Statics is the branch of mechanics Mechanics is the branch of physics concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effect of the bodies on their environment. The discipline has its roots in several ancient civilizations (see History of classical mechanics and Timeline of classical mechanics). During the early modern concerned with the analysis of loads (force In physics, a force is a push or pull that can cause an object with mass to change its velocity. Force has both magnitude and direction, making it a vector quantity. Newton's second law states that an object with a constant mass will accelerate in proportion to the net force acting upon and in inverse proportion to its mass. Equivalently, the net, torque/moment Torque, also called moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist) on physical systems In physics the word system has a technical meaning, namely, it is the portion of the physical universe chosen for analysis. Everything outside the system is known as the environment, which in analysis is ignored except for its effects on the system. The cut between system and environment is a free choice, generally made to simplify the analysis as in static equilibrium However, this definition is of little use in continuum mechanics, for which the idea of a particle is foreign. In addition, this definition gives no information as to one of the most important and interesting aspects of equilibrium states – their stability, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at a constant velocity. When in static equilibrium, the system is either at rest, or its center of mass The center of mass of a system of particles is a specific point at which, for many purposes, the system's mass behaves as if it were concentrated. The center of mass is a function only of the positions and masses of the particles that comprise the system. In the case of a rigid body, the position of its center of mass is fixed in relation to the moves at constant velocity. The study of moving bodies is known as dynamics.
By Newton's first law Newton's laws of motion are three physical laws that form the basis for classical mechanics. They are:, this situation implies that the net force and net torque Torque, also called moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist (also known as moment of force) on every body in the system is zero. From this constraint, such quantities as stress In continuum mechanics, the concept of stress, introduced by Cauchy around 1822, is a measure of the average amount of force exerted per unit area of the surface on which internal forces act within a deformable body . In other words, it is a measure of the intensity, or internal distribution of the total internal forces acting within a deformable or pressure Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure can be derived. The net forces equalling zero is known as the first condition for equilibrium, and the net torque equalling zero is known as the second condition for equilibrium. See statically determinate In statics, a structure is statically indeterminate when the static equilibrium equations are not sufficient for determining the internal forces and reactions on that structure.
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Solids
Statics is used in the analysis of structures, for instance in architectural Architectural engineering, also known as Building Engineering, is the application of engineering principles and technology to building design and construction. Definitions of an architectural engineer may refer to: and structural engineering Structural engineering is a field of engineering dealing with the analysis and design of structures that support or resist loads economically. Structural engineering is usually considered a specialty within civil engineering, but it can also be studied in its own right. Strength of materials In materials science, the strength of a material refers to the material's ability to withstand an applied stress without failure. Yield strength refers to the point on the engineering stress-strain curve beyond which the material begins deformation that cannot be reversed upon removal of the loading. Ultimate strength refers to the point on the is a related field of mechanics that relies heavily on the application of static equilibrium. A key concept is the centre of gravity The center of mass of a system of particles is a specific point at which, for many purposes, the system's mass behaves as if it were concentrated. The center of mass is a function only of the positions and masses of the particles that comprise the system. In the case of a rigid body, the position of its center of mass is fixed in relation to the of a body at rest: it represents an imaginary point at which all the mass Mass is a concept used in the physical sciences to explain a number of observable behaviors, and in everyday usage, it is common to identify mass with those resulting behaviors. In particular, mass is commonly identified with weight. But according to our modern scientific understanding, the weight of an object results from the interaction of its of a body resides. The position of the point relative to the foundations A foundation is a structure that transfers loads to the earth. Foundations are generally broken into two categories: shallow foundations and deep foundations on which a body lies determines its stability towards small movements. If the center of gravity falls outside the foundations, then the body is unstable because there is a torque acting: any small disturbance will cause the body to fall or topple. If the centre of gravity falls within the foundations, the body is stable since no net torque acts on the body. If the center of gravity coincides with the foundations, then the body is said to be metastable Metastability is a general scientific concept which describes states of delicate equilibrium. A system is in a metastable state when it is in equilibrium but is susceptible to fall into lower-energy states with only slight interaction. It is analogous to being at the bottom of a small valley when there is a deeper valley close by - a local.
Fluids
Hydrostatics Fluid statics is the science of fluids at rest, and is a sub-field within fluid mechanics. The term usually refers to the mathematical treatment of the subject. It embraces the study of the conditions under which fluids are at rest in stable equilibrium. The use of fluid to do work is called hydraulics, and the science of fluids in motion is fluid, also known as fluid statics Fluid statics is the science of fluids at rest, and is a sub-field within fluid mechanics. The term usually refers to the mathematical treatment of the subject. It embraces the study of the conditions under which fluids are at rest in stable equilibrium. The use of fluid to do work is called hydraulics, and the science of fluids in motion is fluid, is the study of fluids at rest. This analyzes bodies of fluid in static equilibrium. The characteristic of any fluid at rest is that the force exerted on any particle of the fluid is the same at all points at the same depth (or altitude) within the fluid. If the net force is greater than zero the fluid will move in the direction of the resulting force. This concept was first formulated in a slightly extended form by the French France (pronounced /ˈfræns/ or /ˈfrɑːns/; French: [fʁɑ̃s]), officially the French Republic (French: République française, pronounced: [ʁepyblik fʁɑ̃sɛz]), is a country located in Western Europe, with several overseas islands and territories located on other continents. Metropolitan France extends from the Mediterranean Sea to the mathematician The publication of new discoveries in mathematics continues at an immense rate in hundreds of scientific journals. One of the most exciting recent developments was the proof of Fermat's Last Theorem by Andrew Wiles, following 350 years of the brightest mathematical minds attempting to settle the problem and philosopher Most academic subjects have a philosophy, for example the philosophy of science, the philosophy of mathematics, the philosophy of logic, the philosophy of law, and the philosophy of history. In addition, a range of academic subjects have emerged to deal with areas which would have historically been the subject of philosophy. These include Blaise Pascal Blaise Pascal , (June 19, 1623, in Clermont-Ferrand, France – August 19, 1662) was a French mathematician, physicist, and religious philosopher. He was a child prodigy who was educated by his father, a civil servant. Pascal's earliest work was in the natural and applied sciences where he made important contributions to the construction of in 1647 and would be later known as Pascal's Law Pressure is the result of a force applied over a specific area and that pressure is therefore measured by the formula P = F / A or "pressure equals force divided by area". When a force is applied to an incompressible fluid, the area in question is the contact area between any two molecules of the fluid. That area is the same for any pair. This law has many important applications in hydraulics Hydraulics is a topic in applied science and engineering dealing with the mechanical properties of liquids. Fluid mechanics provides the theoretical foundation for hydraulics, which focuses on the engineering uses of fluid properties. In fluid power, hydraulics is used for the generation, control, and transmission of power by the use of. Archimedes Archimedes of Syracuse (c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and the explanation of the, Abū Rayhān al-Bīrūnī Abū Rayḥān Muḥammad ibn Aḥmad al-Bīrūnī , often known as Alberuni, Al Beruni or variants, (born 5 September 973 in Kath, Khwarezm (now in Uzbekistan), died 13 December 1048 in Ghazni, today's Afghanistan) was a Persian polymath scholar of the 11th century, Al-Khazini "His hydrostatic balance can leave no doubt that as a maker of scientific instruments he is among the greatest of any time."[1] and Galileo Galilei Galileo Galilei was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations, and support for Copernicanism. Galileo has been called the "father of modern observational astronomy," were also major figures in the development of hydrostatics.
See also
- Dynamics
- Mechanical equilibrium However, this definition is of little use in continuum mechanics, for which the idea of a particle is foreign. In addition, this definition gives no information as to one of the most important and interesting aspects of equilibrium states – their stability
- Solid mechanics Solid mechanics is the branch of mechanics, physics, and mathematics that concerns the behavior of solid matter under external actions . It is part of a broader study known as continuum mechanics. One of the most common practical applications of Solid Mechanics is the Euler-Bernoulli beam equation. Solid mechanics extensively uses tensors to
- Cremona diagram
References
Notes
- ^ Mariam Rozhanskaya and I. S. Levinova (1996), "Statics", p. 642, in (Morelon & Rashed 1996, pp. 614-642):
"Using a whole body of mathematical methods (not only those inherited from the antique theory of ratios and infinitesimal techniques, but also the methods of the contemporary algebra and fine calculation techniques), Arabic scientists raised statics to a new, higher level. The classical results of Archimedes in the theory of the centre of gravity were generalized and applied to three-dimensional bodies, the theory of ponderable lever was founded and the 'science of gravity' was created and later further developed in medieval Europe. The phenomena of statics were studied by using the dynamic apporach so that two trends - statics and dynamics - turned out to be inter-related withina single science, mechanics. The combination of the dynamic apporach with Archimedean hydrostatics gave birth to a direction in science which may be called medieval hydrodynamics. [...] Numerous fine experimental methods were developed for determining the specific weight, which were based, in particular, on the theory of balances and weighing. The classical works of al-Biruni and al-Khazini can by right be considered as the beginning of the application of experimental methods in medieval science In the Middle Ages, science progressed dramatically from the time of antiquity in areas as diverse as astronomy, medicine, and mathematics. Whereas the ancient cultures of the world had developed many of the foundations of science, it was during the Middle Ages that the scientific method was born and science became a formal discipline separate."
External links
- Online test of statics conceptual knowledge (meant for teachers)
- Free Statics courseware with about 300 interactive exercises with hints and feedback
- Statics for Robotics
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pwolanin
2009-04-14 00:00:00
Just wondering, if a function has multiple . static. variables, we would need to call clear_cache() multiple times and know how they are called then? A way to clear all . static. vars of a specific function would be nice. ...
