Definition of a physical quantity

Classification of physical quantities.

Classification of units of physical quantities.

SECTION 1. METROLOGY. Theme 3

Topic 3. Physical quantities as an object of measurement. SI system (SI)

Study questions:

1. Definition of a physical quantity.

2. International system of units of physical quantities SI.

A physical quantity (PV) is a property of a physical object ͵ common to many objects in qualitative terms (this is a type of quantity), but individual in quantitative terms (this is the size of a quantity).

Systemic- are included in one of the accepted systems (these are all basic, derivative, multiple and submultiple units).

Off-system- are not included in any of the accepted systems of PV units (liter, nautical mile, carat, horsepower).

Multiple- ϶ᴛᴏ unit of PV, the value of which is an integer number of times greater than a system or non-system unit (for example, a unit of length 1 km = 103 m, that is, a multiple of a meter).

Dolnaya- ϶ᴛᴏ is a unit of PV, the value of which is an integer number of times less than a system or non-system unit (for example, a unit of length 1 mm = 10-3 m, that is, it is a fractional one).

The basic quantities do not depend on each other and serve as the basis for establishing relationships with other physical quantities, which are called derivatives of them. For example, in Einstein's formula E=mc2, mass is the ϶ᴛᴏ base unit and energy is the ϶ᴛᴏ derived unit.

The set of basic and derived units is usually called the system of units of physical quantities. In 1960 ᴦ. The International System of Units (Systeme International d "Unites), designated SI, was adopted. It contains the basic (meter, kilogram, second, ampere, kelvin, mole, candela), additional and derivative (radian, steradian) units of physical quantities.

In science, technology and everyday life, a person deals with various properties of the physical objects around us. Their description is made by means of physical quantities.

A physical quantity (PV) is a property of a physical object ͵ common to many objects in qualitative terms (this is the type of quantity - R), but individual in quantitative terms (this is the size of the quantity - 10 Ohm).

In order to be able to establish for each object differences in the quantitative content of the property displayed by a physical quantity, the concepts of its size and value are introduced in metrology.

The size of the PV is the quantitative content in a given object of a property corresponding to the concept of the PV - all bodies differ in mass, ᴛ.ᴇ. according to the size of this PV.

The PV value is an estimate of its size in the form of a certain number of units accepted for it. It is obtained as a result of measuring or calculating the PV.

A PV unit is a fixed-size PV that is conventionally assigned a numerical value of 1.

Example: PV - mass,

the unit of this PV is 1kᴦ.

value - the mass of the object = 5 kᴦ.

Classification of PV units

1. systemic and non-systemic

Systemic - which are included in one of the accepted systems.

* these are all basic, derivative, multiple and submultiple units.

Non-systemic - which are not included in any of the accepted systems of PV units:

liter (unit of volume),

liter (unit of volume), nautical mile

carat (a unit of mass in jewelry),

carat (unit of mass in jewelry) horsepower (obsolete

unit of power)

Definition of a physical quantity - concept and types. Classification and features of the category "Determination of a physical quantity" 2014, 2015.

Physical quantity (PV) is a property that is common in quality

nominally to many physical objects, but quantitatively

relation is individual for each physical object.

Measurement - a set of operations performed to determine

dividing the quantitative value of the quantity .

Qualitative characteristics of the measured values . quality-

a characteristic characteristic of physical quantities is the size

ness. It is denoted by the symbol dim, which comes from the word

dimension, which, depending on the context, can be translated

both as a size and as a dimension.

Measuring scales. Measurement scale- it is ordered

a set of values ​​of a physical quantity that serves

basis for its measurement.

Measurement classification

Measurements can be classified according to the following features

1. According to the method of obtaining information:

- straight are measurements in which the desired value of fi-

zic value is obtained directly;

- indirect is a measurement in which the definition is artificial

my value of a physical quantity is found on the basis of the result

tat of direct measurements of other physical quantities, functional

but related to the desired value;

- cumulative are simultaneous measurements of non-

how many quantities of the same name for which the desired value of ve-

masks are determined by solving a system of equations obtained

when measuring these quantities in various combinations;

- joint are simultaneous measurements

two or more dissimilar quantities to determine the

dependencies between them.

2. By the amount of measurement information:

Single use;

Multiple.

3. In relation to the main units:

Absolute;

Relative.

4. By the nature of the dependence of the measured value on time

static;

dynamic.

5. Depending on the physical nature of the measured quantities

measurements are divided into types:

Measurement of geometric quantities;

Measurement of mechanical quantities;

Measurement of flow parameters, flow rate, level, volume of

Pressure measurement, vacuum measurements;

Measurement of physical and chemical composition and properties of substances;

Thermophysical and temperature measurements;

Time and frequency measurement;

Measurement of electrical and magnetic quantities;

Radioelectronic measurements;

Measurement of acoustic quantities;

Optical-physical measurements;

Measurement of the characteristics of ionizing radiation and nuclear

constants.

Measurement methods

Measurement method is a technique or set of techniques

comparison of the measured value with its unit in accordance with the re-

alized measurement principle.

Measuring principle is a physical phenomenon or effect

underlying measurements. For example, the phenomenon of electric

resonance in the oscillatory circuit is the basis for measuring

the frequency of the electrical signal by the resonant method.

Methods for measuring specific physical quantities are very

varied. AT general plan distinguish the method of direct

estimates and a method of comparison with a measure.

Direct evaluation method is that the value

measured value is determined directly from the reference

measuring instrument device.

Measure comparison method is that the measured value

the mask is compared with the value reproduced by the measure.

The method of comparison with a measure has a number of varieties. This me-

opposition method, zero method, substitution method, differential

rational method, coincidences.

Contrasting method is that the measured

the value and the value reproduced by the measure, simultaneously

act on the comparison device, with which you can set

there is a relation between these quantities. For example, change

weighing on a balance scale with weights, or

measurement of DC voltage on the compensator

with a known EMF of a normal element.

Zero method is that the resulting effect

the impact of the measured quantity and measure on the comparator do-

lead to zero. For example, electrical resistance measurements

bridge with its full balancing.

substitution method lies in the fact that the measured value

the rank is replaced by a measure with a known value of the quantity. For example,

weighing with alternate placement of the measured mass and weights

on the same scale pan (Borda's method).

Differential Method is that the measured

value is compared with a homogeneous value, which has a known

value, slightly different from the value of the measured

quantities, and at which the difference between these two

quantities. For example, measuring frequency with a digital frequency

rum with a heterodyne frequency carrier.

Match method is that the difference between

measurable value and the value reproduced by the measure,

ryayut using the coincidence of scale marks or periodic signals

cash. For example, measuring the speed with a stroboscope.

It is necessary to distinguish between the measurement method and the technique

measurements.

Measurement technique is an established co-

a set of operations and rules during measurement, the implementation of which

provides measurement results with guaranteed

accuracy in accordance with the accepted method.

Measuring instruments

measuring instrument (SI) is a technical tool used

zable for measurements and having normalized metrological

characteristics.__

Measure is an SI designed to reproduce

physical quantity of a given size. For example, a weight is a measure

mass, a quartz oscillator is a measure of frequency, a ruler is a measure of length.

Multivalued measures:

Smoothly adjustable;

Measure sets;

Stores measures.

A single-valued measure reproduces a physical quantity of a single-valued

size.

A multivalued measure reproduces a series of values ​​of the same

the same physical quantity.

Measuring transducer is an SI intended

to generate a measurement information signal in the form,

convenient for transfer, further transformation, but

not amenable to direct perception by the operator.

Measuring device is an SI designed for

generating a measurement information signal in a form convenient for

for the perception of the operator. For example, voltmeter, frequency counter,

oscilloscope, etc.

Measuring setup is a set of functional

combined SI and auxiliary devices, designed

to measure one or more physical quantities and

located in one place. As a rule, measuring

installations are used for verification of measuring instruments.

Measuring system - a set of functional

combined measures, measuring instruments, measuring

converters, computers and other technical means,

located at different points of the controlled object, etc. With

the purpose of measuring one or more physical quantities,

characteristic of this object, and the generation of measuring signals

in different chains. It differs from the measurement setup in that

which generates measurement information in a form convenient for

for automatic processing and transmission.

INTRODUCTION

A physical quantity is a characteristic of one of the properties of a physical object ( physical system, phenomenon or process), which is qualitatively common to many physical objects, but quantitatively individual for each object.

Individuality is understood in the sense that the value of a quantity or the size of a quantity can be for one object a certain number of times greater or less than for another.

The value of a physical quantity is an estimate of its size in the form of a certain number of units accepted for it or a number according to the scale adopted for it. For example, 120 mm is the value of a linear value; 75 kg is the value of body weight.

There are true and real values ​​of a physical quantity. A true value is a value that ideally reflects a property of an object. Real value - the value of a physical quantity, found experimentally, close enough to the true value that can be used instead.

The measurement of a physical quantity is a set of operations for the use of a technical means that stores a unit or reproduces a scale of a physical quantity, which consists in comparing (explicitly or implicitly) the measured quantity with its unit or scale in order to obtain the value of this quantity in the form most convenient for use.

There are three types of physical quantities, the measurement of which is carried out according to fundamentally different rules.

The first type of physical quantities includes quantities on the set of dimensions of which only the order and equivalence relations are defined. These are relationships like "softer", "harder", "warmer", "colder", etc.

Quantities of this kind include, for example, hardness, defined as the ability of a body to resist the penetration of another body into it; temperature, as the degree of body heat, etc.

The existence of such relationships is established theoretically or experimentally with the help of special means of comparison, as well as on the basis of observations of the results of the impact of a physical quantity on any objects.

For the second type of physical quantities, the relation of order and equivalence takes place both between sizes and between differences in pairs of their sizes.

A typical example is the scale of time intervals. So, the differences of time intervals are considered equal if the distances between the corresponding marks are equal.

The third type is additive physical quantities.

Additive physical quantities are called quantities, on the set of sizes of which not only the order and equivalence relations are defined, but also the operations of addition and subtraction

Such quantities include, for example, length, mass, current strength etc. They can be measured in parts, and also reproduced using a multi-valued measure based on the summation of individual measures.

The sum of the masses of two bodies is the mass of such a body, which is balanced on the first two equal-arm scales.

The dimensions of any two homogeneous PV or any two sizes of the same PV can be compared with each other, i.e., find how many times one is larger (or smaller) than the other. To compare m sizes Q", Q", ... , Q (m) with each other, it is necessary to consider C m 2 of their relationship. It is easier to compare each of them with one size [Q] of a homogeneous PV, if we take it as a unit of the PV size, (abbreviated as a PV unit). As a result of such a comparison, we obtain expressions for the dimensions Q", Q", ... , Q (m) in the form of some numbers n", n", .. . ,n (m) PV units: Q" = n" [Q]; Q" = n"[Q]; ...; Q(m) = n(m)[Q]. If the comparison is carried out experimentally, then only m experiments are required (instead of C m 2), and the comparison of the sizes Q", Q", ... , Q (m) with each other can be performed only by calculations like

where n (i) / n (j) are abstract numbers.

Type equality

is called the basic measurement equation, where n [Q] is the value of the size of the PV (abbreviated as the value of the PV). The PV value is a named number, composed of the numerical value of the PV size, (abbreviated as the numerical value of the PV) and the name of the PV unit. For example, with n = 3.8 and [Q] = 1 gram, the size of the mass Q = n [Q] = 3.8 grams, with n = 0.7 and [Q] = 1 ampere, the size of the current strength Q = n [Q ] = 0.7 amperes. Usually, instead of “the size of the mass is 3.8 grams”, “the size of the current is 0.7 amperes”, etc., they say and write more briefly: “the mass is 3.8 grams”, “the current is 0.7 amperes " etc.

The dimensions of the PV are most often found as a result of their measurement. The measurement of the size of the PV (abbreviated as the measurement of the PV) consists in the fact that by experience, using special technical means, the value of the PV is found and the proximity of this value to the value that ideally reflects the size of this PV is estimated. The PV value found in this way will be called nominal.

The same size Q can be expressed in different values ​​with different numerical values ​​depending on the choice of the PV unit (Q = 2 hours = 120 minutes = 7200 seconds = = 1/12 of a day). If we take two different units and , then we can write Q = n 1 and Q = n 2, whence

n 1 / n 2 \u003d /,

i.e., the numerical values ​​of the PV are inversely proportional to its units.

From the fact that the size of the PV does not depend on its chosen unit, the condition for the unambiguity of measurements follows, which consists in the fact that the ratio of two values ​​of a certain PV should not depend on which units were used in the measurement. For example, the ratio of the speeds of a car and a train does not depend on whether these speeds are expressed in kilometers per hour or meters per second. This condition, which at first glance seems indisputable, unfortunately, cannot yet be met when measuring some PVs (hardness, photosensitivity, etc.).

1. THEORETICAL PART

1.1 The concept of a physical quantity

Weight objects of the surrounding world are characterized by their properties. Property - philosophical category, expressing such a side of an object (phenomenon, process), which determines its difference or commonality with other objects (phenomena, processes) and is found in its relationship to them. The property is a quality category. For a quantitative description of various properties of processes and physical bodies the concept of magnitude is introduced. A value is a property of something that can be distinguished from other properties and evaluated in one way or another, including quantitatively. The value does not exist by itself, it takes place only insofar as there is an object with properties expressed by this value.

An analysis of the values ​​allows us to divide them (Fig. 1) into two types: the values material form(real) and values ​​of ideal models of reality (ideal), which are mainly related to mathematics and are a generalization (model) of specific real concepts.

Real quantities, in turn, are divided into physical and non-physical. A physical quantity in the most general case can be defined as a quantity inherent in material objects (processes, phenomena) studied in the natural (physics, chemistry) and technical sciences. Non-physical quantities should include quantities inherent in the social (non-physical) sciences - philosophy, sociology, economics, etc.

Rice. 1. Classification of quantities.

The document RMG 29-99 interprets a physical quantity as one of the properties of a physical object, which is qualitatively common for many physical objects, but quantitatively individual for each of them. Individuality in quantitative terms is understood in the sense that a property can be for one object a certain number of times more or less than for another.

It is expedient to divide physical quantities into measurable and estimated ones. Measured FIs can be expressed quantitatively as a certain number of established units of measure. The possibility of introducing and using such units is an important distinguishing feature of the measured PV. Physical quantities for which, for one reason or another, a unit of measurement cannot be introduced, can only be estimated. Evaluation is understood as the operation of assigning a certain number to a given value, carried out according to established rules. Evaluation of the value is carried out using scales. A magnitude scale is an ordered set of magnitude values ​​that serves as the initial basis for measuring a given magnitude.

Non-physical quantities, for which a unit of measurement cannot in principle be introduced, can only be estimated. It should be noted that the estimation of non-physical quantities is not included in the tasks of theoretical metrology.

For a more detailed study of PV, it is necessary to classify, to identify the general metrological features of their individual groups. Possible classifications of FI are shown in fig. 2.

According to the types of phenomena, PVs are divided into:

Real, i.e. quantities describing the physical and physico-chemical properties of substances, materials and products from them. This group includes mass, density, electrical resistance, capacitance, inductance, etc. Sometimes these PVs are called passive. To measure them, it is necessary to use an auxiliary energy source, with the help of which a signal of measuring information is formed. In this case, passive PV are converted into active ones, which are measured;

Energy, i.e. quantities describing the energy characteristics of the processes of transformation, transmission and use of energy. These include current, voltage, power, energy. These quantities are called active.

They can be converted into measurement information signals without the use of auxiliary energy sources;

Characterizing the course of processes in time, This group includes different kind spectral characteristics, correlation functions and other parameters.

By belonging to different groups physical processes PVs are divided into space-time, mechanical, electrical and magnetic, thermal, acoustic, light, physico-chemical, ionizing radiation, atomic and nuclear physics.

Rice. 2. Classifications of physical quantities

According to the degree of conditional independence from other values ​​of this group, all PVs are divided into basic (conditionally independent), derivatives (conditionally dependent) and additional. Currently, the SI system uses seven physical quantities chosen as the main ones: length, time, mass, temperature, force electric current, the intensity of light and the amount of matter. Additional PVs include flat and solid angles. According to the presence of dimensions, PVs are divided into dimensional ones, i.e. dimensioned and dimensionless.

1.2 Metric system of measures

The lack of rational justifications for the choice of PV units has led to their great diversity, not only in different countries but even in different areas of the same country. This created great difficulties, especially in international relations. The metric system of measures arose, i.e. a set of PV units recommended instead of those used previously.

Units were adopted: length - meter (m), mass - kilogram (kg), volume - liter (l), time - second (s).

Decimal multiples and submultiples of PV units were also introduced, i.e., PV units that are 10 times larger and smaller to the integer power, and simple rules were established for naming multiple and submultiple units of PV using prefixes: kilo, hecto, deca, deci, centi and milli [e.g. centimeter (cm), millimeter (mm), decaliter (dal), etc.]

This gave units metric system(metric units of PV) a significant advantage over others that existed at that time. In addition, the metric units of PV made it possible not to use composite named numbers (for example, the length of 8 fathoms 3 feet 5 inches) and greatly facilitated the calculations.

1.3 Systems of units of physical quantities

Construction of units and systems of units. Previously, units of various PVs were established, as a rule, independently of each other. The only exceptions were units of length, area and volume. The main feature of modern PV units is that dependencies are established between them. At the same time, several basic units of PV are arbitrarily chosen, and all the rest - derived units of PV are obtained using dependencies (laws and definitions) linking different PV, i.e. defining equations.

Physical quantities, the units of which are taken as the main ones, are called the main PV, and the units of which are derivatives, are called the derivatives of the PV.

The set of basic and derived units of PV, covering all or some areas of physics, is called the system of units of PV.

Let us consider examples of establishing derived units of PV with the length L, mass M and time T chosen as the main PV, i.e. with the selected basic units of PV [L], [M] and [T].

Example 1. Establishing a unit of area. Let's choose some simple geometric figure, for example a circle. The size of the area s of the circle is proportional to the second power of the size of its diameter d: s = k S d 2 , where k S is the coefficient of proportionality. We will take this equation as the determining one. Putting the size of the diameter of the circle equal to the unit length, i.e. d = [L], we get [s] = k S [L] 2 . The choice of the coefficient of proportionality k S is arbitrary. Let k S = l, then [s] = [L] 2 , i.e., the area of ​​a circle with a diameter equal to a unit of length is chosen as a unit area. If [L] = 1 m, then [s] = 1 m 2. The area of ​​a circle in this case must be calculated using the formula s \u003d d 2, and the area of ​​​​a square with side b - using the formula s \u003d (4 / p) b 2.

Usually, instead of such a round unit of area, a more convenient square unit is used, which is the area of ​​a square with a side equal to a unit of length.

If k S = p/4 were adopted when establishing the round unit of area, then it would coincide with the usual square unit.

Example 2. Establishing the unit of speed. As a determining one, we will take an equation showing that the size of the speed and uniform motion is the greater, the larger size l of the distance traveled and the smaller the amount of time T spent on this path:

where k u - coefficient of proportionality.

Assuming l = [L], T = [T], we obtain the unit of speed [u]=k u k u [L] [T] -1 . If, for reasons of convenience, we set k u = l, then the unit of speed will be [u] = [L] [T] -1 . When [L] = 1 mi [T] = 1s according to the last formula [u] = 1 m/s.

Example 3. Establishing the unit of acceleration. As a defining equation, we take the definition of acceleration as the derivative of speed with respect to time: a = du/dT. Setting du = [u], dT = [T], we obtain the unit of acceleration: [a] = When [L] \u003d 1 m and [T] \u003d 1s [a] \u003d 1 m / s 2.

Example 4. Establishing the unit of force. Let us choose as the law of universal gravitation that determines the equation

f = where m 1 and m 2 are the dimensions of the masses of the bodies;

r is the size of the distance between the centers of these masses;

k f - coefficient of proportionality.

Assuming m 1 \u003d m 2 [M], r \u003d [L], we get the unit of force

or when k f =1 [f] = [M] 2 [L] -2 . With [L] = 1 m and [M] = 1 kg according to the last formula [f] = 1 kg 2 /m 2.

Choosing f = k f ma as the defining equation of Newton's second law, we obtain, similarly to the previous one, the unit of force in the form [f] = k f [M] * [a] = k f [M] [L] [T] -2, or in the form [f] \u003d [M] [L] [T] -2. With [M] = 1 kg, [L] = 1 m and [T] = 1s according to the last formula [f] = 1 kg m/s 2 .

Both received units of force are equal, but the second is widespread, and the first is rarely used (mainly in astronomy).

From the examples considered, it can be seen that with the chosen basic PV - length L, mass M and time T, the derivative unit [x] of some PV x is found through the units [L], [M] and [T] according to the formula:

[x] = k x [L] pL [M] pM [T] pT ,

where k x is an arbitrarily chosen proportionality factor;

p L , р М and р Т are positive or negative numbers.

These numbers show how the derived unit of PV changes with a change in the main one. For example, with a change in the basic unit [L] by q times, the derived unit [x] will change by q pL times. Since k x does not affect the change in [x], the nature of the change in the unit [x] with the change in the units [L], [M] and [T] is usually expressed using dimension formulas in which k x \u003d 1. In the case under consideration the dimension formula is

dimx = L pL M pL T pT ,

where the right side is called the dimension of the PV unit; the left part is the designation of this dimension (dimension);

p L , р М and р Т – dimension indicators.

From the dimension formula, it can be seen in the same way how the size of the PV derivative changes with a change in the size of the main PV with the chosen defining equation. The right side of this formula is also called the PV dimension.

Consider the general case when there are several basic PVs A, B, C, D, ..., the units of which are [A], [B], [C], [D], ..... Then, obviously, the establishment of the derivative units of PV x will be reduced to the choice of some defining equation connecting x with other (basic and derivative) PV, to bringing this equation to the form:

x = k x A pA B pB C pC D pD …,

where p A , p B , p C , p D , ... are dimensional indicators, and to the replacement of the main PV by their units:

[x] = k x [A] pA [B] pB [C] pC [D] pD …

The dimension formula in this case will look like:

dim x = A pA B pB C pC D pD …

It is known that the derived unit of the PV x has the dimension p A relative to the basic unit of the PV A, the dimension p B relative to the basic unit of the PV B, etc. (or that the derivative of the PV has the dimension p A relative to the main PV A, the dimension p B relative to the main PV B, etc.). So, having considered the dimension of speed (example 2) LT -1 , or L 1 M 0 T -1 , we can say that the speed has a dimension of 1 with respect to length, a zero dimension with respect to mass and a dimension of -1 with respect to time (a unit of speed has a dimension of 1 with respect to units of length, etc.).

If r A = r B = r C = r D = … = 0, then the derivative of the PV x is called the dimensionless PV, and its unit [x] is the dimensionless unit of the PV.

An example of a dimensionless derivative of the PV unit is the unit [φ] of the plane angle φ – radian. When this unit is established, the equation φ = = k φ (l/r) is taken as the determining one, showing that the size of the angle φ is the larger, the larger the size of the length l, the arc that subtends it, and the smaller the size of the length r of the radius of this arc. The equation accepts k φ = 1, l = [L], r= [L]. Hence [φ] = = [L] 0 and dim φ = L 0 .

If, when establishing a derivative unit of the PV in its expression through the basic units of the PV, k x = 1 is assumed, then it is called a coherent derived unit of the PV. The system of PV units, all of whose derived units are coherent, is called the coherent system of PV units.

The dimensions of the derived units of the PV x, y and z are interconnected as follows. If z = k 1 xy, then

dimz - dimх * dimу. (1.2)

If z = k 2 , then

dimz - dimх/dimу. (1.3)

If z = k 3 x n , then

dimz - (dim x) n . (1.4)

We used equalities (1.2) and (1.3) when establishing the units of acceleration and force, and equality (1.4) is a consequence of equality (1.2).

Dimension formulas can be written only for such PVs, in the measurement of which the condition of unambiguous measurements is satisfied. The dimensions of different PV may coincide (for example, the moment of force and work), and the dimensions of the same PV in different systems ax units of PV may differ (see example 4, where different constitutive equations led us to different dimensions of units of force and, consequently, to different dimensions of force). Therefore, the dimensions do not give a complete picture of the PV. However, the discrepancy between the dimensions of the left and right parts of any formula or any equation indicates the fallacy of this formula or this equation. In addition, the concept of dimension facilitates the solution of many problems. If it is previously known which FIs are involved in the process under study, then it is possible to establish the nature of the relationship between the sizes of these FIs using the analysis of dimensions. In this case, the solution of the problem often turns out to be much simpler than if it were carried out in other ways.

It is important that in the mathematical formulation physical phenomena PV symbols do not mean the PV themselves and not their sizes, but the values ​​of the PV, i.e. named numbers. For example, in the equation f = k f ma, which expresses Newton's second law, the symbols m and a mean not the PVs themselves (mass and acceleration) and not the dimensions of mass and acceleration, which cannot be multiplied by each other, but the values ​​of mass and acceleration, i.e. e. Named numbers that reflect the dimensions of mass and acceleration, and for which the operation of multiplication makes sense.

1.4 Systems of units

The first system of PV units was essentially the metric PV units mentioned above. However, only in 1832, K. Gauss proposed to continue to build systems of PV units as sets of basic and derived units. In the system he built, the basic units of PV were millimeter, milligram and second.

Subsequently, other systems of PV units appeared, also based on metric PV units, but with different base units. The most famous of these systems are as follows.

CGS system (1881). The basic units of PV are centimeter, gram, second. The system has become widespread in physics. Later, some varieties of this system were created for electric and magnetic PVs.

MTS system (1919). The main units of PV are meter, ton (1000 kg), second. This system has not received wide distribution.

ICSS system ( late XIX in). The basic units of PV are the meter, the kilogram-force, and the second. This system has become widespread in technology.

MKSA system (1901). It is sometimes called the Georgie system (after its creator). The basic units of PV are the meter, kilogram, second, and ampere. This system is currently integral part into the new international system of units

All basic and derived units of any system of PV units are called PV system units (in relation to this system). Along with systemic units, there are also so-called non-systemic units, i.e., those that are not included in the system of units of PV. All non-systemic PV units can be divided into two groups: 1) not included in any of the known systems, for example: a unit of length - x-unit, a unit of pressure - a millimeter of mercury, a unit of energy - an electron volt; 2) being non-systemic only in relation to some systems, for example: a unit of length - a centimeter - is non-systemic for all systems, except for the CGS; unit of mass - ton - off-system for all systems, except for MTS; unit of electrical capacitance - centimeter - off-system for all systems, except CGSE.

The presence of different systems of units of PV, as well as a large number off-system units of PV creates inconvenience associated with the calculations required when moving from one unit of PV to another. In connection with the growth of scientific and technical ties between countries, it became necessary to unify the PV units. As a result, a new International System of Units of PhV was created.

International system of units. In 1960, the XI General Conference on Weights and Measures approved international system units of PV SI ·.

In the USSR and in the CMEA member countries - SI is included in the CMEA standard STSEV 1052 - 78 “Metrology. Units of physical quantities” Information about the basic units of the PV SI is given in Table. one.

Two, essentially derivative, units of PV SI: a unit of a flat angle - a radian (Russian designation rad, international - rad) and a unit of solid angle - steradian (Russian designation cf, international - sr) - are not officially considered derivatives and are called additional units of PV SI . The reason for their isolation is that they are established according to the defining equations j = l/r and y = S/R 2 , where j is a flat angle whose vertex coincides with the center of an arc of length l and radius r; y is the solid angle whose vertex coincides with the center of a sphere of radius R, and which cuts out an area S on the surface of the sphere. Units

[j]=0 and [y]=

are dimensionless and, therefore, do not depend on the choice of the basic units of the PV system.

Derived units of PV SI are formed from basic and additional coherent units of PV according to the rules of formation.

Basic units of physical quantities SI Table 1.

For example: angular acceleration - radian per second squared (rad / s 2), tension magnetic field- ampere per meter (A / m), brightness - candela per square meter (cd / m 2).

The units of the FI SI, which have special names, are given in Table. 2.

The international system has the following advantages over other systems of PV units: it is universal, that is, it covers all areas of physics; coherent; its PV units are practically convenient in most cases and were widely used earlier.

Units permitted for use in the CMEA countries. The above advantages of SI as a whole do not yet allow us to assert that its units of PV are in all cases more acceptable than any others. For example, for measuring long periods of time, the month and century may be more convenient units than the second; for measuring large distances, a light year and a parsec may be more convenient units than a meter, etc.

Derived units of physical quantities SI with special names. Table 2.

2. CALCULATION PART

A task. With a voltmeter of accuracy class 4, U n = 150V, the observation result X = 100V was obtained. Determine the range in which the true value is located, the relative and absolute errors.

Solution. k =

Relative error:

True value: X and = (100 ± 6) V.

All technological human activity is associated with the measurement of various physical quantities.

A set of physical quantities is a certain system in which individual quantities are interconnected by a system of equations.

Each physical quantity must have a unit of measure. An analysis of the relationships between physical quantities shows that, independently of each other, it is possible to establish units of measurement for only a few physical quantities, and the rest can be expressed through them. The number of independently established quantities is equal to the difference between the number of quantities included in the system and the number of independent equations of connection between the quantities.

For example, if the speed of a body is determined by the formula v=L/t, then only two quantities can be set independently, and the third can be expressed through them.

Physical quantities, the units of which are established independently of others, are called basic quantities, and their units are called basic units.

The dimension of a physical quantity is an expression in the form of a power monomial, composed of the products of the symbols of the main physical quantities in various degrees and reflecting the relationship of this quantity with the physical quantities accepted in this system of quantities as the main ones and with a proportionality coefficient equal to one.

The degrees of symbols of the basic quantities included in the monomial can be integer, fractional, positive and negative. In accordance with the international standard ISO 31/0, the dimension of quantities should be denoted by the sign dim. In the LMT system, the dimension of X will be:

dimX = L l M m T t ,

where L.M.T - symbols of quantities taken as the main ones (respectively, length, mass, time);

l, m, t - integer or fractional, positive or negative real numbers, which are indicators of dimension.

The dimension of a physical quantity is more than general characteristics than the equation that determines the quantity, since the same dimension can be inherent in quantities that have a different qualitative side.

For example, the work of a force F is defined by the equation A = Fl; kinetic energy moving body - by the equation E k =mv 2 /2, and the dimensions of both are the same.

Multiplication, division, exponentiation and root extraction can be performed on dimensions.

An indicator of the dimension of a physical quantity is an indicator of the degree to which the dimension of the main physical quantity, which is included in the dimension of the derivative of the physical quantity, is raised.

Dimensions are widely used in the formation of derived units and checking the homogeneity of equations. If all exponents of the degree of dimension are equal to zero, then such a physical quantity is called dimensionless. All relative values(the ratio of like quantities) are dimensionless.

Physical - quantity (PV) - a property that is qualitatively common for many physical objects (their states and processes occurring in them), but quantitatively individual for each of them.

Qualitatively general properties characterize the genus PV. Qualitatively common can also be different in name (opposite) PVs: either length, width, height, depth, distance, or electromotive force, electrical voltage, electric potential, or work, energy, amount of heat. Such PVs are said to be of the same genus, or homogeneous. Physical quantities that are not homogeneous are called heterogeneous, or inhomogeneous.

Quantitatively, an individual property is characterized by the size of the PV. For example, speed, temperature, viscosity are properties inherent in a wide variety of objects, but some objects have more of this property, others have less. Consequently, the dimensions of speed, temperature, viscosity for some physical objects are greater than for others.

BIBLIOGRAPHY

1. Kuznetsov V.A., Yalunina G.V. Basics of metrology. Tutorial. – M.: Ed. Standards, 1995. - 280 p.

2. Pronenko V.I., Yakirin R.V. Metrology in industry. - Kyiv: Technique, 1979. - 223 p.

3. Laktionov B.I., Radkevich Ya.M. Metrology and interchangeability. - M.: Publishing house of the Moscow State Mining University, 1995. - 216 p.

It would be more correct to say “dimensionless unit of PV”, since the dimension is equal to zero, and not the size. However, the term "dimensionless PV unit" is widely used. The same applies to the term "dimensionless PV".

GSSE is one of the varieties of the GSES system.

SI stands for Systeme International. Instead of SI, you can write SI (International System).

2.2 Units of physical quantities

2.3. International PV system (SI)

2.4. Physical quantities of technological processes of food production

2.1 Physical quantities and scales

Physical quantity(PV) is one of the properties of a physical object (physical system, phenomenon or process), which 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 should be understood in such a way that the same property for one object can be a certain number of times more 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.

It is advisable to divide the physical quantities into 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, for example, using magnitude scales– an ordered sequence of its values, adopted by agreement on the basis of the results of precise measurements.

By type of event FV is divided into:

- real, i.e. describing the physical and physico-chemical properties of substances, materials and products from them. This group includes mass, density, specific surface, etc.

energy, i.e. quantities describing the energy characteristics of the processes of transformation, transmission and use of energy. These include, for example, current, voltage, power. These are active quantities that 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.

By belonging to different groups of physical processes PVs are divided into space-time, mechanical, thermal, electrical and magnetic, acoustic, light, physico-chemical, ionizing radiation, atomic and nuclear physics.

By degree of conditional independence from other values ​​of this group PV are divided into basic (conditionally independent), derivatives (conditionally dependent) and additional. Basic physical quantity is a physical quantity included in the system of quantities and conditionally accepted as independent of other quantities of this system. 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.

Derived physical quantity is a physical quantity included in the system of quantities and determined through the basic quantities of this system. For example, a derived physical quantity is density, which is determined through the mass and volume of a body.

Additional physical quantities include flat and solid angles.

The set of basic and derivative PV, formed in accordance with accepted principles, is called system of physical quantities.

By dimension PV are divided into dimensional, i.e. dimensioned and dimensionless.

In cases where it is necessary to emphasize that the quantitative content of a physical quantity in a given object is meant, the concept of p should be used. PV size(quantity size) - the quantitative certainty of PV inherent in a particular material object, system, phenomenon, process.

PV value(Q) is an expression of the size of a physical quantity in the form of a certain number of units accepted for it. The value of a physical quantity is obtained as a result of measurement or calculation, for example, 12 kg is the value of body weight.

Numerical value of FV (q) - an abstract number included in the value of the quantity

The equation

is called the basic measurement equation.

There is a fundamental difference between size and value. The size of a quantity does not depend on whether we know it or not. We can express the size using any of the units of a given quantity and a numerical value (except for the unit of mass - kg, you can use, for example, g). The sizes of different units of the same value are different.

The relationship between the basic and derived quantities of the system is expressed using dimensional equations.

Dimension of a physical quantity(dimQ) is an expression in the form of a power monomial, which reflects the relationship of a quantity with the basic units of the system and in which the proportionality coefficient is taken equal to one. The dimension of a quantity is the product of the basic physical quantities raised to the appropriate powers

dimQ = L α M β N γ I η , (2.2)

where L, M, N, I are the symbols of the main PVs, and α, β, γ, η are real numbers.

Dimension indicator of a physical quantity– an indicator of the degree to which the dimension of the basic physical quantity, which is included in the dimension of the derivative physical quantity, is raised. Dimension indicators can take different values: integer or fractional, positive or negative.

The concept of "dimension" extends to both basic and derived physical quantities. The dimension of the main quantity in relation to itself is equal to one and does not depend on other quantities, i.e. the formula for the dimension of the main quantity coincides with its symbol, for example: the dimension of length is L, the dimension of mass is M, etc.

To find the dimension of the derivative of a physical quantity in a certain system of quantities, one should substitute their dimension instead of the designation of quantities in the right side of the defining equation of this quantity. So, for example, substituting the dimension of length L instead of dl into the governing equation of the uniform motion velocity V = l/t and the dimension of time T instead of dt, we get - dim Q = L/T = LT - 1 .

The following operations can be performed on dimensions: multiplication, division, exponentiation, and root extraction.

Dimensional physical quantity- a physical quantity in the dimension of which at least one of the basic physical quantities is raised to a power that is not equal to zero. If all exponents of the degree of dimension of quantities are equal to zero, then such a physical quantity is called dimensionless. All relative quantities are dimensionless, i.e., the ratio of the same quantities. For example, relative density r is a dimensionless quantity. Indeed, r = L -3 M/L -3 M=L 0 M 0 = 1.

The value of a physical quantity can be true, real and measured. True PV value(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 true value of a certain quantity exists, it is constant and can be correlated with the concept of absolute truth. It can only be obtained as a result of an endless process of measurements with endless improvement of methods and measuring instruments. For each level of development of measuring technology, we can only know 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. Measured value of a physical quantity- the value of a physical quantity obtained using a specific technique.

In practice, it is necessary to measure various physical quantities. Various manifestations (quantitative or qualitative) of any property form sets, the mapping of whose elements onto an ordered set of numbers or, in a more general case, conventional signs form a scale for measuring these properties.

Scale of a physical quantity is an ordered set of PV values ​​that serves as the initial basis for measuring a given quantity. In accordance with the logical structure of the manifestation of properties, five main types of measurement scales are distinguished: names, order, conditional intervals, relations.

Name scale (classification scale). Such scales are used to classify empirical objects, the properties of which are manifested only in relation to equivalence, these properties cannot be considered physical quantities, therefore scales of this type are not PV scales. This is the simplest type of scale, based on attributing numbers to the qualitative properties of objects, playing the role of names. In the naming scales, in which the assignment of the reflected property to one or another equivalence class is carried out with the help of the human senses, this is the most adequate result chosen by the majority of experts. In this case, the correct choice of classes of the equivalent scale is of great importance - they must be distinguished by observers, experts evaluating this property. The numbering of objects according to the scale of names is carried out according to the principle: "do not attribute the same number to different objects." The numbers assigned to objects can only be used to determine the probability or frequency of occurrence of a given object, but they cannot be used for summation or other mathematical operations. Since these scales are characterized only by equivalence relations, they do not contain the concepts of zero, "more or less" and units of measurement. An example of naming scales are widespread color atlases designed to identify colors.

If the property of a given empirical object manifests itself in terms of equivalence and order in ascending or descending quantitative manifestation of the property, then a scale of order (ranks). It is monotonically increasing or decreasing and allows you to set the ratio more/less between the quantities characterizing the specified property. In order scales, zero exists or does not exist, but in principle it is impossible to introduce units of measurement, since a proportionality relation has not been established for them and, accordingly, it is not possible to judge how many times more or less specific manifestations of a property are.

In cases where the level of knowledge of the phenomenon does not allow to accurately establish the relationship that exists between the values ​​of this characteristic, or the use of the scale is convenient and sufficient for practice, use conditional (empirical) scale according torow. This is the PV scale, the initial values ​​of which are expressed in arbitrary units, for example, the Engler viscosity scale, the 12-point Beaufort scale for measuring the strength of the sea wind.

Interval scales (difference scale are a further development of scales of order and are applied to objects whose properties satisfy the relations of equivalence, order, and additivity. The interval scale consists of identical intervals, has a unit of measurement and an arbitrarily chosen beginning - a zero point. These scales include chronology according to various calendars, in which either the creation of the world, or the Nativity of Christ, etc. is taken as the starting point. The Celsius, Fahrenheit, and Réaumur temperature scales are also interval scales.

Relationship scale describe the properties of empirical objects that satisfy the relations of equivalence, order and additivity (scales of the second kind are additive), and in some cases proportionality (scales of the first kind are proportional). Their examples are the scale of mass (of the second kind), thermodynamic temperature (of the first kind).

In relation scales, there is an unambiguous natural criterion for the zero quantitative manifestation of a property and a unit of measurement. From a formal point of view, the scale of ratios is a scale of intervals with a natural reference point. All arithmetic operations are applicable to the values ​​obtained on this scale, which is important when measuring the EF. For example, the scale of the scale, starting from the zero mark, can be graduated in different ways, depending on the required weighing accuracy.

Absolute scales. Absolute scales are understood as scales that have all the features of ratio scales, but additionally have a natural unambiguous definition of the unit of measurement and do not depend on the accepted system of units of measurement. Such scales correspond to relative values: gain, attenuation, etc. For the formation of many derived units in the SI system, dimensionless and counting units of absolute scales are used.

Note that the scales of names and order are called notmetric (conceptual), and the scales of intervals and ratios - metric (material). Absolute and metric scales are classified as linear. The practical implementation of measurement scales is carried out by standardizing both the scales and units of measurement themselves, and, if necessary, the methods and conditions for their unambiguous reproduction.