton in his work Philosophiæ Naturalis Principia Mathematica and his three laws are, A body either is at rest or moves with constant velocity, until and unless an outer force is applied to it. An object will travel in one direction only until an outer force changes its direction, whenever one body exerts a force F onto a second body, the second body exerts the force −F on the first body. F and −F are equal in magnitude and opposite in sense, so, the body which exerts F will go backwards. Newtons three laws of motion, along with his Newtons law of motion, which were the first to provide a mathematical model for understanding orbiting bodies in outer space. This explanation unified the motion of bodies and motion of objects on earth. Classical mechanics was later enhanced by Albert Einsteins special relativity. Motion of objects with a velocity, approaching the speed of light
8.
Impact (mechanics)
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In mechanics, an impact is a high force or shock applied over a short time period when two or more bodies collide. Such a force or acceleration usually has an effect than a lower force applied over a proportionally longer period. The effect depends critically on the velocity of the bodies to one another. At normal speeds, during a perfectly inelastic collision, an object struck by a projectile will deform, however, these deformations and vibrations cannot occur instantaneously. A high-velocity collision does not provide sufficient time for these deformations and vibrations to occur, thus, the struck material behaves as if it were more brittle than it would otherwise be, and the majority of the applied force goes into fracturing the material. Or, another way to look at it is that actually are more brittle on short time scales than on long time scales. Impact resistance decreases with an increase in the modulus of elasticity, resilient materials will have better impact resistance. Different materials can behave in different ways in impact when compared with static loading conditions. Ductile materials like steel tend to become brittle at high loading rates. The way in which the energy is distributed through the section is also important in determining its response. Projectiles apply a Hertzian contact stress at the point of impact to a body, with compression stresses under the point. Since most materials are weaker in tension than compression, this is the zone where cracks tend to form, a nail is pounded with a series of impacts, each by a single hammer blow. These high velocity impacts overcome the friction between the nail and the substrate. A pile driver achieves the same end, although on a larger scale. An impact wrench is a designed to impart torque impacts to bolts to tighten or loosen them. At normal speeds, the applied to the bolt would be dispersed, via friction. However, at speeds, the forces act on the bolt to move it before they can be dispersed. In ballistics, bullets utilize impact forces to puncture surfaces that could otherwise resist substantial forces, a rubber sheet, for example, behaves more like glass at typical bullet speeds
9.
Mechanics
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Mechanics is an area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment. The scientific discipline has its origins in Ancient Greece with the writings of Aristotle, during the early modern period, scientists such as Khayaam, Galileo, Kepler, and Newton, laid the foundation for what is now known as classical mechanics. It is a branch of physics that deals with particles that are either at rest or are moving with velocities significantly less than the speed of light. It can also be defined as a branch of science which deals with the motion of, historically, classical mechanics came first, while quantum mechanics is a comparatively recent invention. Classical mechanics originated with Isaac Newtons laws of motion in Philosophiæ Naturalis Principia Mathematica, both are commonly held to constitute the most certain knowledge that exists about physical nature. Classical mechanics has especially often been viewed as a model for other so-called exact sciences, essential in this respect is the relentless use of mathematics in theories, as well as the decisive role played by experiment in generating and testing them. Quantum mechanics is of a scope, as it encompasses classical mechanics as a sub-discipline which applies under certain restricted circumstances. According to the principle, there is no contradiction or conflict between the two subjects, each simply pertains to specific situations. The correspondence principle states that the behavior of systems described by quantum theories reproduces classical physics in the limit of quantum numbers. Quantum mechanics has superseded classical mechanics at the level and is indispensable for the explanation and prediction of processes at the molecular, atomic. However, for macroscopic processes classical mechanics is able to solve problems which are difficult in quantum mechanics and hence remains useful. Modern descriptions of such behavior begin with a definition of such quantities as displacement, time, velocity, acceleration, mass. Until about 400 years ago, however, motion was explained from a different point of view. He showed that the speed of falling objects increases steadily during the time of their fall and this acceleration is the same for heavy objects as for light ones, provided air friction is discounted. The English mathematician and physicist Isaac Newton improved this analysis by defining force and mass, for objects traveling at speeds close to the speed of light, Newton’s laws were superseded by Albert Einstein’s theory of relativity. For atomic and subatomic particles, Newton’s laws were superseded by quantum theory, for everyday phenomena, however, Newton’s three laws of motion remain the cornerstone of dynamics, which is the study of what causes motion. In analogy to the distinction between quantum and classical mechanics, Einsteins general and special theories of relativity have expanded the scope of Newton, the differences between relativistic and Newtonian mechanics become significant and even dominant as the velocity of a massive body approaches the speed of light. Relativistic corrections are also needed for quantum mechanics, although general relativity has not been integrated, the two theories remain incompatible, a hurdle which must be overcome in developing a theory of everything
10.
Secondary school
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A secondary school is both an organization that delivers level 2 junior secondary education or level 3 secondary education phases of the ISCED scale, and the building where this takes place. Level 2 junior secondary education is considered to be the second, Secondary schools typically follow on from primary schools and lead into vocational and tertiary education. Attendance is compulsory in most countries for students between the ages 11 and 16, the systems and terminology remain unique to each country. School building design does not happen in isolation, schools need to accommodate students, staff, storage, mechanical and electrical systems, storage, support staff, ancillary staff and administration. The number of rooms required can be determined from the roll of the school. A general classroom for 30 students needs to be 55m2, or more generously 62m2, a general art room for 30 students needs to be 83m2, but 104 m2 for 3D textile work. A drama studio or a specialist science laboratory for 30 needs to be 90 m2, examples are given on how this can be configured for a 1,200 place secondary. The building providing the education has to fulfil the needs of, The students, the teachers, the support staff, the adminstrators. It has to should meet health requirements, minimal functional requirements- such as classrooms, toilets and showers, electricity, textbooks, Government accountants having read the advice then publish minimum guidelines on schools. These enable environmental modelling and establish building costs. Future plans are audited to ensure that standards are not exceeded. The UK government published this downwardly revised space formula in 2014 and it said the floor area should be 1050m² +6. 3m²/pupil place for 11- to 16-year-olds + 7m²/pupil place for post-16s. The external finishes were to be downgraded to meet a build cost of £1113/m², a secondary school, locally may be called high school, junior high school, senior high school. Sweden, gymnasium Switzerland, gymnasium, secondary school, collège or lycée Taiwan, Junior High School, Senior High School, Vocational High School, Military School, in Nigeria, secondary school starts from JSS1 until SSS3. Most students start at the age of 10 or 11 and finish at 16 or 17, Students are required to sit for the West African Senior Secondary Certificate Examination. To progress to university students must obtain at least a credit in Maths, English, in Somalia, secondary school starts from 9th grade until 12th. Students start it when they are around 14 to 15 years of age, Students are required to study Somali and Arabic, with the option of either English or Italian depending on the type of school. Religion, chemistry, physics, biology, physical education, textile, art, design, when secondary school has been completed, students are sent to national training camp before going to either college, or military training. In South Africa, high school begins at grade 8, Students study for five years, at the end of which they write a Matriculation examination
11.
Projectile motion
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A special case of a ballistic trajectory for a rocket is a lofted trajectory, a trajectory with an apogee greater than the minimum-energy trajectory to the same range. In other words, the rocket higher and by doing so it uses more energy to get to the same landing point. This may be done for reasons such as increasing distance to the horizon to give greater viewing/communication range or for changing the angle with which a missile will impact on landing. Lofted trajectories are sometimes used in both missile rocketry and in spaceflight, the following applies for ranges which are small compared to the size of the Earth. For longer ranges see sub-orbital spaceflight, in the equations on this page, the following variables will be used, g, the gravitational acceleration—usually taken to be 9. A ballistic missile is a missile only guided during the brief initial powered phase of flight. These formulae ignore aerodynamic drag and also assume that the area is at uniform height 0. This distance is, d = v 2 g For explicit derivations of these results, the time of flight is the time it takes for the projectile to finish its trajectory. The above results are found in Range of a projectile, the third term is the deviation from traveling in a straight line. The magnitude, | v |, of the velocity of the projectile at distance x is given by | v | = v 2 −2 g x tan θ +2. The magnitude |v| of the velocity is given by | v | = V x 2 + V y 2, here the x-velocity remains constant, it is always equal to v cos θ. The y-velocity can be using the formula v f = v i + a t by setting vi = v sin θ, a = -g. Then, V y = v sin θ − g x v cos θ and | v | =2 +2, the formula above is found by simplifying. This formula allows one to find the angle of launch needed without the restriction of y =0, the tangent of the angle of elevation is proportional to the time since the ball was sent into the air, usually by being struck with a bat. Even when the ball is really descending, near the end of its flight, the player therefore sees it in line with a point ascending vertically from the batsman at constant speed. Finding the place from which the ball appears to rise steadily helps the player to position himself correctly to make the catch, if he is too close to the batsman who has hit the ball, it will appear to rise at an accelerating rate. If he is too far from the batsman, it appear to slow rapidly. Proof Suppose the ball starts with a component of velocity of v y upward
12.
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
13.
Magnus effect
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The Magnus effect is the commonly observed effect in which a spinning ball curves away from its principal flight path. It is important in many ball sports and it affects spinning missiles, and has some engineering uses, for instance in the design of rotor ships and Flettner aeroplanes. In terms of games, topspin is defined as spin about an axis perpendicular to the direction of travel. Under the Magnus effect, topspin produces a downward swerve of a ball, greater than would be produced by gravity alone. Likewise side-spin causes swerve to either side as seen during some baseball pitches, the overall behaviour is similar to that around an aerofoil with a circulation which is generated by the mechanical rotation, rather than by airfoil action. The Magnus effect is named after Heinrich Gustav Magnus, the German physicist who investigated it, the force on a rotating cylinder is known as Kutta–Joukowski lift, after Martin Wilhelm Kutta and Nikolai Zhukovsky, who first analyzed the effect. The body pushes the air down, and the air pushes the body upward, as a particular case, a lifting force is accompanied by a downward deflection of the air-flow. It is a deflection in the fluid flow, aft of the body. In fact there are ways in which the rotation might cause such a deflection. By far the best way to know what happens in typical cases is by wind tunnel experiments. Lyman Briggs made a wind tunnel study of the Magnus effect on baseballs. The studies show a turbulent wake behind the spinning ball, the wake is to be expected and is the cause of aerodynamic drag. However there is an angular deflection in the wake and the deflection is in the direction of the spin. The process by which a turbulent wake develops aft of a body in an air-flow is complex and it is found that the thin boundary layer detaches itself from the body at some point and this is where the wake begins to develop. The boundary layer itself may be turbulent or not, this has a significant effect on the wake formation, quite small variations in the surface conditions of the body can influence the onset of wake formation and thereby have a marked effect on the downstream flow pattern. The influence of the rotation is of this kind. It is said that Magnus himself wrongly postulated a theoretical effect with laminar flow due to skin friction, such effects are physically possible but slight in comparison to what is produced in the Magnus effect proper. In some circumstances the causes of the Magnus effect can produce a deflection opposite to that of the Magnus effect, the diagram at the head of this article shows lift being produced on a back-spinning ball
14.
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
15.
Coefficient of restitution
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The coefficient of restitution is the ratio of the final to initial velocity difference between two objects after they collide. It normally ranges from 0 to 1 where 1 would be a perfectly elastic collision, a perfectly inelastic collision has a coefficient of 0, but a 0 value does not have to be perfectly inelastic. It is measured in the Leeb rebound hardness test, expressed as 1000 times the COR, the value is almost always less than one due to initial translational kinetic energy being lost to rotational kinetic energy, plastic deformation, and heat. It is also known as Newtons experimental law, line of impact – It is the line along which e is defined or in absence of tangential reaction force between colliding surfaces, force of impact is shared along this line between bodies. During physical contact between bodies during impact its line along common normal to pair of surfaces in contact of colliding bodies, hence e is defined as a dimensionless one-dimensional parameter. E is usually a positive, real number between 0 and 1.0, e =0, This is an inelastic collision. The objects do not move apart after the collision, but instead they coalesce, kinetic energy is converted to heat or work done in deforming the objects. 0 < e <1, This is an inelastic collision. E =1, This is an elastic collision, in which no kinetic energy is dissipated. This may also be thought of as a transfer of momentum. E >1, This would represent a collision in which energy is released, for example, also, some recent articles have described superelastic collisions in which it is argued that the COR can take a value greater than one in a special case of oblique collisions. These phenomena are due to the change of rebound trajectory caused by friction, in such collision kinetic energy is increased in a manner energy is released in some sort of explosion. It is possible that e = ∞ for an explosion of a rigid system. For this short duration this collision e=0 and may be referred as inelastic phase, the COR is a property of a pair of objects in a collision, not a single object. If a given object collides with two different objects, each collision would have its own COR, a perfectly rigid wall is not possibly but can be approximated by a steel block if investigating the COR of spheres with a much smaller modulus of elasticity. Otherwise, the COR will rise and then based on collision velocity in a more complicated manner. In a one-dimensional collision, the two key principles are, conservation of energy and conservation of momentum, a third equation can be derived from these two, which is the restitution equation as stated above. When solving problems, any two of the three equations can be used, the advantage of using the restitution equation is that it sometimes provides a more convenient way to approach the problem
16.
Temperature
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A temperature is an objective comparative measurement of hot or cold. It is measured by a thermometer, several scales and units exist for measuring temperature, the most common being Celsius, Fahrenheit, and, especially in science, Kelvin. Absolute zero is denoted as 0 K on the Kelvin scale, −273.15 °C on the Celsius scale, the kinetic theory offers a valuable but limited account of the behavior of the materials of macroscopic bodies, especially of fluids. Temperature is important in all fields of science including physics, geology, chemistry, atmospheric sciences, medicine. The Celsius scale is used for temperature measurements in most of the world. Because of the 100 degree interval, it is called a centigrade scale.15, the United States commonly uses the Fahrenheit scale, on which water freezes at 32°F and boils at 212°F at sea-level atmospheric pressure. Many scientific measurements use the Kelvin temperature scale, named in honor of the Scottish physicist who first defined it and it is a thermodynamic or absolute temperature scale. Its zero point, 0K, is defined to coincide with the coldest physically-possible temperature and its degrees are defined through thermodynamics. The temperature of zero occurs at 0K = −273. 15°C. For historical reasons, the triple point temperature of water is fixed at 273.16 units of the measurement increment, Temperature is one of the principal quantities in the study of thermodynamics. There is a variety of kinds of temperature scale and it may be convenient to classify them as empirically and theoretically based. Empirical temperature scales are historically older, while theoretically based scales arose in the middle of the nineteenth century, empirically based temperature scales rely directly on measurements of simple physical properties of materials. For example, the length of a column of mercury, confined in a capillary tube, is dependent largely on temperature. Such scales are only within convenient ranges of temperature. For example, above the point of mercury, a mercury-in-glass thermometer is impracticable. A material is of no use as a thermometer near one of its phase-change temperatures, in spite of these restrictions, most generally used practical thermometers are of the empirically based kind. Especially, it was used for calorimetry, which contributed greatly to the discovery of thermodynamics, nevertheless, empirical thermometry has serious drawbacks when judged as a basis for theoretical physics. Theoretically based temperature scales are based directly on theoretical arguments, especially those of thermodynamics, kinetic theory and they rely on theoretical properties of idealized devices and materials
17.
Pressure
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Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the relative to the ambient pressure. Various units are used to express pressure, Pressure may also be expressed in terms of standard atmospheric pressure, the atmosphere is equal to this pressure and the torr is defined as 1⁄760 of this. Manometric units such as the centimetre of water, millimetre of mercury, Pressure is the amount of force acting per unit area. The symbol for it is p or P, the IUPAC recommendation for pressure is a lower-case p. However, upper-case P is widely used. The usage of P vs p depends upon the field in one is working, on the nearby presence of other symbols for quantities such as power and momentum. Mathematically, p = F A where, p is the pressure, F is the normal force and it relates the vector surface element with the normal force acting on it. It is incorrect to say the pressure is directed in such or such direction, the pressure, as a scalar, has no direction. The force given by the relationship to the quantity has a direction. If we change the orientation of the element, the direction of the normal force changes accordingly. Pressure is distributed to solid boundaries or across arbitrary sections of normal to these boundaries or sections at every point. It is a parameter in thermodynamics, and it is conjugate to volume. The SI unit for pressure is the pascal, equal to one newton per square metre and this name for the unit was added in 1971, before that, pressure in SI was expressed simply in newtons per square metre. Other units of pressure, such as pounds per square inch, the CGS unit of pressure is the barye, equal to 1 dyn·cm−2 or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre, but using the names kilogram, gram, kilogram-force, or gram-force as units of force is expressly forbidden in SI. The technical atmosphere is 1 kgf/cm2, since a system under pressure has potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume. It is therefore related to density and may be expressed in units such as joules per cubic metre. Similar pressures are given in kilopascals in most other fields, where the prefix is rarely used
18.
Sportsmanship
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A sore loser refers to one who does not take defeat well, whereas a good sport means being a good winner as well as being a good loser. Sportsmanship is also looked at as being the way one reacts to a sport/game/player, the four elements of sportsmanship are often shown being good form, the will to win, equity and fairness. All four elements are critical and a balance must be found all four for true sportsmanship to be illustrated. These elements may also cause conflict, as a person may desire to win more than play in equity and fairness and thus resulting in a clash within the aspects of sportsmanship. This will cause problems as the person believes they are being a good sportsman, when athletes become too self-centred, the idea of sportsmanship is dismissed. Todays sporting culture, in particular the base of elite sport, places great importance on the idea of competition and winning and thus sportsmanship takes a back seat as a result. In most, if not all sports, sportsmen at the elite level make the standards on sportsmanship and no matter whether they like it or not, they are seen as leaders and role models in society. Since every sport is rule driven, the most common offence of bad sportsmanship is the act of cheating or breaking the rules to gain an unfair advantage, a competitor who exhibits poor sportsmanship after losing a game or contest is often called a sore loser. There are six different categories relating to sportsmanship, the elements of sports, all six of these characterize a person with good sportsmanship. Even though there is some affinity between some of the categories, they are distinct elements, in essence, play has for its directed and immediate end joy, pleasure, and delights and which is dominated by a spirit of moderation and generosity. Athletics, on the hand, is essentially a competitive activity, which has for its end victory in the contest. Hence, the virtues of a player are different from the virtues of an athlete. The handshaking was banned because of fights that were ensuing after the handshake, most players are influenced by the leaders around them such as coaches and older players, if there are coaches and administrators who dont understand sportsmanship, then what about the players. There are various ways that sportsmanship is practiced in different sports, being a good sport often includes treating others as you would also like to be treated, cheer for good plays, accept responsibility for your mistakes, and keep your perspective. To accept responsibility for your mistakes will entail not placing the blame on other people, most importantly it is often encouraged and said regarding sportsmanship that Its not whether you win or lose, its how you play the game. Sportsmanship can be manifested in different ways depending on the game itself or the culture of the group, sportsmanship can be affected by a few contributing factors such as the players values and attitudes towards the sport and also the professional role models that are shown to the public. Role models in sport are expected to act in a moral, when elite sporting role models do not encourage sportsmanship this can also encourage people in society to act in similar ways to the athletes that they look up to and idolize. Having a positive environment in your team will therefore create good sportsmanship from the individuals
19.
Mesoamerican ballgame
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The Mesoamerican ballgame was a sport with ritual associations played since 1400 BCE by the pre-Columbian peoples of Ancient Mesoamerica. The sport had different versions in different places during the millennia, the rules of ōllamaliztli are not known, but judging from its descendant, ulama, they were probably similar to racquetball, where the aim is to keep the ball in play. The stone ballcourt goals are an addition to the game. In the most common theory of the game, the struck the ball with their hips, although some versions allowed the use of forearms, rackets, bats. The ball was made of rubber and weighed as much as 4 kg. The game had important ritual aspects, and major formal ballgames were held as ritual events, Late in the history of the game, some cultures occasionally seem to have combined competitions with religious human sacrifice. The sport was also played casually for recreation by children and may have played by women as well. Pre-Columbian ballcourts have been found throughout Mesoamerica, as for example at Copán, as far south as modern Nicaragua and these ballcourts vary considerably in size, but all have long narrow alleys with slanted side-walls against which the balls could bounce. It is not known precisely when or where ōllamaliztli originated, although it is likely that the game originated earlier than 1400 BCE in the tropical zones home to the rubber tree. One candidate for the birthplace of the ballgame is the Soconusco coastal lowlands along the Pacific Ocean, here, at Paso de la Amada, archaeologists have found the oldest ballcourt yet discovered, dated to approximately 1400 BCE. The other major candidate is the Olmec heartland, across the Isthmus of Tehuantepec along the Gulf Coast, the Aztecs referred to their Postclassic contemporaries who then inhabited the region as the Olmeca since the region was strongly identified with latex production. The earliest-known rubber balls come from the bog at El Manatí. Villagers, and subsequently archaeologists, have recovered a dozen balls ranging in diameter from 10 to 22 cm from the spring there. Five of these balls have been dated to the occupational phase for the site. These rubber balls were found with other ritual offerings buried at the site, indicating that even at this early date ōllamaliztli had religious, excavations at the nearby Olmec site of San Lorenzo Tenochtitlán have also uncovered a number of ballplayer figurines, radiocarbon-dated as far back as 1250–1150 BCE. A rudimentary ballcourt, dated to an occupation at San Lorenzo. From the tropical lowlands, ōllamaliztli apparently moved into central Mexico, starting around 1000 BCE or earlier, ballplayer figurines were interred with burials at Tlatilco and similarly styled figurines from the same period have been found at the nearby Tlapacoya site. It was about this period, as well, that the so-called Xochipala-style ballplayer figurines were crafted in Guerrero and it is known in Spanish as juego de pelota, in Classic Maya as pitz, and in modern Nahuatl as ōllamaliztli
20.
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
21.
Norm (mathematics)
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A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors. A norm must also satisfy certain properties pertaining to scalability and additivity which are given in the definition below. A simple example is the 2-dimensional Euclidean space R2 equipped with the Euclidean norm, elements in this vector space are usually drawn as arrows in a 2-dimensional cartesian coordinate system starting at the origin. The Euclidean norm assigns to each vector the length of its arrow, because of this, the Euclidean norm is often known as the magnitude. A vector space on which a norm is defined is called a vector space. Similarly, a space with a seminorm is called a seminormed vector space. It is often possible to supply a norm for a vector space in more than one way. If p =0 then v is the zero vector, by the first axiom, absolute homogeneity, we have p =0 and p = p, so that by the triangle inequality p ≥0. A seminorm on V is a p, V → R with the properties 1. and 2. Every vector space V with seminorm p induces a normed space V/W, called the quotient space, the induced norm on V/W is clearly well-defined and is given by, p = p. A topological vector space is called if the topology of the space can be induced by a norm. If a norm p, V → R is given on a vector space V then the norm of a vector v ∈ V is usually denoted by enclosing it within double vertical lines, such notation is also sometimes used if p is only a seminorm. For the length of a vector in Euclidean space, the notation | v | with single vertical lines is also widespread, in Unicode, the codepoint of the double vertical line character ‖ is U+2016. The double vertical line should not be confused with the parallel to symbol and this is usually not a problem because the former is used in parenthesis-like fashion, whereas the latter is used as an infix operator. The double vertical line used here should not be confused with the symbol used to denote lateral clicks. The single vertical line | is called vertical line in Unicode, the trivial seminorm has p =0 for all x in V. Every linear form f on a vector space defines a seminorm by x → | f |, the absolute value ∥ x ∥ = | x | is a norm on the one-dimensional vector spaces formed by the real or complex numbers. The absolute value norm is a case of the L1 norm
22.
Rotation
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A rotation is a circular movement of an object around a center of rotation. A three-dimensional object always rotates around a line called a rotation axis. If the axis passes through the center of mass, the body is said to rotate upon itself. A rotation about a point, e. g. the Earth about the Sun, is called a revolution or orbital revolution. The axis is called a pole, mathematically, a rotation is a rigid body movement which, unlike a translation, keeps a point fixed. This definition applies to rotations within both two and three dimensions All rigid body movements are rotations, translations, or combinations of the two, a rotation is simply a progressive radial orientation to a common point. That common point lies within the axis of that motion, the axis is 90 degrees perpendicular to the plane of the motion. If the axis of the rotation lies external of the body in question then the body is said to orbit, there is no fundamental difference between a “rotation” and an “orbit” and or spin. The key distinction is simply where the axis of the rotation lies and this distinction can be demonstrated for both “rigid” and “non rigid” bodies. If a rotation around a point or axis is followed by a rotation around the same point/axis. The reverse of a rotation is also a rotation, thus, the rotations around a point/axis form a group. However, a rotation around a point or axis and a rotation around a different point/axis may result in something other than a rotation, Rotations around the x, y and z axes are called principal rotations. Rotation around any axis can be performed by taking a rotation around the x axis, followed by a rotation around the y axis and that is to say, any spatial rotation can be decomposed into a combination of principal rotations. In flight dynamics, the rotations are known as yaw, pitch. This terminology is used in computer graphics. In astronomy, rotation is an observed phenomenon. Stars, planets and similar bodies all spin around on their axes, the rotation rate of planets in the solar system was first measured by tracking visual features. Stellar rotation is measured through Doppler shift or by tracking active surface features and this rotation induces a centrifugal acceleration in the reference frame of the Earth which slightly counteracts the effect of gravity the closer one is to the equator
23.
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
24.
Acceleration
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Acceleration, in physics, is the rate of change of velocity of an object with respect to time. An objects acceleration is the net result of any and all forces acting on the object, the SI unit for acceleration is metre per second squared. Accelerations are vector quantities and add according to the parallelogram law, as a vector, the calculated net force is equal to the product of the objects mass and its acceleration. For example, when a car starts from a standstill and travels in a line at increasing speeds. If the car turns, there is an acceleration toward the new direction, in this example, we can call the forward acceleration of the car a linear acceleration, which passengers in the car might experience as a force pushing them back into their seats. When changing direction, we call this non-linear acceleration, which passengers might experience as a sideways force. If the speed of the car decreases, this is an acceleration in the direction from the direction of the vehicle. Passengers may experience deceleration as a force lifting them forwards, mathematically, there is no separate formula for deceleration, both are changes in velocity. Each of these accelerations might be felt by passengers until their velocity matches that of the car, an objects average acceleration over a period of time is its change in velocity divided by the duration of the period. Mathematically, a ¯ = Δ v Δ t, instantaneous acceleration, meanwhile, is the limit of the average acceleration over an infinitesimal interval of time. The SI unit of acceleration is the metre per second squared, or metre per second per second, as the velocity in metres per second changes by the acceleration value, every second. An object moving in a circular motion—such as a satellite orbiting the Earth—is accelerating due to the change of direction of motion, in this case it is said to be undergoing centripetal acceleration. Proper acceleration, the acceleration of a relative to a free-fall condition, is measured by an instrument called an accelerometer. As speeds approach the speed of light, relativistic effects become increasingly large and these components are called the tangential acceleration and the normal or radial acceleration. Geometrical analysis of space curves, which explains tangent, normal and binormal, is described by the Frenet–Serret formulas. Uniform or constant acceleration is a type of motion in which the velocity of an object changes by an amount in every equal time period. A frequently cited example of uniform acceleration is that of an object in free fall in a gravitational field. The acceleration of a body in the absence of resistances to motion is dependent only on the gravitational field strength g
25.
Velocity
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The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of its speed and direction of motion, Velocity is an important concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity is a vector quantity, both magnitude and direction are needed to define it. The scalar absolute value of velocity is called speed, being a coherent derived unit whose quantity is measured in the SI system as metres per second or as the SI base unit of. For example,5 metres per second is a scalar, whereas 5 metres per second east is a vector, if there is a change in speed, direction or both, then the object has a changing velocity and is said to be undergoing an acceleration. To have a constant velocity, an object must have a constant speed in a constant direction, constant direction constrains the object to motion in a straight path thus, a constant velocity means motion in a straight line at a constant speed. For example, a car moving at a constant 20 kilometres per hour in a path has a constant speed. Hence, the car is considered to be undergoing an acceleration, Speed describes only how fast an object is moving, whereas velocity gives both how fast and in what direction the object is moving. If a car is said to travel at 60 km/h, its speed has been specified, however, if the car is said to move at 60 km/h to the north, its velocity has now been specified. The big difference can be noticed when we consider movement around a circle and this is because the average velocity is calculated by only considering the displacement between the starting and the end points while the average speed considers only the total distance traveled. Velocity is defined as the rate of change of position with respect to time, average velocity can be calculated as, v ¯ = Δ x Δ t. The average velocity is less than or equal to the average speed of an object. This can be seen by realizing that while distance is always strictly increasing, from this derivative equation, in the one-dimensional case it can be seen that the area under a velocity vs. time is the displacement, x. In calculus terms, the integral of the velocity v is the displacement function x. In the figure, this corresponds to the area under the curve labeled s. Since the derivative of the position with respect to time gives the change in position divided by the change in time, although velocity is defined as the rate of change of position, it is often common to start with an expression for an objects acceleration. As seen by the three green tangent lines in the figure, an objects instantaneous acceleration at a point in time is the slope of the tangent to the curve of a v graph at that point. In other words, acceleration is defined as the derivative of velocity with respect to time, from there, we can obtain an expression for velocity as the area under an a acceleration vs. time graph
26.
Position (vector)
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Usually denoted x, r, or s, it corresponds to the straight-line distances along each axis from O to P, r = O P →. The term position vector is used mostly in the fields of geometry, mechanics. Frequently this is used in two-dimensional or three-dimensional space, but can be generalized to Euclidean spaces in any number of dimensions. These different coordinates and corresponding basis vectors represent the position vector. More general curvilinear coordinates could be used instead, and are in contexts like continuum mechanics, linear algebra allows for the abstraction of an n-dimensional position vector. The notion of space is intuitive since each xi can be any value, the dimension of the position space is n. The coordinates of the vector r with respect to the vectors ei are xi. The vector of coordinates forms the coordinate vector or n-tuple, each coordinate xi may be parameterized a number of parameters t. One parameter xi would describe a curved 1D path, two parameters xi describes a curved 2D surface, three xi describes a curved 3D volume of space, and so on. The linear span of a basis set B = equals the position space R, position vector fields are used to describe continuous and differentiable space curves, in which case the independent parameter needs not be time, but can be arc length of the curve. In the case of one dimension, the position has only one component and it could be, say, a vector in the x-direction, or the radial r-direction. Equivalent notations include, x ≡ x ≡ x, r ≡ r, s ≡ s ⋯ For a position vector r that is a function of time t and these derivatives have common utility in the study of kinematics, control theory, engineering and other sciences. Velocity v = d r d t where dr is a small displacement. By extension, the higher order derivatives can be computed in a similar fashion, study of these higher order derivatives can improve approximations of the original displacement function. Such higher-order terms are required in order to represent the displacement function as a sum of an infinite sequence, enabling several analytical techniques in engineering. A displacement vector can be defined as the action of uniformly translating spatial points in a given direction over a given distance, thus the addition of displacement vectors expresses the composition of these displacement actions and scalar multiplication as scaling of the distance. With this in mind we may define a position vector of a point in space as the displacement vector mapping a given origin to that point. Note thus position vectors depend on a choice of origin for the space, affine space Six degrees of freedom Line element Parametric surface Keller, F. J, Gettys, W. E. et al
27.
Time
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Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future. Time is often referred to as the dimension, along with the three spatial dimensions. Time has long been an important subject of study in religion, philosophy, and science, nevertheless, diverse fields such as business, industry, sports, the sciences, and the performing arts all incorporate some notion of time into their respective measuring systems. Two contrasting viewpoints on time divide prominent philosophers, one view is that time is part of the fundamental structure of the universe—a dimension independent of events, in which events occur in sequence. Isaac Newton subscribed to this realist view, and hence it is referred to as Newtonian time. This second view, in the tradition of Gottfried Leibniz and Immanuel Kant, holds that time is neither an event nor a thing, Time in physics is unambiguously operationally defined as what a clock reads. Time is one of the seven fundamental physical quantities in both the International System of Units and International System of Quantities, Time is used to define other quantities—such as velocity—so defining time in terms of such quantities would result in circularity of definition. The operational definition leaves aside the question there is something called time, apart from the counting activity just mentioned, that flows. Investigations of a single continuum called spacetime bring questions about space into questions about time, questions that have their roots in the works of early students of natural philosophy. Furthermore, it may be there is a subjective component to time. Temporal measurement has occupied scientists and technologists, and was a motivation in navigation. Periodic events and periodic motion have long served as standards for units of time, examples include the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum, and the beat of a heart. Currently, the unit of time, the second, is defined by measuring the electronic transition frequency of caesium atoms. Time is also of significant social importance, having economic value as well as value, due to an awareness of the limited time in each day. In day-to-day life, the clock is consulted for periods less than a day whereas the calendar is consulted for periods longer than a day, increasingly, personal electronic devices display both calendars and clocks simultaneously. The number that marks the occurrence of an event as to hour or date is obtained by counting from a fiducial epoch—a central reference point. Artifacts from the Paleolithic suggest that the moon was used to time as early as 6,000 years ago. Lunar calendars were among the first to appear, either 12 or 13 lunar months, without intercalation to add days or months to some years, seasons quickly drift in a calendar based solely on twelve lunar months
28.
Stokes' law
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Stokes law is derived by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations. In SI units, Fd is given in Newtons, η in Pa·s, r in meters, Stokes law makes the following assumptions for the behavior of a particle in a fluid, Laminar Flow Spherical particles Homogeneous material Smooth surfaces Particles do not interfere with each other. Note that for molecules Stokes law is used to define their Stokes radius, the CGS unit of kinematic viscosity was named stokes after his work. Stokes law is the basis of the viscometer, in which the fluid is stationary in a vertical glass tube. A sphere of size and density is allowed to descend through the liquid. If correctly selected, it reaches terminal velocity, which can be measured by the time it takes to pass two marks on the tube, electronic sensing can be used for opaque fluids. Knowing the terminal velocity, the size and density of the sphere, a series of steel ball bearings of different diameters are normally used in the classic experiment to improve the accuracy of the calculation. The school experiment uses glycerine or golden syrup as the fluid, several school experiments often involve varying the temperature and/or concentration of the substances used in order to demonstrate the effects this has on the viscosity. Industrial methods include many different oils, and polymer liquids such as solutions, the importance of Stokes law is illustrated by the fact that it played a critical role in the research leading to at least three Nobel Prizes. Stokes law is important for understanding the swimming of microorganisms and sperm, also, in air, the same theory can be used to explain why small water droplets can remain suspended in air until they grow to a critical size and start falling as rain. Similar use of the equation can be made in the settlement of fine particles in water or other fluids, requiring the force balance Fd = Fg and solving for the velocity V gives the terminal velocity Vs. Note that since buoyant force increases as R3 and Stokes drag increases as R, the terminal velocity increases as R2 and thus varies greatly with particle size as shown below. This velocity V is given by, V =29 μ g R2, in Stokes flow, at very low Reynolds number, the convective acceleration terms in the Navier–Stokes equations are neglected. By using some vector calculus identities, these equations can be shown to result in Laplaces equations for the pressure and each of the components of the vorticity vector, ∇2 ω =0 and ∇2 p =0. For the case of a sphere in a uniform far field flow, the z–axis is through the centre of the sphere and aligned with the mean flow direction, while r is the radius as measured perpendicular to the z–axis. The origin is at the sphere centre, because the flow is axisymmetric around the z–axis, it is independent of the azimuth φ. The azimuthal velocity component in the φ–direction is equal to zero, the volume flux, through a tube bounded by a surface of some constant value ψ, is equal to 2π ψ and is constant. The Laplace operator, applied to the vorticity ωφ, becomes in this coordinate system with axisymmetry
29.
Newtonian fluid
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That is equivalent to saying that those forces are proportional to the rates of change of the fluids velocity vector as one moves away from the point in question in various directions. Newtonian fluids are the simplest mathematical models of fluids that account for viscosity, while no real fluid fits the definition perfectly, many common liquids and gases, such as water and air, can be assumed to be Newtonian for practical calculations under ordinary conditions. However, non-Newtonian fluids are relatively common, and include oobleck, other examples include many polymer solutions, molten polymers, many solid suspensions, blood, and most highly viscous fluids. Newtonian fluids are named after Isaac Newton, who first postulated the relation between the strain rate and shear stress for such fluids in differential form. An element of a liquid or gas will suffer forces from the surrounding fluid. These forces can be approximated to first order by a viscous stress tensor. The deformation of that element, relative to some previous state. The tensors τ and ∇ v can be expressed by 3×3 matrices, one also defines a total stress tensor σ ) that combines the shear stress with conventional pressure p. The diagonal components of viscosity tensor is molecular viscosity of a liquid, and not diagonal components – turbulence eddy viscosity
30.
Earth
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Earth, otherwise known as the World, or the Globe, is the third planet from the Sun and the only object in the Universe known to harbor life. It is the densest planet in the Solar System and the largest of the four terrestrial planets, according to radiometric dating and other sources of evidence, Earth formed about 4.54 billion years ago. Earths gravity interacts with objects in space, especially the Sun. During one orbit around the Sun, Earth rotates about its axis over 365 times, thus, Earths axis of rotation is tilted, producing seasonal variations on the planets surface. The gravitational interaction between the Earth and Moon causes ocean tides, stabilizes the Earths orientation on its axis, Earths lithosphere is divided into several rigid tectonic plates that migrate across the surface over periods of many millions of years. About 71% of Earths surface is covered with water, mostly by its oceans, the remaining 29% is land consisting of continents and islands that together have many lakes, rivers and other sources of water that contribute to the hydrosphere. The majority of Earths polar regions are covered in ice, including the Antarctic ice sheet, Earths interior remains active with a solid iron inner core, a liquid outer core that generates the Earths magnetic field, and a convecting mantle that drives plate tectonics. Within the first billion years of Earths history, life appeared in the oceans and began to affect the Earths atmosphere and surface, some geological evidence indicates that life may have arisen as much as 4.1 billion years ago. Since then, the combination of Earths distance from the Sun, physical properties, in the history of the Earth, biodiversity has gone through long periods of expansion, occasionally punctuated by mass extinction events. Over 99% of all species that lived on Earth are extinct. Estimates of the number of species on Earth today vary widely, over 7.4 billion humans live on Earth and depend on its biosphere and minerals for their survival. Humans have developed diverse societies and cultures, politically, the world has about 200 sovereign states, the modern English word Earth developed from a wide variety of Middle English forms, which derived from an Old English noun most often spelled eorðe. It has cognates in every Germanic language, and their proto-Germanic root has been reconstructed as *erþō, originally, earth was written in lowercase, and from early Middle English, its definite sense as the globe was expressed as the earth. By early Modern English, many nouns were capitalized, and the became the Earth. More recently, the name is simply given as Earth. House styles now vary, Oxford spelling recognizes the lowercase form as the most common, another convention capitalizes Earth when appearing as a name but writes it in lowercase when preceded by the. It almost always appears in lowercase in colloquial expressions such as what on earth are you doing, the oldest material found in the Solar System is dated to 4. 5672±0.0006 billion years ago. By 4. 54±0.04 Gya the primordial Earth had formed, the formation and evolution of Solar System bodies occurred along with the Sun
31.
Mechanical energy
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In the physical sciences, mechanical energy is the sum of potential energy and kinetic energy. It is the associated with the motion and position of an object. The principle of conservation of energy states that in an isolated system that is only subject to conservative forces the mechanical energy is constant. In elastic collisions, the energy is conserved but in inelastic collisions. The equivalence between lost mechanical energy and an increase in temperature was discovered by James Prescott Joule and it is defined as the objects ability to do work and is increased as the object is moved in the opposite direction of the direction of the force. On the contrary, when a force acts upon an object. Though energy cannot be created or destroyed in an isolated system, the pendulum reaches greatest kinetic energy and least potential energy when in the vertical position, because it will have the greatest speed and be nearest the Earth at this point. On the other hand, it will have its least kinetic energy and greatest potential energy at the positions of its swing. However, when taking the forces into account, the system loses mechanical energy with each swing because of the work done by the pendulum to oppose these non-conservative forces. This equivalence between mechanical energy and heat is especially important when considering colliding objects, in an elastic collision, mechanical energy is conserved – the sum of the mechanical energies of the colliding objects is the same before and after the collision. After an inelastic collision, however, the energy of the system will have changed. Usually, the energy before the collision is greater than the mechanical energy after the collision. In inelastic collisions, some of the energy of the colliding objects is transformed into kinetic energy of the constituent particles. This increase in energy of the constituent particles is perceived as an increase in temperature. The collision can be described by saying some of the energy of the colliding objects has been converted into an equal amount of heat. Thus, the energy of the system remains unchanged though the mechanical energy of the system has reduced. A satellite of mass m at a distance r from the centre of Earth possesses both kinetic energy, K, and gravitational energy, U. These devices can be placed in categories, An electric motor converts electrical energy into mechanical energy
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Conservation of energy
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In physics, the law of conservation of energy states that the total energy of an isolated system remains constant—it is said to be conserved over time. Energy can neither be created nor destroyed, rather, it transforms from one form to another, for instance, chemical energy can be converted to kinetic energy in the explosion of a stick of dynamite. A consequence of the law of conservation of energy is that a perpetual motion machine of the first kind cannot exist and that is to say, no system without an external energy supply can deliver an unlimited amount of energy to its surroundings. Ancient philosophers as far back as Thales of Miletus c.550 BCE had inklings of the conservation of some underlying substance of everything is made. However, there is no reason to identify this with what we know today as mass-energy. Empedocles wrote that in his system, composed of four roots, nothing comes to be or perishes, instead. In 1605, Simon Stevinus was able to solve a number of problems in statics based on the principle that perpetual motion was impossible. Essentially, he pointed out that the height a moving body rises is equal to the height from which it falls, and used this observation to infer the idea of inertia. The remarkable aspect of this observation is that the height that a moving body ascends to does not depend on the shape of the surface that the body is moving on. In 1669, Christian Huygens published his laws of collision, among the quantities he listed as being invariant before and after the collision of bodies were both the sum of their linear momentums as well as the sum of their kinetic energies. However, the difference between elastic and inelastic collision was not understood at the time and this led to the dispute among later researchers as to which of these conserved quantities was the more fundamental. In his Horologium Oscillatorium, he gave a much clearer statement regarding the height of ascent of a moving body, Huygens study of the dynamics of pendulum motion was based on a single principle, that the center of gravity of heavy objects cannot lift itself. The fact that energy is scalar, unlike linear momentum which is a vector. It was Leibniz during 1676–1689 who first attempted a mathematical formulation of the kind of energy which is connected with motion. Using Huygens work on collision, Leibniz noticed that in mechanical systems. He called this quantity the vis viva or living force of the system, the principle represents an accurate statement of the approximate conservation of kinetic energy in situations where there is no friction. Many physicists at that time, such as Newton, held that the conservation of momentum and it was later shown that both quantities are conserved simultaneously, given the proper conditions such as an elastic collision. In 1687, Isaac Newton published his Principia, which was organized around the concept of force and momentum
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Range of a projectile
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In physics, assuming a flat Earth with a uniform gravity field, and no air resistance, a projectile launched with specific initial conditions will have a predictable range. The following applies for ranges which are compared to the size of the Earth. For longer ranges see sub-orbital spaceflight, the maximum horizontal distance traveled by the projectile g, the gravitational acceleration—usually taken to be 9. This assumption simplifies the mathematics greatly, and is an approximation of actual projectile motion in cases where the distances travelled are small. Ideal projectile motion is also an introduction to the topic before adding the complications of air resistance. This is due to the nature of right triangles, additionally, from the equation for the range, R = v 2 sin 2 θ g We can see that the range will be maximum when the value of sin 2 θ is the highest. Clearly,2 θ has to be 90 degrees and that is to say, θ is 45 degrees. First we examine the case where is zero, let tg be any time when the height of the projectile is equal to its initial value. The second solution is the one for determining the range of the projectile. In addition to air resistance, which slows a projectile and reduces its range, generally speaking, a projectile with greater volume faces greater air resistance, reducing the range of the projectile. This can be modified by the shape, a tall and wide, but short projectile will face greater air resistance than a low and narrow. However, certain irregularities such as dimples on a ball may actually increase its range by reducing the amount of turbulence caused behind the projectile as it travels. Mass also becomes important, as a massive projectile will have more kinetic energy. The distribution of mass within the projectile can also be important, as an unevenly weighted projectile may spin undesirably, if a projectile is given rotation along its axes of travel, irregularities in the projectiles shape and weight distribution tend to be cancelled out. See rifling for a greater explanation, for projectiles that are launched by firearms and artillery, the nature of the guns barrel is also important. Longer barrels allow more of the energy to be given to the projectile. Rifling, while it may not increase the range of many shots from the same gun, will increase the accuracy
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Time of flight
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Time of flight describes a variety of methods that measure the time that it takes for an object, particle or acoustic, electromagnetic or other wave to travel a distance through a medium. This measurement can be used for a standard, as a way to measure velocity or path length through a given medium. The traveling object may be detected directly or indirectly, in electronics, the TOF method is used to estimate the electron mobility. Originally, it was designed for measurement of low-conductive thin films and this experimental technique is used for metal-dielectric-metal structures as well as organic field-effect transistors. The excess charges are generated by application of the laser or voltage pulse, in time-of-flight mass spectrometry, ions are accelerated by an electrical field to the same kinetic energy with the velocity of the ion depending on the mass-to-charge ratio. Thus the time-of-flight is used to measure velocity, from which the ratio can be determined. The time-of-flight of electrons is used to measure their kinetic energy, in ultrasonic flow meter measurement, TOF is used to measure speed of signal propagation upstream and downstream of flow of a media, in order to estimate total flow velocity. This measurement is made in a direction with the flow. In planar Doppler velocimetry, TOF measurements are made perpendicular to the flow by timing when individual particles cross two or more locations along the flow, such methods are used in laser radar and laser tracker systems for medium-long range distance measurement. In Neutron time-of-flight scattering, a monochromatic neutron beam is scattered by a sample. The energy spectrum of the neutrons is measured via time of flight. In kinematics, TOF is the duration in which a projectile is traveling through the air, time-of-flight mass spectrometry is a method of mass spectrometry in which ions are accelerated by an electric field of known strength. This acceleration results in an ion having the same energy as any other ion that has the same charge. The velocity of the ion depends on the mass-to-charge ratio, the time that it subsequently takes for the particle to reach a detector at a known distance is measured. This time will depend on the ratio of the particle. From this time and the experimental parameters one can find the mass-to-charge ratio of the ion. The elapsed time from the instant a particle leaves a source to the instant it reaches a detector, an ultrasonic flow meter measures the velocity of a liquid or gas through a pipe using acoustic sensors. This has some advantages over other measurement techniques, the results are slightly affected by temperature, density or conductivity
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Wind
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Wind is the flow of gases on a large scale. On the surface of the Earth, wind consists of the movement of air. Winds are commonly classified by their scale, their speed, the types of forces that cause them, the regions in which they occur. The strongest observed winds on a planet in the Solar System occur on Neptune, Winds have various aspects, an important one being its velocity, another the density of the gas involved, another its energy content or wind energy. In meteorology, winds are referred to according to their strength. Short bursts of high speed wind are termed gusts, strong winds of intermediate duration are termed squalls. Long-duration winds have various names associated with their strength, such as breeze, gale, storm. The two main causes of large-scale atmospheric circulation are the differential heating between the equator and the poles, and the rotation of the planet, within the tropics, thermal low circulations over terrain and high plateaus can drive monsoon circulations. In coastal areas the sea breeze/land breeze cycle can define local winds, in areas that have variable terrain, mountain, Wind powers the voyages of sailing ships across Earths oceans. Hot air balloons use the wind to take trips, and powered flight uses it to increase lift. Areas of wind caused by various weather phenomena can lead to dangerous situations for aircraft. When winds become strong, trees and man-made structures are damaged or destroyed, Winds can shape landforms, via a variety of aeolian processes such as the formation of fertile soils, such as loess, and by erosion. Wind also affects the spread of wildfires, Winds can disperse seeds from various plants, enabling the survival and dispersal of those plant species, as well as flying insect populations. When combined with temperatures, wind has a negative impact on livestock. Wind affects animals food stores, as well as their hunting, Wind is caused by differences in the atmospheric pressure. When a difference in atmospheric pressure exists, air moves from the higher to the pressure area. On a rotating planet, air will also be deflected by the Coriolis effect, globally, the two major driving factors of large-scale wind patterns are the differential heating between the equator and the poles and the rotation of the planet. Outside the tropics and aloft from frictional effects of the surface, near the Earths surface, friction causes the wind to be slower than it would be otherwise
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Laminar flow
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In fluid dynamics, laminar flow occurs when a fluid flows in parallel layers, with no disruption between the layers. At low velocities, the fluid tends to flow without lateral mixing, there are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow, the motion of the particles of the fluid is very orderly with particles close to a surface moving in straight lines parallel to that surface. Laminar flow is a flow regime characterized by high momentum diffusion, Laminar flow tends to occur at lower velocities, below a threshold at which it becomes turbulent. Turbulent flow is an orderly flow regime that is characterised by eddies or small packets of fluid particles which result in lateral mixing. In non-scientific terms, laminar flow is smooth while turbulent flow is rough, the type of flow occurring in a fluid in a channel is important in fluid dynamics problems and subsequently affects heat and mass transfer in fluid systems. The dimensionless Reynolds number is an important parameter in the equations that describe whether fully developed flow conditions lead to laminar or turbulent flow, Laminar flow generally occurs when the fluid is moving slowly or the fluid is very viscous. If the Reynolds number is small, much less than 1, then the fluid will exhibit Stokes or creeping flow. The specific calculation of the Reynolds number, and the values where laminar flow occurs, will depend on the geometry of the flow system, Q is the volumetric flow rate. A is the pipes cross-sectional area, V is the mean velocity of the fluid. μ is the viscosity of the fluid. ν is the viscosity of the fluid, ν = μ/ρ. ρ is the density of the fluid, for such systems, laminar flow occurs when the Reynolds number is below a critical value of approximately 2,040, though the transition range is typically between 1,800 and 2,100. For fluid systems occurring on external surfaces, such as flow past objects suspended in the fluid, the particle Reynolds number Rep would be used for particle suspended in flowing fluids, for example. As with flow in pipes, laminar flow typically occurs with lower Reynolds numbers, while turbulent flow and related phenomena, such as vortex shedding, a common application of laminar flow is in the smooth flow of a viscous liquid through a tube or pipe. In that case, the velocity of flow varies from zero at the walls to a maximum along the centre of the vessel. The flow profile of laminar flow in a tube can be calculated by dividing the flow into thin cylindrical elements, another example is the flow of air over an aircraft wing. The boundary layer is a thin sheet of air lying over the surface of the wing
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Turbulence
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Turbulence or turbulent flow is a flow regime in fluid dynamics characterized by chaotic changes in pressure and flow velocity. It is in contrast to a flow regime, which occurs when a fluid flows in parallel layers. Turbulence is caused by kinetic energy in parts of a fluid flow. For this reason turbulence is easier to create in low viscosity fluids, in general terms, in turbulent flow, unsteady vortices appear of many sizes which interact with each other, consequently drag due to friction effects increases. This would increase the energy needed to pump fluid through a pipe, however this effect can also be exploited by such as aerodynamic spoilers on aircraft, which deliberately spoil the laminar flow to increase drag and reduce lift. The onset of turbulence can be predicted by a constant called the Reynolds number. However, turbulence has long resisted detailed physical analysis, and the interactions within turbulence creates a complex situation. Richard Feynman has described turbulence as the most important unsolved problem of classical physics, smoke rising from a cigarette is mostly turbulent flow. However, for the first few centimeters the flow is laminar, the smoke plume becomes turbulent as its Reynolds number increases, due to its flow velocity and characteristic length increasing. If the golf ball were smooth, the boundary layer flow over the front of the sphere would be laminar at typical conditions. However, the layer would separate early, as the pressure gradient switched from favorable to unfavorable. To prevent this happening, the surface is dimpled to perturb the boundary layer. This results in higher skin friction, but moves the point of boundary layer separation further along, resulting in form drag. The flow conditions in industrial equipment and machines. The external flow over all kind of such as cars, airplanes, ships. The motions of matter in stellar atmospheres, a jet exhausting from a nozzle into a quiescent fluid. As the flow emerges into this external fluid, shear layers originating at the lips of the nozzle are created and these layers separate the fast moving jet from the external fluid, and at a certain critical Reynolds number they become unstable and break down to turbulence. Biologically generated turbulence resulting from swimming animals affects ocean mixing, snow fences work by inducing turbulence in the wind, forcing it to drop much of its snow load near the fence
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Reynolds number
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The Reynolds number is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations. It has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. The concept was introduced by George Gabriel Stokes in 1851, but the Reynolds number was named by Arnold Sommerfeld in 1908 after Osborne Reynolds, who popularized its use in 1883. A similar effect is created by the introduction of a stream of higher velocity fluid and this relative movement generates fluid friction, which is a factor in developing turbulent flow. Counteracting this effect is the viscosity of the fluid, which as it increases, progressively inhibits turbulence, the Reynolds number quantifies the relative importance of these two types of forces for given flow conditions, and is a guide to when turbulent flow will occur in a particular situation. Such scaling is not linear and the application of Reynolds numbers to both situations allows scaling factors to be developed, the Reynolds number can be defined for several different situations where a fluid is in relative motion to a surface. These definitions generally include the properties of density and viscosity, plus a velocity. This dimension is a matter of convention – for example radius and diameter are equally valid to describe spheres or circles, for aircraft or ships, the length or width can be used. For flow in a pipe or a sphere moving in a fluid the internal diameter is used today. Other shapes such as pipes or non-spherical objects have an equivalent diameter defined. For fluids of variable density such as gases or fluids of variable viscosity such as non-Newtonian fluids. The velocity may also be a matter of convention in some circumstances, in practice, matching the Reynolds number is not on its own sufficient to guarantee similitude. Fluid flow is chaotic, and very small changes to shape. Nevertheless, Reynolds numbers are an important guide and are widely used. Osborne Reynolds famously studied the conditions in which the flow of fluid in pipes transitioned from laminar flow to turbulent flow, when the velocity was low, the dyed layer remained distinct through the entire length of the large tube. When the velocity was increased, the broke up at a given point. The point at which this happened was the point from laminar to turbulent flow. From these experiments came the dimensionless Reynolds number for dynamic similarity—the ratio of forces to viscous forces
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Density of air
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The density of air is the mass per unit volume of Earths atmosphere. Air density, like air pressure, decreases with increasing altitude and it also changes with variation in temperature or humidity. At sea level and at 15 °C air has a density of approximately 1.225 kg/m3 according to ISA.058 J/ in SI units and this quantity may vary slightly depending on the molecular composition of air at a particular location. Therefore, At IUPAC standard temperature and pressure, dry air has a density of 1.2754 kg/m3, at 20 °C and 101.325 kPa, dry air has a density of 1.2041 kg/m3. At 70 °F and 14.696 psi, dry air has a density of 0.074887 lb/ft3 and this occurs because the molar mass of water is less than the molar mass of dry air. For any gas, at a temperature and pressure, the number of molecules present is constant for a particular volume. So when water molecules are added to a volume of air. Hence the mass per volume of the gas decreases. The density of air may be calculated as a mixture of ideal gases. In this case, the pressure of water vapor is known as the vapor pressure. One formula used to find the saturation pressure is, p s a t =6.1078 ×107.5 T T +237.3 where T = is in degrees C. Despite minor differences to define all formulations the predicted mass of dry air. Importantly, some of the examples are not normalized so that the composition is equal to unity, air Density Atmosphere of Earth International Standard Atmosphere U. S
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Dynamic viscosity
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The viscosity of a fluid is a measure of its resistance to gradual deformation by shear stress or tensile stress. For liquids, it corresponds to the concept of thickness, for example. Viscosity is a property of the fluid which opposes the motion between the two surfaces of the fluid in a fluid that are moving at different velocities. For a given velocity pattern, the stress required is proportional to the fluids viscosity, a fluid that has no resistance to shear stress is known as an ideal or inviscid fluid. Zero viscosity is observed only at low temperatures in superfluids. Otherwise, all fluids have positive viscosity, and are said to be viscous or viscid. A fluid with a high viscosity, such as pitch. The word viscosity is derived from the Latin viscum, meaning mistletoe, the dynamic viscosity of a fluid expresses its resistance to shearing flows, where adjacent layers move parallel to each other with different speeds. It can be defined through the situation known as a Couette flow. This fluid has to be homogeneous in the layer and at different shear stresses, if the speed of the top plate is small enough, the fluid particles will move parallel to it, and their speed will vary linearly from zero at the bottom to u at the top. Each layer of fluid will move faster than the one just below it, in particular, the fluid will apply on the top plate a force in the direction opposite to its motion, and an equal but opposite one to the bottom plate. An external force is required in order to keep the top plate moving at constant speed. The magnitude F of this force is found to be proportional to the u and the area A of each plate. The proportionality factor μ in this formula is the viscosity of the fluid, the ratio u/y is called the rate of shear deformation or shear velocity, and is the derivative of the fluid speed in the direction perpendicular to the plates. Isaac Newton expressed the forces by the differential equation τ = μ ∂ u ∂ y, where τ = F/A. This formula assumes that the flow is moving along parallel lines and this equation can be used where the velocity does not vary linearly with y, such as in fluid flowing through a pipe. Use of the Greek letter mu for the dynamic viscosity is common among mechanical and chemical engineers. However, the Greek letter eta is used by chemists, physicists