The study of physical phenomena and their regularities, as well as the use of these regularities in human practical activity, is associated with the measurement of physical quantities.

A physical quantity is a property qualitatively common to many physical objects (physical systems, their states and processes occurring in them), but quantitatively individual for each object.

A physical quantity is, for example, mass. Different physical objects have mass: all bodies, all particles of matter, particles electromagnetic field and others. Qualitatively, all concrete realizations of mass, i.e., the masses of all physical objects, are the same. But the mass of one object can be a certain number of times greater or less than the mass of another. And in this quantitative sense, mass is a property that is individual for each object. Physical quantities are also length, temperature, electric field strength, oscillation period, etc.

Specific realizations of the same physical quantity are called homogeneous quantities. For example, the distance between the pupils of your eyes and the height eiffel tower there are specific realizations of one and the same physical quantity - length, and therefore they are homogeneous quantities. The mass of this book and the mass of the Earth's satellite Kosmos-897 are also homogeneous physical quantities.

Homogeneous physical quantities differ from each other in size. The size of a physical quantity is

quantitative content in this object of a property corresponding to the concept of "physical quantity".

The sizes of homogeneous physical quantities of various objects can be compared with each other if the values ​​of these quantities are determined.

The value of a physical quantity is an estimate of a physical quantity in the form of a certain number of units accepted for it (see p. 14). For example, the value of the length of a certain body, 5 kg is the value of the mass of a certain body, etc. An abstract number included in the value of a physical quantity (in our examples 10 and 5) is called a numerical value. In the general case, the value X of a certain quantity can be expressed as the formula

where is the numerical value of the quantity, its unit.

It is necessary to distinguish between the true and actual values ​​of a physical quantity.

The true value of a physical quantity is the value of the quantity that perfect way would reflect in qualitative and quantitative terms the corresponding property of the object.

The actual value of a physical quantity is the value of the quantity found experimentally and so close to the true value that it can be used instead of it for a given purpose.

Finding the value of a physical quantity empirically using special technical means is called measurement.

The true values ​​of physical quantities are, as a rule, unknown. For example, no one knows the true values ​​of the speed of light, the distance from the Earth to the Moon, the mass of an electron, proton and other elementary particles. We do not know the true value of our height and body weight, we do not know and cannot find out the true value of the air temperature in our room, the length of the table at which we work, etc.

However, using special technical means, it is possible to determine the actual

all these and many other values. At the same time, the degree of approximation of these actual values ​​to the true values ​​of physical quantities depends on the perfection of the technical means of measurement used in this case.

Measuring instruments include measures, measuring instruments, etc. A measure is understood as a measuring instrument designed to reproduce a physical quantity of a given size. For example, a weight is a measure of mass, a ruler with millimeter divisions is a measure of length, a measuring flask is a measure of volume (capacity), a normal element is a measure of electromotive force, a quartz oscillator is a measure of the frequency of electrical oscillations, etc.

A measuring device is a measuring instrument designed to generate a signal of measuring information in a form accessible for direct perception by observation. Measuring instruments include dynamometer, ammeter, manometer, etc.

There are direct and indirect measurements.

A direct measurement is a measurement in which the desired value of a quantity is found directly from experimental data. Direct measurements include, for example, the measurement of mass on an equal-arm scale, temperature - with a thermometer, length - with a scale ruler.

Indirect measurement is a measurement in which the desired value of a quantity is found on the basis of a known relationship between it and the quantities subjected to direct measurements. Indirect measurements are, for example, finding the density of a body by its mass and geometric dimensions, finding the electrical resistivity of a conductor by its resistance, length and cross-sectional area.

Measurements of physical quantities are based on various physical phenomena. For example, thermal expansion of bodies or the thermoelectric effect is used to measure temperature, gravity is used to measure the mass of bodies by weighing, etc. The set of physical phenomena on which measurements are based is called the principle of measurement. Measurement principles are not covered in this manual. Metrology deals with the study of the principles and methods of measurements, types of measuring instruments, measurement errors and other issues related to measurements.

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 lesser degree 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 ground level with hot air balloon or measurement constant voltage 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, measuring the linear size of a manufactured product with 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(compound, 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 various systems units units of the same value 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 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 values ​​of the scale are, respectively, the smallest and highest value 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 according to 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 the general qualitatively physical properties, 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 important hallmark 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 characteristic 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.

IN Lately All greater distribution gets the subdivision of quantities by 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 physical world and are applied 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 social sciences, economics, 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 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.

Physics, as we have already established, studies the general patterns in the world around us. To do this, scientists conduct observations of physical phenomena. However, when describing phenomena, it is customary to use not everyday language, but special words that have a strictly defined meaning - terms. Some physical terms have already met you in the previous paragraph. Many terms you just have to learn and remember their meanings.

In addition, physicists need to describe various properties (characteristics) of physical phenomena and processes, and characterize them not only qualitatively, but also quantitatively. Let's take an example.

We investigate the dependence of the time of the fall of the stone from the height from which it falls. Experience shows what more height, the longer the fall time. This is a qualitative description, it does not allow a detailed description of the result of the experiment. To understand the regularity of such a phenomenon as a fall, you need to know, for example, that with a fourfold increase in height, the time it takes for a stone to fall usually doubles. This is an example of quantitative characteristics of the properties of a phenomenon and the relationship between them.

In order to quantitatively describe the properties (characteristics) of physical objects, processes or phenomena, physical quantities are used. Examples of physical quantities known to you are length, time, mass, speed.

Physical quantities quantitatively describe properties physical bodies, processes, phenomena.

Some of the quantities you have encountered before. In mathematics lessons, when solving problems, you measured the lengths of segments, determined the distance traveled. In this case, you used the same physical quantity - length. In other cases, you found the duration of the movement of various objects: a pedestrian, a car, an ant - and also used only one physical quantity for this - time. As you have already noticed, for different objects the same physical quantity takes various meanings. For example, the lengths of different segments may not be the same. Therefore, the same value can take different meanings and be used to characterize a variety of objects and phenomena.

The need to introduce physical quantities also lies in the fact that they are used to write down the laws of physics.

In formulas and calculations, physical quantities are denoted by letters of the Latin and Greek alphabets. There are generally accepted designations, for example, length - l or L, time - t, mass - m or M, area - S, volume - V, etc.

If you write down the value of a physical quantity (the same length of the segment, having received it as a result of the measurement), you will notice that this value is not just a number. Having said that the length of the segment is 100, it is imperative to clarify in what units it is expressed: in meters, centimeters, kilometers, or something else. Therefore, they say that the value of a physical quantity is a named number. It can be represented as a number followed by the name of the unit of this quantity.

The value of a physical quantity = Number * Unit of quantity.

The units of many physical quantities (for example, length, time, mass) originally arose from the needs of everyday life. For them in different times different peoples invented different units. It is interesting that the names of many units of quantities are the same among different peoples, because when choosing these units, the dimensions of the human body were used. For example, a unit of length called a cubit was used in Ancient Egypt, Babylon, the Arab world, England, Russia.

But the length was measured not only in cubits, but also in inches, feet, leagues, etc. It should be said that even with the same names, units of the same size were different for different peoples. In 1960, scientists developed the International System of Units (SI, or SI). This system has been adopted by many countries, including Russia. Therefore, the use of units of this system is mandatory.
It is customary to distinguish between basic and derived units of physical quantities. In SI, the basic mechanical units are length, time, and mass. Length is measured in meters (m), time - in seconds (s), mass - in kilograms (kg). Derived units are formed from the basic ones, using the ratios between physical quantities. For example, a unit of area - a square meter (m 2) - is equal to the area of ​​​​a square with a side length of one meter.

In measurements and calculations, one often has to deal with physical quantities whose numerical values ​​differ many times from the unit of magnitude. In such cases, a prefix is ​​added to the name of the unit, meaning the multiplication or division of the unit by a certain number. Very often they use the multiplication of the accepted unit by 10, 100, 1000, etc. (multiple values), as well as the division of the unit by 10, 100, 1000, etc. (multiple values, i.e., fractions). For example, a thousand meters is one kilometer (1000 m = 1 km), the prefix is ​​​​kilo-.

Prefixes, meaning the multiplication and division of units of physical quantities by ten, one hundred and one thousand, are shown in Table 1.
Results

A physical quantity is a quantitative characteristic of the properties of physical objects, processes or phenomena.

A physical quantity characterizes the same property of a variety of physical objects and processes.

The value of a physical quantity is a named number.
The value of a physical quantity = Number * Unit of quantity.

Questions

1. What are physical quantities for? Give examples of physical quantities.
2. Which of the following terms are physical quantities and which are not? Ruler, car, cold, length, speed, temperature, water, sound, mass.
3. How are physical quantities recorded?
4. What is SI? What is it for?
5. Which units are called basic and which are derivatives? Give examples.
6. The mass of a body is 250 g. Express the mass of this body in kilograms (kg) and milligrams (mg).
7. Express the distance 0.135 km in meters and millimeters.
8. In practice, an off-system unit of volume is often used - a liter: 1 l \u003d 1 dm 3. In SI, the unit of volume is called the cubic metre. How many liters are in one cubic meter? Find the volume of water contained in a cube with an edge of 1 cm, and express this volume in liters and cubic meters, using the necessary prefixes.
9. Name the physical quantities that are necessary to describe the properties of such physical phenomenon like the wind. Use the information received in science lessons, as well as the results of your observations. Plan a physical experiment to measure these quantities.
10. What old and modern units length and time you know?

Physical quantities

Physical quantity– it is a characteristic of physical objects or phenomena of the material world, common to many objects or phenomena in qualitative terms, but individual in quantitative terms for each of them. For example, mass, length, area, temperature, etc.

Each physical quantity has its own qualitative and quantitative characteristics .

Qualitative characteristic is determined by what property of a material object or what feature of the material world this value characterizes. Thus, the property "strength" quantitatively characterizes such materials as steel, wood, fabric, glass and many others, while the quantitative value of strength for each of them is completely different.

To identify a quantitative difference in the content of a property in any object, displayed by a physical quantity, the concept is introduced the size of a physical quantity . This size is set during measurements- a set of operations performed to determine the quantitative value of a quantity (FZ "On ensuring the uniformity of measurements"

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.). Between the sizes of each physical quantity there are relations in the form of numerical forms (such as "greater than", "less than", "equality", "sum", etc.), which can serve as a model of this quantity.

Depending on the degree of approximation to objectivity, there are true, actual and measured values ​​of a physical quantity .

The true value of a physical quantity - this value, ideally reflecting in qualitative and quantitative terms the corresponding property of the object. 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.

The actual value of the physical quantity - it is the value of a quantity found experimentally and so close to the true value that it can be used instead of it for this purpose.

Measured value of a physical quantity - this is the value obtained during the measurement using specific methods and measuring instruments.

When planning measurements, one should strive to ensure that the range of measured quantities meets the requirements of the measurement task (for example, when monitoring, the measured quantities should reflect the relevant indicators of product quality).

For each product parameter, the following requirements must be met:

The correctness of the formulation of the measured quantity, excluding the possibility various interpretations(for example, it is necessary to clearly define in which cases the "mass" or "weight" of the product, the "volume" or "capacity" of the vessel, etc. is determined);

The certainty of the properties of the object to be measured (for example, "the temperature in the room is not more than ... ° C" allows for different interpretations. It is necessary to change the wording of the requirement in such a way that it is clear whether this requirement is established for maximum or for average temperature premises, which will be further taken into account when performing measurements);

Use of standardized terms.

Physical units

A physical quantity, which by definition is assigned a numerical value equal to one, is called unit of physical quantity.

Many units of physical quantities are reproduced by the measures used for measurements (for example, meter, kilogram). On early stages development of material culture (in slave and feudal societies) there were units for a small range of physical quantities - length, mass, time, area, volume. Units of physical quantities were chosen out of connection with each other, and, moreover, different in different countries and geographic areas. That's how it came about a large number of often identical in name, but different in size units - cubits, feet, pounds.

With the expansion of trade relations between peoples and the development of science and technology, the number of units of physical quantities increased and the need for unification of units and the creation of systems of units was increasingly felt. About units of physical quantities and their systems began to conclude special international agreements. In the 18th century In France, the metric system of measures was proposed, which later received international recognition. On its basis, a number of metric systems of units were built. Currently, there is a further ordering of units of physical quantities on the basis of international system units (SI).

Units of physical quantities are divided into systemic, i.e., units included in any system, and non-system units (for example, mm Hg, horsepower, electron volts).

System units physical quantities are divided into main, chosen arbitrarily (meter, kilogram, second, etc.), and derivatives, formed according to the equations of connection between quantities (meter per second, kilogram per cubic meter, newton, joule, watt, etc.).

For the convenience of expressing quantities that are many times larger or smaller than units of physical quantities, we use multiple units (for example, kilometer - 10 3 m, kilowatt - 10 3 W) and submultiples (for example, a millimeter is 10 -3 m, a millisecond is 10-3 s)..

In metric systems of units, multiple and unit units of physical quantities (with the exception of units of time and angle) are formed by multiplying the system unit by 10 n, where n is a positive integer or a negative number. Each of these numbers corresponds to one of the decimal prefixes used to form multiples and divisional units.

In 1960, at the XI General Conference on Weights and Measures of the International Organization of Weights and Measures (MOMV), the International System was adopted units(SI).

Basic units in the international system of units are: meter (m) - length, kilogram (kg) - mass, second (s) - time, ampere (A) - the strength of the electric current, kelvin (K) – thermodynamic temperature, candela (cd) - light intensity, mole - amount of substance.

Along with systems of physical quantities, so-called off-system units are still used in measurement practice. These include, for example: units of pressure - atmosphere, millimeter of mercury column, unit of length - angstrom, unit of heat - calorie, units of acoustic quantities - decibel, background, octave, units of time - minute and hour, etc. However, in currently there is a tendency to reduce them to a minimum.

The international system of units has a number of advantages: universality, unification of units for all types of measurements, coherence (consistency) of the system (proportionality coefficients in physical equations are dimensionless), better mutual understanding between various specialists in the process of scientific, technical and economic relations between countries.

At present, the use of units of physical quantities in Russia is legalized by the Constitution of the Russian Federation (Article 71) (standards, standards, the metric system and timekeeping are under the jurisdiction of Russian Federation) And federal law"On Ensuring the Uniformity of Measurements". Article 6 of the Law determines the use in the Russian Federation of units of the International System of Units adopted by the General Conference on Weights and Measures and recommended for use international organization legal metrology. At the same time, in the Russian Federation, non-systemic units of quantities, the name, designations, rules for writing and using which are established by the Government of the Russian Federation, may be allowed to be used along with SI units of quantities.

In practice, one should be guided by the units of physical quantities regulated by GOST 8.417-2002 “State system for ensuring the uniformity of measurements. Units of values.

Standard along with mandatory application basic and derivative units of the International System of Units, as well as decimal multiples and submultiples of these units, it is allowed to use some units that are not included in the SI, their combinations with SI units, as well as some decimal multiples and submultiples of the listed units that are widely used in practice.

The standard defines the rules for the formation of names and symbols for decimal multiples and submultiples of SI units using multipliers (from 10 -24 to 10 24) and prefixes, rules for writing unit designations, rules for the formation of coherent derived SI units

The multipliers and prefixes used to form the names and symbols of decimal multiples and submultiples of the SI units are given in Table.

Multipliers and prefixes used to form the names and symbols of decimal multiples and submultiples of SI units

Coherent derived units The international system of units, as a rule, is formed using the simplest equations of connection between quantities (defining equations), in which the numerical coefficients are equal to 1. To form derived units, the designations of quantities in the connection equations are replaced by the designations of SI units.

If the connection equation contains a numerical coefficient other than 1, then to form a coherent derivative of the SI unit, the notation of quantities with values ​​in SI units is substituted on the right side, giving, after multiplication by the coefficient, a total numerical value equal to 1.

The size of a physical quantity- quantitative certainty of a physical quantity inherent in a specific material object, system, phenomenon or process.

The broad use of the word "size" is sometimes objected to, arguing that it only refers to length. However, we note that each body has a certain mass, as a result of which bodies can be distinguished by their mass, i.e. by the size of the physical quantity (mass) of interest to us. Looking at things A And IN, one can, for example, argue that they differ from each other in length or size of length (for example, A > B). A more accurate estimate can only be obtained after measuring the length of these objects.

Often in the phrase “size of a quantity”, the word “size” is omitted or replaced by the phrase “value of a quantity”.

In mechanical engineering, the term "size" is widely used, meaning by it the value of a physical quantity - the length inherent in any part. This means that two terms (“size” and “value”) are used to express one concept “the value of a physical quantity”, which cannot contribute to the ordering of terminology. Strictly speaking, it is necessary to clarify the concept of "size" in mechanical engineering so that it does not contradict the concept of "size of a physical quantity" adopted in metrology. GOST 16263-70 gives a clear explanation on this issue.

A quantitative assessment of a specific physical quantity, expressed as a certain number of units of a given quantity, is called "the value of a physical quantity".

An abstract number included in the "value" of a quantity is called a numerical value.

There is a fundamental difference between size and value. The size of a quantity really exists, whether we know it or not. You can express the size of a quantity using any of the units of a given quantity, in other words, using a numerical value.

It is characteristic of a numerical value that when a different unit is used, it changes, while physical size magnitude remains unchanged.

If we designate the measured value through x, the unit of magnitude - through x 1 , and their ratio through q 1, then x = q 1 x 1  .

The size of x does not depend on the choice of unit, which cannot be said about numerical value q , which is entirely determined by the choice of the unit. If to express the size of the quantity x instead of the unit x 1 , use the unit x 2  , then the unchanged size x will be expressed by a different value:

x = q 2 x 2  , where n 2 n 1 .

If q = 1 is used in the above expressions, then the sizes of the units

x 1 = 1x 1  and x 2 = 1x 2 .

The sizes of different units of the same value are different. Thus, the size of a kilogram is different from the size of a pound; the size of a meter is from the size of a foot, etc.

1.6. Dimension of physical quantities

Dimension of physical quantities - this is the ratio between the units of quantities included in the equation, connecting the given quantity with other quantities through which it is expressed.

The dimension of a physical quantity is denoted dim A(from lat. dimension - dimension). Let us assume that the physical quantity A associated with x, Equation A = F(X, Y). Then the quantities X, Y, A can be represented as

X = x [X]; Y=y [Y];A = a [A],

Where A, X, Y - symbols denoting a physical quantity; a, x, y - numerical values ​​of quantities (dimensionless); [A];[X]; [Y]- corresponding units of data of physical quantities.

The dimensions of the values ​​of physical quantities and their units are the same. For example:

A=X/Y; dim(a) = dim(X/Y) = [X]/[Y].

Dimension - a qualitative characteristic of a physical quantity, giving an idea of ​​the type, nature of the quantity, its relationship with other quantities, the units of which are taken as the main ones.