The following are categorized as being part of Quantum mechanics:
Particle physics, the motion, structure, and reactions of particles
Nuclear physics, the motion, structure, and reactions of nuclei
Condensed matter physics, quantum gases, solids, liquids, etc.
Quantum statistical mechanics, large assemblies of particles
Professional organizations
Applied Mechanics Division, American Society of Mechanical Engineers
Fluid Dynamics Division, American Physical Society
Institution of Mechanical Engineers is the United Kingdom's qualifying body for Mechanical Engineers and has been the home of Mechanical Engineers for over 150 years
See also
Analytical mechanics
Applied mechanics
Dynamics
Engineering
Kinematics
Kinetics
Further reading
Landau, L. D.; Lifshitz, E. M. (1972). Mechanics and Electrodynamics, Vol. 1. Franklin Book Company, Inc. ISBN 0-08-016739-X.
External links
iMechanica: the web of mechanics and mechanicians
Mechanics Blog by a Purdue University Professor
The Mechanics program at Virginia Tech
Physclips: Mechanics with animations and video clips from the University of New South Wales
U.S. National Committee on Theoretical and Applied Mechanics
Interactive learning resources for teaching Mechanics
Sunday, August 30, 2009
Einsteinian versus Newtonian
Analogous to the quantum versus classical reformation, Einstein's general and special theories of relativity have expanded the scope of mechanics beyond the mechanics of Newton and Galileo, and made fundamental corrections to them, that become significant and even dominant as speeds of material objects approach the speed of light, which cannot be exceeded. 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 the Grand Unified Theory.
Types of mechanical bodies
Thus the often-used term body needs to stand for a wide assortment of objects, including particles, projectiles, spacecraft, stars, parts of machinery, parts of solids, parts of fluids (gases and liquids), etc.
Other distinctions between the various sub-disciplines of mechanics, concern the nature of the bodies being described. Particles are bodies with little (known) internal structure, treated as mathematical points in classical mechanics. Rigid bodies have size and shape, but retain a simplicity close to that of the particle, adding just a few so-called degrees of freedom, such as orientation in space.
Otherwise, bodies may be semi-rigid, i.e. elastic, or non-rigid, i.e. fluid. These subjects have both classical and quantum divisions of study.
For instance, the motion of a spacecraft, regarding its orbit and attitude (rotation), is described by the relativistic theory of classical mechanics, while the analogous movements of an atomic nucleus are described by quantum mechanics.
Sub-disciplines in mechanics
The following are two lists of various subjects that are studied in mechanics.
Note that there is also the "theory of fields" which constitutes a separate discipline in physics, formally treated as distinct from mechanics, whether classical fields or quantum fields. But in actual practice, subjects belonging to mechanics and fields are closely interwoven. Thus, for instance, forces that act on particles are frequently derived from fields (electromagnetic or gravitational), and particles generate fields by acting as sources. In fact, in quantum mechanics, particles themselves are fields, as described theoretically by the wave function.
Classical mechanics
The following are described as forming Classical mechanics:
Newtonian mechanics, the original theory of motion (kinematics) and forces (dynamics)
Hamiltonian mechanics, a theoretical formalism, based on the principle of conservation of energy
Lagrangian mechanics, another theoretical formalism, based on the principle of the least action
Celestial mechanics, the motion of heavenly bodies: planets, comets, stars, galaxies, etc.
Astrodynamics, spacecraft navigation, etc.
Solid mechanics, elasticity, the properties of (semi-)rigid bodies
Acoustics, sound ( = density variation propagation) in solids, fluids and gases.
Statics, semi-rigid bodies in mechanical equilibrium
Fluid mechanics, the motion of fluids
Types of mechanical bodies
Thus the often-used term body needs to stand for a wide assortment of objects, including particles, projectiles, spacecraft, stars, parts of machinery, parts of solids, parts of fluids (gases and liquids), etc.
Other distinctions between the various sub-disciplines of mechanics, concern the nature of the bodies being described. Particles are bodies with little (known) internal structure, treated as mathematical points in classical mechanics. Rigid bodies have size and shape, but retain a simplicity close to that of the particle, adding just a few so-called degrees of freedom, such as orientation in space.
Otherwise, bodies may be semi-rigid, i.e. elastic, or non-rigid, i.e. fluid. These subjects have both classical and quantum divisions of study.
For instance, the motion of a spacecraft, regarding its orbit and attitude (rotation), is described by the relativistic theory of classical mechanics, while the analogous movements of an atomic nucleus are described by quantum mechanics.
Sub-disciplines in mechanics
The following are two lists of various subjects that are studied in mechanics.
Note that there is also the "theory of fields" which constitutes a separate discipline in physics, formally treated as distinct from mechanics, whether classical fields or quantum fields. But in actual practice, subjects belonging to mechanics and fields are closely interwoven. Thus, for instance, forces that act on particles are frequently derived from fields (electromagnetic or gravitational), and particles generate fields by acting as sources. In fact, in quantum mechanics, particles themselves are fields, as described theoretically by the wave function.
Classical mechanics
The following are described as forming Classical mechanics:
Newtonian mechanics, the original theory of motion (kinematics) and forces (dynamics)
Hamiltonian mechanics, a theoretical formalism, based on the principle of conservation of energy
Lagrangian mechanics, another theoretical formalism, based on the principle of the least action
Celestial mechanics, the motion of heavenly bodies: planets, comets, stars, galaxies, etc.
Astrodynamics, spacecraft navigation, etc.
Solid mechanics, elasticity, the properties of (semi-)rigid bodies
Acoustics, sound ( = density variation propagation) in solids, fluids and gases.
Statics, semi-rigid bodies in mechanical equilibrium
Fluid mechanics, the motion of fluids
Friday, August 28, 2009
Classical mechanics
In the fields of physics, classical mechanics is one of the two major sub-fields of study in the science of mechanics, which is concerned with the set of physical laws governing and mathematically describing the motions of bodies and aggregates of bodies geometrically distributed within a certain boundary under the action of a system of forces. The other sub-field is quantum mechanics.
Classical mechanics is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. It produces very accurate results within these domains, and is one of the oldest and largest subjects in science, engineering and technology.
Besides this, many related specialties exist, dealing with gases, liquids, and solids, and so on. Classical mechanics is enhanced by special relativity for objects moving with high velocity, approaching the speed of light; general relativity is employed to handle gravitation at a deeper level; and quantum mechanics handles the wave-particle duality of atoms and molecules.
The term classical mechanics was coined in the early 20th century to describe the system of mathematical physics begun by Isaac Newton and many contemporary 17th century natural philosophers, building upon the earlier astronomical theories of Johannes Kepler, which in turn were based on the precise observations of Tycho Brahe and the studies of terrestrial projectile motion of Galileo, but before the development of quantum physics and relativity. Therefore, some sources exclude so-called "relativistic physics" from that category. However, a number of modern sources do include Einstein's mechanics, which in their view represents classical mechanics in its most developed and most accurate form. The initial stage in the development of classical mechanics is often referred to as Newtonian mechanics, and is associated with the physical concepts employed by and the mathematical methods invented by Newton himself, in parallel with Leibniz, and others. This is further described in the following sections. More abstract and general methods include Lagrangian mechanics and Hamiltonian mechanics. Much of the content of classical mechanics was created in the 18th and 19th centuries and extends considerably beyond (particularly in its use of analytical mathematics) the work of Newton.
1 Description of the theory
1.1 Position and its derivatives
1.1.1 Velocity and speed
1.1.2 Acceleration
1.1.3 Frames of reference
1.2 Forces; Newton's Second Law
1.3 Energy
1.4 Beyond Newton's Laws
1.5 Classical transformations
2 History
3 Limits of validity
3.1 The Newtonian approximation to special relativity
3.2 The classical approximation to quantum mechanics
4 Branches
5 See also
6 Notes
7 References
8 Further reading
9 External links
Description of the theory
The following introduces the basic concepts of classical mechanics. For simplicity, it often models real-world objects as point particles, objects with negligible size. The motion of a point particle is characterized by a small number of parameters: its position, mass, and the forces applied to it. Each of these parameters is discussed in turn.
In reality, the kind of objects which classical mechanics can describe always have a non-zero size. (The physics of very small particles, such as the electron, is more accurately described by quantum mechanics). Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional degrees of freedom—for example, a baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as composite objects, made up of a large number of interacting point particles. The center of mass of a composite object behaves like a point particl Position and its derivatives
Monday, August 24, 2009
Stainless Steel - Mechanical Properties
Background
The mechanical properties of stainless steels are almost always requirements of the product specifications used to purchase the product. For flat rolled products the properties usually specified are tensile strength, yield stress (or proof stress), elongation and Brinell or Rockwell hardness. Much less frequently there are requirements for impact resistance, either Charpy or Izod. Bar, tube, pipe, fittings etc. also usually require at least tensile strength and yield stress. These properties give a guarantee that the material in question has been correctly produced, and are also used by engineers to calculate the working loads or pressures that the product can safely carry in service.
Typical Properties
Typical mechanical properties of annealed materials are as in the graph of Figure 1. Note that the high cold work hardening rate of the austenitic grades in particular results in actual properties of some commercial products being significantly higher than these values. The yield stress (usually measured as the 0.2% proof stress) is particularly increased by even quite minor amounts of cold work. More details of the work hardening of stainless steels are given in the section of this handbook on fabrication.
Yield Strength
An unusual feature of annealed austenitic stainless steels is that the yield strength is a very low proportion of the tensile strength, typically only 40-45%. The comparable figure for a mild steel is about 65-70%. As indicated above a small amount of cold work greatly increases the yield (much more so than the tensile strength), so the yield also increases to a higher proportion of tensile. Only a few % of cold work will increase the yield by 200 or 300MPa, and in severely cold worked material like spring temper wire or strip, the yield is usually about 80-95% of the tensile strength.
Ductility
The other mechanical property of note is the ductility, usually measured by % elongation during a tensile test. This shows the amount of deformation a piece of metal will withstand before it fractures. Austenitic stainless steels have exceptionally high elongations, usually about 60-70% for annealed products, as shown in figure 2. It is the combination of high work hardening rate and high elongation that permits the severe fabrication operations which are routinely carried out, such as deep drawing of kitchen sinks and laundry troughs.
Hardness
Hardness (measured by Brinell, Rockwell or Vickers machines) is another value for the strength of a material. Hardness is usually defined as resistance to penetration, so these test machines measure the depth to which a very hard indenter is forced into a material under the action of a known force. Each machine has a different shaped indenter and a different force application system, so conversion between hardness scales is not generally very accurate. Although conversion tables have been produced these conversions are only approximate, and should not be used to determine conformance to standards.
It is also sometimes convenient to do a hardness test and then convert the result to tensile strength. Although the conversions for carbon and low alloy steels are fairly reliable, those for stainless steels are much less so.
Mechanical Properties of Wire and Bar
The mechanical properties of the majority of the stainless steel wire and bar products are generally sufficiently described by the tensile strength. These products require mechanical properties which are carefully chosen to enable the product to be fabricated into the finished component and also to withstand the loads which will be applied during service. Spring wire has the highest tensile strength of the wire generally manufactured; it must be suitable for coiling into tension or compression springs without breaking during forming. However, such high tensile strengths would be completely unsuitable for forming or weaving applications because the wire would break on forming. Weaving wires are supplied in a variety of tensile strengths carefully chosen so that the finished woven screen will have adequate strength to withstand the service loads, and yet soft enough to be crimped and to be formed into the screen satisfactorily. Mechanical properties of wire for fasteners are another example where a careful balance in mechanical properties is required. In this type of product the wire must be ductile enough to form a quite complex head but the wire must be hard enough so that the threads will not deform when the screw or bolt is assembled into the component. Good examples are roofing bolts, wood screws and self-tapping screws; to achieve the mechanical properties required for such components requires careful consideration of the composition of the steel so that the work hardening rate will be sufficiently high to form hard threads on thread rolling and yet not so high as to prevent the head from being formed.For bar products a compromise must also be made; a large proportion of bar will be machined, so it is important that the hardness be not too high, but better load carrying capacity is achieved if the strength is high, and for drawn bar a good bright finish is achieved only by a reduction which significantly increases strength levels.
The mechanical properties of stainless steels are almost always requirements of the product specifications used to purchase the product. For flat rolled products the properties usually specified are tensile strength, yield stress (or proof stress), elongation and Brinell or Rockwell hardness. Much less frequently there are requirements for impact resistance, either Charpy or Izod. Bar, tube, pipe, fittings etc. also usually require at least tensile strength and yield stress. These properties give a guarantee that the material in question has been correctly produced, and are also used by engineers to calculate the working loads or pressures that the product can safely carry in service.
Typical Properties
Typical mechanical properties of annealed materials are as in the graph of Figure 1. Note that the high cold work hardening rate of the austenitic grades in particular results in actual properties of some commercial products being significantly higher than these values. The yield stress (usually measured as the 0.2% proof stress) is particularly increased by even quite minor amounts of cold work. More details of the work hardening of stainless steels are given in the section of this handbook on fabrication.
Yield Strength
An unusual feature of annealed austenitic stainless steels is that the yield strength is a very low proportion of the tensile strength, typically only 40-45%. The comparable figure for a mild steel is about 65-70%. As indicated above a small amount of cold work greatly increases the yield (much more so than the tensile strength), so the yield also increases to a higher proportion of tensile. Only a few % of cold work will increase the yield by 200 or 300MPa, and in severely cold worked material like spring temper wire or strip, the yield is usually about 80-95% of the tensile strength.
Ductility
The other mechanical property of note is the ductility, usually measured by % elongation during a tensile test. This shows the amount of deformation a piece of metal will withstand before it fractures. Austenitic stainless steels have exceptionally high elongations, usually about 60-70% for annealed products, as shown in figure 2. It is the combination of high work hardening rate and high elongation that permits the severe fabrication operations which are routinely carried out, such as deep drawing of kitchen sinks and laundry troughs.
Hardness
Hardness (measured by Brinell, Rockwell or Vickers machines) is another value for the strength of a material. Hardness is usually defined as resistance to penetration, so these test machines measure the depth to which a very hard indenter is forced into a material under the action of a known force. Each machine has a different shaped indenter and a different force application system, so conversion between hardness scales is not generally very accurate. Although conversion tables have been produced these conversions are only approximate, and should not be used to determine conformance to standards.
It is also sometimes convenient to do a hardness test and then convert the result to tensile strength. Although the conversions for carbon and low alloy steels are fairly reliable, those for stainless steels are much less so.
Mechanical Properties of Wire and Bar
The mechanical properties of the majority of the stainless steel wire and bar products are generally sufficiently described by the tensile strength. These products require mechanical properties which are carefully chosen to enable the product to be fabricated into the finished component and also to withstand the loads which will be applied during service. Spring wire has the highest tensile strength of the wire generally manufactured; it must be suitable for coiling into tension or compression springs without breaking during forming. However, such high tensile strengths would be completely unsuitable for forming or weaving applications because the wire would break on forming. Weaving wires are supplied in a variety of tensile strengths carefully chosen so that the finished woven screen will have adequate strength to withstand the service loads, and yet soft enough to be crimped and to be formed into the screen satisfactorily. Mechanical properties of wire for fasteners are another example where a careful balance in mechanical properties is required. In this type of product the wire must be ductile enough to form a quite complex head but the wire must be hard enough so that the threads will not deform when the screw or bolt is assembled into the component. Good examples are roofing bolts, wood screws and self-tapping screws; to achieve the mechanical properties required for such components requires careful consideration of the composition of the steel so that the work hardening rate will be sufficiently high to form hard threads on thread rolling and yet not so high as to prevent the head from being formed.For bar products a compromise must also be made; a large proportion of bar will be machined, so it is important that the hardness be not too high, but better load carrying capacity is achieved if the strength is high, and for drawn bar a good bright finish is achieved only by a reduction which significantly increases strength levels.
Friday, August 14, 2009
MECHANICAL PROPERTIES
Strength, hardness, toughness, elasticity, plasticity, brittleness, and ductility and malleability are mechanical properties used as measurements of how metals behave under a load. These properties are described in terms of the types of force or stress that the metal must withstand and how these are resisted.
Common types of stress are compression, tension, shear, torsion, impact, 1-2 or a combination of these stresses, such as fatigue. (See
Compression stresses develop within a material when forces compress or crush the material. A column that supports an overhead beam is in compression, and the internal stresses that develop within the column are compression.
Tension (or tensile) stresses develop when a material is subject to a pulling load; for example, when using a wire rope to lift a load or when using it as a guy to anchor an antenna. "Tensile strength" is defined as resistance to longitudinal stress or pull and can be measured in pounds per square inch of cross section. Shearing stresses occur within a material when external forces are applied along parallel lines in opposite directions. Shearing forces can separate material by sliding part of it in one direction and the rest in the opposite direction.
Some materials are equally strong in compression, tension, and shear. However, many materials show marked differences; for example, cured concrete has a maximum strength of 2,000 psi in compression, but only 400 psi in tension. Carbon steel has a maximum strength of 56,000 psi in tension and compression but a maximum shear strength of only 42,000 psi; therefore, when dealing with maximum strength, you should always state the type of loading.
A material that is stressed repeatedly usually fails at a point considerably below its maximum strength in tension, compression, or shear. For example, a thin steel rod can be broken by hand by bending it back and forth several times in the same place; however, if the same force is applied in a steady motion (not bent back and forth), the rod cannot be broken. The tendency of a material to fail after repeated bending at the same point is known as fatigue.
Common types of stress are compression, tension, shear, torsion, impact, 1-2 or a combination of these stresses, such as fatigue. (See
Compression stresses develop within a material when forces compress or crush the material. A column that supports an overhead beam is in compression, and the internal stresses that develop within the column are compression.
Tension (or tensile) stresses develop when a material is subject to a pulling load; for example, when using a wire rope to lift a load or when using it as a guy to anchor an antenna. "Tensile strength" is defined as resistance to longitudinal stress or pull and can be measured in pounds per square inch of cross section. Shearing stresses occur within a material when external forces are applied along parallel lines in opposite directions. Shearing forces can separate material by sliding part of it in one direction and the rest in the opposite direction.
Some materials are equally strong in compression, tension, and shear. However, many materials show marked differences; for example, cured concrete has a maximum strength of 2,000 psi in compression, but only 400 psi in tension. Carbon steel has a maximum strength of 56,000 psi in tension and compression but a maximum shear strength of only 42,000 psi; therefore, when dealing with maximum strength, you should always state the type of loading.
A material that is stressed repeatedly usually fails at a point considerably below its maximum strength in tension, compression, or shear. For example, a thin steel rod can be broken by hand by bending it back and forth several times in the same place; however, if the same force is applied in a steady motion (not bent back and forth), the rod cannot be broken. The tendency of a material to fail after repeated bending at the same point is known as fatigue.
Tuesday, August 4, 2009
Mechanical Advantages
Man first started using machines to make work easier and faster. How much easier and faster a machine makes your work is the mechanical advantage of that machine. In science terms, the mechanical advantage is the number of times a machine multiplies your effort force.
To find the MA of a machine, you can divide the resistance force by the effort force. Most of the time the resistance force is the weight of the object in Newtons.
To find the MA of a machine, you can divide the resistance force by the effort force. Most of the time the resistance force is the weight of the object in Newtons.
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