Physical quantity called physical property material object, process, physical phenomenon, quantified.
The value of a physical quantity expressed by one or more numbers characterizing this physical quantity, indicating the unit of measurement.
The size of a physical quantity are the values of the numbers appearing in the meaning of the physical quantity.
Units of measurement of physical quantities.
The unit of measurement of a physical quantity is a fixed size value that is assigned a numeric value, equal to one. It is used for the quantitative expression of physical quantities homogeneous with it. A system of units of physical quantities is a set of basic and derived units based on a certain system of quantities.
Only a few systems of units have become widespread. In most cases, many countries use the metric system.
Basic units.
Measure physical quantity - means to compare it with another similar physical quantity, taken as a unit.
The length of an object is compared with a unit of length, body weight - with a unit of weight, etc. But if one researcher measures the length in sazhens, and another in feet, it will be difficult for them to compare these two values. Therefore, all physical quantities around the world are usually measured in the same units. In 1963, the International System of Units SI (System international - SI) was adopted.
For each physical quantity in the system of units, an appropriate unit of measurement must be provided. Standard units is its physical realization.
The length standard is meter- the distance between two strokes applied on a specially shaped rod made of an alloy of platinum and iridium.
Standard time is the duration of any correctly repeating process, which is chosen as the movement of the Earth around the Sun: the Earth makes one revolution per year. But the unit of time is not a year, but give me a sec.
For a unit speed take the speed of such uniform rectilinear motion, at which the body makes a movement of 1 m in 1 s.
A separate unit of measurement is used for area, volume, length, etc. Each unit is determined when choosing one or another standard. But the system of units is much more convenient if only a few units are chosen as the main ones, and the rest are determined through the main ones. For example, if the unit of length is meter, then the unit of area is square meter, volume - cubic meter, speed - meter per second, etc.
Basic units The physical quantities in the International System of Units (SI) are: meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), candela (cd) and mole (mol).
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Basic SI units |
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Value |
Unit |
Designation |
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Name |
Russian |
international |
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Power electric current |
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Thermodynamic temperature |
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The power of light |
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Amount of substance |
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There are also derived SI units, which have their own names:
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SI derived units with their own names |
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Unit |
Derived unit expression |
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Value |
Name |
Designation |
Via other SI units |
Through basic and additional SI units |
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Pressure |
m -1 ChkgChs -2 |
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Energy, work, amount of heat |
m 2 ChkgChs -2 |
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Power, energy flow |
m 2 ChkgChs -3 |
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Quantity of electricity, electric charge |
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Electrical voltage, electrical potential |
m 2 ChkgChs -3 CHA -1 |
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Electrical capacitance |
m -2 Chkg -1 Hs 4 CHA 2 |
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Electrical resistance |
m 2 ChkgChs -3 CHA -2 |
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electrical conductivity |
m -2 Chkg -1 Hs 3 CHA 2 |
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Flux of magnetic induction |
m 2 ChkgChs -2 CHA -1 |
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Magnetic induction |
kghs -2 CHA -1 |
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Inductance |
m 2 ChkgChs -2 CHA -2 |
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Light flow |
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illumination |
m 2 ChkdChsr |
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Radioactive source activity |
becquerel |
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Absorbed radiation dose |
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ANDmeasurements. To obtain an accurate, objective and easily reproducible description of a physical quantity, measurements are used. Without measurements, a physical quantity cannot be quantified. Definitions such as "low" or "high" pressure, "low" or "high" temperature reflect only subjective opinions and do not contain comparison with reference values. When measuring a physical quantity, it is assigned a certain numerical value.
Measurements are made using measuring instruments. There is quite a large number of measuring instruments and fixtures, from the simplest to the most complex. For example, length is measured with a ruler or tape measure, temperature with a thermometer, width with calipers.
Measuring instruments are classified: according to the method of presenting information (indicating or recording), according to the method of measurement (direct action and comparison), according to the form of presentation of indications (analog and digital), etc.
The measuring instruments are characterized by the following parameters:
Measuring range- the range of values of the measured quantity, on which the device is designed during its normal operation (with a given measurement accuracy).
Sensitivity threshold- the minimum (threshold) value of the measured value, distinguished by the device.
Sensitivity- relates the value of the measured parameter and the corresponding change in instrument readings.
Accuracy- the ability of the device to indicate the true value of the measured indicator.
Stability- the ability of the device to maintain a given measurement accuracy for a certain time after calibration.
In principle, one can imagine any large number different systems units, but only a few are widely used. All over the world, for scientific and technical measurements, and in most countries in industry and everyday life, the metric system is used.
Basic units.
In the system of units for each measured physical quantity, an appropriate unit of measurement must be provided. Thus, a separate unit of measure is needed for length, area, volume, speed, etc., and each such unit can be determined by choosing one or another standard. But the system of units turns out to be much more convenient if in it only a few units are chosen as the main ones, and the rest are determined through the main ones. So, if the unit of length is a meter, the standard of which is stored in the State Metrological Service, then the unit of area can be considered a square meter, the unit of volume is a cubic meter, the unit of speed is a meter per second, etc.
The convenience of such a system of units (especially for scientists and engineers, who are much more familiar with measurements than other people) is that the mathematical relationships between the basic and derived units of the system turn out to be simpler. At the same time, a unit of speed is a unit of distance (length) per unit of time, a unit of acceleration is a unit of change in speed per unit of time, a unit of force is a unit of acceleration per unit of mass, etc. In mathematical notation, it looks like this: v = l/t, a = v/t, F = ma = ml/t 2. The presented formulas show the "dimension" of the quantities under consideration, establishing relationships between units. (Similar formulas allow you to define units for quantities such as pressure or electric current.) Such ratios are general character and are performed regardless of the units in which the length is measured (meter, foot or arshin) and which units are chosen for other quantities.
In engineering, the basic unit of measurement of mechanical quantities is usually taken not as a unit of mass, but as a unit of force. Thus, if in the system most used in physical research, a metal cylinder is taken as a standard of mass, then in a technical system it is considered as a standard of force that balances the force of gravity acting on it. But since the force of gravity is not the same at different points on the surface of the Earth, for the exact implementation of the standard, it is necessary to indicate the location. Historically, the location was at sea level at geographical latitude 45° . At present, such a standard is defined as the force necessary to give the indicated cylinder a certain acceleration. True, in technology, measurements are carried out, as a rule, not with such high precision, so that you have to take care of the variations in gravity (if we are not talking about the calibration of measuring instruments).
A lot of confusion is associated with the concepts of mass, force and weight. The fact is that there are units of all these three quantities that have the same name. Mass is the inertial characteristic of a body, showing how difficult it is to derive it external force from a state of rest or uniform and rectilinear motion. A unit of force is a force that, acting on a unit of mass, changes its speed by a unit of speed per unit of time.
All bodies are attracted to each other. Thus, any body near the Earth is attracted to it. In other words, the Earth creates the force of gravity acting on the body. This force is called its weight. The force of weight, as mentioned above, is not the same at different points on the surface of the Earth and on different height above sea level due to differences in gravitational pull and in the manifestation of the Earth's rotation. However, the total mass of a given amount of substance is unchanged; it is the same in interstellar space and at any point on Earth.
Precise experiments have shown that the force of gravity acting on different bodies(i.e. their weight) is proportional to their mass. Therefore, masses can be compared on a balance, and masses that are the same in one place will be the same in any other place (if the comparison is carried out in a vacuum to exclude the influence of the displaced air). If a certain body is weighed on a spring balance, balancing the force of gravity with the force of an extended spring, then the results of the weight measurement will depend on the place where the measurements are taken. Therefore, spring scales must be adjusted at each new location so that they correctly show the mass. The simplicity of the weighing procedure itself was the reason that the force of gravity acting on the reference mass was taken as an independent unit of measurement in technology. HEAT.
Metric system of units.
The metric system is the common name for the international decimal system units, the basic units of which are the meter and the kilogram. With some differences in details, the elements of the system are the same all over the world.
Story.
The metric system grew out of the decrees adopted by the National Assembly of France in 1791 and 1795 to define the meter as one ten-millionth of the length of the earth's meridian from the North Pole to the equator.
By a decree issued on July 4, 1837, the metric system was declared mandatory for use in all commercial transactions in France. It has gradually supplanted local and national systems elsewhere in Europe and has been legally accepted in the UK and the US. An agreement signed on May 20, 1875 by seventeen countries created international organization, designed to preserve and improve the metric system.
It is clear that by defining the meter as a ten millionth of a quarter of the earth's meridian, the creators of the metric system sought to achieve invariance and exact reproducibility of the system. They took the gram as a unit of mass, defining it as the mass of one millionth cubic meter water at its maximum density. Since it would not be very convenient to make geodetic measurements of a quarter of the earth's meridian with each sale of a meter of cloth or to balance a basket of potatoes in the market with an appropriate amount of water, metal standards were created that reproduce these ideal definitions with the utmost accuracy.
It soon became clear that metal standards of length could be compared with each other, introducing a much smaller error than when comparing any such standard with a quarter of the earth's meridian. In addition, it became clear that the accuracy of comparing metal mass standards with each other is much higher than the accuracy of comparing any such standard with the mass of the corresponding volume of water.
In this regard, the International Commission on the Meter in 1872 decided to take the “archival” meter stored in Paris “as it is” as the standard of length. Similarly, the members of the Commission took the archival platinum-iridium kilogram as the standard of mass, “considering that the simple ratio established by the creators of the metric system between a unit of weight and a unit of volume represents the existing kilogram with an accuracy sufficient for ordinary applications in industry and commerce, and accurate science needs not a simple numerical ratio of this kind, but an extremely perfect definition of this ratio. In 1875, many countries of the world signed an agreement on the meter, and this agreement established the procedure for coordinating metrological standards for the world scientific community through the International Bureau of Weights and Measures and the General Conference on Weights and Measures.
The new international organization immediately took up the development of international standards of length and mass and the transfer of their copies to all participating countries.
Length and mass standards, international prototypes.
International prototypes of standards of length and mass - meters and kilograms - were deposited with the International Bureau of Weights and Measures, located in Sevres, a suburb of Paris. The standard of the meter was a ruler made of an alloy of platinum with 10% iridium, the cross section of which was given a special X-shape to increase flexural rigidity with a minimum volume of metal. There was a longitudinal flat surface in the groove of such a ruler, and the meter was defined as the distance between the centers of two strokes applied across the ruler at its ends, at a standard temperature of 0 ° C. The mass of a cylinder made from the same platinum was taken as the international prototype of the kilogram. iridium alloy, which is the standard of the meter, with a height and diameter of about 3.9 cm. The weight of this standard mass, equal to 1 kg at sea level at a geographical latitude of 45 °, is sometimes called a kilogram-force. Thus, it can be used either as a standard of mass for the absolute system of units, or as a standard of force for the technical system of units, in which one of the basic units is the unit of force.
The International Prototypes were selected from a significant batch of identical standards made at the same time. The other standards of this batch were transferred to all participating countries as national prototypes (state primary standards), which are periodically returned to the International Bureau for comparison with international standards. Comparisons made in different time since then, show that they do not detect deviations (from international standards) that go beyond the limits of measurement accuracy.
International SI system.
The metric system was very favorably received by scientists of the 19th century. partly because it was proposed as an international system of units, partly because its units were theoretically supposed to be independently reproducible, and also because of its simplicity. Scientists began to derive new units for the various physical quantities they were dealing with, based on the elementary laws of physics and relating these units to the units of length and mass of the metric system. The latter increasingly won various European countries, in which many unrelated units for different quantities were previously in circulation.
Although in all countries that adopted the metric system of units, the standards of metric units were almost the same, there were various discrepancies in the derived units between different countries and different disciplines. In the field of electricity and magnetism, two separate systems of derived units have emerged: the electrostatic one, based on the force with which two electric charges act on each other, and the electromagnetic one, based on the force of the interaction of two hypothetical magnetic poles.
The situation became even more complicated with the advent of the so-called. practical electrical units, introduced in the middle of the 19th century. British Association for the Advancement of Science to meet the demands of rapidly developing wire telegraph technology. Such practical units do not coincide with the units of the two systems named above, but differ from the units of the electromagnetic system only by factors equal to integer powers of ten.
Thus, for such common electrical quantities, like voltage, current and resistance, there were several options for the accepted units of measurement, and each scientist, engineer, teacher had to decide for himself which of these options he should use. In connection with the development of electrical engineering in the second half of the 19th and first half of the 20th centuries. more and more practical units were used, which eventually came to dominate the field.
To eliminate such confusion in the early 20th century. a proposal was put forward to combine practical electrical units with the corresponding mechanical units based on metric units of length and mass, and to build some kind of consistent (coherent) system. In 1960, the XI General Conference on Weights and Measures adopted a unified International System of Units (SI), defined the basic units of this system and prescribed the use of some derived units, "without prejudice to the question of others that may be added in the future." Thus, for the first time in history, an international coherent system of units was adopted by international agreement. It is now accepted as the legal system of units of measurement by most countries in the world.
The International System of Units (SI) is a harmonized system in which for any physical quantity, such as length, time or force, there is one and only one unit of measure. Some of the units are given specific names, such as the pascal for pressure, while others are named after the units from which they are derived, such as the unit of speed, the meter per second. The main units, together with two additional geometric ones, are presented in Table. 1. Derived units for which special names are adopted are given in Table. 2. Of all the derived mechanical units, the most important are the newton unit of force, the joule unit of energy, and the watt unit of power. Newton is defined as the force that gives a mass of one kilogram an acceleration equal to one meter per second squared. A joule is equal to the work done when the point of application of a force equal to one Newton moves one meter in the direction of the force. A watt is the power at which work of one joule is done in one second. Electrical and other derived units will be discussed below. The official definitions of primary and secondary units are as follows.
A meter is the distance traveled by light in a vacuum in 1/299,792,458 of a second. This definition was adopted in October 1983.
The kilogram is equal to the mass of the international prototype of the kilogram.
A second is the duration of 9,192,631,770 periods of radiation oscillations corresponding to transitions between two levels of the hyperfine structure of the ground state of the cesium-133 atom.
Kelvin is equal to 1/273.16 of the thermodynamic temperature of the triple point of water.
The mole is equal to the amount of a substance, which contains as many structural elements as there are atoms in the carbon-12 isotope with a mass of 0.012 kg.
A radian is a flat angle between two radii of a circle, the length of the arc between which is equal to the radius.
The steradian is equal to the solid angle with the vertex at the center of the sphere, which cuts out on its surface an area equal to the area of a square with a side equal to the radius of the sphere.
For the formation of decimal multiples and submultiples, a number of prefixes and multipliers are prescribed, indicated in Table. 3.
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Table 3 INTERNATIONAL SI DECIMAL MULTIPLES AND MULTIPLE UNITS AND MULTIPLIERS |
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| exa | deci | ||||
| peta | centi | ||||
| tera | Milli | ||||
| giga | micro |
mk |
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| mega | nano | ||||
| kilo | pico | ||||
| hecto | femto | ||||
| soundboard |
Yes |
atto | |||
Thus, a kilometer (km) is 1000 m, and a millimeter is 0.001 m. (These prefixes apply to all units, such as kilowatts, milliamps, etc.)
Initially, one of the basic units was supposed to be the gram, and this was reflected in the names of the units of mass, but now the basic unit is the kilogram. Instead of the name of megagrams, the word "ton" is used. In physical disciplines, for example, to measure the wavelength of visible or infrared light, a millionth of a meter (micrometer) is often used. In spectroscopy, wavelengths are often expressed in angstroms (Å); An angstrom is equal to one tenth of a nanometer, i.e. 10 - 10 m. For radiation with a shorter wavelength, such as X-rays, in scientific publications it is allowed to use a picometer and an x-unit (1 x-unit \u003d 10 -13 m). A volume equal to 1000 cubic centimeters (one cubic decimeter) is called a liter (l).
Mass, length and time.
All the basic units of the SI system, except for the kilogram, are currently defined in terms of physical constants or phenomena, which are considered to be invariable and reproducible with high accuracy. As for the kilogram, a method for its implementation with the degree of reproducibility that is achieved in the procedures for comparing various mass standards with the international prototype of the kilogram has not yet been found. Such a comparison can be carried out by weighing on a spring balance, the error of which does not exceed 1×10–8. The standards of multiples and submultiples for a kilogram are established by combined weighing on a balance.
Because the meter is defined in terms of the speed of light, it can be reproduced independently in any well-equipped laboratory. So, by the interference method, dashed and end gauges, which are used in workshops and laboratories, can be checked by comparing directly with the wavelength of light. The error with such methods in optimal conditions does not exceed one billionth (1H 10 -9). With development laser technology such measurements have been greatly simplified, and their range has been significantly expanded.
Similarly, the second, in accordance with its modern definition, can be independently realized in a competent laboratory in an atomic beam facility. The beam atoms are excited by a high-frequency generator tuned to the atomic frequency, and the electronic circuit measures time by counting the oscillation periods in the generator circuit. Such measurements can be carried out with an accuracy of the order of 1×10 -12 - much better than was possible with previous definitions of the second, based on the rotation of the Earth and its revolution around the Sun. Time and its reciprocal, frequency, are unique in that their references can be transmitted by radio. Thanks to this, anyone with the appropriate radio receiving equipment can receive accurate time and reference frequency signals that are almost identical in accuracy to those transmitted on the air.
Mechanics.
temperature and warmth.
Mechanical units do not allow solving all scientific and technical problems without involving any other ratios. Although the work done when moving a mass against the action of a force and the kinetic energy of a certain mass are equivalent in nature to the thermal energy of a substance, it is more convenient to consider temperature and heat as separate quantities that do not depend on mechanical ones.
Thermodynamic temperature scale.
The thermodynamic temperature unit Kelvin (K), called the kelvin, is determined by the triple point of water, i.e. the temperature at which water is in equilibrium with ice and steam. This temperature is taken equal to 273.16 K, which determines the thermodynamic temperature scale. This scale, proposed by Kelvin, is based on the second law of thermodynamics. If there are two heat reservoirs at a constant temperature and a reversible heat engine transferring heat from one of them to the other in accordance with the Carnot cycle, then the ratio of the thermodynamic temperatures of the two reservoirs is given by T 2 /T 1 = –Q 2 Q 1 , where Q 2 and Q 1 - the amount of heat transferred to each of the reservoirs (the minus sign indicates that heat is taken from one of the reservoirs). Thus, if the temperature of the warmer reservoir is 273.16 K, and the heat taken from it is twice the heat transferred to another reservoir, then the temperature of the second reservoir is 136.58 K. If the temperature of the second reservoir is 0 K, then it no heat will be transferred at all, since all the energy of the gas has been converted into mechanical energy in the adiabatic expansion section of the cycle. This temperature is called absolute zero. The thermodynamic temperature commonly used in scientific research, coincides with the temperature included in the equation of state ideal gas PV = RT, where P- pressure, V- volume and R is the gas constant. The equation shows that for an ideal gas, the product of volume and pressure is proportional to temperature. For any of the real gases, this law is not exactly fulfilled. But if we make corrections for virial forces, then the expansion of gases allows us to reproduce the thermodynamic temperature scale.
International temperature scale.
In accordance with the above definition, the temperature can be measured with a very high accuracy (up to about 0.003 K near the triple point) by gas thermometry. A platinum resistance thermometer and a gas reservoir are placed in a heat-insulated chamber. When the chamber is heated, the electrical resistance of the thermometer increases and the gas pressure in the reservoir rises (in accordance with the equation of state), and when cooled, the reverse picture is observed. By simultaneously measuring resistance and pressure, it is possible to calibrate a thermometer according to gas pressure, which is proportional to temperature. The thermometer is then placed in a thermostat in which liquid water can be maintained in equilibrium with its solid and vapor phases. By measuring its electrical resistance at this temperature, a thermodynamic scale is obtained, since the temperature of the triple point is assigned a value equal to 273.16 K.
There are two international temperature scales - Kelvin (K) and Celsius (C). The Celsius temperature is obtained from the Kelvin temperature by subtracting 273.15 K from the latter.
Accurate temperature measurements using gas thermometry require a lot of work and time. Therefore, in 1968 the International Practical Temperature Scale (IPTS) was introduced. Using this scale, thermometers of various types can be calibrated in the laboratory. This scale was established using a platinum resistance thermometer, a thermocouple and a radiation pyrometer used in the temperature intervals between some pairs of constant reference points (temperature benchmarks). The MTS was supposed to correspond with the greatest possible accuracy to the thermodynamic scale, but, as it turned out later, its deviations are very significant.
Fahrenheit temperature scale.
The Fahrenheit temperature scale, which is widely used in conjunction with the British technical system units, as well as in non-scientific measurements in many countries, it is customary to determine by two constant reference points - the melting temperature of ice (32 ° F) and the boiling point of water (212 ° F) at normal (atmospheric) pressure. Therefore, to get the Celsius temperature from the Fahrenheit temperature, subtract 32 from the latter and multiply the result by 5/9.
Heat units.
Since heat is a form of energy, it can be measured in joules, and this metric unit has been adopted by international agreement. But since the amount of heat was once determined by changing the temperature of a certain amount of water, a unit called a calorie and equal to the amount of heat needed to raise the temperature of one gram of water by 1 ° C has become widespread. Due to the fact that the heat capacity of water depends on temperature , I had to specify the value of the calorie. There were at least two different calories- "thermochemical" (4.1840 J) and "steam" (4.1868 J). The “calorie” used in dieting is actually a kilocalorie (1000 calories). The calorie is not an SI unit and has fallen into disuse in most areas of science and technology.
electricity and magnetism.
All common electrical and magnetic units of measurement are based on metric system. In accordance with modern definitions of electrical and magnetic units, they are all derived units derived from certain physical formulas from metric units of length, mass and time. Since most electrical and magnetic quantities are not so easy to measure using the standards mentioned, it was considered that it was more convenient to establish, by appropriate experiments, derived standards for some of the indicated quantities, and measure others using such standards.
SI units.
Below is a list of electrical and magnetic units of the SI system.
The ampere, the unit of electric current, is one of the six basic units of the SI system. Ampere - the strength of an unchanging current, which, when passing through two parallel straight conductors of infinite length with a negligibly small circular cross-sectional area, located in vacuum at a distance of 1 m from one another, would cause an interaction force equal to 2 × 10 on each section of the conductor 1 m long - 7 N.
Volt, unit of potential difference and electromotive force. Volt - electrical voltage on the site electrical circuit with a direct current of 1 A with a power consumption of 1 W.
Coulomb, a unit of quantity of electricity (electric charge). Coulomb - the amount of electricity passing through the cross section of the conductor when DC with a force of 1 A in a time of 1 s.
Farad, unit of electrical capacitance. Farad is the capacitance of a capacitor, on the plates of which, with a charge of 1 C, an electric voltage of 1 V arises.
Henry, unit of inductance. Henry is equal to the inductance of the circuit in which an EMF of self-induction of 1 V occurs with a uniform change in the current strength in this circuit by 1 A per 1 s.
Weber, unit of magnetic flux. Weber - a magnetic flux, when it decreases to zero in a circuit coupled to it, having a resistance of 1 Ohm, flows electric charge, equal to 1 C.
Tesla, unit of magnetic induction. Tesla - magnetic induction of a homogeneous magnetic field, in which the magnetic flux through a flat area of 1 m 2, perpendicular to the lines of induction, is 1 Wb.
Practical standards.
Light and illumination.
The units of luminous intensity and illuminance cannot be determined on the basis of mechanical units alone. It is possible to express the energy flux in a light wave in W/m 2 and the intensity of a light wave in V/m, as in the case of radio waves. But the perception of illumination is a psychophysical phenomenon in which not only the intensity of the light source is essential, but also the sensitivity of the human eye to the spectral distribution of this intensity.
By international agreement, the unit of luminous intensity is the candela (formerly called a candle), equal to strength light in a given direction of a source emitting monochromatic radiation with a frequency of 540×10 12 Hz ( l\u003d 555 nm), the energy strength of the light radiation of which in this direction is 1/683 W / sr. This roughly corresponds to the light intensity of the spermaceti candle, which once served as a standard.
If the luminous intensity of the source is one candela in all directions, then the total luminous flux is 4 p lumens Thus, if this source is located in the center of a sphere with a radius of 1 m, then the illumination of the inner surface of the sphere is equal to one lumen per square meter, i.e. one suite.
X-ray and gamma radiation, radioactivity.
Roentgen (R) is an obsolete unit of exposure dose of X-ray, gamma and photon radiation, equal to the amount of radiation, which, taking into account secondary electron radiation, forms ions in 0.001 293 g of air, carrying a charge equal to one CGS charge unit of each sign. In the SI system, the unit of absorbed radiation dose is the gray, which is equal to 1 J/kg. The standard of the absorbed dose of radiation is the installation with ionization chambers, which measure the ionization produced by radiation.
Measurements are based on comparison of identical properties of material objects. For properties that are quantitatively compared physical methods, in metrology a single generalized concept is established - a physical quantity. Physical quantity- a property that is qualitatively common to many physical objects, but quantitatively individual for each object, for example, length, mass, electrical conductivity and heat capacity of bodies, gas pressure in a vessel, etc. But smell is not a physical quantity, since it is established through subjective sensations.
A measure for quantitative comparison of the same properties of objects is unit of physical quantity - a physical quantity, which, by agreement, is assigned a numerical value equal to 1. The units of physical quantities are assigned a full and abbreviated symbolic designation - dimension. For example, mass is kilogram (kg), time is second (s), length is meter (m), force is Newton (N).
The value of the physical quantity - evaluation of a physical quantity in the form of a certain number of units accepted for it - characterizes the quantitative individuality of objects. For example, the diameter of the hole is 0.5 mm, the radius of the globe is 6378 km, the speed of the runner is 8 m/s, the speed of light is 3 10 5 m/s.
by measurement is called finding the value of a physical quantity using special technical means. For example, measuring the shaft diameter with a caliper or micrometer, liquid temperature with a thermometer, gas pressure with a pressure gauge or vacuum gauge. The value of a physical quantity x^, obtained during the measurement, is determined by the formula x^ = ai, where a- numerical value (size) of a physical quantity; and - unit of physical quantity.
Since the values of physical quantities are found empirically, they contain measurement errors. In this regard, the true and actual values of physical quantities are distinguished. True value - the value of a physical quantity, which ideally reflects the corresponding property of the object in qualitative and quantitative terms. It is the limit to which the value of a physical quantity approaches with increasing measurement accuracy.
Actual value - the value of a physical quantity found experimentally and so close to the true value that it can be used instead of it for a specific purpose. This value varies depending on the required measurement accuracy. In technical measurements, the value of a physical quantity found with an allowable error is taken as a real value.
Measurement error is the deviation of the measurement result from the true value of the measured quantity. Absolute error called the measurement error, expressed in units of the measured value: Oh = x^-x, where X- the true value of the measured quantity. Relative error - the ratio of the absolute measurement error to the true value of the physical quantity: 6=Ax/x. The relative error can also be expressed as a percentage.
Since the true value of the measurement remains unknown, in practice only an approximate estimate of the measurement error can be found. In this case, instead of the true value, the actual value of the physical quantity is taken, obtained by measuring the same quantity with a higher accuracy. For example, the error in measuring linear dimensions with a caliper is ±0.1 mm, and with a micrometer - ± 0.004 mm.
The measurement accuracy can be expressed quantitatively as the reciprocal of the modulus of relative error. For example, if the measurement error is ±0.01, then the measurement accuracy is 100.
INTRODUCTION
A physical quantity is a characteristic of one of the properties of a physical object (physical system, phenomenon or process), which is qualitatively common to many physical objects, but quantitatively individual for each object.
Individuality is understood in the sense that the value of a quantity or the size of a quantity can be for one object a certain number of times greater or less than for another.
The value of a physical quantity is an estimate of its size in the form of a certain number of units accepted for it or a number according to the scale adopted for it. For example, 120 mm is the value of a linear value; 75 kg is the value of body weight.
There are true and real values of a physical quantity. A true value is a value that ideally reflects a property of an object. Real value - the value of a physical quantity, found experimentally, close enough to the true value that can be used instead.
The measurement of a physical quantity is a set of operations for the use of a technical means that stores a unit or reproduces a scale of a physical quantity, which consists in comparing (explicitly or implicitly) the measured quantity with its unit or scale in order to obtain the value of this quantity in the form most convenient for use.
There are three types of physical quantities, the measurement of which is carried out according to fundamentally different rules.
The first type of physical quantities includes quantities on the set of dimensions of which only the order and equivalence relations are defined. These are relationships like "softer", "harder", "warmer", "colder", etc.
Quantities of this kind include, for example, hardness, defined as the ability of a body to resist the penetration of another body into it; temperature, as the degree of body heat, etc.
The existence of such relations is established theoretically or experimentally using special means comparisons, as well as on the basis of observations of the results of the impact of a physical quantity on any objects.
For the second type of physical quantities, the relation of order and equivalence takes place both between sizes and between differences in pairs of their sizes.
A typical example is the scale of time intervals. So, the differences of time intervals are considered equal if the distances between the corresponding marks are equal.
The third type is additive physical quantities.
Additive physical quantities are called quantities, on the set of sizes of which not only the order and equivalence relations are defined, but also the operations of addition and subtraction
Such quantities include, for example, length, mass, current strength, etc. They can be measured in parts, and also reproduced using a multi-valued measure based on the summation of individual measures.
The sum of the masses of two bodies is the mass of such a body, which is balanced on the first two equal-arm scales.
The dimensions of any two homogeneous PV or any two sizes of the same PV can be compared with each other, i.e., find how many times one is larger (or smaller) than the other. To compare m sizes Q", Q", ... , Q (m) with each other, it is necessary to consider C m 2 of their relationship. It is easier to compare each of them with one size [Q] of a homogeneous PV, if we take it as a unit of the PV size, (abbreviated as a PV unit). As a result of such a comparison, we obtain expressions for the dimensions Q", Q", ... , Q (m) in the form of some numbers n", n", .. . ,n (m) PV units: Q" = n" [Q]; Q" = n"[Q]; ...; Q(m) = n(m)[Q]. If the comparison is carried out experimentally, then only m experiments are required (instead of C m 2), and the comparison of the sizes Q", Q", ... , Q (m) with each other can be performed only by calculations like
where n (i) / n (j) are abstract numbers.
Type equality
is called the basic measurement equation, where n [Q] is the value of the size of the PV (abbreviated as the value of the PV). The PV value is a named number, composed of the numerical value of the PV size, (abbreviated as the numerical value of the PV) and the name of the PV unit. For example, with n = 3.8 and [Q] = 1 gram, the size of the mass Q = n [Q] = 3.8 grams, with n = 0.7 and [Q] = 1 ampere, the size of the current strength Q = n [Q ] = 0.7 amperes. Usually, instead of “the size of the mass is 3.8 grams”, “the size of the current is 0.7 amperes”, etc., they say and write more briefly: “the mass is 3.8 grams”, “the current is 0.7 amperes " etc.
The dimensions of the PV are most often found as a result of their measurement. The measurement of the size of the PV (abbreviated as the measurement of the PV) consists in the fact that by experience, using special technical means, the value of the PV is found and the proximity of this value to the value that ideally reflects the size of this PV is estimated. The PV value found in this way will be called nominal.
The same Q dimension can be expressed different values with different numerical values depending on the choice of the PV unit (Q = 2 hours = 120 minutes = 7200 seconds = = 1/12 days). If we take two different units and , then we can write Q = n 1 and Q = n 2, whence
n 1 / n 2 \u003d /,
i.e. numerical values PV is inversely proportional to its units.
From the fact that the size of the PV does not depend on its chosen unit, the condition for the unambiguity of measurements follows, which consists in the fact that the ratio of two values of a certain PV should not depend on which units were used in the measurement. For example, the ratio of the speeds of a car and a train does not depend on whether these speeds are expressed in kilometers per hour or meters per second. This condition, which at first glance seems indisputable, unfortunately, cannot yet be met when measuring some PVs (hardness, photosensitivity, etc.).
1. THEORETICAL PART
1.1 The concept of a physical quantity
Weight objects of the surrounding world are characterized by their properties. Property is a philosophical category that expresses such a side of an object (phenomenon, process) that determines its difference or commonality with other objects (phenomena, processes) and is found in its relationship to them. The property is a quality category. For a quantitative description of various properties of processes and physical bodies the concept of magnitude is introduced. A value is a property of something that can be distinguished from other properties and evaluated in one way or another, including quantitatively. The value does not exist by itself, it takes place only insofar as there is an object with properties expressed by this value.
The analysis of quantities allows us to divide (Fig. 1) them into two types: quantities of a material form (real) and quantities of ideal models of reality (ideal), which mainly relate to mathematics and are a generalization (model) of specific real concepts.
Real quantities, in turn, are divided into physical and non-physical. A physical quantity in the most general case can be defined as a quantity inherent in material objects (processes, phenomena) studied in the natural (physics, chemistry) and technical sciences. Non-physical quantities should include quantities inherent in the social (non-physical) sciences - philosophy, sociology, economics, etc.
Rice. 1. Classification of quantities.
The document RMG 29-99 interprets a physical quantity as one of the properties of a physical object, which is qualitatively common for many physical objects, but quantitatively individual for each of them. Individuality in quantitative terms is understood in the sense that a property can be for one object a certain number of times more or less than for another.
Physical quantities it is advisable to divide into measured and evaluated. Measured FIs can be expressed quantitatively as a certain number of established units of measurement. The possibility of introducing and using such units is important hallmark measured PV. Physical quantities for which, for one reason or another, a unit of measurement cannot be introduced, can only be estimated. Evaluation is the operation of assigning a certain number to a given value, carried out according to established rules. Evaluation of the value is carried out using scales. A magnitude scale is an ordered set of magnitude values that serves as the initial basis for measuring a given magnitude.
Non-physical quantities, for which a unit of measurement cannot in principle be introduced, can only be estimated. It should be noted that the estimation of non-physical quantities is not included in the tasks of theoretical metrology.
For a more detailed study of PV, it is necessary to classify, to identify the general metrological features of their individual groups. Possible classifications of FI are shown in fig. 2.
According to the types of phenomena, PVs are divided into:
Real, i.e. quantities describing the physical and physico-chemical properties of substances, materials and products from them. This group includes mass, density, electrical resistance, capacitance, inductance, etc. Sometimes these PVs are called passive. To measure them, it is necessary to use an auxiliary energy source, with the help of which a signal of measuring information is formed. In this case, passive PV are converted into active ones, which are measured;
Energy, i.e. quantities describing the energy characteristics of the processes of transformation, transmission and use of energy. These include current, voltage, power, energy. These quantities are called active.
They can be converted into measurement information signals without the use of auxiliary energy sources;
Characterizing the course of processes in time, This group includes different kind spectral characteristics, correlation functions and other parameters.
1. The concept of magnitude. Basic properties of homogeneous quantities.
2. Measurement of magnitude. The numerical value of the quantity.
3. Length, area, mass, time.
4. Dependencies between quantities.
4.1. The concept of magnitude
The value is one of the basic mathematical concepts that arose in antiquity and underwent a number of generalizations in the process of long development. Length, area, volume, mass, speed and many others are all quantities.
Value - it is a special property of real objects or phenomena. For example, the property of objects "to have extension" is called "length". The value is considered as a generalization of the properties of some objects and as an individual characteristic of the properties of a particular object. The values can be quantified based on the comparison.
For example, the concept length occurs:
when designating the properties of a class of objects (“many objects around us have a length”);
when designating a property of a particular object from this class (“this table has a length”);
when comparing objects by this property ("the length of the table is greater than the length of the desk").
Homogeneous quantities - quantities that express the same property of objects of a certain class.
Heterogeneous quantities express various properties of objects (one object can have mass, volume, etc.).
Properties of homogeneous quantities:
1. Homogeneous quantities can be compare.
For any values a and b, only one of the relations is true: a < b, a > b, a = b.
For example, the mass of a book is greater than the mass of a pencil, and the length of a pencil is less than the length of a room.
2. Homogeneous quantities can be add and subtract. As a result of addition and subtraction, a value of the same kind is obtained.
The quantities that can be added are called additivenym. For example, you can add the lengths of objects. The result is a length. There are quantities that are not additive, such as temperature. When water of different temperatures is combined from two vessels, a mixture is obtained, the temperature of which cannot be determined by adding the values.
We will consider only additive quantities.
Let: a- the length of the fabric, b- the length of the piece that was cut off, then: ( a - b) is the length of the remaining piece.
3. The value can be multiply by a real number. The result is a quantity of the same kind.
Example: "Pour 6 glasses of water into a jar."
If the volume of water in the glass is V, then the volume of water in the bank is 6V .
4. Homogeneous quantities share. The result is a non-negative real number, it is called attitudequantities.
Example: "How many ribbons of length b can be obtained from a ribbon of length a?" ( X = a : b)
5. The value can be measure.
4.2. Value measurement
Comparing the quantities directly, we can establish their equality or inequality. For example, by comparing the lengths of the strips by overlay or application, one can determine whether they are equal or not:
If the ends match, then the strips are of equal length;
If the left ends coincide, and the right end of the lower strip protrudes, then its length is greater.
For more exact result magnitude comparisons are measured.
Measurement consists in comparing a given value with somea value taken as a unit.
Measuring the mass of watermelon on the scales, compare it with the mass of the kettlebell.
Measuring the length of the room in steps, compare it with the length of the step.
The comparison process depends on the kind of quantity: length is measured using a ruler, mass - using scales. Whatever this process, as a result of the measurement, a certain number is obtained, depending on the chosen unit of quantity.
The purpose of the measurement is get a numerical characteristic of the given quantity with the selected unit.
If the quantity a is given and the unit of quantity e is chosen, then in reas a result of measuring the quantity a, they find such a realthe number x such that a = x e. This number x is called the numerical valuethe value of a when the value of e is unity.
1) The mass of a melon is 3 kg.
3kg \u003d 3 ∙ 1 kg, where 3 is the numerical value of the melon mass with a mass unit of 1 kg.
2) The length of the segment is 10cm.
10cm \u003d 10 1cm, where 10 is the numerical value of the length of the segment with a unit of length of 1cm.
Quantities determined by one numerical value are called scalar(length, volume, mass, etc.). There are more vector quantities, which are determined by numerical value and direction (speed, force, etc.).
Measurement allows you to reduce the comparison of values to a comparison of numbers, and actions with values - to actions on numbers.
1. If the values a and b measured using a unit of quantity e, then the relationship between the quantities a and b will be the same as the ratios between their numerical values (and vice versa):
Let a= t e,b= n e, then a=b<= > m = n,
a >b < = > m > p,
a< b < = > T< п.
Example: “The mass of a watermelon is 5 kg. The weight of the melon is 3 kg. The mass of a watermelon is greater than the mass of a melon, because 5 > 3".
2. If the values a and b measured using a unit of quantity e, then to find the numerical value of the sum (a+ b), it suffices to add the numerical values of the quantities a and b.
Let a=t e,b\u003d p e, c \u003dke, then a +b= with< = > t + p= k.
For example, to determine the mass of purchased potatoes, poured into two bags, it is not necessary to pour them together and weigh them, it is enough to add the numerical values of the mass of each bag.
3. If the values a and b are such that b = x a, where X - positive real number, and the value a measured using a unit of quantity e, then to find the numerical value of the quantity b with a unit e, a number is sufficient X multiply by the numerical value of the quantity a.
Let a= t e,b= x a, then b=(x t) e.
Example: “The length of the blue strip is 2 dm. The length of the yellow is 3 times longer. What is the length of the yellow stripe?
2dm 3 = (2 1dm) 3 = (2 3) 1dm = 6 1dm = 6dm.
Preschoolers get acquainted with the measurement of quantities first with the help of conditional measures. In the process of practical activity, they are aware of the relationship between the value and its numerical value, as well as the numerical value of the quantity from the selected unit of measure.
“Measure in steps the length of the path from the house to the tree, and now from the tree to the fence. What is the length of the entire track?
(Children add values using their numerical values.)
What is the length of the track, measured by Masha's steps? (5 steps of Masha.)
What is the length of the same track, measured by Kolya's steps? (4 steps Kolya.)
Why did we measure the length of the same track, but get different results?
(The length of the track is measured in different steps. Kolya's steps are longer, so there are fewer of them).
The numerical values of the road length differ due to the use of different units of measurement.
The need for measuring quantities arose in the practical activity of man in the process of his development. The measurement result is expressed as a number and makes it possible to better understand the essence of the concept of number. The measurement process itself teaches children to think logically, forms practical skills, and enriches cognitive activity. In the process of measuring, children can get not only natural numbers, but also fractions.