statics

The branch of mechanics that describes bodies which are acted upon by balanced forces and torques so that they remain at rest or in uniform motion. This includes point particles, rigid bodies, fluids, and deformable solids in general. Static point particles, however, are not very interesting, and special branches of mechanics are devoted to fluids and deformable solids. For example, hydrostatics is the study of static fluids, and elasticity and plasticity are two branches devoted to deformable bodies. Therefore this article will be limited to the discussion of the statics of rigid bodies in two- and three-space dimensions. See also Buoyancy; Elasticity; Hydrostatics; Mechanics.

In statics the bodies being studied are in equilibrium. The equilibrium conditions are very similar in the planar, or two-dimensional, and the three-dimensional rigid body statics. These are that the vector sum of all forces acting upon the body must be zero; and the resultant of all torques about any point must be zero. Thus it is necessary to understand the vector sums of forces and torques.

In studying statics problems, two principles, superposition and transmissibility, are used repeatedly on force vectors. They are applicable to all vectors, but specifically to forces and torques (first moments of forces). The principle of superposition of vectors is that the sum of any two vectors is another vector. The principle of transmissibility of a force applied to a rigid body is that the same mechanical effect is produced by any shift of the application of the force along its line of action. To use the superposition principle to add two vectors, the principle of transmissibility is used to move some vectors along their line of action in order to add to their components.

The moment of a force about a directed line is a signed number whose value can be obtained by applying these two rules: (1) The moment of a force about a line parallel to the force is zero. (2) The moment of a force about a line normal to a plane containing the force is the product of the magnitude of the force and the least distance from the line to the line of the force. See also Equilibrium of forces; Force; Torque.

That branch of the science of mechanics concerned with forces acting on bodies in equilibrium.

A division of rigid-body mechanics dealing with objects at rest or moving at a constant velocity. Compare dynamics.

For static analysis in economics, see Comparative statics.

For the technique of static correction used in exploration geophysics, see Reflection seismology.

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Example of a beam in static equilibrium. The sum of force and moment is zero.

Statics is the branch of mechanics concerned with the analysis of loads (force, torque/moment) on physical systems in static equilibrium, 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 moves at constant velocity. The study of moving bodies is known as dynamics.

By Newton's first law, this situation implies that the net force and net torque (also known as moment of force) on every body in the system is zero. From this constraint, such quantities as stress or 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.

Contents 1 Solids 2 Fluids 3 See also 4 References 4.1 Notes 5 External links

Solids

Statics is used in the analysis of structures, for instance in architectural and structural engineering. Strength of materials is a related field of mechanics that relies heavily on the application of static equilibrium. A key concept is the center of gravity of a body at rest: it represents an imaginary point at which all the mass of a body resides. The position of the point relative to the foundations on which a body lies determines its stability towards small movements. If the center of gravity exists 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 center of gravity exists 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.

Fluids

Hydrostatics, also known as fluid statics, 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 mathematician and philosopher Blaise Pascal in 1647 and would be later known as Pascal's Law. This law has many important applications in hydraulics. Archimedes, Abū Rayhān al-Bīrūnī, Al-Khazini^[1] and Galileo Galilei were also major figures in the development of hydrostatics.

See also

Physics portal

• Dynamics
• Mechanical equilibrium
• Solid mechanics
• Cremona diagram

References

• Beer, F.P. and Johnston Jr, E.R. (1992). Statics and Mechanics of Materials. McGraw-Hill, Inc. 

Notes

1. ^ 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."

External links

Wikimedia Commons has media related to: Statics

Look up statics in Wiktionary, the free dictionary.

• Online test of statics conceptual knowledge (meant for teachers)
• Free engineering Statics courseware with about 300 interactive exercises with hints and feedback : Carnegie Mellon Open Learning Initiative
• Statics for Robotics

Wikibooks has a book on the topic of Statics

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