Physical quantities. Basic physical quantities and units of their measurement Through basic and additional SI units
Physical quantity called the physical property of a material object, process, physical phenomenon, characterized quantitatively.
The value of a physical quantity expressed by one or more numbers characterizing this physical quantity, indicating the unit of measurement.
The size of a physical quantity are the values of the numbers appearing in the meaning of the physical quantity.
Units of measurement of physical quantities.
The unit of measurement of a physical quantity is a fixed size value that is assigned a numeric value equal to one. It is used for the quantitative expression of physical quantities homogeneous with it. A system of units of physical quantities is a set of basic and derived units based on a certain system of quantities.
Only a few systems of units have become widespread. In most cases, many countries use the metric system.
Basic units.
Measure physical quantity - means to compare it with another similar physical quantity, taken as a unit.
The length of an object is compared with a unit of length, body weight - with a unit of weight, etc. But if one researcher measures the length in sazhens, and another in feet, it will be difficult for them to compare these two values. Therefore, all physical quantities around the world are usually measured in the same units. In 1963, the International System of Units SI (System international - SI) was adopted.
For each physical quantity in the system of units, an appropriate unit of measurement must be provided. Standard units is its physical realization.
The length standard is meter- the distance between two strokes applied on a specially shaped rod made of an alloy of platinum and iridium.
Standard time is the duration of any correctly repeating process, which is chosen as the movement of the Earth around the Sun: the Earth makes one revolution per year. But the unit of time is not a year, but give me a sec.
For a unit speed take the speed of such uniform rectilinear motion, at which the body makes a movement of 1 m in 1 s.
A separate unit of measurement is used for area, volume, length, etc. Each unit is determined when choosing one or another standard. But the system of units is much more convenient if only a few units are chosen as the main ones, and the rest are determined through the main ones. For example, if the unit of length is a meter, then the unit of area is a square meter, volume is a cubic meter, speed is a meter per second, and so on.
Basic units The physical quantities in the International System of Units (SI) are: meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), candela (cd) and mole (mol).
Basic SI units |
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Value |
Unit |
Designation |
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Name |
Russian |
international |
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The strength of the electric current |
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Thermodynamic temperature |
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The power of light |
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Amount of substance |
There are also derived SI units, which have their own names:
SI derived units with their own names |
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Unit |
Derived unit expression |
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Value |
Name |
Designation |
Via other SI units |
Through basic and additional SI units |
Pressure |
m -1 ChkgChs -2 |
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Energy, work, amount of heat |
m 2 ChkgChs -2 |
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Power, energy flow |
m 2 ChkgChs -3 |
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Quantity of electricity, electric charge |
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Electrical voltage, electrical potential |
m 2 ChkgChs -3 CHA -1 |
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Electrical capacitance |
m -2 Chkg -1 Hs 4 CHA 2 |
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Electrical resistance |
m 2 ChkgChs -3 CHA -2 |
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electrical conductivity |
m -2 Chkg -1 Hs 3 CHA 2 |
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Flux of magnetic induction |
m 2 ChkgChs -2 CHA -1 |
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Magnetic induction |
kghs -2 CHA -1 |
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Inductance |
m 2 ChkgChs -2 CHA -2 |
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Light flow |
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illumination |
m 2 ChkdChsr |
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Radioactive source activity |
becquerel |
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Absorbed radiation dose |
ANDmeasurements. To obtain an accurate, objective and easily reproducible description of a physical quantity, measurements are used. Without measurements, a physical quantity cannot be quantified. Definitions such as "low" or "high" pressure, "low" or "high" temperature reflect only subjective opinions and do not contain comparison with reference values. When measuring a physical quantity, it is assigned a certain numerical value.
Measurements are made using measuring instruments. There is a fairly large number of measuring instruments and fixtures, from the simplest to the most complex. For example, length is measured with a ruler or tape measure, temperature with a thermometer, width with calipers.
Measuring instruments are classified: according to the method of presenting information (indicating or recording), according to the method of measurement (direct action and comparison), according to the form of presentation of indications (analog and digital), etc.
The measuring instruments are characterized by the following parameters:
Measuring range- the range of values of the measured quantity, on which the device is designed during its normal operation (with a given measurement accuracy).
Sensitivity threshold- the minimum (threshold) value of the measured value, distinguished by the device.
Sensitivity- relates the value of the measured parameter and the corresponding change in instrument readings.
Accuracy- the ability of the device to indicate the true value of the measured indicator.
Stability- the ability of the device to maintain a given measurement accuracy for a certain time after calibration.
Physical quantity- this is such a physical quantity, which, by agreement, is assigned a numerical value equal to one.
The tables show the basic and derived physical quantities and their units adopted in the International System of Units (SI).
Correspondence of a physical quantity in the SI system
Basic quantities
Value | Symbol | SI unit | Description |
Length | l | meter (m) | The length of an object in one dimension. |
Weight | m | kilogram (kg) | The value that determines the inertial and gravitational properties of bodies. |
Time | t | second (s) | Event duration. |
The strength of the electric current | I | ampere (A) | Charge flowing per unit time. |
thermodynamic temperature | T | kelvin (K) | The average kinetic energy of the object's particles. |
The power of light | candela (cd) | The amount of light energy emitted in a given direction per unit time. | |
Amount of substance | ν | mole (mol) | The number of particles referred to the number of atoms in 0.012 kg 12 C |
Derived quantities
Value | Symbol | SI unit | Description |
Area | S | m 2 | The extent of an object in two dimensions. |
Volume | V | m 3 | The extent of an object in three dimensions. |
Speed | v | m/s | The speed of changing body coordinates. |
Acceleration | a | m/s² | The rate of change in the speed of an object. |
Pulse | p | kg m/s | The product of mass and velocity of a body. |
Strength | kg m / s 2 (newton, N) | The external cause of acceleration acting on the object. | |
mechanical work | A | kg m 2 / s 2 (joule, J) | The scalar product of force and displacement. |
Energy | E | kg m 2 / s 2 (joule, J) | The ability of a body or system to do work. |
Power | P | kg m 2 / s 3 (watt, W) | Rate of energy change. |
Pressure | p | kg / (m s 2) (Pascal, Pa) | Force per unit area. |
Density | ρ | kg / m 3 | Mass per unit volume. |
Surface density | ρ A | kg/m2 | Mass per unit area. |
Line Density | ρl | kg/m | Mass per unit length. |
Quantity of heat | Q | kg m 2 / s 2 (joule, J) | Energy transferred from one body to another by non-mechanical means |
Electric charge | q | A s (coulomb, C) | |
Voltage | U | m 2 kg / (s 3 A) (volt, V) | The change in potential energy per unit of charge. |
Electrical resistance | R | m 2 kg / (s 3 A 2) (ohm, Ohm) | resistance of an object to the passage of electric current |
magnetic flux | Φ | kg/(s 2 A) (weber, Wb) | A value that takes into account the intensity of the magnetic field and the area it occupies. |
Frequency | ν | s −1 (hertz, Hz) | The number of repetitions of an event per unit of time. |
Injection | α | radian (rad) | The amount of change in direction. |
Angular velocity | ω | s −1 (radians per second) | Angle change rate. |
Angular acceleration | ε | s −2 (radian per second squared) | Rate of change of angular velocity |
Moment of inertia | I | kg m 2 | A measure of the inertia of an object during rotation. |
angular momentum | L | kg m 2 /s | A measure of the rotation of an object. |
Moment of power | M | kg m 2 / s 2 | The product of a force times the length of the perpendicular from a point to the line of action of the force. |
Solid angle | Ω | steradian (sr) |
According to their purpose and requirements, the following types of standards are distinguished.
Primary standard - provides reproduction and storage of a unit of physical quantity with the highest accuracy in the country (in comparison with other standards of the same quantity). Primary standards are unique measuring complexes created taking into account the latest achievements of science and technology and ensuring the uniformity of measurements in the country.
Special standard - ensures the reproduction of a unit of a physical quantity under special conditions in which a direct transfer of the size of a unit from a primary standard with the required accuracy is not feasible, and serves as a primary standard for these conditions.
The primary or special standard, officially approved as the initial one for the country, is called the state standard. State standards are approved by the State Standard, and for each of them the state standard is approved. State standards are created, stored and used by the central scientific metrological institutes of the country.
Secondary standard - stores the dimensions of a unit of a physical quantity obtained by comparison with the primary standard of the corresponding physical quantity. Secondary standards refer to subordinate means of storing units and transferring their sizes during verification work and ensure the safety and minimum wear of state primary standards.
According to their metrological purpose, secondary standards are divided into copy standards, comparison standards, witness standards and working standards.
Reference copy - designed to transfer the size of a unit of physical quantity as a working standard with a large amount of verification work. It is a copy of the state primary standard only for metrological purposes, but is not always a physical copy.
Comparison standard - It is used to compare standards that, for one reason or another, cannot be directly compared with each other.
Standard-witness - designed to check the safety and invariance of the state standard and replace it in case of damage or loss. Since the majority of state standards were created on the basis of the most stable physical phenomena and are therefore indestructible, at present only the kilogram standard has a witness standard.
Working standard - is used to transfer the size of a unit of physical quantity by a working measuring instrument. This is the most common type of standards that are used for verification work by territorial and departmental metrological services. Working standards are divided into categories that determine the order of their subordination in accordance with the verification scheme.
Standards of basic SI units.
Standard unit of time. The unit of time, the second, has long been defined as 1/86400 of a mean solar day. Later it was discovered that the rotation of the Earth around its axis is non-uniform. Then the basis for determining the unit of time was the period of rotation of the Earth around the Sun - a tropical year, i.e. the interval of time between two vernal equinoxes following one after the other. The size of a second was defined as 1/31556925.9747 of a tropical year. This made it possible to increase the accuracy of determining the unit of time by almost 1000 times. However, in 1967, the 13th General Conference on Weights and Measures adopted a new definition of the second as the time interval during which 9192631770 oscillations occur, corresponding to the resonant frequency of the energy transition between the levels of the hyperfine structure of the ground state of the cesium-133 atom in the absence of perturbation by external fields. This definition is implemented using cesium frequency references.
In 1972, the transition to the coordinated universal time system was carried out. Since 1997, the state primary control and the state verification scheme for time and frequency measuring instruments are determined by the rules of interstate standardization PMG18-96 "Interstate verification scheme for time and frequency measuring instruments".
The state primary standard of the unit of time, consisting of a set of measuring instruments, ensures the reproduction of units of time with a standard deviation of the measurement result not exceeding 1 * 10 -14 for three months.
Standard unit of length. In 1889, the meter was taken to be equal to the distance between two strokes on a metal rod with an X-shaped cross section. Although the international and national standards of the meter were made of an alloy of platinum and iridium, which is distinguished by significant hardness and high resistance to oxidation, however, there was no complete certainty that the length of the standard would not change over time. In addition, the error of comparing platinum-iridium line meters with each other is + 1.1 * 10 -7 m (+0.11 microns), and since the lines have a significant width, it is impossible to significantly improve the accuracy of this comparison.
After studying the spectral lines of a number of elements, it was found that the orange line of the krypton-86 isotope provides the greatest accuracy in reproducing a unit length. In 1960, the 11th General Conference on Weights and Measures adopted the expression of the size of the meter in terms of these wavelengths as its most accurate value.
The krypton meter made it possible to increase the accuracy of reproduction of a unit of length by an order of magnitude. However, further research made it possible to obtain a more accurate standard of the meter, based on the wavelength in vacuum of monochromatic radiation generated by a stabilized laser. The development of new reference complexes for reproducing the meter led to the definition of the meter as the distance traveled by light in vacuum in 1/299792458 of a second. This definition of the meter was enshrined in law in 1985.
The new reference complex for reproducing the meter, in addition to increasing the accuracy of measurement, in necessary cases, also allows you to monitor the constancy of the platinum-iridium standard, which has now become a secondary standard used to transfer the size of a unit to a working standard.
Standard unit of mass. When establishing the metric system of measures, the mass of one cubic decimeter of pure water at the temperature of its highest density (4 0 C) was taken as a unit of time.
During this period, accurate determinations of the mass of a known volume of water were made by successively weighing an empty bronze cylinder in air and water, the dimensions of which were carefully determined.
Based on these weighings, the first prototype of the kilogram was a platinum cylindrical weight 39 mm high, equal to its diameter. Like the prototype of the meter, it was deposited in the National Archives of France. In the 19th century, several careful measurements of the mass of one cubic decimeter of pure water at a temperature of 4 0 C were repeatedly carried out. At the same time, it was found that this mass is slightly (approximately 0.028 g) less than the prototype kilogram of the Archive. In order not to change the value of the initial unit of mass during further, more accurate weighings, the International Commission on the Prototypes of the Metric System in 1872. it was decided to take the mass of the prototype kilogram of the Archive as a unit of mass.
In the manufacture of platinum-iridium kilogram standards, the international prototype was taken to be the one whose mass differed the least from the mass of the Archive's kilogram prototype.
In connection with the adoption of a conditional prototype of the unit of mass, a liter was not equal to a cubic decimeter. The value of this deviation (1l=1.000028 dm 3) corresponds to the difference between the mass of the international prototype of the kilogram and the mass of a cubic decimeter of water. In 1964, the 12th General Conference on Weights and Measures decided to equate the volume of 1 liter to 1 dm 3.
It should be noted that at the time of the establishment of the metric system of measures, there was no clear distinction between the concepts of mass and weight, therefore the international prototype of the kilogram was considered the standard of the unit of weight. However, already with the approval of the international prototype of the kilogram at the 1st General Conference on Weights and Measures in 1889, the kilogram was approved as the prototype of the mass.
A clear distinction between the kilogram as a unit of mass and the kilogram as a unit of force was given in the decisions of the 3rd General Conference on Weights and Measures (1901).
The state primary standard and the verification scheme for means of changing the mass is determined by GOST 8.021 - 84. The state standard consists of a set of measures and measuring instruments:
· the national prototype of the kilogram - copy No. 12 of the international prototype of the kilogram, which is a weight made of a platinum-iridium alloy and designed to transfer the size of a mass unit to the weight R1;
national prototype of the kilogram - copy No. 26 of the international prototype of the kilogram, which is a weight made of a platinum-iridium alloy and designed to check the invariability of the size of the unit of mass, reproduced by the national prototype of the kilogram - copy No. 12, and replacing the latter during its comparisons in the International Bureau of Measures and Measures scales;
· weights R1 and a set of weights made of platinum-iridium alloy and designed to transfer the size of a mass unit to standards - copies;
reference weights.
The nominal value of the mass reproduced by the standard is 1 kg. The state primary standard ensures the reproduction of a unit of mass with a standard deviation of the measurement result when compared with the international prototype of the kilogram, not exceeding 2 * 10 -3 mg.
Reference scales, which are used to compare the mass standard, with a weighing range of 2 * 10 -3 ... 1 kg, have a standard deviation of the observation result on the scales of 5 * 10 -4 ... 3 * 10 -2 mg.
The objects of measurement are the properties of objective realities (bodies, substances, phenomena, processes). A property is an expression of some side of a thing or phenomenon. Each thing has many properties in which its quality is manifested. Some properties are essential, others are non-essential. A change in essential properties is equivalent to a change in the qualitative state of a thing or phenomenon.
Technological human activity is associated with the measurement of various physical quantities.
A physical quantity is a characteristic of one of the properties of a physical object (phenomenon or process), which is qualitatively common to many physical objects, but quantitatively individual for each object.
The value of a physical quantity is an estimate of its magnitude 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 a linear value; 75 kg - body weight value, HB190 - Brinell hardness number.
A distinction is made between the true value of a physical quantity, which ideally reflects the properties of the measured object in a qualitative and quantitative sense, and the actual value found experimentally, but which is close enough to the true value of the physical quantity and can be used instead of the actual value.
A measurement of a physical quantity is a set of operations performed with the help 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 most convenient form. for use.
In the theory of measurements, there are mainly five types of scales: names, order, intervals, ratios, and absolute.
Name scales are characterized only by the equivalence relation. In its essence, it is of high quality, does not contain zero and unit of measure. An example of such a scale is the assessment of color by name (color atlases). Since each color has many variations, such a comparison can only be performed by an experienced expert with the appropriate visual capabilities.
Order scales are characterized by equivalence and order relations. For the practical use of such a scale, it is necessary to establish a number of standards. Classification of objects is carried out by comparing the intensity of the evaluated property with its reference value. Order scales include, for example, the scale of earthquakes, the scale of wind strength, the scale of the hardness of bodies, etc.
The difference scale differs from the order scale in that, in addition to equivalence and order relations, the equivalence of intervals (differences) between various quantitative manifestations of a property is added. It has conditional zero values, and the intervals are set by agreement. A typical example of such a scale is the time interval scale. Time intervals can be summed up (subtracted).
Ratio scales describe the properties to which equivalence, order, and summation relations, and hence subtraction and multiplication, apply. These scales have a natural zero value, and the units of measurement are established by agreement. For the ratio scale, one standard is enough to distribute all the objects under study according to the intensity of the property being measured. An example of a ratio scale is the mass scale. The mass of two objects is equal to the sum of the masses of each of them.
Absolute scales have all the features of ratio scales, but additionally they have a natural unambiguous definition of the unit of measure. Such scales correspond to relative quantities (the ratios of physical quantities of the same name described by ratio scales). Among the absolute scales, absolute scales are distinguished, the values of which are in the range from 0 to 1. Such a value is, for example, the efficiency factor.
Most of the properties that are considered in metrology are described by one-dimensional scales. However, there are properties that can only be described using multidimensional scales. For example, three-dimensional color scales in colorimetry.
The practical implementation of scales of specific properties is achieved by standardizing units of measurement, scales and (or) methods and conditions for their unambiguous reproduction. The concept of a unit of measurement unchanged for any points of the scale makes sense only for scales of ratios and intervals (differences). In scales of order, you can only talk about the numbers assigned to specific manifestations of a property. It is impossible to say that such numbers differ by a certain number of times or by so many percent. For scales of ratios and differences, sometimes it is not enough to establish only the unit of measurement. So, even for such quantities as time, temperature, luminous intensity (and other light quantities), which in the International System of Units (SI) correspond to the basic units - second, Kelvin and candela, practical measurement systems also rely on special scales. In addition, the SI units themselves are in some cases based on fundamental physical constants.
In this regard, three types of physical quantities can be distinguished, the measurement of which is carried out according to 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 heating of the body, 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. So, the differences of time intervals are considered equal if the distances between the corresponding marks are equal.
The third type is made up of additive physical quantities.
Additive physical quantities are 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 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. For example, the sum of the masses of two bodies is the mass of such a body that balances the first two on equal-arm scales.
Topic: VALUES AND THEIR MEASUREMENTS
Target: Give the concept of quantity, its measurement. To acquaint with the history of the development of the system of units of quantities. Summarize knowledge about the quantities that preschoolers get acquainted with.
Plan:
The concept of magnitude, their properties. The concept of measuring a quantity. From the history of the development of the system of units of quantities. International system of units. The quantities that preschoolers get acquainted with and their characteristics.
1. The concept of magnitude, their properties
The value is one of the basic mathematical concepts that arose in antiquity and underwent a number of generalizations in the process of long development.
The initial idea of the size is associated with the creation of a sensory basis, the formation of ideas about the size of objects: show and name the length, width, height.
The value refers to the special properties of real objects or phenomena of the surrounding world. The size of an object is its relative characteristic, emphasizing the length of individual parts and determining its place among homogeneous ones.
Values that have only a numerical value are called scalar(length, mass, time, volume, area, etc.). In addition to scalars in mathematics, they also consider vector quantities, which are characterized not only by number, but also by direction (force, acceleration, electric field strength, etc.).
Scalars can be homogeneous or heterogeneous. Homogeneous quantities express the same property of objects of a certain set. Heterogeneous quantities express different properties of objects (length and area)
Scalar properties:
§ any two quantities of the same kind are comparable or they are equal, or one of them is less (greater than) the other: 4t5ts …4t 50kgÞ 4t5c=4t500kg Þ 4t500kg>4t50kg, because 500kg>50kg
4t5c >4t 50kg;
§ Values of the same genus can be added, resulting in a value of the same genus:
2km921m+17km387mÞ 2km921m=2921m, 17km387m=17387m Þ 17387m+2921m=20308m; means
2km921m+17km387m=20km308m
§ A value can be multiplied by a real number, resulting in a value of the same kind:
12m24cm× 9 Þ 12m24m=1224cm, 1224cm×9=110m16cm, so
12m24cm× 9=110m16cm;
4kg283g-2kg605gÞ 4kg283g=4283g, 2kg605g=2605g Þ 4283g-2605g=1678g, so
4kg283g-2kg605g=1kg678g;
§ quantities of the same kind can be divided, resulting in a real number:
8h25min: 5 Þ 8h25min=8×60min+25min=480min+25min=505min, 505min : 5=101min, 101min=1h41min, so 8h25min: 5=1h41min.
The value is a property of an object perceived by different analyzers: visual, tactile and motor. In this case, most often the value is perceived simultaneously by several analyzers: visual-motor, tactile-motor, etc.
The perception of magnitude depends on:
§ the distance from which the object is perceived;
§ the size of the object with which it is compared;
§ its location in space.
The main properties of the quantity:
§ Comparability- the definition of the value is possible only on the basis of comparison (directly or by comparing with a certain way).
§ Relativity- the characteristic of the magnitude is relative and depends on the objects chosen for comparison; the same object can be defined by us as larger or smaller, depending on the size of the object it is compared with. For example, a bunny is smaller than a bear, but larger than a mouse.
§ Variability- the variability of quantities is characterized by the fact that they can be added, subtracted, multiplied by a number.
§ measurability- measurement makes it possible to characterize the magnitude of the comparison of numbers.
2. The concept of measuring a quantity
The need to measure all kinds of quantities, as well as the need to count objects, arose in the practical activity of man at the dawn of human civilization. Just as to determine the number of sets, people compared different sets, different homogeneous quantities, determining first of all which of the compared quantities is larger, which is smaller. These comparisons were not measurements yet. Subsequently, the procedure for comparing values was improved. One quantity was taken as the standard, and other quantities of the same kind were compared with the standard. When people mastered the knowledge about numbers and their properties, the number 1 was attributed to the value - the standard, and this standard became known as the unit of measurement. The purpose of measurement has become more specific – to evaluate. How many units are in the measurand. the result of the measurement began to be expressed as a number.
The essence of measurement is the quantitative fragmentation of the measured objects and the establishment of the value of this object in relation to the accepted measure. By means of the measurement operation, the numerical ratio of the object between the measured value and a pre-selected unit of measure, scale or standard is established.
The measurement includes two logical operations:
the first is the process of separation, which allows the child to understand that the whole can be divided into parts;
the second is the replacement operation, which consists in connecting separate parts (represented by the number of measures).
The measurement activity is quite complex. It requires certain knowledge, specific skills, knowledge of the generally accepted system of measures, the use of measuring instruments.
In the process of forming measuring activity among preschoolers by means of conditional measurements, children must understand that:
§ measurement gives an accurate quantitative characteristic of the value;
§ for measurement, it is necessary to choose an adequate measure;
§ the number of measures depends on the measured value (the larger the value, the greater its numerical value and vice versa);
§ the measurement result depends on the chosen measure (the larger the measure, the smaller the numerical value and vice versa);
§ To compare quantities, it is necessary to measure them with the same standards.
3. From the history of the development of the system of units of quantities
Man has long realized the need to measure different quantities, and to measure as accurately as possible. The basis of accurate measurements are convenient, well-defined units of quantities and accurately reproducible standards (samples) of these units. In turn, the accuracy of standards reflects the level of development of science, technology and industry of the country, speaks of its scientific and technical potential.
In the history of the development of units of quantities, several periods can be distinguished.
The most ancient is the period when units of length were identified with the name of the parts of the human body. So, the palm (the width of four fingers without the thumb), the elbow (the length of the elbow), the foot (the length of the foot), the inch (the length of the knuckle of the thumb), etc. were used as units of length. The units of area during this period were: , which can be watered from one well), plow or plow (average area cultivated per day with a plow or plow), etc.
In the XIV-XVI centuries. appear in connection with the development of trade so-called objective units of measurement. In England, for example, an inch (the length of three barley grains placed side by side), a foot (the width of 64 barley grains laid side by side).
Gran (mass of grain) and carat (mass of the seed of one of the bean species) were introduced as units of mass.
The next period in the development of units of quantities is the introduction of units interconnected with each other. In Russia, for example, such units were mile, verst, sazhen and arshin; 3 arshins made up a sazhen, 500 sazhens - a verst, 7 versts - a mile.
However, the connections between units of quantities were arbitrary, their measures of length, area, mass were used not only by individual states, but also by individual regions within the same state. Particular discord was observed in France, where each feudal lord had the right to establish his own measures within the limits of his possessions. Such a variety of units of quantities hindered the development of production, hindered scientific progress and the development of trade relations.
The new system of units, which later became the basis for the international system, was created in France at the end of the 18th century, during the era of the French Revolution. The basic unit of length in this system was meter- one forty-millionth part of the length of the earth's meridian passing through Paris.
In addition to the meter, the following units were also installed:
§ ar is the area of a square whose side length is 10 m;
§ liter- volume and capacity of liquids and loose bodies, equal to the volume of a cube with an edge length of 0.1 m;
§ gram is the mass of pure water occupying the volume of a cube with an edge length of 0.01 m.
Decimal multiples and submultiples were also introduced, formed with the help of prefixes: myria (104), kilo (103), hecto (102), deca (101), deci, centi, milli
The kilogram mass unit was defined as the mass of 1 dm3 of water at a temperature of 4 °C.
Since all units of quantities turned out to be closely related to the unit of length, the meter, the new system of quantities was called metric system.
In accordance with the accepted definitions, platinum standards of the meter and kilogram were made:
§ the meter was represented by a ruler with strokes applied at its ends;
§ kilogram - a cylindrical weight.
These standards were transferred to the National Archives of France for storage, in connection with which they received the names "archival meter" and "archival kilogram".
The creation of the metric system of measures was a great scientific achievement - for the first time in history, measures appeared that form a harmonious system, based on a model taken from nature, and closely related to the decimal number system.
But soon this system had to be changed.
It turned out that the length of the meridian was not determined accurately enough. Moreover, it became clear that with the development of science and technology, the value of this quantity will be refined. Therefore, the unit of length, taken from nature, had to be abandoned. The meter began to be considered the distance between the strokes applied at the ends of the archival meter, and the kilogram - the mass of the standard of the archive kilogram.
In Russia, the metric system of measures began to be used on a par with Russian national measures starting in 1899, when a special law was adopted, the draft of which was developed by an outstanding Russian scientist. By special decrees of the Soviet state, the transition to the metric system of measures was legalized, first by the RSFSR (1918), and then completely by the USSR (1925).
4. International system of units
International System of Units (SI)- this is a single universal practical system of units for all branches of science, technology, the national economy and teaching. Since the need for such a system of units, which is uniform for the whole world, was great, in a short time it received wide international recognition and distribution throughout the world.
This system has seven basic units (meter, kilogram, second, ampere, kelvin, mole and candela) and two additional units (radian and steradian).
As you know, the unit of length, the meter, and the unit of mass, the kilogram, were also included in the metric system of measures. What changes did they undergo when they entered the new system? A new definition of the meter has been introduced - it is considered as the distance that a plane electromagnetic wave travels in vacuum in a fraction of a second. The transition to this definition of the meter is caused by an increase in the requirements for measurement accuracy, as well as the desire to have a unit of magnitude that exists in nature and remains unchanged under any conditions.
The definition of the unit of mass of the kilogram has not changed, as before, the kilogram is the mass of a cylinder made of platinum-iridium alloy, made in 1889. This standard is stored at the International Bureau of Weights and Measures in Sevres (France).
The third basic unit of the International System is the second unit of time. She is much older than a meter.
Prior to 1960, a second was defined as 0 " style="border-collapse:collapse;border:none">
Prefix names
Prefix designation
Factor
Prefix names
Prefix designation
Factor
For example, a kilometer is a multiple of a unit, 1 km = 103×1 m = 1000 m;
millimeter is a submultiple, 1 mm=10-3×1m = 0.001 m.
In general, for length, a multiple unit is a kilometer (km), and longitude units are centimeter (cm), millimeter (mm), micrometer (µm), nanometer (nm). For mass, the multiple unit is the megagram (Mg), and the submultiples are the gram (g), milligram (mg), microgram (mcg). For time, the multiple unit is the kilosecond (ks), and the submultiples are the millisecond (ms), microsecond (µs), nanosecond (not).
5. The quantities that preschoolers get acquainted with and their characteristics
The purpose of preschool education is to acquaint children with the properties of objects, to teach them to differentiate them, highlighting those properties that are commonly called quantities, to introduce the very idea of measurement through intermediate measures and the principle of measuring quantities.
Length is a characteristic of the linear dimensions of an object. In the preschool methodology for the formation of elementary mathematical representations, it is customary to consider “length” and “width” as two different qualities of an object. However, in school, both linear dimensions of a flat figure are more often called "side length", the same name is used when working with a three-dimensional body that has three dimensions.
The lengths of any objects can be compared:
§ approximately;
§ application or overlay (combination).
In this case, it is always possible either approximately or precisely to determine "by how much one length is greater (less) than the other."
Weight is a physical property of an object, measured by weighing. Distinguish between mass and weight of an object. With a concept item weight children get acquainted in the 7th grade in a physics course, since weight is the product of mass and acceleration of free fall. The terminological incorrectness that adults allow themselves in everyday life often confuses the child, because we sometimes say without hesitation: "The weight of an object is 4 kg." The very word "weighing" encourages the use of the word "weight" in speech. However, in physics, these quantities differ: the mass of an object is always constant - this is a property of the object itself, and its weight changes if the force of attraction (free fall acceleration) changes.
In order for the child not to learn the wrong terminology, which will confuse him later in elementary school, you should always say: mass of the object.
In addition to weighing, mass can be approximately determined by an estimate on the arm (“baric feeling”). Mass is a category that is difficult from a methodological point of view for organizing classes with preschoolers: it cannot be compared by eye, application, or measured by an intermediate measure. However, any person has a "pressure feeling", and using it, you can build a number of tasks that are useful for the child, leading him to an understanding of the meaning of the concept of mass.
The basic unit of mass is kilogram. From this basic unit, other units of mass are formed: grams, tons, etc.
Area- this is a quantitative characteristic of a figure, indicating its dimensions on a plane. The area is usually determined for flat closed figures. To measure the area as an intermediate measure, you can use any flat shape that fits snugly into this figure (without gaps). In elementary school, children are introduced to palette - a piece of transparent plastic coated with a grid of squares of equal size (usually 1 cm2 in size). Overlaying a palette on a flat figure makes it possible to calculate the approximate number of squares that fit in it to determine its area.
At preschool age, children compare the areas of objects without naming this term, using the imposition of objects or visually, by comparing the space they occupy on the table, on the ground. The area is a convenient value from a methodological point of view, since it allows organizing various productive exercises for comparing and equalizing areas, determining the area by laying down intermediate measures and through a system of tasks for equal composition. For example:
1) comparison of the areas of figures by the overlay method:
The area of a triangle is less than the area of a circle, and the area of a circle is greater than the area of a triangle;
2) comparison of the areas of figures by the number of equal squares (or any other measurements);
The areas of all figures are equal, since the figures consist of 4 equal squares.
When performing such tasks, children indirectly get acquainted with some area properties:
§ The area of a figure does not change when its position on the plane changes.
§ A part of an object is always less than the whole.
§ The area of the whole is equal to the sum of the areas of its constituent parts.
These tasks also form in children the concept of area as a number of measures contained in a geometric figure.
Capacity is a characteristic of liquid measures. At school, capacity is considered sporadically in one lesson in grade 1. They introduce children to a measure of capacity - a liter in order to use the name of this measure in the future when solving problems. The tradition is such that capacity is not associated with the concept of volume in elementary school.
Time is the duration of the process. The concept of time is more complex than the concept of length and mass. In everyday life, time is what separates one event from another. In mathematics and physics, time is considered as a scalar quantity, because time intervals have properties similar to those of length, area, mass:
§ Time spans can be compared. For example, a pedestrian will spend more time on the same path than a cyclist.
§ Time intervals can be added. Thus, a lecture in college lasts the same amount of time as two lessons in high school.
§ Time intervals are measured. But the process of measuring time is different from measuring length. You can repeatedly use a ruler to measure length by moving it from point to point. The time interval taken as a unit can be used only once. Therefore, the unit of time must be a regularly repeating process. Such a unit in the International System of Units is called second. Along with the second, other units of time: minute, hour, day, year, week, month, century .. Such units as year and day were taken from nature, and hour, minute, second were invented by man.
A year is the time it takes for the Earth to revolve around the Sun. A day is the time it takes the Earth to rotate around its axis. A year consists of approximately 365 days. But a year of human life consists of a whole number of days. Therefore, instead of adding 6 hours to each year, they add a whole day to every fourth year. This year consists of 366 days and is called a leap year.
A calendar with such an alternation of years was introduced in 46 BC. e. Roman emperor Julius Caesar in order to streamline the very confusing calendar that existed at that time. Therefore, the new calendar is called the Julian. According to him, the new year begins on January 1 and consists of 12 months. It also preserved such a measure of time as a week, invented by the Babylonian astronomers.
Time sweeps away both physical and philosophical meaning. Since the sense of time is subjective, it is difficult to rely on feelings in its evaluation and comparison, as can be done to some extent with other quantities. In this regard, at school, almost immediately, children begin to get acquainted with devices that measure time objectively, that is, regardless of human sensations.
When getting acquainted with the concept of "time" at first, it is much more useful to use an hourglass than a watch with arrows or an electronic one, since the child sees how the sand is poured and can observe the "flow of time". An hourglass is also convenient to use as an intermediate measure when measuring time (in fact, this is precisely what they were invented for).
Working with the value of "time" is complicated by the fact that time is a process that is not directly perceived by the child's sensory system: unlike mass or length, it cannot be touched or seen. This process is perceived by a person indirectly, in comparison with the duration of other processes. At the same time, the usual stereotypes of comparisons: the course of the sun across the sky, the movement of the hands in a clock, etc. - as a rule, are too long for a child of this age to really be able to trace them.
In this regard, "Time" is one of the most difficult topics in both preschool mathematics and elementary school.
The first ideas about time are formed at preschool age: the change of seasons, the change of day and night, children get acquainted with the sequence of concepts: yesterday, today, tomorrow, the day after tomorrow.
By the beginning of schooling, children form ideas about time as a result of practical activities related to the duration of processes: performing routine moments of the day, keeping a weather calendar, getting to know the days of the week, their sequence, children get acquainted with the clock and orientate themselves in connection with visiting kindergarten. It is quite possible to introduce children to such units of time as a year, month, week, day, to clarify the idea of the hour and minute and their duration in comparison with other processes. The instruments for measuring time are the calendar and the clock.
Speed is the path traveled by the body per unit of time.
Speed is a physical quantity, its names contain two quantities - units of length and units of time: 3 km / h, 45 m / min, 20 cm / s, 8 m / s, etc.
It is very difficult to give a visual representation of speed to a child, since this is the ratio of path to time, and it is impossible to depict or see it. Therefore, when getting acquainted with speed, one usually refers to a comparison of the time it takes objects to travel an equal distance or the distances they cover in the same time.
Named numbers are numbers with the names of units of measurement. When solving problems at school, you have to perform arithmetic operations with them. The acquaintance of preschoolers with named numbers is provided in the programs "School 2000" ("One - a step, two - a step ...") and "Rainbow". In the School 2000 program, these are tasks of the form: "Find and correct errors: 5 cm + 2 cm - 4 cm = 1 cm, 7 kg + 1 kg - 5 kg = 4 kg." In the Rainbow program, these are tasks of the same type, but by “names” there is meant any name with numerical values, and not just the names of measures of quantities, for example: 2 cows + 3 dogs + + 4 horses \u003d 9 animals.
Mathematically, you can perform an action with named numbers in the following way: perform actions with the numerical components of named numbers, and add a name when writing the answer. This method requires compliance with the rule of a single name in the components of the action. This method is universal. In elementary school, this method is also used when performing actions with composite named numbers. For example, to add 2 m 30 cm + 4 m 5 cm, children replace the composite named numbers with numbers of the same name and perform the action: 230 cm + 405 cm = 635 cm = 6 m 35 cm or add the numerical components of the same names: 2 m + 4 m = 6 m, 30 cm + 5 cm = 35 cm, 6 m + 35 cm = 6 m 35 cm.
These methods are used when performing arithmetic operations with numbers of any names.
Units of some quantities
Units of length 1 km = 1,000 m 1 m = 10 dm = 100 m 1 dm = 10 cm 1cm=10mm | Mass units 1 t = 1,000 kg 1 kg = 1,000 g 1 g = 1,000 mg | Ancient measures of length 1 verst = 500 fathoms = 1,500 arshins = = 3,500 feet = 1,066.8 m 1 sazhen = 3 arshins = 48 vershoks = 84 inches = 2.1336 m 1 yard = 91.44cm 1 arshin \u003d 16 inches \u003d 71.12 cm 1 inch = 4.450 cm 1 inch = 2.540 cm 1 weave = 2.13 cm |
area units 1 m2 = 100 dm2 = cm2 1 ha = 100 a = m2 1 a (ar) = 100m2 | Volume units 1 m3 = 1,000 dm3 = 1,000,000 cm3 1 dm3 = 1,000 cm3 1 bbl (barrel) = 158.987 dm3 (l) | Mass measures 1 pood = 40 pounds = 16.38 kg 1 lb = 0.40951 kg 1 carat = 2×10-4 kg |