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Static Structure
Statics is the branch of classical mechanics that is concerned with the analysis of force and torque (also called moment) acting on physical systems that do not experience an acceleration (''a''=0), but rather, are in static equilibrium with their environment. The application of Newton's second law to a system gives: : \textbf F = m \textbf a \, . Where bold font indicates a vector that has magnitude and direction. \textbf F is the total of the forces acting on the system, m is the mass of the system and \textbf a is the acceleration of the system. The summation of forces will give the direction and the magnitude of the acceleration and will be inversely proportional to the mass. The assumption of static equilibrium of \textbf a = 0 leads to: : \textbf F = 0 \, . The summation of forces, one of which might be unknown, allows that unknown to be found. So when in static equilibrium, the acceleration of the system is zero and the system is either at rest, or its center of m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility). The earliest development of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on foundational works of Sir Isaac Newton, and the mathematical methods invented by Gottfried Wilhelm Leibniz, Joseph-Louis Lagrange, Leonhard Euler, and other contemporaries, in the 17th century to describe the motion of bodies under the influence of a system of forces. Later, more abstract methods were developed, leading to the reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances, ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector (mathematics And Physics)
In mathematics and physics, vector is a term that refers colloquially to some quantities that cannot be expressed by a single number (a scalar), or to elements of some vector spaces. Historically, vectors were introduced in geometry and physics (typically in mechanics) for quantities that have both a magnitude and a direction, such as displacements, forces and velocity. Such quantities are represented by geometric vectors in the same way as distances, masses and time are represented by real numbers. The term ''vector'' is also used, in some contexts, for tuples, which are finite sequences of numbers of a fixed length. Both geometric vectors and tuples can be added and scaled, and these vector operations led to the concept of a vector space, which is a set equipped with a vector addition and a scalar multiplication that satisfy some axioms generalizing the main properties of operations on the above sorts of vectors. A vector space formed by geometric vectors is called a Euclidean ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hot Air Balloon
A hot air balloon is a lighter-than-air aircraft consisting of a bag, called an envelope, which contains heated air. Suspended beneath is a gondola or wicker basket (in some long-distance or high-altitude balloons, a capsule), which carries passengers and a source of heat, in most cases an open flame caused by burning liquid propane. The heated air inside the envelope makes it buoyant, since it has a lower density than the colder air outside the envelope. As with all aircraft, hot air balloons cannot fly beyond the atmosphere. The envelope does not have to be sealed at the bottom, since the air inside the envelope is at about the same pressure as the surrounding air. In modern sport balloons the envelope is generally made from nylon fabric, and the inlet of the balloon (closest to the burner flame) is made from a fire-resistant material such as Nomex. Modern balloons have been made in many shapes, such as rocket ships and the shapes of various commercial products, though the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guy Wires
A guy-wire, guy-line, guy-rope, or stay, also called simply a guy, is a tensioned cable designed to add stability to a free-standing structure. They are used commonly for ship masts, radio masts, wind turbines, utility poles, and tents. A thin vertical mast supported by guy wires is called a guyed mast. Structures that support antennas are frequently of a lattice construction and are called "towers". One end of the guy is attached to the structure, and the other is anchored to the ground at some distance from the mast or tower base. The tension in the diagonal guy-wire, combined with the compression and buckling strength of the structure, allows the structure to withstand lateral loads such as wind or the weight of cantilevered structures. They are installed radially, usually at equal angles about the structure, in trios and quads. As the tower leans a bit due to the wind force, the increased guy tension is resolved into a compression force in the tower or mast and a late ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Varignon's Theorem (mechanics)
Varignon's theorem is a theorem of French mathematician Pierre Varignon (1654–1722), published in 1687 in his book ''Projet d'une nouvelle mécanique''. The theorem states that the torque of a resultant of two concurrent forces about any point is equal to the algebraic sum of the torques of its components about the same point. In other words, "If many concurrent forces are acting on a body, then the algebraic sum of torques of all the forces about a point in the plane of the forces is equal to the torque of their resultant about the same point." Proof Consider a set of ''N'' force vectors \mathbf_1, \mathbf_2, ..., \mathbf_N that concur at a point \mathbf in space. Their resultant is: :\mathbf=\sum_^N \mathbf_i . The torque of each vector with respect to some other point \mathbf_1 is : \mathbf_^ = (\mathbf-\mathbf_1) \times \mathbf_i . Adding up the torques and pulling out the common factor (\mathbf-\mathbf), one sees that the result may be expressed solely in terms of \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cross Product
In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and is denoted by the symbol \times. Given two linearly independent vectors and , the cross product, (read "a cross b"), is a vector that is perpendicular to both and , and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with the dot product (projection product). If two vectors have the same direction or have the exact opposite direction from each other (that is, they are ''not'' linearly independent), or if either one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diagram Of The Moment Arm Of A Force F
A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment. Sometimes, the technique uses a three-dimensional visualization which is then projected onto a two-dimensional surface. The word ''graph'' is sometimes used as a synonym for diagram. Overview The term "diagram" in its commonly used sense can have a general or specific meaning: * ''visual information device'' : Like the term "illustration", "diagram" is used as a collective term standing for the whole class of technical genres, including graphs, technical drawings and tables. * ''specific kind of visual display'' : This is the genre that shows qualitative data with shapes that are connected by lines, arrows, or other visual links. In science the term is used in both ways. For example, Anderson (1997) stated more generally: "diagrams are pictorial, yet abstract, representatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Of Action
In physics, the line of action (also called line of application) of a force ''(F)'' is a geometric representation of how the force is applied. It is the line through the point at which the force is applied in the same direction as the vector .Mungan, Carl E. "Acceleration of a pulled spool." The Physics Teacher 39.8 (2001): 481-485. https://www.usna.edu/Users/physics/mungan/_files/documents/Publications/TPT.pdf The concept is essential, for instance, for understanding the net effect of multiple forces applied to a body. For example, if two forces of equal magnitude act upon a rigid body along the same line of action but in opposite directions, they cancel and have no net effect. But if, instead, their lines of action are not identical, but merely parallel, then their effect is to create a moment on the body, which tends to rotate it. Calculation of torque For the simple geometry associated with the figure, there are three equivalent equations for the magnitude of the torque ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Force Field (physics)
In physics, a force field is a vector field corresponding with a non-contact force acting on a particle at various positions in space. Specifically, a force field is a vector field \vec, where \vec(\vec) is the force that a particle would feel if it were at the point \vec. Examples *Gravity is the force of attraction between two objects. A gravitational force field models this influence that a massive body (or more generally, any quantity of energy) extends into the space around itself. In Newtonian gravity, a particle of mass ''M'' creates a gravitational field \vec=\frac\hat, where the radial unit vector \hat points away from the particle. The gravitational force experienced by a particle of light mass ''m'', close to the surface of Earth is given by \vec = m \vec, where ''g'' is the standard gravity. *An electric field \vec is a vector field. It exerts a force on a point charge ''q'' given by \vec = q\vec. Work Work is dependent on the displacement as well as the force ac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contact Force
A contact force is any force that occurs as a result of two objects making contact with each other. Contact forces are ubiquitous and are responsible for most visible interactions between macroscopic collections of matter. Pushing a car or kicking a ball are some of the everyday examples where contact forces are at work. In the first case the force is continuously applied to the car by a person, while in the second case the force is delivered in a short impulse. Contact forces are often decomposed into orthogonal components, one perpendicular to the surface(s) in contact called the normal force, and one parallel to the surface(s) in contact, called the friction force. Not all forces are contact forces; for example, the weight of an object is the force between the object and the Earth, even though the two do not need to make contact. Gravitational forces, electrical forces and magnetic forces are body forces and can exist without contact occurring. Origin of contact forces The m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Coordinate System
A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. Each reference coordinate line is called a ''coordinate axis'' or just ''axis'' (plural ''axes'') of the system, and the point where they meet is its ''origin'', at ordered pair . The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin. One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, ''n'' Cartesian coordinates (an element of real ''n''-space) specify the point in an ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonal
In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''. By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in other fields including art and chemistry. Etymology The word comes from the Ancient Greek ('), meaning "upright", and ('), meaning "angle". The Ancient Greek (') and Classical Latin ' originally denoted a rectangle. Later, they came to mean a right triangle. In the 12th century, the post-classical Latin word ''orthogonalis'' came to mean a right angle or something related to a right angle. Mathematics Physics * In optics, polarization states are said to be orthogonal when they propagate independently of each other, as in vertical and horizontal linear polarization or right- and left-handed circular polarization. * In special relativity, a time axis determined by a rapidity of motion is hyperbolic-orthogonal to a space axis of s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
