Measurements in physics. Direct Assessment Method

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1. Basic concepts and definitions in information and measuring processes

What is a measurement, control, testing, what do they differ about each other in content and what is in them?

Measure it is called experienced by the value of the physical quantity (FV) with the help of special technical means. The purpose of measurement is to extract information about the input (measured) value from the output signal of the measurement tool (C), taking into account its properties and characteristics.

The information flow diagram is shown in Figure 1.

Picture 1.

Test according to GOST 16504-81, the experimental determination of the quantitative and / or qualitative characteristics of the properties of the test object as a result of the impact on it when it is functioning, when modeling an object and / or influences. When testing. As a rule, measurement tools are used, other technical devices, substances and / or materials.

Control call the product compliance check, process or services to the established requirements. Control, as a rule, is carried out in two stages. At the first stage, the value of the controlled characteristic (quantitative - by measuring) is determined, on the second, they compare the resulting value with the norm. Sometimes both stages are combined in one action. For example, when controlling the size of parts by calibers. Thus, control is a validation check. The norm is set in advance, and the verification of compliance to it ends with the decision-making: "corresponds to, does not match"; "Suitable marriage", etc.

The presence of the norm implies the gradation of the quantitative characteristics of any property and causes the ability to make a decision.

Analyzing the procedures and tasks of "measuring" "control" and "tests", you can establish their relationship, which is shown in Figure 2.

Figure 2. Relationship of concepts "Measurement", "Control" and "Test"

Measurement can be both part of the intermediate transformation in the control process and the final stage of obtaining information during the test. The test is the stage of obtaining primary information in the control process using measuring operations.

What is "unity of measurements"?

In almost all spheres of human activity, it is necessary to deal with measurements of physical quantities and ensuring their unity. The meaning of the unity of measurement is so highly that a special law "On ensuring the unity of measurements" / 1 / is published in Russia.

Unity of measurements - This is a state of measurements in which their results are expressed in legalized units, and measurement errors are known with a given probability.

The unity of measurements is necessary in order to compare the measurement results performed in different places in different timeVarious measurement means. It is important both within the country and in the interaction between countries. An example of this can be the fact that the quality indicators of imported goods are checked in the countries where they are implemented.

What values \u200b\u200bare subject to measurements?

The values \u200b\u200bthat operate a person in real reality can be divided into two types, as shown in Figure 3.

Figure 3. Classification of values

In the studied course "Methods and measuring instruments, tests and controls", we deal with physical quantities inherent in specific subjects, phenomena, processes that are, values \u200b\u200bof limited sizes and being measured. The measured physical value is the value for which you can choose a unit of measurements and embody this unit in the measurement means.

What " physical quantity» and "physical parameter"?

According to the RMG 29-99 / 2 / physical quantity (FV) One of the properties of the physical object (physical system, phenomena or process), common in qualitative relation for many physical objects, but individual in quantitative terms for each of them.

Size FV - Quantitative content in this object property corresponding to the concept of "physical value". Considering objects a and b, different one of their physical properties (for example by weight), we can say that they are different sized (weight) and differ from each other (A\u003e B or A<Б).

Value of FV - expression of the size of the FV in the form of a certain number of units taken for her. The FV value is obtained as a result of its measurement or calculation in accordance with the basic equation of measurement.

Q. change = A.U.,

where Q.change- the value of FV;

BUT - the numerical value of the measured physical quantity, expressed in the adopted unit;

U. - Selected unit of FV.

The numerical value of PV is an abstrused number that is included in the value of the value of FV. For example: L \u003d 20 mm, where 20 is a numerical value.

In the practice of measurements, the measurement is very often the measurement, but physical parameters.

Physical parameter (Briefly - parameter) - FV, considered when measuring another physical size as auxiliary. The physical parameter characterizes the private feature of the measured physical quantity. for exampleWhen measuring the voltage of alternating current, the amplitude and frequency of this current are considered as voltage parameters.

What is called "true" and "valid" values \u200b\u200bof physical quantity?

True value of FV - The value of FV, which would ideally reflect the existing FV in a qualitative and quantitative relationship. This concept is correlated with the concept of "absolute truth", which is impossible in reality.

Valid value of FV - The value of the FV found experimentally and is so close to the true value that it may replace it for the measuring task. In repeated measurements, the average arithmetic value from a number of measured values \u200b\u200bof the value is taken for the actual value. With single measurements - the value of the value obtained by measurements is the most accurate C.

What is the dimension of physical size and how is it determined?

Dimension - formalized reflection of high-quality differences in physical quantities is their . The dimension is indicated by the symbol dim, What is happening from the word dimension, which, depending on the context, can be translated and as size, and as dimension.

The dimension of the basic physical quantities is denoted by the corresponding capital letters. For length, mass and time, for example,

dim L \u003d L; dim m \u003d m; Dim T \u003d T.

When determining dimension derivatives Values \u200b\u200bare guided by the following rules:

1. The dimension of the right and left parts of the equation cannot but coincide, because Only identical properties can be compared with each other. Thus, algebraically, only the values \u200b\u200bhaving the same dimension can be summed up.

2. Algebra of the dimensions of multiplicative, i.e. It consists of one single multiplication action.

2.1. The dimension of the product of several quantities is equal to the product of their dimensions. So, if the dependence between the values \u200b\u200bof Q, and, B, C has the view Q \u003d ABC, then

dim Q \u003d Dim Achdim Vchdim C.

2.2. The dimension of the private in the division of one value to another is equal to the ratio of their dimensions, i.e. if q \u003d a / b, then

dim Q \u003d Dim A / Dim V.

2.3. The dimension of any value erected into some degree is equal to its dimension to the same extent. So, if q \u003d a n, then

dim Q \u003d Dim A \u003d dim n A.

For example, if the speed is determined by the formula V \u003d S / T, then

dIM V \u003d DIM S / DIM T \u003d L / T \u003d LT -1.

If the force according to the second law of Newton F \u003d MA, where a \u003d V / T - the acceleration of the body, then

dIM f \u003d dim m dim a \u003d ml / t 2 \u003d MLT -2.

Thus, it is always possible to express the dimension of the physical size of the physical size through the dimension of the main physical quantities with the help of power unoblane:

where L, M, T, - the dimension of the corresponding major physical quantities; - indicators of dimension. Each of the indicators of the dimension can be a positive or negative, integer or fractional number, zero.

If all dimension indicators are zero, then this value is called dimensionless. She may be relative defined as the ratio of the same names (for example, relative dielectric constant), and logarithmic Defined as a relative value logarithm (for example, the logarithm of power relations or voltages).

The theory of dimension is everywhere applied to operational verification of the correctness of the formulas (according to rule 1). The formal application of the dimension algebra sometimes allows you to determine the unknown relationship between physical quantities.

What is a unit of measurement of physical quantity?

Unit of measuring physical quantity The physical value of the fixed size, which is conditionally assigned a numerical value equal to one, and used for the quantitative expression of homogeneous physical quantities. Units of measurements of some values \u200b\u200bmay differ in its size, for example, meter, foot and inches, being units of length, have a different size: 1 foot \u003d 0.3048 m, 1 inch \u003d 0.254 m.

What is a system of units of physical quantities?

To ensure the unity of measurements from 1.01.82 years in our country, GOS 8.417-81 GCI "Units of physical quantities" is enacted. The standard meets the requirements of the international units (SI) system and contains:

Units C (main, additional, derivatives);

Introduction units allowed on par with SI units and in combination with them;

Rule of formation of multiple and dolle units;

Name of units, their designations and other provisions.

The standard does not apply to units used in research and development in the publications of their results, as well as by the units of values \u200b\u200bassessed by conditional scales (metal hardness scales, earthquake, unrest, photosensitivity, etc.).

In this way, fromextent of units of physical quantities the combination of basic and derivative units of physical quantities formed in accordance with the principles for a given system of physical quantities. For example, an international system of units (C) adopted in 1960

What are the basic units of the SI system?

The main unit of the system of units of physical quantities the unit of the main physical quantity in this system of units.

The main units of the international system system are: meter, kilogram, second, amp, degrees Kelvin, candela, mole. When choosing these units, only practical feasibility were guided, i.e. Ease of use of units in human activity.

The meter is a unit of length equal to the path in a vacuum with light for 1/299792458 share of a second. Initially, the meter was defined as the length of 1/40000000 share of the length of the Paris Meridian and was reproduced as the distance between the risks applied on platinum, and later the platinumiridium bruse of the X-shaped section. But this value was unstable, so the meter began to express with the length of the radiation wavelength of the red line of cadmium, and at present the orange line of the radiation of the crypton-86 atom. 1 meter corresponds to 1650763.73 radiation wavelengths in vacuo, corresponding to the transition between the level 2p 10 and 5d 5 of the KR-86 atom.

The meter is determined by indirect methods on radiometric bridges. They consist of a series of consistently located radiotechnical generators and lasers with a frequency multiply between them. The input is fed by a reference frequency of 5 MHz from the generator, synchronized through the frequency multiplier system with hydrogen generators of the time and frequency referenced, calibrated in the cesium frequency regiment. The bridge multiplies this frequency to a value of about 1 * 10 14 Hz. The task is to measure the frequencies of stabilized lasers. Knowing them, they calculate the wavelengths of their radiation and with the help of optical interferometers are certified and the various lengths of length are certified.

Kilogram is a mass unit equal to the mass of 1.000028 dm 3 of water at the temperature of its highest density 4 єС.

The standard kilogram in Russia is a cylinder height and a diameter of 39 mm with rounded ribs. Work is underway to determine the kilogram through the volt and Ohm using advanced amps scales.

Second - a time unit equal to 9192631770 radiation periods corresponding to the transition between two ultra-thin levels of the main state of the cesium-133 atom. The standard of seconds was established in 1967. It is based on the ability of atoms to emit and absorb energy during the transition between the two energy states in the field of radio frequencies. Reper, or quantum frequency standard, is a device for accurate reproduction of the frequency of electromagnetic oscillations in ultra-frequency and optical spectra, based on measuring the frequency of quantum transitions of atoms, ions or molecules. In passive quantum standards, the frequencies of spectral absorption lines are used, in active - forced emission of photon particles. Active quantum frequency standards on the beam of ammonia molecules (so-called molecular generators) and hydrogen atoms (hydrogen generators) are used. Passive frequency standards - on the beam of cesium atoms (frequency cesium reper)

To play seconds, cesium generators (standards) of frequencies are used - these are highly stable monochromatic radiation generators (signal) with a frequency of 9192631770 Hz; The frequency error does not exceed 1.5 * 10 -13. In the state standard of Russia, hydrogen generators are periodically pulmoned with cesium, their long-term frequency is not postulated, but instability is less than 3 * 10 -14. In addition, the standard contains the formation and storage equipment. The main scale of such a uniform atomic time with a fixed zero, not related to the rotation and position in the space of the Earth. Other scales: UT0 - World Time (average solar "C"); UT1 adjusted to the oscillations of the Poles of the Earth; UT2 - with an amendment for the seasonal unevenness of the rotation of the Earth. These are worldwide scales, gradually diverged due to slowing the speed of the earth's rotation. To match them, the UTC scale was introduced, in which 1C UTC \u003d 1C TA, and the beginning of the account may vary for 1C from the 1st day of each month (1.01 or 1.06) in Russia on the UTC scale transmit time signals to TV or radio.

Amp - unit of power of electric current. The ampere is equal to the power of an immutable current, which, passing along two parallel straight-line conductors of an infinite length and a negligible area of \u200b\u200ba circular cross section, located in a vacuum at a distance of 1 m one from the other, would cause 1 m long of the interaction force, equal to 2 · 10 -7 N.

Ampere-scales that implement the force are used as the measurements of the amper, or by measuring the moment of force acting onto the coil with a current placed in the magnetic field of another coil. These are precise equal departure scales made of non-magnetic materials. At one end of the rocker, a cup is suspended for placing permanent and additional balancing cargo. A movable coil is hung to another end of the rocker, incoming coaxially in a fixed coil of larger diameter. Coil windings (in the simplest case) are connected sequentially. In a de-energized mode, the scales are balanced. When passing through the electric current coil, the movable coil is drawn into a fixed (or pushed out of it). For equilibrium recovery, it serves an additional balanced cargo. According to the results of metrological research, the value of the mass of this cargo corresponding to, for example, the power of electric current 1a is calculated. Turning on the coil chain the reference resistor, you can calibrate the reference measures of EDC (the reference measures of current force are not yet applied).

More accurate standards based on the measurements of magnetic induction by the nuclear magnetic resonance method are used so far only as secondary. In 1992, the National Standard AP was approved in Russia, the size of which is reproduced using Volt and Ohm elements. Argent quadratic deviation (approximation) no more than 1 · 10 -8, not excluded systematic errors (NSP) no more than 1 · 10 -7 (in amp-weights CKO? 4 · 10 -6, HCP? 8 · 10 -6).

Kelvin is a unit of thermodynamic temperature, equal to 1/273,16 parts of the thermodynamic temperature of the triple point of water. The triple point of water is the condition of water in a sealed glass vessel, in which ice, water and her pairs are in equilibrium: water does not freeze, does not evaporate, the ice does not melt, steam is not condensed.

State primary standards of Russia reproduce the international degree of MGS-90 in two subbands: 0.8 ... 273.16 K and 373,16 ... 2773 K. In the composition of the low-temperature reference, it includes two groups of iron and platinum resistance thermometers as the main part. The calibration dependences of which are determined by the results of the comparisons of the results obtained in the laboratories of Russia, England, the United States, Australia and Holland. Each group contains two platinum and two iron-rhodium thermometers constantly in the comparison unit - a massive cylinder with four longitudinal channels for thermometers. The transmission of the scale thermometers - secondary and working standards is carried out by bringing them into thermal contact with the reference comparison unit and comparison in the cryostat. In addition to devices for accurate measurements of resistance, the set of installations for realizing the temperature points, a gas interpolation thermometer with a unique mercury gauge and comparison cryostat, includes a set of accurate resistance measurements. EKT standard 0.3 ... 1.0 MK, NSP 0.4 ... 1.5 MK The smallest value of the reproducible temperature is 0.8 K.

The second standard includes platinum resistance thermometers, temperature lamps, reference dot playing equipment in the range of 273.16 ... 1355.77 K, (approx. 5 · 10 -5 ... 1 · 10 -2; NSP? 1 · 10 - 45 ... 10 -3). The following ratios are installed on various temperature ranges:

celsius scale: C \u003d K \u003d T with +273,16

the Raida scale: 1R \u003d 1.25 C; t C \u003d 1.25 T R; T \u003d 1.25 T R +273,16

fahrenheit scale: 1F \u003d 5/9C \u003d 5 / 9K; t c \u003d 5/9 (t f -32); T \u003d 5/9 (t f -32) +273,16

Candela is a unit of light, equal to the power of light in a predetermined direction of the source emitting a monochromatic radiation with a frequency of 540 · 10 12 Hz, the energy force of which in this direction is 1/683 W / cf. The initiators of the introduction of this unit were astronomers. In the state standard, the light is emitted from a certain surface of the solidification platinum under certain external conditions and is perceived by the primary photometer created on the basis of a non-selective radiometer, the spectral sensitivity of which is correlated on a special filter for a functional dependence on the wavelength. The standard reproduces the unit of light power in the range of 30 ... 110 kD from the speed? 0.1 · 10 -2 and NSP? 0.25 · 10 -2.

Mol is a unit of a substance equal to the amount of substance containing as many structural elements (atoms, molecules), how many are contained in 0.012 kg of carbon-12. The standards praying were never created, as the mass of one praying of various substances or structures, numerically equal to the number of Avogadro - 6,025 · 10 23 particles; Measuring instruments that are separated in moles are not available. There are reasonable proposals to eliminate mole from major SI units and to admit it to apply on a par with SI units as a special unit of mass, convenient for chemical calculations.

The reference base of Russia has 114 state standards and more than 250 secondary benchmarks of units of FV. Of these, 52 are in Vnie. D.I. Mendeleeva (S.-PB.), incl. standards m, kg, a, k, glad; 25 - in VNIIFTRI (physico-technical and radio engineering measurements, Moscow, incl. Standards of time and frequency units; 13 - in the VNII of optical-physical measurements, incl. Candelas; respectively, 5 and 6 - in Ural and Siberian Nii of Metrology.

What is derivative units C?

Derivative unit of units of physical quantities - the unit of the derivative of the physical size of the units system formed in accordance with the equation connecting it with the main units or with the main and already certain derivatives.

The derivatives of the C units are formed from the main, additional and previously formed derivatives of the SI units using the equations of communication between the physical quantities in which the numerical coefficients are equal to one. For this value in the right and left parts of the equation of communication are taken equal to units of C. For example, for a derivative of a velocity unit determined from the equation V \u003d L / T, the equation of units [v] \u003d [L] / [T] is recorded, and instead of the symbols of Li ts, they substitute their units (1 m and 1 s) and obtain [v ] \u003d 1 m / 1 C \u003d 1 m / s. This means that the unit of speed in C is a meter per second. The derivatives of units may be assigned to the names in honor of the well-known scientists. Thus, the equation of communication between values \u200b\u200bfor determining the pressure unit P \u003d F / S, the equation of communication between pressure units, strength and area [p] \u003d [F] / [S]. Substituting instead F. and S units of these values \u200b\u200bin C (1 H and 1 m 2), we obtain [p] \u003d 1 n / 1 m 2 \u003d 1 n / m 2. This unit was awarded the name - Pascal (PA) named French mathematics and blouse physics Pascal.

What is multiple and dolle units, and what are the rules for their education?

At the XI General Conference on measures and weights, together with the adoption of SI, 12 multiple and dolly consoles were adopted, to which new ones were added at subsequent conferences. The consoles made an opportunity to form decimal multiple and dolly units from SI units.

Multiple unity of physical quantity Unit of physical quantity, for an integer time a large system or non-system unit. For example, the unit of length is 1 km (kilometer) \u003d 10 3 m, i.e., a multiple meter; 1 MHz frequency unit (megahertz) \u003d 10 6 Hz, multiple hertz; The unit of activity of radionuclides is 1 MBK (megabekkequer) \u003d 10 6 VC, multiple Becker.

Dolly Unit of Physical Size - unit of physical quantity, for an integer, a smaller system or non-system unit.

The names of multiple and dolle units are formed using the consoles shown in Table 3.

Table 3 - multipliers and consoles to SI units

What is a "non-systemic unit of physical quantity"?

Introduced Unit of Physical - Unit of FV, not incorporated into any of the adopted systems of units. In relation to the units of X, non-system units of physical quantities are divided into four types: permissible on par with basic units; allowable to use in special areas; outdated (invalid); temporarily allowed.

To non-system units allowed on a par with units , relate: ton - a unit of mass; degrees, minute, second - unit of a flat angle; liter - unit of capacity; Minute, day, week, month, year, century - time units.

To the extra system, allowable to use in special areas, units include: in physics - electron volts; in agriculture - hectare; in astronomy - light year; In optics - diopter.

For non-system units, temporarily used on par with SI units include: in marine navigation: - Sea mile - a unit of length; Node - a unit of speed; For precious stones, a mass unit - carat; In other areas: turnover per minute (rpm) - a unit of rotation frequency; Bar (bar) - a pressure unit.

Temporarily applied units must be drawn (and are withdrawn) from consumption in accordance with international agreements.

Contributed units seized from use include: kilogram-force - a unit of force, weight; Centner - unit of mass; Horsepower - unit of power, etc.

What is the measurement?

Measure Physical quantities are a combination of operations on the use of a technical means that stores the unit of physical quantity that ensures that the ratio (explicitly and implicit form) of the measured value with its unit and obtaining the value of this magnitude.

The measurement result is recorded as a general measurement equation:

Q change \u003d n [q],

where q ism - the measured physical value; p - number of units; [Q] - Unit of physical size.

Note. Since not only physical quantities are measured, there is another interpretation of the concept of "measurement". Measurement is a set of operations performed in order to determine the value of the value. Here, the definition of the concept of "measurement" is not limited to finding the value of the physical quantity, there is no mention of technical means. This interpretation of the concept is suitable for physical and non-physical quantities. Consequently, the measurements include various types of quantitative estimation of quantities.

How are the measurements classified?

With all the variety of measurements, they can be classified on six signs.

As a feature of 1 dependence of the measured value of time, measurements are divided into static and dynamic.

Static dimension Measurement of FV, taken into line with a specific measuring task for the constant measurement time. For example, measuring the constant voltage of the electric current. Measuring the dimensions of the land.

Dynamic dimension - Measurement variable in size of physical, magnitude. For example, measuring the height of a declining aircraft, that is, with a continuous change in the size of the measured value; Measurement of alternating voltage of electric current.

As a characteristic of the 2 - the accuracy of measurement results, measurements are divided into equal and inequalization.

Equal measurements - measurements of the values \u200b\u200bperformed by the same measurement with the accuracy of measurements, in the same conditions, with one operator, with the same thoroughness and one and the same number of measurements.

Alignment measurements - measurements of the values \u200b\u200bperformed by the measurement differences in accuracy, in different conditions, with different operators, with different number of measurements. So that the measurement results are inequalized, it is often enough to have one of the listed factors.

As a characteristic of 3, the conditions determining the accuracy of the result, the measurements are divided into technical and metrological.

Technical dimensions Measurements using measurement tests. Technical measurements are performed in order to control and control technological processes, scientific experiments, diagnosis of diseases, and so on. An example of technical measurements is to measure the speed of the bus, the aircraft, that is, any moving body.

Metrological measurements These are measurements performed using the standards and exemplary measurement tools in order to reproduce units of physical quantities or transmitting them to the size of the measurement tools. For example, verification or calibration of the working weight of the 2nd grade accuracy according to the calibration scheme is performed by exemplary weighting of the 1st discharge on the weights of the 1st discharge. Such measurements are manufactured in order to establish the accuracy of the standards and working tools of measurements, that is, are metrological. Metrological measurements are divided into measurements of the highest possible accuracy and test measurements.

As a feature of 4, measurements performed to obtain the result, measurements are divided into one-time (ordinary) and multiple (statistical).

Single dimension This measurement performed once. for example, Measurement of a specific point in time by the hour.

Multiple measurements This measurement of the same physical size of a constant size, the result of which is obtained from several measurements following each other, that is, a measurement consisting of a number of single measurements. For the result of repeated measurement, medium-ray value is usually taken from the results of single measurements included in the row. Multiple consider measuring with the number of individual measurements n\u003e 4.

As a feature 5, a method for obtaining a result (by type), measurements are divided into direct, indirect, cumulative and joint.

Direct measurement This measurement in which the desired physical value is obtained directly from the experimental data. For example, measuring machine speed speedometer, an angle measurement with a measurement, measuring the current force by an ammeter.

Indirect measurement It is the definition of a physical quantity based on the results of direct measurements of other physical quantities that are functionally related to the desired magnitude. For example, the length of hypotenuse rectangular triangle (c) can be determined by direct measurements of two cathets (A and B), which are mathematically connected with the hypothenoise formula:

Cumulative measurements This measurements of several of the same names performed simultaneously. In this case, the desired values \u200b\u200bof values \u200b\u200bare determined by solving the system of equations obtained by measuring these values \u200b\u200bin various states.

Joint measurements These are measuring two or more non-values \u200b\u200bthat are performed simultaneously to determine the relationship between them.

The main equations in cumulative and joint dimensions are:

where w. 1 ... W. n. - the desired values;

x. 1 ... H. m. - parameters or values \u200b\u200bestablished on the basis of direct or indirect measurement;

F. 1 ... F. n. - known communication functions.

known functional connection of the form:

that is, the relationship between the resistance R t is known at any temperature of R 0 at T \u003d 0 and constant coefficients and.

At three known values t.1, t.2, t.3 Measure R. tL , R. t. 2 , R. t. 3 .

Compile equations:

The resulting system of equations is solved, since the number of equations is equal to the number of unknown.

As a feature of 6, the method of expressing the measurement results, the measurements are divided into absolute and relative.

Absolute measurement This is a measurement based on direct measurements of one or more values \u200b\u200bin its units.

Concept absolute measurement It is used as opposite to the concept of relative dimension.

Relative dimension Measurement of the ratio of the value to the same name, which plays the role of a unit, or measure the change in the value with respect to the same name taken for the original.

For example, the measurement of the electric current force ammeter, when the measurement result is expressed in a unit of measured value (in amperes) is a direct dimension.

Measurement on the two-stage mass weights, the value of which is greater than the measurement limit on the scale of the scale, is relative. On the scale of the scales there will be an indication corresponding to the difference in the mass of mass and mass of the initial weights less weighable, installed on the weighting area.

What is the connection between the concepts of "Methods", "Method" and "principle" of measurements?

Each measuring process, regardless of the purpose of it and end result, It consists of the following main stages: preparation for measurements, measurement, measurement results processing. In order to ensure proper measurement quality, each stage of the measuring process must be performed in accordance with the established rules that are defined by the measurement methodology.

Methods of performing measurements This is the established set of operations and rules when measuring, the execution of which ensures that the necessary measurement results are obtained in accordance with this method.

Measuring methods involves: analysis of the measuring task; the choice of principle, method and measurement means; preparation of measuring instruments for work; requirements for measurement conditions; measurements indicating their number; Processing measurement results, including calculation, introduction of amendments and ways to express errors.

Usually, measurement techniques are governed by any regulatory and technical document. Many measurement techniques are unified, since their unification is important in ensuring the unity of measurements.

The choice of the principle and method of measurement is carried out on the basis of the analysis of the measuring task, in which the following questions are solved: what physical values \u200b\u200band object parameters are subject to measurement; What accuracy should be the measurement result; In what form it should be submitted that this corresponds to the purpose of the measuring task.

Principle of measurements This is a physical phenomenon or effect based on measurements in one way or another type of measurement.

For example, according to the phenomenon of Seebek, in a closed electrical circuit formed by two heterogeneous conductors, thermo-e-ds occurs. DC, proportional difference in the temperatures of the ends of the sword conductors. The magnitude of this thermo-e.d. can be represented by the function E. aB= f.(t. a.- t. b.) where t. a. and t. b. Temperature of the ends of the soldered conductors BUT and IN. This physical phenomenon is based on thermocouple temperature measurements.

Measurement method j. Reception or a set of comparison methods of a measured physical value with its unit in accordance with the realizable measurement principle. Measurement methods are methods for solving measurement tasks characterized by their theoretical substantiations and the development of basic techniques for the use of measuring instruments. Measurement methods are very diverse. Their appearance is due to scientific and technical progress.

The classification of basic measurement methods is shown in Figure 5. The classification feature in such a separation of measurement methods is the presence or absence of measure when measuring. In this regard, measurement methods are divided into direct assessment method and the comparison method with measure.

Direct rating method (reference) The measurement method in which the FV value is determined directly by the measuring instrument device (Figure 6).

Comparison method with measure The measurement method in which the measured value is compared with the value reproduced by measure.

The comparison method, depending on the presence or absence, when comparing the difference between the measured value and the magnitude reproducible by the measure, is divided into zero and differential methods.

Zero measurement method The comparison method with a measure in which the resulting effect of the measured value and the measure on the comparison device is adjusted to zero (Figure 7).

Differential measurement method The measurement method at which the measured value is compared with a homogeneous value having a known value, originally differing from the measured value and in which the difference between these two values \u200b\u200bis measured.

Measurements with zero and differential methods can be carried out by methods of opposition, substitution, coincidence.

Method of opposition The comparison method with a measure in which the measured value and the value reproduced by the measure simultaneously affect the comparison tool with which the relationship between these values \u200b\u200bis established (Figure 8, a).

Method of substitution - The comparison method with a measure in which the measured value is replaced by a measurable measure (Figures 7, b and 8, b).

Method of coincidence (method - "Nonius") - The comparison method with a measure in which the difference between the measured value and the magnitude of the reproducible measure is measured using the coincidence of the marks of the scale or periodic signals.

Direct evaluation method.

The weight of the cargo x is determined on the basis of the measuring transformation by the value of the springs deformation.

Figure 6. Measurement diagram by direct assessment.

Comparison methods with measure.

Cargo x is barely bastily.

Figure 7. Measurement schemes with zero method:

a) the method of opposition; b) Recognition method.

Figure 8. Measurement schemes by a differential method:

From the figures shown in Figures 7 and 8 it follows that the distinctive feature of these methods is the simultaneity of the impact of the measured value and measure. When the substitution method, the measured value (measurement object) and the measure affect the measurement means alternately.

2 . Measurement conditions

For what purpose and how normalize the measurement conditions?

During the measurements, along with the measured physical quantity, other FVs are involved, the action of which can distort the measurement result. These accompanying values \u200b\u200bare called influencing them, first of all include: temperature ambient, atmospheric, humidity, amplitude and frequency of oscillations during vibration, voltage and frequency of alternating current, magnetic induction, etc. In the measurement process, the change in the values \u200b\u200bof the influential values \u200b\u200bis extremely undesirable, since this leads to a decrease in the measurement accuracy.

To increase the accuracy of measurements, the values \u200b\u200bof influencing values \u200b\u200bare normalized. At the same time, for each type of measurement, a set of influencing values \u200b\u200band their meanings are set.

As normal values \u200b\u200bof some influencing values \u200b\u200bare taken:

Ambient temperature (20 ± 2) ° C;

Barometric pressure (101,325 + 3, h) kPa;

Supply voltage (22010) in,

AC frequency (505) Hz, etc.

The normal values \u200b\u200bof influencing values \u200b\u200busually calculate the main (limit) error of measuring instruments, they are given the results of measurements performed in different conditions.

The limits of normal values \u200b\u200bof the influencing values \u200b\u200bare defined by GOST 8.395-80 "Normal conditions for calibration".

Normal conditions for the use of measuring instruments are not working conditions. For each type of measurement tools in standards or technical conditions, establish an extended (operating) area of \u200b\u200bvalues \u200b\u200bof influencing values, within which the value of an additional error is normalized.

As a working area of \u200b\u200bvalues \u200b\u200bof influencing values, for example:

Ambient temperature from 5 to 50 ° C (-50 to + 50 ° C);

Relative humidity from 30 to 80% (or from 30 to 98%);

Supply voltage from 187 to 242V, etc.

In the working conditions there may be external phenomena, impact
which does not directly influence the instrument readings (the output signal of the converter), but there may be a cause of damage and disruption of the performance of blocks of measurement tools (aggressive gases, dust, water, etc.). From the effects of these factors, measurement means are protected by protective buildings, covers, and the like. In addition, external mechanical forces (vibration, shaking, blows) can affect measurement tools (vibration, shaking) leading to the distortion of their testimony and the impossibility of reporting. Measurement facilities operating under mechanical exposure conditions are protected by special devices from a destructive action or increase their strength.

Depending on the degree of protectedness from external influences and resistance to them, devices and converters are divided into ordinary, vibration-resistant, dust-absorbing, splashing, hermetic, gas-protected, explosion-proof, etc. This makes it possible to choose si applied to working conditions.

What are the measuring instruments?

Measurement means - this is a technical means (or a complex of technical means) intended for measurements having normalized specificationsreproducing and / or staining one or more physical quantities whose dimensions are accepted unchanged over a certain period of time (intermediate interval).

Speaking of measurement tools, use the concepts: view Si, type si.

View measurement tools - A combination of measuring instruments intended to measure this type of FV.

A type measurement tools - A combination of measuring instruments, one and the same purpose based on the same principle of action with the same design, manufactured by the same technical documentation, but having various modifications (for example, differing from measurement limits). The type of measurement tools may include several of their types, type - several modifications.

The classification of measuring instruments can be carried out on various features. In the metrology of the SI, it is customary to classify, the principle of operation and metrological purpose (Figure 10).

All measurement tools are divided into two types: measures and measuring devices. In turn, the latter, depending on the form of the presentation of the measuring information, are divided into measuring transducers, measuring instruments, measuring installations and measuring systems.

Measure - Measurement tool intended for playing and / or storage of FV of one or more specified sizes, the values \u200b\u200bof which are expressed in the conditioned units and are known with the necessary accuracy. Distinguish the following varieties of measures:

- unambiguous measure - measure that reproduces the physical quantity of the same size (for example, a 1kg weight);

- multivalued measure - measure that reproduces the physical size of different sizes (for example, a barrier period of lengths - line);

- set of Mer. - a set of measures of different sizes of the same physical quantity intended for measurement in practice, both individually and in various combinations (for example, a set of end measures);

- store Mer. - A set of measures constructively combined into a single device in which there are devices for their compound in various combinations (for example, an electrical resistance store).

Measuring converter - Measurement means serving to convert the measured value to another value or measured signal, convenient for processing, storage, further transformations, indication or transmission, but not directly perceived by the observer.

Measuring device - Measurement tool intended to generate a signal about the value of the measured physical value in the extentual range in the form available for direct perception by the observer.

Measuring Installation - A combination of functionally combined measures, measuring instruments, measuring transducers and other devices intended for measuring one or more physical quantities and located in one place.

Measuring installations are commonly used in scientific researchimplemented in laboratories when monitoring quality and in metrological services to determine the metrological characteristics of measuring instruments. They are intended to withdraw the measuring information in the form, convenient for direct perception by the operator.

Measuring system - a set of functionally combined measures, measuring instruments, measuring transducers, computers, other technical means located at various points of the controlled object, in order to measure one or more physical quantities, characteristic of this object, and intended for the production of measuring signals in a form convenient for transferable , storage, processing and use in automatic control systems.

Depending on the purpose, the measuring systems are divided into measuring information, measuring controlling, measuring control, measuring computing, etc. An example is the measuring system of thermal power plant containing a large number of measuring channels, whose sensors are separated in space for a significant distance from each other.

What major parts are the measuring devices?

Measuring devices (IU) Consist from elements that perform the functions of conversion of the input signal in the form or type of energy, reassuring oscillations, protection against noiseing fields, circuit switching, representations, information processing, etc.

The measurement devices include:

- converting elementin which one of the variance transformations is happening;

- measuring chain - a set of elements of measuring instruments that form a continuous path of passing the measuring signal of one FV from the input before the exit; (for the measuring system, it was called the measuring channel);

- sensitive element - part of the measuring converter in the measuring circuit, which perceives the input measuring signal;

- measuring mechanism - a set of measurement tool elements that provide the necessary movement of the pointer (arrows, light spots, etc.). For example, for the malelololtmeter, the measuring mechanism consists of a permanent magnet and a movable frame;

- showing device- a set of elements of measuring instruments that provide visual perception of values \u200b\u200bof the measured value or associated values;

- pointer- Part of the showing device whose position relative to the marks of the scale determines the measurement tool readings. The pointer can be an arrow, light beam, the surface of the liquid column in the thermometer, etc.

- registering device- a set of elements of measuring instruments that register the value of the measured or associated magnitude.

What are the structural schemes of measuring devices?

For convenience of analyzing various compounds of measuring devices with each other and with offline controls, any measuring device is considered as a converter for converting the input signal (input effects) x in the output signal (response)

Figure 10 shows the structural diagrams of measuring instruments based on the direct conversion method (A) - direct action, and the reverse conversion (comparison) (b) is balancing or compensatory transformation. The structural circuit of a particular device is fully determined by the transformation method.

Figure 10 - Structural diagrams of measuring devices: a) direct conversion; b) reverse transformation (comparison)

The measuring device based on the direct conversion method works as follows. The measured value x enters the sensitive element 1, where it is converted to another physical value, convenient for further use (current, voltage, pressure, movement, force), and enters the intermediate element 2, which is usually either increasing the incoming signal, or converts it to form. Sometimes item 2 may be absent. The output signal of the element 2 enters the measuring mechanism 3, the movement of the elements of which is determined using the reading device 4. The output signal y (indication), formed by the measuring mechanism, can be perceived by the human sense organ.

A distinctive feature of comparison devices is the presence of a negative feedback (Figure 10, b). The z signal, which occurs when the sensing element is released, enters the conversion element of comparison 5 (comparing element), which is capable of comparing two quantities entering its input. In addition to z, the input of the element 5 is fed with the opposite sign, balancing the Z Ur signal., Which is formed at the output of the reverse conversion element 6. At the output of the element 5, a signal is formed, a proportional difference of z z values. It enters the intermediate converter element 2, the output of which comes simultaneously to the measuring mechanism 3 and to the input of the element 6. Depending on the type of intermediate transformations of the element 2, with each value of the measured parameter and the corresponding value of the z difference (ZZ UR) entering the input Element 5, can be reduced to 0 or have some small value proportional to the measured value.

With what elements of the counting devices receive the measurement tools?

The indication is called the value of the value or the number on the device showing the measurement tool, expressed in the received units of this magnitude. The reading device is a digital scoreboard, and more often - a scale with a pointer. For the scale counting devices, it is customary to use a number of concepts illustrated in Figure 11.

Scalemeasurement tools - Part of the showing device, which is an ordered number of marks together with the associated numbering. Marks can be applied evenly or uneven depending on the type of scale.

Scale mark - Sign on the scale of measuring instruments (kid, prong, point, etc.), which makes up a certain value of physical quantity.

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"Science begins with how to measure. Accurate science is unthinkable without measure.

In the nature of the measure and weight - the essence of the main instruments of knowledge. "

/D.I. Inendeev/

a) educational

the student must learn:

The concept of physical magnitude and units of measurement;

Methods for measuring physical quantities;

Algorithm for determining the price of division and error.

b) Developing

the student should be able to:

Determine the price of fission and testing of measuring instruments;

Record indications of measurement results taking into account errors.

c) Educational:

education of patriotism and citizenship when studying historical aspects of the topic; Development of communicativeness in the process of joint activity.

LESSON STRUCTURE:

№	Stage lesson	Form of activity	Time
1	Org.Moment	Creating a working environment	1-2 min.
2	Checking the house	Test	5 minutes.
3	Actualization of knowledge	Experiment	5 minutes
4	Studying a new meatrial	Heuristic conversation, View Film Fragment, Working with Fiz. Pribers and Didactic Cards	20 minutes.
5	Fixing	Self-execution of tasks on the topic	10 min.
6	Reflection	Answers on questions	2-3 min.

Equipment:

• multimedia projector to demonstrate a presentation;
• three glasses with hot, warm and cold water for the experiment,
• rule, pencil, thermometer (C \u003d 1 ° C), Menzurka.
• individual didactic cards to determine the price of the division of minzur and thermometer.

During the classes

1) Orgmant.

2) Checking homework:

Control test based on the materials of the previous lesson (see Appendix No. 1).

3) the actualization of knowledge.

Conduct an experiment. In three glasses of nanite hot, warm and cold water. Lower one finger of the left hand in hot water, hold a little, and lower in warm. Warm water will seem to you ... (Cold). Now lower your finger right hand in cold waterAnd then in warm. What kind of water will appear? ... (hot). But the water has not changed? What needs to be done to absolutely definitely determine what is the water in a glass? (In the process of the conversation we come to the conclusion):

Conclusion: Sometimes our feelings can deceive us, and therefore it is simply necessary in the process of observations and experiments to make measurements of some values.

4) Studying a new material.

These values \u200b\u200bare called physical, and many are already familiar to you from mathematics, natural science (for example: length, weight, area, speed, etc.). Measurements are extremely important in science, and in the surrounding life.

Great Russian scientist D.I. Mendeleev said this: (slide 1) "Science begins since they begin to measure. Accurate science is unthinkable without measure. In the nature of the measure and weight - the essence of the main instruments of knowledge. "

And therefore the topic of the lesson today: "Measurement of physical quantities"

(Slide 3). Today we must answer the following questions:

• Why do you need measurements?
• What is a physical value?
• How to measure physical size?

We have already answered the first question in the process of discussing the experiment, so we go to the second issue:

What is a physical value?

Let's return to the experience. Take the thermometer in your hands, lower it into the first cup with water, wait a bit and name the water temperature. ( at this stage of the lesson, this measurement may be inaccurate, but it will allow you to introduce the concept of physical quantity as a quantitative characteristic of the class)

Now just measure the temperature in the remaining glasses. Write down the results in the notebook in ascending order.

/ For example: 20 °, 40 °, 60 ° /

Now we will easily define where what water is. The temperature is determined by the number, and the number more, the warmer water. And we can write to the notebook general definition: (Slide 4)

PHS.Veechine is a quantitative (numerical) characteristic of the body or substance. It is denoted by the letters of the Latin alphabet, for example:

m - Weight, T - Time, L - Length.

Any physician except numerical value has a measurement unit.

For example: on wrapped chocolate chocolates: "Mass of 100 g".

Weight is .. (physical value)

100 is ... (numerical meaning)

mr. Gram is ... (Unit of measurement).

Now try yourself:

My height is 164 cm.

Growth (length) is ... (physical value)

164 - this is .., (numeric value)

cm - this .. (Unit of measurement)

Therefore, when we measure some value, we compare it with certain units of measurements. We write a definition: (slide 5)

Measure physician-value-to compare it with a homogeneous value adopted per unit of measurements. Now we have the main question: how to measure the physical size? Let's see how learned to measure the cartoon characters. You will need to answer questions: (Slide 6).

• What physical size was the film characters?
• What units?
• And what was measured?
• Is it correct? Why?

Slide 7 (viewing a cartoon fragment). Discussion of answers / We return to the slide 6 /.

With such difficulties there were not only the boa and his friends. In Russia, since ancient times, there were their units of measurement of distances, masses and volume (slide 8). And although we now almost do not use, in proverbs and sayings, fairy tales and verses they have survived. Explain the meaning of these statements.To not be confused in measurements. In Russia, in the 16th and 17th centuries, a system of measures for the whole country was created. In 1736, the Senate decided to form the Scales and Measures Commission. The Commission has created exemplary measures - standards. By 1807, three planes were made by Arshin (kept in St. Petersburg): crystal, steel and copper. They were already aligned with English lengths of length - feet and inch. This required the need to develop trade relations with other countries - because at the beginning of the 18th century in different countries There have been 400 different in the magnitude of units! To understand each other well, an international system of units (SI) was created, where each magnitude was assigned their designation and a unit of measurement. (Stand "International System Units") All physical quantities are indicated here, and in the course of physics we will study them. Today we will pay attention to the most important, values \u200b\u200bare the main and derivatives. Write in the notebook units of measurement of basic physical survivors:

Mass - kg (kilogram), length - m (meter), time - c (second)

But the mass can be measured more ... (in grams, milligrams, tons).You have already studied it in the course of mathematics. And in which units measure the length? Time? System C is called decimal. All homogeneous values \u200b\u200bare interconnected.

1 kilogram \u003d 1000 (10 3) g 1 kilometer \u003d 1000 (10 3) m

1 milligram \u003d 0.001 g 1 millimeter \u003d 0.001m

There is a special table that is used to translate units of measurement: (see Appendix 2)

Today we must learn to use the measurement instruments correctly.

You have already measured the water temperature today. So what is needed for measurements? First, have a device, secondly, you need to be able to use it. Well familiar ruler is a device for measuring length. The temperature is measured by another instrument - thermometer.

The measuring device is a device for measuring any physical quantity.

(Slide 9.) Here you see various measuring instruments: Thermometer, speedometer, water meter, pressure gauge.

All of them are very different, but they have similarities. Each device necessarily has a scale with divisions and numbers.

Most great importance On the scale is called the upper limit, the smallest - the lower limit. Name the limits of those devices that you have on the desk.

Today we have already measured the temperature with you. Now let's try to determine the volume of water using a special device - mins. We measure the volume in ml or cubic. CM. How much water in this minzur? / 200 ml/. And now the stone lowered the stone, and the water has become more. How many? / Answers will certainly be different, which will allow you to introduce the concept of division price /

To answer this question correctly, you need to determine the price of division, i.e. the value of the smallest gap on the scale.

For this you need: (slide 11)

• Select two nearest numbers (for example, 400 ml and 200 ml)
• Find a difference between them (400 ml - 200 ml \u003d 200 ml)
• Count the number of divisions between them (10)
• Divide the difference in the number of divisions (200 ml: 10 \u003d 20 ml)

We write the formula to determine the division of the device:

c \u003d 400 -200/10 \u003d 20 ml

Now try yourself: (slide12)

Knowing the division price, you can define the instrument readings. If the thermometer shows 5 divisions above 25 °, and one division of 1 °, then the final result will be ... (25 °). A medical thermometer shows for one division less than 37 °, its division price is 0.1 °, which means the temperature is 36.9 °.

Alone on the card determine the price of the division of the thermometer ( for those who have learned well and fulfilled the task quickly, you can offer tasks with a menzur in the same cards)

Measurement error.

Now, please define the width of the textbook "Physics 7" and write down your result in the notebook. Let's compare your measurements.

Why is the same textbook, and the lengths of length are different?

/ During the discussion, we conclude: /

Unfortunately, any measurements have error, Ie Error (Slide 13). Error depends on the device itself (instrumental error), and on how we measure (measurement error). Measurement error is indicated? (Delta) and equal to half the price of division:

The error shows how mistaken we are mistaken (in a large or smaller side). Therefore, the final measurement result is accepted so:

t \u003d 25 ° ± 0, 5 ° (for the first thermometer)

t \u003d 36.9 ° ± 0.05 ° (for the second thermometer)

This means that in fact the temperature ranges from 24.5 ° to 25.5 ° for the first thermometer and from 36.85 ° to 36.95 ° for the second.

And now tell me: Which thermometer is more accurate to measure the temperature?

We write to the notebook:

The less the price of division, the more accurate the device measures.

The measurements that we today did in the lesson are called straight. They are made using instruments. Some values \u200b\u200bcannot be immediately determined. For example: how do you determine the area of \u200b\u200bthe party?That's right, you need to measure the length and width. Such measurements are called indirect.

5. Fastening.

Today at the lesson you learned a lot of new things. Let's remember the most important thing again:

What it is? Replies options:

Minute - ... 1. Unit for measurement

Scales - ... 2. Physical Size

Time - ... 3. Measuring device

Balance - ... 4. physical phenomenon

Weight - ...

Now execute the following tasks: (Slide 14-15)

6. Reflection:

Continue offer:

Now I know…

And I can ...

It would be interesting to learn ...

7. Homework: (Slide 16). § 4.5 (Textbook "Physics 7" Pyryshkin A.V.)

Literature

1. Pyryshkin A.V. Physics 7, Enlightenment, 2008

2. Fireplace A.L. Physics. Educational training. Grade 7, Phoenix, 2003

3. Gentendstein L.E., Kirik L.A., Gelfgat I.M. Tasks in physics for the primary school with examples of solutions, Ilex, 2005

4. Hannanov N.K., Hannanova TA. Physics. Tests. 7, Drop, 2005

The measurement of physical quantities is to compare any value with a homogeneous value adopted per unit. In metrology, the term "measurement" is used, under which it means to find the value of the physical quantity by experimentally through special technical means.

Measurement performed using special technical means is called tool. The simplest example of such measurements is to determine the size of the part with divisions with divisions, that is, a component of the size of the part with a unit of length, stored ruler.

The term derived from the term "measurement" is the term "measure", widely used in practice. There are term "measure", "measure", "measure", but their use in metrology is unacceptable.

To streamline measuring measurement activities, are classified according to the following features:

General techniques for obtaining results - direct, indirect, compatible, cumulative;

The number of measurements in the series is single and multiple;

Metrological appointment - technical, metrological;

Characteristic of accuracy is equal and inequalous;

Relation to the change in the measured value - statistical and dynamic;

The expression of the measurement result is absolute and relative;

Direct measurements - measurements in which the desired value of the magnitude is directly from the experimental data (measuring the mass on the scales, temperature of thermometers, lengths using linear measures). With direct measurements, the research object leads to interaction with measurement tools and according to the latter indications, the value of the measured value is counted. Sometimes the instrument readings multiplied by the coefficient, appropriate corrections are introduced, etc. These measurements can be written in the form of equation: x \u003d · x n,

where x is the value of the measured value in the units taken for it;

C is the price of dividing the scale or a single reading of the digital reading device in units of the measured value;

X P - counting on the indicator device in the division of the scale.

Indirect measurements - measurementsin which the desired value is found on the basis of the known relationship between this magnitude and the values \u200b\u200bobtained by direct measurements (determining the density of the homogeneous body by weight and geometric dimensions, the electrical resistance of the conductor by its resistance, the length and the cross-sectional area). In general, this dependence can be represented as a function x \u003d (x1, x2, ...., Xn), in which the value of the arguments X1, X2, ...., Xn are found as a result of direct, and sometimes indirect, joint or cumulative measurements. .

For example, the density of homogeneous solid ρ is found as the ratio of mass M to its volume V, and the mass and volume of the body are measured directly: ρ \u003d m / v.

To increase the accuracy of measurements of the density ρ of measuring the mass M and volume V produce many times. In this case, body density

ρ \u003d m / v, m - the result of measuring body weight, m \u200b\u200b\u003d 1 / n Σ m i;

V \u003d σvi / n - the result of measuring the volume of the body π.

The total measurements of measurements of several homogeneous values \u200b\u200bin which the desired value of the values \u200b\u200bare found by the solution of the system of equations obtained by direct measurements of various combinations of these values \u200b\u200b(measurements in which the mass of individual dialing weights are located in the well-known mass of one of them and according to the results of direct comparisons of masses of various combinations of weights ).

Joint measurements - simultaneous measurements of two or more different variance values \u200b\u200bfor finding the dependence between them (performed simultaneously measuring the increment of the sample length depending on changes in its temperature and determining the linear extension coefficient).

Joint and cumulative measurements in ways of finding the desired values \u200b\u200bof the measured values \u200b\u200bare very close. The difference is that in total measurements, several single-names are measured simultaneously, and with collaborative - multimedial. The values \u200b\u200bof the measured values \u200b\u200bof x1, ..., CP are determined on the basis of the cumulative equations;

F1 (X1, ..., xm, x11, ..., x1n);

F2 (x1, ..., xm, x21, ..., x1n);

Fn (x1, ..., xm, hk1, ..., hkn),

where x11, x21, ...................hk n is the values \u200b\u200bintended direct methods.

Joint measurements are based on known equations reflecting existing communication between object properties in nature, i.e. Between values.

Absolute measurements - measurements based on direct measurements of one or more of the main values \u200b\u200band use of physical constants.

Relative measurements - obtaining the ratio of the value to the same name, which plays the role of a unit, or a change in the value with respect to the same-name value taken for the original.

Single measurements - the measurement performed once (measuring the specific time by the clock).

Multiple measurements of measurements of the same physical quantity, the result of which is obtained from several measurements following each other. Typically, the multiple dimensions are considered those that are produced over three times.

TECHNICAL MEASUREMENTS - Measurements performed using operations of measurements in order to control and control scientific experiments, control of product parameters, etc. (Air pressure measurement in the automotive chamber).

Metrological measurements - measurements with the help of standards and exemplary measuring instruments for the purpose of innovation of units of physical quantities or transmitting their size to the measurement tools.

Equimed measurements - a number of measurements of any magnitude made by the same measurement to the same conditions in the same conditions.

Alignment measurements - a number of measurements of any magnitude made different with accuracy with measurement tools and in different conditions.

Static measurements - measurements of the physical quantity taken in accordance with a specific measuring task for the constant measurement time (measuring the size of the part at normal temperature).

Dynamic measurements of the measurements of the physical size, the size of which changes over time (measurement of the distance to the ground level with a declining aircraft).

Measurement tools

Measures are the technical means used in measurements and having normalized metrological properties. The correct definition of the measured value in the process of its measurements depends on the measurement tools. Measurement tools include: Measures: Measuring instruments, Measuring Installations, Measuring systems.

Measure - measurement means intended to reproduce the physical size of the specified size (weight measure weight, the generator is a measure of the frequency of electrical oscillations). Measures, in turn, are divided into unambiguous and multivalued.

Unambiguous mea Merareproducing the physical size of the same size (flat-parallel terminal measure length, normal element, constant capacity capacitor),

the multi-valued measure that reproduces a number of single physical quantities of various sizes (ruler: millimeter divisions, condenser variable capacity).

A set of measures is a specially selected set of measures applied not only separately, but also in various combinations in order to reproduce a number of single-dimensional values \u200b\u200bof various sizes (a set of giri, a set of flat-parallel terminal lengths).

Measuring instrument Measurement means intended to generate a signal of measuring information in the form available for direct perception by the observer. Measurement results are issued in detaching devices that can be scales, digital and recorded.

The scale counting devices consist of a scale representing the set of marks and numbers depicting a number of consecutive values \u200b\u200bof the measured value, and the pointer (arrows, the electron beam and others) associated with the movable instrument system.

Scale marks with presented numeric values \u200b\u200bare called numeric marks. The main characteristics of the scale - the length of the scale dividing the distance between the axes of two adjacent scales, and the division price of the scale representing the value of the measured value causing the movement of the pointer to one division.

It is also accepted to allocate concepts: measurement range and indication range.

The measurement range is a part of the test range for which the limits of the permissible errors of measuring instruments are normalized. The smallest I. the greatest value The measurement range is called the lower and upper measurement limits accordingly.

The value of the value determined by the measurement toilet device and expressed in the adopted units of this value is called the measurement tool.

The measured value is determined or by multiplying the number of divisions of the scale on the price of dividing the scale or multiplying the numerical value, read on the scale, on a permanent scale.

Currently, either mechanical or light digital reading devices have widespread.

Registering reading devices consist of a writing or printing mechanism and tape. The simplest writing device is a feather filled with ink, fixing the measurement result on paper tape. In more complex devices, recording the measurement result can be carried out by a light or electronic beam, the movement of which depends on the values \u200b\u200bof the measured values.

Physics is experimental science. Its laws are based on the facts established by the experimental way. However, only experimental methods physical research It is not enough to get a complete picture of the phenomena studied by physics.

Modern physics widely uses theoretical methods of physical research that provide for the analysis of data obtained as a result of experiments, the formulation of the laws of nature, an explanation of concrete phenomena based on these laws, and most importantly - predictions and theoretical justification (with extensive use mathematical methods) New phenomena.

Theoretical studies are conducted not with a specific physical body, but with its idealized analogue - physical modelwhich has a small number of basic properties of the body under study. For example, during the study of certain types of mechanical movement, the physical body model is used - a material point.

This model is used if the sizes of the body are not essential for theoretical description of its movement, that is, in the model " material point»Consider only body weight, and do not take into account the body shape and its size.

How to measure physical quantity

Definition 1.

The physical value is a characteristic that is common to many material objects or phenomena in qualitative terms, but may acquire an individual value for each of them.

The measurement of physical quantities is called the sequence of experimental operations to find the physical size characterizing the object or phenomenon. Measure means to compare the measured value on the other, uniform with it the value adopted for the standard.

The measurement is completed by determining the degree of approximation of the value found to the true or to true average. True averages are characterized by values \u200b\u200bthat are statistical, for example, medium height Human, average energy of gas molecules and the like. Parameters such as body weight or its volume are characterized by a true value. In this case, we can talk about the degree of approximation of the found medium value of the physical value to its true meaning.

Measurements can be as direct when the desired value is found directly according to the experimental data and indirectly, when the final answer to the question is found through the known relationships between the physical quantity. We are also interested in the values \u200b\u200bthat can be obtained experimentally using direct measurements.

The path, weight, time, strength, tension, density, pressure, temperature, illumination are far from all examples of the physical quantities with which many met during the study of physics. Measure physical quantity - it means to compare it with a homogeneous value taken per unit.

Measurement are straight and indirect. In the case of direct measurements, the magnitude is compared with its unit (meter, second, kilogram, amp, etc.) with a measuring instrument, chanting in relevant units.

The main experimentally measured values \u200b\u200bare the distance, time and weight. They are measured, for example, with the help of roulette, hours and scales (or weights), respectively. There are also instruments for measuring complex quantities: speedometers are used to measure the speed of movement of the body, for determining the power of the electric current - ammeters, etc.

Main types of measurement errors

The imperfection of measuring instruments and human senses, and often - and the nature of the most measured value leads to the fact that the result for any measurement is obtained with a certain accuracy, that is, the experiment does not give the true meaning of the measured value, but rather close.

The accuracy of measurement is determined by the proximity of this result to the true value of the measured value or to the true average, the quantitative measure of the measurement accuracy is the error. In general, indicate absolute error Measurements.

The main types of measurement errors include:

1. Rough errors (misses), which arise as a result of negligence or inattention experimenter. For example, the countdown of the measured value is randomly spent without the necessary devices, the figure is incorrectly read on the scale and the like. These errors are easy to avoid.
2. Random errors occur for various reasons whose action is different in each of the experiments, they cannot be provided in advance. These errors are subject to statistical laws and are calculated using mathematical statistics methods.
3. Systematic errors occur as a result of the wrong method of measurement, malfunction of instruments, etc. One of the types of systematic errors - the errors of the instruments that determine the accuracy of the measurement of the instruments. When reading the measurement result is inevitably rounded, given the price of fission and, accordingly, the accuracy of the device. These types of errors cannot be avoided and they must be taken into account along with random errors.

In the proposed methodical instructions The final formulas of the theory of the errors necessary for mathematical processing of measurement results are presented.

Square in the SI system

The area, volume and speed are derived units, their dimension occurs from the main units of measurement.

Calculations also use multiple units, to a whole degree of dozens exceed the main unit of measurement. For example: 1 km \u003d 1000 m, 1 dm \u003d 10 cm (centimeters), 1 m \u003d 100 cm, 1 kg \u003d 1000 or private units, to a whole degree of dozens of less than the set unit of measurement: 1 cm \u003d 0.01 m , 1 mm \u003d 0.1 cm.

One-time units are somewhat different: 1 min. \u003d 60 s, 1 h. \u003d 3600 s. Private is only 1 ms (millisecond) \u003d 0.001 s and 1 μs (microsecond) \u003d 10-6c.

Figure 1. List of physical quantities. Author24 - Internet Exchange student work

Measurements and measuring instruments

Measurements and measuring instruments include:

1. Measuring instruments - devices that measure physical quantities.
2. Scalar physical quantities are physical quantities that only specify numerical values.
3. Physical quantity - physical property The material object, physical phenomenon, a process that can be characterized quantitatively.
4. Vector physical quantities - physical quantities characterizing a numerical value and direction. The value of the vector value is called its module.
5. Length is the distance from the point to the point.
6. The area is the value that determines the size of the surface, one of the main properties of geometric shapes.
7. The volume is the capacity of the geometric body, or part of the space bounded by closed surfaces.
8. The movement of the body is a directional segment, carried out from the initial position of the body in its final position.
9. Mass - the physical value, which is one of the main characteristics of the body, is usually indicated by the Latin letter M.
10. The force of attraction is the force with which the Earth attracts objects.