Lecture Property. Value. Basic measurement equation. Measurements. Review the definition of scoring, scoring, and measurement. Highlight their common and distinctive features The term physical quantity denotes a property
Download from Depositfiles
Lecture 1.Property. Value. Basic measurement equation
2. Measurements
Quantities, measurements and measuring instruments are studied in detail in the course "Metrology", which will be read to you in the fourth year. Here we will consider the main points, the knowledge of which we will need in the course "Geodesic Instruments and Measurements".
1. Property. Value. Basic measurement equation
All objects of the surrounding world are characterized by their properties.
For example, you can name such properties of objects as color, weight, length, height, density, hardness, softness, etc. However, from the fact that an object is colored or long, we learn nothing more than that it has the property of color or extension.
For a quantitative description various properties, processes and physical bodies the concept of magnitude is introduced.
All quantities can be divided into two types:real And ideal .
Ideal quantities relate mainly to mathematics and are a generalization (model) of specific real concepts. We are not interested in them.
Real values are divided, in turn, byphysical And non-physical .
TO non-physical it is necessary to attribute the values inherent in the social (non-physical) sciences - philosophy, sociology, economics, etc. These values are of no interest to us.
Physical a quantity in the general case can be defined as a quantity inherent in material objects (processes, phenomena) studied in the natural (physics, chemistry) and technical sciences. It is these values that are of interest to us.
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.
For example, every object on Earth has such a property as weight. If you take several apples, then each of them has a weight. But, at the same time, the weight of each apple will be different from the weight of other apples.
Physical quantities can be divided intomeasurable And evaluated.
Physical quantities for which, for one reason or another, a measurement cannot be performed or a unit of measurement cannot be entered, can only be estimated. These physical quantities are called evaluated . evaluation of such physical quantities produced using conditional scales. For example, the intensity of earthquakes is estimated by Richter scale, the hardness of minerals - on the Mohs scale.
According to the degree of conditional independence from other quantities, physical quantities are divided into main (conditionally independent),derivatives (conditionally dependent) andadditional .
All modern physics can be built on seven basic quantities that characterize the fundamental properties of the material world. These includeseven physical quantities chosen inSI system as major , And two additional physical quantities.
With the help of seven basic and two additional quantities, introduced solely for convenience, the whole variety of derivative physical quantities is formed and a description of the properties of physical objects and phenomena is provided.
According to the presence of dimensions, physical quantities are divided intodimensional , i.e. having dimensions, anddimensionless .
concept dimensions of a physical quantity was introduced Fourier in 1822.
Dimension
quality
its characteristic and is indicated by the symbol 
derived from the word dimension
(English - size, dimension). Dimension major
physical quantities are denoted by the corresponding capital letters. For example, for length, mass and time
The dimension of a derivative of a physical quantity is expressed in terms of the dimensions of the basic physical quantities using a power monomial:
Where 
, 
,
, … are the dimensions of the main physical quantities;
, 
,
, … are dimensional indicators.
Moreover, each of the dimension indicators can be positive or negative, integer or fractional number, as well as zero.
If all dimensions zero , then this quantity is called dimensionless .
Size measured value isquantitative her characteristic.
For example, the length of a board is a quantitative characteristic of a board. The very same length can be determined only as a result of measurement.
A set of numbers representing homogeneous quantities of different sizes should be a set of identically named numbers. This naming is unit of physical quantity or her share. The same example with the length of the board. There is a set of numbers characterizing the length of various boards: 110, 115, 112, 120, 117. All numbers are called centimeters. The naming centimeter is a unit of physical quantity, in this case a unit of length.
For example, meter, kilogram, second.
For example, 54.3 meters, 76.8 kilograms, 516 seconds.
For example, 54.3, 76.8, 516.
All three of these parameters are related to each other by the relation
, (3.1) which is calledbasic measurement equation
.
2. Measurements
It follows from the basic measurement equation thatdimension - this is the definition of the value of a quantity, or, in other words, it is a comparison of a quantity with its unit. Physical quantities are measured using technical means. We can give the following definition of a dimension.
This definition contains four features of the concept of measurement.
1. Only physical quantities can be measured(i.e. properties of material objects, phenomena, processes).
2. Measurement is the evaluation of a quantity by experience., i.e. it's always an experiment.
It is impossible to call a measurement the calculated determination of a quantity according to formulas and known initial data.
3. The measurement is carried out using special technical means - carriers of the sizes of units or scales, called measuring instruments.
4. Measurement is the determination of the value of a quantity, i.e. is the comparison of a quantity with its unit or scale. This approach has been developed by centuries of measurement practice. It fully corresponds to the content of the concept of “measurement”, which was given more than 200 years ago by L. Euler: “ It is impossible to determine or measure one quantity otherwise than by taking as known another quantity of the same kind and indicating the ratio in which it is to it. » .
The measurement of a physical quantity includes two (in general, there may be several) stages:
A) comparison of the measured value with the unit;
b) converting to a usable form (various ways indication).
The measurements are:
A) measuring principle is the physical phenomenon or effect underlying the measurements;
b) measurement method– reception or a set of methods for comparing the measured physical quantity with its unit in accordance with the implemented measurement principle. The measurement method is usually determined by the design of measuring instruments.
All possible measurements encountered in human practice can be classified in several directions.
1. Classification by types of measurements :
A) direct measurement - a measurement in which the desired value of a physical quantity is obtained directly.
Examples: measuring the length of a line with a measuring tape, measuring horizontal or vertical angles with a theodolite;
b) indirect measurement – determination of the desired value of a physical quantity based on the results of direct measurements of other physical quantities functionally related to the sought value.
Example 1. Measurement of line lengths by the parallax method, in which the horizontal angle is measured on marks of the base rail, the distance between which is known; the desired length is calculated by formulas relating this length to the horizontal angle and basis.
Example 2. Measuring the length of a line with a rangefinder. In this case, not the length of the line itself is directly measured, but the time of passage of an electromagnetic pulse between the emitter and the reflector installed above the points between which the line length is measured.
Example 3. Determining the spatial coordinates of a point earth's surface using the Global Navigation Satellite System (GNSS). In this case, it is not the coordinates or even the lengths that are measured, but again the time it takes for the signal to travel from each satellite to the receiver. According to the measured time, the distances from the satellites to the receiver are indirectly determined, and then, again, indirectly, the coordinates of the standing point.
V) joint measurements - simultaneous measurements of two or more dissimilar quantities to determine the relationship between them.
Example. Measurement of the length of a metal rod and the temperature at which the length of the rod is measured. The result of such measurements is the determination of the coefficient of linear expansion of the metal from which the rod is made, due to temperature changes.
G) aggregate measurements - simultaneous measurements of several quantities of the same name, in which the desired values of the quantities are determined by solving a system of equations obtained by measuring these quantities in various combinations.
2. Classification by measurement methods :
A) direct evaluation method- a method in which the value of a quantity is determined directly by the indicating measuring instrument;
examples measuring pressure with a barometer or temperature with a thermometer;
b) measure comparison method– a method of measurement in which the quantity being measured is compared with the quantity reproducible by the measure;
examples:
applying a ruler with divisions to any part, in fact, they compare its size with the unit stored by the ruler, and, having counted, they get the value of the quantity (length, height, thickness and other parameters);
by using measuring device compare the size of the value (for example, the angle) converted into the movement of the pointer (alidade), with the unit stored by the scale of this device (horizontal circle, the division of the circle is a measure), and take a reading.
A characteristic of measurement accuracy is its error or uncertainty.
When making measurements, the real object of measurement is always replaced by its model, which, due to its imperfection, differs from the real object. As a result, the values characterizing the real object will also differ from the similar values of the same object. This leads to inevitable measurement errors, which are generally divided into random and systematic.
Measurement method. The choice of the measurement method is determined by the accepted model of the measurement object and available means measurements. When choosing a measurement method, they ensure that the error of the measurement method, i.e. the component of the systematic measurement error, due to the imperfection of the accepted model and measurement method (otherwise, the theoretical error), did not noticeably affect the resulting measurement error, i.e. did not exceed 30% from her.
Object model. Changes in the measured parameters of the model during the observation cycle, as a rule, should not exceed 10% from the given measurement error. If alternatives are possible, then economic considerations are also taken into account: unnecessary overestimation of the accuracy of the model and measurement method leads to unreasonable costs. The same applies to the choice of measuring instruments.
Measuring instruments. The choice of measuring instruments and auxiliary devices is determined by the measured value, the accepted measurement method and the required accuracy of the measurement results (accuracy standards). Measurements using measuring instruments of insufficient accuracy are of little value (even meaningless), since they can lead to incorrect conclusions. The use of overly accurate measuring instruments is economically unprofitable. The range of changes in the measured value, the measurement conditions, the performance of measuring instruments, and their cost are also taken into account.
The main attention is paid to the errors of measuring instruments. It is necessary that the total error of the measurement result 
was less than the maximum permissible measurement error 
, i.e.
— marginal error due to the operator.<
Physical quantity and its characteristics.
All objects of the material world have a number of properties that make it possible to distinguish one object from another.
Property object - ϶ᴛᴏ an objective feature that manifests itself during its creation, operation and consumption.
The property of an object must be expressed qualitatively - in the form of a verbal description, and quantitatively - in the form of graphs, numbers, diagrams, tables.
Metrological science deals with the measurement of the quantitative characteristics of material objects - physical quantities.
Physical quantity- ϶ᴛᴏ property, qualitatively inherent in many objects, and quantitatively individual for each of them.
Eg, mass have all material objects, but each of them mass value individual.
Physical quantities are divided into measurable And evaluated.
measured physical quantities are expressed quantitatively in the form of a certain number of established units of measurement.
Eg, the voltage value in the network is 220 IN.
Physical quantities that do not have a unit of measurement are only estimated. For example, smell, taste. Their evaluation is carried out by tasting.
Some quantities can be estimated on a scale. For example: the hardness of the material - on the Vickers, Brinell, Rockwell scale, the strength of the earthquake - on the Richter scale, the temperature - on the Celsius (Kelvin) scale.
Physical quantities can be qualified by metrological features.
By types of events they are divided into
A) real describing the physical and physico-chemical properties of substances, materials and products from them.
For example, mass, density, electrical resistance (to measure the resistance of a conductor, a current must pass through it, such a measurement is called passive).
b) energy describing the characteristics of the processes of transformation, transmission and use of energy.
These include: current, voltage, power, energy. These physical quantities are called active. Οʜᴎ do not require an auxiliary power source.
There is a group of physical quantities that characterize the course of processes in time, for example, spectral characteristics, correlation functions.
By accessories to different groups of physical processes, the quantities are
spatio-temporal
mechanical,
electrical,
magnetic,
thermal,
acoustic,
light,
physicochemical,
· ionizing radiation, atomic and nuclear physics.
By degree of conditional independence physical quantities are divided by
main (independent),
Derivatives (dependent),
additional.
By dimension physical quantities are divided into dimensional and dimensionless.
An example dimensional magnitude is force, dimensionless- level sound power.
To quantify a physical quantity, the concept is introduced size physical quantity.
The size of a physical quantity- this is the quantitative certainty of a physical quantity inherent in a particular material object, system, process or phenomenon.
Eg, each body has a certain mass, therefore, they can be distinguished by mass, ᴛ.ᴇ. according to the size of the physical quantity.
The expression of the size of a physical quantity in the form of a certain number of units accepted for it is defined as the value of a physical quantity.
The value of the physical quantity - this is an expression of a physical quantity in the form of a certain number of units of measurement accepted for it.
Measurement process - ϶ᴛᴏ the procedure for comparing an unknown quantity with a known physical quantity (comparable) and in this connection the concept is introduced true value physical quantity.
The true value of a physical quantity- ϶ᴛᴏ the value of a physical quantity, ĸᴏᴛᴏᴩᴏᴇ characterizes the corresponding physical quantity in a qualitative and quantitative way.
The true value of independent physical quantities is reproduced in their standards.
The true value is rarely used, more used actual value physical quantity.
The actual value of a physical quantity- ϶ᴛᴏ value obtained experimentally and somewhat close to the true value.
Previously, there was the concept of ʼʼmeasured parametersʼʼ, now, according to the regulatory document RMG 29-99, the concept of ʼʼmeasured valuesʼʼ is recommended.
There are many physical quantities and they are systematized. A system of physical quantities is a set of physical quantities formed in accordance with accepted rules, when some quantities are taken as independent, while others are defined as functions of independent quantities.
In the name of the system of physical quantities, the symbols of quantities are used, which are accepted as the main ones.
For example, in mechanics, where the length is taken as basic - L , weight - m and time - t , the name of the system, respectively - Lm t .
The system of base quantities corresponding to the international system of units SI is expressed by the symbols LmtIKNJ , ᴛ.ᴇ. symbols of base units are applied: length - L , weight - M , time - t , current strength - I , temperature - K, the amount of substance - N , the power of light - J .
Basic physical quantities do not depend on the values of other quantities of this system.
Derived physical quantity- ϶ᴛᴏ is a physical quantity included in the system of quantities and determined through the main quantities of this system. For example, force is defined as mass times acceleration.
3. Units of measurement of physical quantities.
A unit of measurement of a physical quantity is usually called a quantity, which, by definition, is assigned a numerical value equal to 1 and which is used for the quantitative expression of physical quantities homogeneous with it.
Units of physical quantities are combined into a system. The first system was proposed by Gauss K (millimeter, milligram, second). Now the SI system is in effect, previously there was a standard of the CMEA countries.
Units of measurement are divided into basic, additional, derivative and off-system.
In the SI system seven basic units:
· length (meter),
· mass (kilogram),
· time (second),
· thermodynamic temperature (kelvin),
· amount of substance (mol),
· electric current (ampere),
· light intensity (candela).
Table 1
Designation of base units of the SI system
| Physical quantity | Unit of measurement | |||
| Name | Designation | Name | Designation | |
| Russian | international | |||
| main | ||||
| Length | L | meter | m | m |
| Weight | m | kilogram | kg | kg |
| Time | t | second | With | s |
| The strength of the electric current | I | ampere | A | A |
| Thermodynamic temperature | T | kelvin | TO | TO |
| Amount of substance | n,v | mole | mole | mol |
| The power of light | J | candela | cd | cd |
| additional | ||||
| flat corner | - | radian | glad | rad |
| Solid angle | - | steradian | Wed | sr |
Note. A radian is the angle between two radii of a circle, the arc between which is equal in length to the radius. In degrees, a radian is 57 0 17 ’ 48 ’’ .
Steradian - ϶ᴛᴏ solid angle, the vertex of which is located in the center of the sphere and which cuts out on the surface of the sphere an area equal to the area of a square with a side length equal to the radius of the sphere. The solid angle is measured by determining flat angles and performing additional calculations using the formula:
Q \u003d 2p (1 - cosa / 2),
Where Q- solid angle,a - flat angle at the top of the cone formed inside the sphere by the given solid angle.
Body corner 1 Wed corresponds to a flat angle equal to 65 0 32 ’ , cornerp cf - flat corner 120 0 , corner2pav - 180 0 .
Additional SI units are used to form units of angular velocity, angular acceleration, and some other quantities.
By themselves, radians and steradians are mainly used for theoretical constructions and calculations, because most practical angle values (full angle, right angle, etc.) in radians are expressed in transcendental numbers ( 2p, p/2).
Derivatives call the units of measurement obtained using the equations of communication between physical quantities. For example, the SI unit of force is Newton ( H ):
H = kg∙m/s 2 .
Despite the fact that the SI system is universal, it allows the use of some off-system units, which have found wide practical application (for example, a hectare).
Off-system called units that are not included in any of the generally accepted systems of units of physical quantities.
For many practical cases, the chosen sizes of physical quantities are inconvenient - too small or too large. For this reason, in the practice of measurements, they often use multiples And valley units.
Multiple It is customary to call a unit an integer number of times greater than a system or non-system unit. For example, a multiple unit 1km = 1000 m.
Dolny It is customary to call a unit, an integer number of times less than a system or non-system unit. For example, a fractional unit 1 cm = 0,01 m.
After the adoption of the metric system of measures, a decimal system for the formation of multiples and submultiples was adopted, corresponding to the decimal system of our numerical account. Eg, 10 6 – mega, A 10 -6 – micro.
Physical quantity and its characteristics. - concept and types. Classification and features of the category "Physical quantity and its characteristics." 2017, 2018.
Measurement- a set of predominantly experimental operations performed with the help of a technical tool that stores a unit of quantity, which allows you to compare the measured value with its unit and obtain
the desired value of the quantity. This value is called the measurement result.
To establish the difference in the quantitative value of the displayed object, the concept of a physical quantity is introduced.
Physical quantity (PV) one of the properties of a physical object (phenomenon, process) is called, which is qualitatively common for many physical objects, but quantitatively individual for each object (Fig. 4.1).
For example, density, voltage, refractive index, etc.
So, using a measuring device, for example, a DC voltmeter, we measure the voltage in volts of a particular electrical circuit, comparing the position of the pointer (arrow) with the unit of electrical voltage stored by the voltmeter scale. The voltage value found as a number of volts represents the result of the measurement.
Rice. 4.1.
The hallmark of a quantity can be a unit of measurement, a measurement procedure, a reference material, or a combination of both.
With practical necessity, it is possible to measure not only a physical quantity, but also any physical and non-physical object.
If the mass of a body is 50 kg, then we are talking about the size of a physical quantity.
The size of a physical quantity- quantitative certainty of a physical quantity inherent in a specific material object (phenomenon, process).
true size physical quantity is an objective reality, which does not depend on whether the corresponding characteristic of the object's properties is measured or not. Actual value physical quantity is found experimentally. It differs from the true value by the magnitude of the error.
The size of the quantity depends on which unit is used in the measurement of the quantity.
The size can be expressed as an abstract number, without specifying the unit of measurement, which corresponds to the numerical value of a physical quantity. A quantitative assessment of a physical quantity, represented by a number indicating the unit of this quantity, is called the value of a physical quantity.
We can talk about the sizes of different units of a given physical quantity. In this case, the size of, for example, a kilogram differs from the size of a pound (1 lb. = 32 lots = 96 spools = 409.512 g), a pood (1 p. = 40 lb. = 1280 lots = 16.3805 kg), etc. d.
Consequently, different interpretations of physical quantities in different countries must be taken into account, otherwise this can lead to insurmountable difficulties, even to catastrophes.
For example, in 1984, a Canadian Boeing-647 passenger aircraft made an emergency landing at an automobile test site after the engines failed while flying at an altitude of 10,000 meters due to spent fuel. The explanation for this incident was that the instruments on the plane were calibrated in liters, while the instruments of the Canadian airline that refueled the aircraft were calibrated in gallons (approximately 3.8 liters). Thus, almost four times less fuel was filled than required.
So, if there is some value x, the unit of measurement accepted for it is [X], then the value of a specific physical quantity can be calculated by the formula
X = q [X], (4.1)
Where q- numerical value of a physical quantity; [ X] is a unit of physical quantity.
For example, pipe length l= 5m, where l is the length value, 5 is its numerical value, m is the unit of length accepted in this case.
Equation (4.1) is called the main measurement equation, showing that the numerical value of the quantity depends on the size of the accepted unit of measurement.
Depending on the area of comparison, the values can be homogeneous And heterogeneous. For example, diameter, circumference, wavelength, as a rule, are considered as homogeneous quantities related to the quantity called length.
Within the framework of one system of quantities, homogeneous quantities have the same dimension. However, quantities of the same dimension are not always homogeneous. For example, the moment of force and energy are not homogeneous quantities, but have the same dimension.
Value system is a set of quantities together with a set of consistent equations relating these quantities.
Basic quantity represents a value that is conditionally chosen for a given system of quantities and is included in the set of basic quantities. For example, the basic quantities of the SI system. The main quantities are not related to each other.
Derived value system of quantities is determined through the basic quantities of this system. For example, in a system of quantities where the main quantities are length and mass, mass density is a derived quantity, which is defined as the quotient of mass divided by volume (length to the third power).
Multiple unit obtained by multiplying the given unit of measure by an integer greater than one. For example, a kilometer is a decimal multiple of a meter; and the hour is a non-decimal multiple of the second.
submultiple unit is obtained by dividing the unit of measure by an integer greater than one. For example, a millimeter is a decimal unit, a fraction of a meter.
Off-system unit measurement does not belong to this system of units. For example, day, hour, minute are non-systemic units of measurement in relation to the SI system.
Let's introduce another important concept - measurement conversion.
It is understood as the process of establishing a one-to-one correspondence between the sizes of two quantities: the converted value (input) and the one transformed as a result of the measurement (input).
The set of sizes of the input variable subjected to transformation with the help of a technical device - a measuring transducer, is called conversion range.
Measuring transformation can be carried out in different ways depending on the types of physical quantities, which are usually divided into three groups.
First group represents quantities on the set of sizes of which only their ratios are defined in the form of comparisons "weaker - stronger", "softer - harder", "colder - warmer", etc.
These relationships are established on the basis of theoretical or experimental studies and are called order relations(equivalence relations).
To quantities first group include, for example, the strength of the wind (weak, strong, moderate, storm, etc.), hardness, characterized by the ability of the body under study to resist indentation or scratching.
Second group represents quantities for which order (equivalence) relations are determined not only between the sizes of the quantities, but also between the differences in the quantities in pairs of their sizes.
These include, for example, time, energy, temperature, determined by the scale of a liquid thermometer.
The possibility of comparing the differences in the sizes of these values lies in the determination of the values of the second group.
So, when using a mercury thermometer, temperature differences (for example, in the range from +5 to +10 ° C) are considered equal. Thus, in this case, both the ratio of the order of magnitude (25 "warmer" than 10°С) and the equivalence relation between the differences in pairs of sizes of quantities take place: the difference of the pair (25–20°С) corresponds to the difference of the pair (10– 5°C).
In both cases, the order relation is unambiguously established by means of a measuring instrument (measuring transducer), which is said liquid thermometer.
It is easy to conclude that temperature belongs to the values of both the first and second groups.
Third group quantities is characterized by the fact that on the set of their sizes (except for the indicated order and equivalence relations inherent in the quantities of the second group), it is possible to perform operations similar to addition or subtraction (additivity property).
The values of the third group include a significant number of physical quantities, for example, length, mass.
So, two bodies weighing 0.5 kg each, placed on one of the cups of equal-arm scales, are balanced by a weight of 1 kg, placed on the other bowl.
A physical quantity is one of the properties of a physical object (phenomenon, process), which is qualitatively common for many physical objects, while differing in quantitative value.
The purpose of measurements is to determine the value of a physical quantity - a certain number of units adopted for it (for example, the result of measuring the mass of a product is 2 kg, the height of a building is 12 m, etc.).
Depending on the degree of approach to objectivity, the true, actual and measured values of a physical quantity are distinguished.
This is a value that ideally reflects the corresponding property of the object in qualitative and quantitative terms. Due to the imperfection of the means and methods of measurement, the true values of the quantities cannot practically be obtained. They can only be imagined theoretically. And the values of the quantity obtained during the measurement, only to a greater or lesser extent approach the true value.
This is the value of a quantity found experimentally and so close to the true value that it can be used instead for this purpose.
This is the value obtained by measurement using specific methods and measuring instruments.
9. Classification of measurements according to the dependence of the measured value on time and according to the totality of the measured values.
By the nature of the change in the measured value - static and dynamic measurements.
Dynamic measurement - measurement of a quantity whose size changes over time. A rapid change in the size of the measured value requires its measurement with the most accurate determination of the moment in time. For example, measuring the distance to the level of the Earth's surface from a balloon or measuring the direct voltage of an electric current. Essentially, a dynamic measurement is a measurement of the functional dependence of the measurand over time.
Static measurement - measurement of a quantity that is accepted in in accordance with the set measurement task for not changing during the measurement period. For example, the measurement of the linear size of a manufactured product at normal temperature can be considered static, since temperature fluctuations in the workshop at the level of tenths of a degree introduce a measurement error of no more than 10 µm/m, which is insignificant compared to the manufacturing error of the part. Therefore, in this measurement task, the measured quantity can be considered unchanged. When calibrating a line measure of length on the state primary standard, thermostating ensures the stability of maintaining the temperature at the level of 0.005 °C. Such temperature fluctuations cause a thousand times smaller measurement error - no more than 0.01 µm/m. But in this measurement task, it is essential, and taking into account temperature changes in the measurement process becomes a condition for ensuring the required measurement accuracy. Therefore, these measurements should be carried out according to the method of dynamic measurements.
According to the established sets of measured values on electrical ( current, voltage, power) , mechanical ( mass, number of products, efforts); , heat power(temperature, pressure); , physical(density, viscosity, turbidity); chemical(composition, chemical properties, concentration) , radio engineering etc.
Classification of measurements according to the method of obtaining the result (by type).
According to the method of obtaining measurement results, there are: direct, indirect, cumulative and joint measurements.
Direct measurements are those in which the desired value of the measured quantity is found directly from the experimental data.
Indirect measurements are those in which the desired value of the measured quantity is found on the basis of a known relationship between the measured quantity and the quantities determined using direct measurements.
Aggregate measurements are those in which several quantities of the same name are measured simultaneously and the determined value is found by solving a system of equations that is obtained on the basis of direct measurements of the quantities of the same name.
Joint measurements are called two or more dissimilar quantities to find the relationship between them.
Classification of measurements according to the conditions that determine the accuracy of the result and according to the number of measurements to obtain the result.
According to the conditions that determine the accuracy of the result, measurements are divided into three classes:
1. Measurements of the highest possible accuracy achievable with the current state of the art.
These include, first of all, reference measurements related to the maximum possible accuracy of reproduction of the established units of physical quantities, and, in addition, measurements of physical constants, primarily universal ones (for example, the absolute value of the acceleration of gravity, the gyromagnetic ratio of the proton, etc.).
Some special measurements requiring high accuracy also belong to this class.
2. Control and verification measurements, the error of which, with a certain probability, should not exceed a certain specified value.
These include measurements performed by laboratories of state supervision over the implementation and observance of standards and the state of measuring equipment and factory measuring laboratories, which guarantee the error of the result with a certain probability, not exceeding some predetermined value.
3. Technical measurements, in which the error of the result is determined by the characteristics of the measuring instruments.
Examples of technical measurements are measurements performed during the production process at machine-building enterprises, on switchboards of power plants, etc.
According to the number of measurements, measurements are divided into single and multiple.
A single measurement is a measurement of one quantity made once. Single measurements in practice have a large error, in this regard, it is recommended to perform measurements of this type at least three times to reduce the error, and take their arithmetic mean as a result.
Multiple measurements are measurements of one or more quantities taken four or more times. A multiple measurement is a series of single measurements. The minimum number of measurements for which a measurement can be considered multiple is four. The result of multiple measurements is the arithmetic mean of the results of all measurements taken. With repeated measurements, the error is reduced.
Classification of random measurement errors.
Random error - a component of the measurement error that changes randomly during repeated measurements of the same quantity.
1) Rough - does not exceed the permissible error
2) Miss - gross error, depends on the person
3) Expected - obtained as a result of the experiment when creating. conditions
The concept of metrology
Metrology- the science of measurements, methods and means of ensuring their unity and ways to achieve the required accuracy. It is based on a set of terms and concepts, the most important of which are given below.
Physical quantity- a property that is qualitatively common to many physical objects, but quantitatively individual for each object. Physical quantities are length, mass, density, force, pressure, etc.
Unit of physical quantity that value is considered, which, by definition, is assigned a value equal to 1. For example, mass is 1kg, force is 1N, pressure is 1Pa. In different systems of units, units of the same quantity may differ in size. For example, for a force of 1kgf ≈ 10N.
The value of a physical quantity– numerical assessment of the physical value of a particular object in the accepted units. For example, the value of the mass of a brick is 3.5 kg.
Technical Dimension- determination of the values of various physical quantities by special technical methods and means. In the course of laboratory tests, the values of geometric dimensions, mass, temperature, pressure, force, etc. are determined. All technical measurements must meet the requirements of uniformity and accuracy.
Direct measurement– experimental comparison of a given value with another, taken as a unit, by reading on the scale of the device. For example, measuring length, mass, temperature.
Indirect measurements– results obtained using the results of direct measurements by calculations using known formulas. For example, determining the density, strength of the material.
Unity of measurements- the state of measurements, in which their results are expressed in legal units and measurement errors are known with a given probability. The unity of measurements is necessary in order to be able to compare the results of measurements made in different places, at different times, using a variety of instruments.
Accuracy of measurements– the quality of measurements, reflecting the closeness of the obtained results to the true value of the measured quantity. Distinguish between the true and actual value of physical quantities.
true value physical quantity ideally reflects in qualitative and quantitative terms the corresponding properties of the object. The true value is free from measurement errors. Since all values of a physical quantity are found empirically and they contain measurement errors, the true value remains unknown.
Actual value physical quantities are found experimentally. It is so close to the true value that for certain purposes it can be used instead. In technical measurements, the value of a physical quantity found with an error allowed by technical requirements is taken as a real value.
Measurement error– deviation of the measurement result from the true value of the measured quantity. Since the true value of the measured quantity remains unknown, in practice the measurement error is only approximately estimated by comparing the measurement results with the value of the same quantity obtained with an accuracy several times higher. So the error in measuring the dimensions of the sample with a ruler, which is ± 1 mm, can be estimated by measuring the sample with a caliper with an error of no more than ± 0.5 mm.
Absolute error expressed in units of the measured quantity.
Relative error- the ratio of the absolute error to the actual value of the measured quantity.
Measuring instruments - technical means used in measurements and having normalized metrological properties. Measuring instruments are divided into measures and measuring instruments.
Measure- a measuring instrument designed to reproduce a physical quantity of a given size. For example, a weight is a measure of mass.
Measuring device- a measuring instrument that serves to reproduce measurement information in a form accessible to the perception of an observer. The simplest measuring instruments are called measuring instruments. For example, ruler, caliper.
The main metrological indicators of measuring instruments are:
The scale division value is the difference in the values of the measured value corresponding to two adjacent scale marks;
The initial and final value of the scale - respectively, the smallest and largest value of the measured value indicated on the scale;
Measurement range - the range of values of the measured quantity, for which the permissible errors are normalized.
Measurement error- the result of the mutual superposition of errors caused by various reasons: the error of the measuring instruments themselves, the errors that arise when using the device and reading the measurement results and errors from non-compliance with the measurement conditions. With a sufficiently large number of measurements, the arithmetic mean of the measurement results approaches the true value, and the error decreases.
Systematic error- an error that remains constant or regularly changes during repeated measurements and occurs for well-known reasons. For example, the offset of the instrument scale.
Random error - an error in the occurrence of which there is no regular connection with previous or subsequent errors. Its appearance is caused by many random causes, the influence of which on each dimension cannot be taken into account in advance. The reasons leading to the appearance of a random error include, for example, the inhomogeneity of the material, violations during sampling, and an error in the instrument readings.
If the so-called gross error, which significantly increases the error expected under given conditions, then such measurement results are excluded from consideration as unreliable.
The unity of all measurements is ensured by the establishment of units of measurement and the development of their standards. Since 1960, the International System of Units (SI) has been operating, which has replaced a complex set of systems of units and individual non-systemic units that have developed on the basis of the metric system of measures. In Russia, the SI system has been adopted as standard, and its use has been regulated in the field of construction since 1980.
Lecture 2. PHYSICAL QUANTITIES. UNITS OF MEASUREMENT
2.1 Physical quantities and scales
2.2 Units of physical quantity
2.3. International system of units (SI system
2.4 Physical quantities of technological processes
food production
2.1 Physical quantities and scales
A physical quantity is a property that is qualitatively common for many physical objects (physical systems, their states and processes occurring in them), but quantitatively individual for each of them.
Individual in quantitative terms it should be understood that the same property for one object can be a certain number of times greater or less than for another.
Typically, the term "physical quantity" is applied to properties or characteristics that can be quantified. Physical quantities include mass, length, time, pressure, temperature, etc. All of them determine physical properties that are common in qualitative terms, their quantitative characteristics may be different.
It is advisable to distinguish physical quantities on measurable and valued. Measured FIs can be expressed quantitatively as a certain number of established units of measure. The possibility of introducing and using the latter is an important distinguishing feature of the measured PV.
However, there are properties such as taste, smell, etc. for which units cannot be entered. Such quantities can be estimated. Values are evaluated using scales.
By result accuracy There are three types of values of physical quantities: true, real, measured.
The true value of a physical quantity(true value of a quantity) - the value of a physical quantity, which in qualitative and quantitative terms would ideally reflect the corresponding property of the object.
The postulates of metrology include
The true value of a certain quantity exists and it is constant
The true value of the measured quantity cannot be found.
The true value of a physical quantity can only be obtained as a result of an endless process of measurements with an endless improvement in methods and measuring instruments. For each level of development of measuring technology, we can only know the actual value of the physical quantity, which is used instead of the true one.
The actual value of a physical quantity- the value of a physical quantity found experimentally and so close to the true value that it can replace it for the set measurement task. A typical example illustrating the development of measuring technology is the measurement of time. At one time, the unit of time - the second was defined as 1/86400 of the mean solar day with an error of 10 -7 . Currently, a second is determined with an error of 10 -14 , i.e., 7 orders of magnitude closer to the true value of the definition of time at the reference level.
The real value of a physical quantity is usually taken as the arithmetic mean of a series of values of the quantity obtained with equally accurate measurements, or the arithmetic weighted average with unequal measurements.
Measured value of a physical quantity- the value of a physical quantity obtained using a specific technique.
By types of PV phenomena divided into the following groups :
- real , those. describing the physical and physico-chemical properties of substances. Materials and products from them. These include mass, density, etc. These are passive PVs, tk. to measure them, it is necessary to use auxiliary energy sources, with the help of which a signal of measuring information is formed.
- energy - describing the energy characteristics of the processes of conversion, transmission and use of energy (energy, voltage, power. These quantities are active. They can be converted into measurement information signals without the use of auxiliary energy sources;
- characterizing the course of time processes . This group includes various kinds of spectral characteristics, correlation functions, etc.
According to the degree of conditional dependence on other PV values divided into basic and derivative
Basic physical quantity is a physical quantity included in the system of quantities and conditionally accepted as independent of other quantities of this system.
The choice of physical quantities taken as basic, and their number is carried out arbitrarily. First of all, the quantities characterizing the main properties of the material world were chosen as the main ones: length, mass, time. The remaining four basic physical quantities are chosen so that each of them represents one of the sections of physics: current strength, thermodynamic temperature, amount of matter, light intensity.
Each basic physical quantity of the system of quantities is assigned a symbol in the form of a lowercase letter of the Latin or Greek alphabet: length - L, mass - M, time - T, electric current - I, temperature - O, amount of substance - N, light intensity - J. These symbols are included in the name of the system of physical quantities. Thus, the system of physical quantities of mechanics, the main quantities of which are length, mass and time, is called the "LMT system".
Derived physical quantity is a physical quantity included in the system of quantities and determined through the basic quantities of this system.
1.3 Physical quantities and their measurements
Physical quantity - one of the properties of a physical object (physical system, phenomenon or process), which is qualitatively common for many physical objects, but quantitatively individual for each of them. It can also be said that a physical quantity is a quantity that can be used in the equations of physics, moreover, physics here means science and technology in general.
Word " magnitude" is often used in two senses: as a property in general, to which the concept of more or less is applicable, and as a quantity of this property. In the latter case, one would have to talk about the “magnitude of a quantity”, therefore, in what follows, we will talk about a quantity precisely as a property of a physical object, in the second sense - as a value of a physical quantity.
Recently, the division of quantities into physical and non-physical , although it should be noted that so far there is no strict criterion for such a division of quantities. At the same time, under physical understand the quantities that characterize the properties of the physical world and are used in the physical sciences and technology. They have units of measurement. Physical quantities, depending on the rules for their measurement, are divided into three groups:
Values characterizing the properties of objects (length, mass);
quantities characterizing the state of the system (pressure,
temperature);
Quantities characterizing processes (speed, power).
TO non-physical refer quantities for which there are no units of measurement. They can characterize both the properties of the material world and the concepts used in the social sciences, economics, and medicine. In accordance with this division of quantities, it is customary to single out measurements of physical quantities and non-physical measurements . Another expression of this approach are two different understandings of the concept of measurement:
measurement in narrow sense as an experimental comparison
one measurable quantity with another known quantity
the same quality, taken as a unit;
measurement in broad sense how to find matches
between numbers and objects, their states or processes according to
known rules.
The second definition appeared in connection with the recent widespread use of measurements of non-physical quantities that appear in biomedical research, in particular, in psychology, economics, sociology and other social sciences. In this case, it would be more correct to speak not about measurement, but about estimation of quantities , understanding evaluation as establishing the quality, degree, level of something in accordance with established rules. In other words, this is an operation of attributing by calculating, finding or determining a number to a value that characterizes the quality of an object, according to established rules. For example, determining the strength of a wind or an earthquake, grading skaters or grading students' knowledge on a five-point scale.
concept evaluation quantities should not be confused with the concept of estimating quantities, related to the fact that as a result of measurements we actually get not the true value of the measured quantity, but only its estimate, to some extent close to this value.
The concept discussed above dimension”, suggesting the presence of a unit of measurement (measure), corresponds to the concept of measurement in the narrow sense and is more traditional and classical. In this sense, it will be understood below - as a measurement of physical quantities.
The following are about basic concepts related to a physical quantity (hereinafter, all the basic concepts of metrology and their definitions are given according to the above-mentioned recommendation on interstate standardization RMG 29-99):
- the size of a physical quantity - quantitative certainty of a physical quantity inherent in a particular material object, system, phenomenon or process;
- value of a physical quantity - expression of the size of a physical quantity in the form of a certain number of units accepted for it;
- true value of a physical quantity - the value of a physical quantity, which ideally characterizes the corresponding physical quantity in qualitative and quantitative terms (can be correlated with the concept of absolute truth and obtained only as a result of an endless measurement process with endless improvement of methods and measuring instruments);
actual value of a physical quantity the value of a physical quantity obtained experimentally and so close to the true value that it can be used instead of it in the set measurement task;
unit of measurement of a physical quantity a physical quantity of a fixed size, which is conditionally assigned a numerical value equal to 1, and used to quantify physical quantities homogeneous with it;
system of physical quantities a set of physical quantities formed in accordance with accepted principles, when some quantities are taken as independent, and others are determined as functions of these independent quantities;
main physical quantity – a physical quantity included in a system of quantities and conditionally accepted as independent of other quantities of this system.
derivative physical quantity – a physical quantity included in the system of quantities and determined through the basic quantities of this system;
unit system of physical units - a set of basic and derived units of physical quantities, formed in accordance with the principles for a given system of physical quantities.
