Physical quantities. Measurement of physical quantities

22.01.202427.05.2017

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“Science begins as soon as they begin to measure. Exact science is unthinkable without measure.

In nature, measure and weight are the main instruments of knowledge.”

/D.I.Mendeleev/

a) educational

the student must learn:

The concept of physical quantity and units of measurement;

Methods of measuring physical quantities;

Algorithm for determining the division price and error.

b) developing

the student must be able to:

Determine the division price and readings of measuring instruments;

Record the measurement results taking into account errors.

c) educational:

education of patriotism and citizenship while studying the historical aspects of the topic; development of communication in the process of joint activities.

Lesson structure:

№	Lesson stage	Form of activity	Time
1	Organizational moment	Creating a work environment	1-2 min.
2	Checking homework	Test	5 minutes.
3	Updating knowledge	Experiment	5 minutes
4	Exploring new meat material	Heuristic conversation, watching a film fragment, working with physical instruments and flashcards	20 minutes.
5	Consolidation	Independent completion of tasks on the topic	10 min.
6	Reflection	Answers on questions	2-3 min.

Equipment:

multimedia projector for demonstrating presentations;
three glasses of hot, warm and cold water for the experiment,
ruler, pencil, thermometer (c = 1°C), beaker.
individual educational cards for determining the price of dividing a beaker and a thermometer.

During the classes

1) Organizational moment.

2) Checking homework:

A control test based on the materials from the previous lesson (see Appendix No. 1).

3) Updating knowledge.

Let's conduct an experiment. Three glasses contain hot, warm and cold water. Dip one finger of your left hand into hot water, hold it a little, and lower it into warm water. Warm water will seem...(cold) to you. Now dip the finger of your right hand into cold water, and then into warm water. How will the water seem?... (hot). But the water hasn't changed, has it? What needs to be done to determine absolutely exactly what kind of water is in the glass? (during the conversation we come to the conclusion):

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

4) Studying new material.

These quantities are called physical, and many are already familiar to you from mathematics and natural science (for example: length, mass, area, speed, etc.). Measurements are extremely important both in science and in life around us.

The great Russian scientist D.I. Mendeleev said this: (Slide 1) “Science begins as soon as they begin to measure. Exact science is unthinkable without measure. In nature, measure and weight are the main instruments of knowledge.”

And that’s why the topic of today’s lesson is: “Measurement of physical quantities”

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

Why do you need measurements?
What is a physical quantity?
How to measure a physical quantity?

We have already answered the first question in the process of discussing the experiment, so let’s move on to the second question:

What is a physical quantity?

Let's return to experience once again. Take a thermometer in your hands, lower it into the first glass of water, wait a little and tell the temperature of the water. ( at this stage of the lesson, this measurement may not be accurate, but it will allow us to introduce the concept of a physical quantity as a quantitative characteristic of an object)

Now measure the temperature in the remaining glasses in the same way. Write the results in your notebook in ascending order.

/ For example: 20°, 40°, 60°/

Now we can easily determine which water is which. Temperature is determined by a number, and the higher the number, the warmer the water. And we can write down the general definition in a notebook: (Slide 4)

A physical quantity is a quantitative (numerical) characteristic of a body or substance. It is indicated by letters of the Latin alphabet, for example:

m – mass, t – time, l – length.

Any physical quantity, except a numerical value, has units of measurement.

For example: On the wrapper of a chocolate bar it is written: “Weight 100 g.”

Mass is.. (physical quantity)

100 is...(numeric value)

g - gram is... (unit of measurement).

Now try it yourself:

My height is 164 cm.

Height (length) is... (physical quantity)

164 is.., (numeric value)

cm is..(unit of measurement)

Therefore, when we measure a quantity, we compare it with certain units of measurement. Let's write down the definition: (Slide 5)

To measure a physical quantity means to compare it with a homogeneous value taken as a unit of measurement. Now we are left with the main question: How to measure a physical quantity? Let's see how cartoon characters learned to measure. You will have to answer the questions: (Slide 6).

What physical quantity did the characters in the film measure?
In what units?
What did you measure with?
Is it correct? Why?

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

It was not only Boa Constrictor and his friends who encountered such difficulties. Since ancient times, Rus' has had its own units of measurement for distances, mass and volume (Slide 8). And although we hardly use them now, they have been preserved in proverbs and sayings, fairy tales and poems. Explain the meaning of these statements. To avoid confusion in measurements. In Russia, back in the 16th and 17th centuries, a unified system of measures was created for the entire country. In 1736, the Senate decided to form the Commission of Weights and Measures. The commission created exemplary measures - standards. By 1807, three arshin standards were made (stored in St. Petersburg): crystal, steel and copper. They had already been brought into line with the English measures of length - feet and inches. This was required by the need to develop trade relations with other countries - after all, already at the beginning of the 18th century there were 400 units of different sizes in different countries! In order to understand each other well, the International System of Units (SI) was created, where each quantity was assigned its own designation and unit of measurement. (stand “International System of Units”) All physical quantities are indicated here, and we will study them in the physics course. Today let’s pay attention to the most important thing. Quantities are basic and derivative. Write down the units of measurement of basic physical quantities in your notebook:

Mass – kg (kilogram), length – m (meter), time – s (second)

But mass can also be measured... (in grams, milligrams, tons). You already studied this in your math course. In what units is length measured? Time? The SI system is called the decimal system. All homogeneous quantities are interconnected.

1 kilo gram = 1000 (10 3) g 1 kilo meter = 1000 (10 3) m

1 Milli gram = 0.001 g 1 Milli meter = 0.001m

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

Today we must learn how to use measuring instruments correctly.

You have already measured the water temperature today. So, what do you need to measure? Firstly, you need to have a device, and secondly, you need to be able to use it. A well-known ruler is a device for measuring length. Temperature is measured with another device - a thermometer.

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

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

They are all very different, but they have similarities. Each device must have a scale with divisions and numbers.

The largest value on the scale is called the upper limit, the smallest is called the lower limit. Name the limits of the devices that you have on your desk.

Today we have already measured your temperature. Now let's try to determine the volume of water using a special device - a beaker. Volume is measured in ml or cubic cm. How much water is in this beaker? / 200 ml/. And now they lowered a stone into the beaker, and there was more water. How many? / The answers will probably be different, which will allow us to introduce the concept of division price/

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

To do this you need: (slide 11)

Select the two closest numbers (for example, 400 ml and 200 ml)

Find the difference between them (400 ml - 200 ml = 200 ml)

Count the number of divisions between them (10)

Divide the difference by the number of divisions (200 ml: 10 = 20 ml)

Let's write down the formula for determining the division price of the device:

c = 400 -200/10 = 20 ml

Now try it yourself: (Slide 12)

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

Use the card to independently determine the price of thermometer division ( for those who have mastered the task well and completed the task quickly, you can offer tasks with a beaker using the same cards)

Measurement error.

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

Why is the textbook the same, but the length values are different?

/During the discussion we come to the conclusion:/

Unfortunately, any measurements have error, i.e. error (Slide 13). The error depends both on the device itself (instrumental error) and on how we measure (measurement error). Is the measurement error indicated? (delta) and is equal to half the division price:

The error shows how much we made a mistake (up or down). Therefore, the final measurement result is usually written as follows:

t = 25°± 0.5° (for the first thermometer)

t = 36.9° ± 0.05° (for the second thermometer)

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

Now tell me: which thermometer will measure temperature more accurately?

Let's write down the conclusion in our notebook:

The lower the division value, the more accurately the device measures.

The measurements we made today in class are called direct. They are made using devices. Some quantities cannot be determined immediately. For example: How do you determine the area of the desk? That's right, you need to measure the length and width. Such measurements are called indirect.

5. Consolidation.

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

What it is? Possible answers:

Minute – ... 1. unit of measurement

Libra –... 2. physical quantity

Time – ... 3. measuring device

Balancing –... 4. physical phenomenon

Weight - ...

Now let's complete the following tasks: (Slide 14-15)

6. Reflection:

Continue the sentence:

Now I know…

And I can also...

It would be interesting to know more...

7. Homework: (Slide 16). § 4.5 (textbook “Physics 7” Peryshkin A.V.)

Literature

1. Peryshkin A.V. Physics 7, Education, 2008

2. Fireplace A.L. Physics. Developmental training. 7th grade, Phoenix, 2003

3. Gendenshtein L.E., Kirik L.A., Gelfgat I.M. Physics problems for primary school with examples of solutions, Ilexa, 2005.

4. Khannanov N.K., Khannanova T.A. Physics. Tests. 7, Bustard, 2005

The task of a physical experiment is to establish and study connections between various physical quantities. Moreover, during the experiment it is often necessary to measure these physical quantities. To measure a physical quantity means to compare it with an identical physical quantity taken as a unit.

Measurement is the experimental determination of the value of a physical quantity using measuring instruments. Measuring instruments include: 1) measures (weights, measuring cups, etc.); 2) measuring instruments with a scale or digital display (stopwatches, ammeters, voltmeters, etc.); 3) measuring and computing systems, including measuring instruments and computer equipment.

To measure a physical quantity, you must: 1) select a unit of measurement for this quantity; 2) select measuring instruments calibrated in established units with the required accuracy; 3) choose the most appropriate measurement technique; 4) carry out, using available means, a measurement of a given value; 5) give an assessment of the error allowed in the measurements.

Depending on the method of obtaining the result, measurements are divided into straight And indirect. Direct measurements are carried out using measuring instruments that directly determine the value under study (for example, measuring length using a ruler, body weight using scales, time using a stopwatch). However, direct measurements are not always feasible, convenient, or have the necessary accuracy and reliability. In these cases use indirect measurements in which the desired value of a quantity is found by a known relationship between this quantity and quantities whose values can be found by direct measurements. For example, volume can be calculated from the measured linear dimensions of an object, body mass from known density and volume, etc. Thus, the value of any quantity can be obtained both by direct measurements and by indirect ones. For example, the resistance value of a wire can be determined both using a device - an ohmmeter, and using calculations based on the measured values of the current flowing through the conductor and the voltage drop across it. The choice of method for measuring a physical quantity for each specific case is decided separately, taking into account convenience, speed of obtaining results, required accuracy and reliability.

Each physical experiment consists of preparing the object under study and measuring instruments, monitoring the progress of the experiment and instrument readings, recording readings and measurement results.

Measuring instrument called a device that allows you to directly determine the values of the measured quantity.

Each measuring device has a reading device for displaying information about measurement results. The simplest reading device consists of a scale and a pointer.

Scale is a set of marks applied across a certain line. The spaces between the marks are called scale divisions. For ease of reference, individual marks are isolated, increasing their length or thickness, and marked with numbers.

Pointer performed in the form of an arrow or a stroke that can move along the scale. In some devices, a light spot containing an image of a line moves along the scale.

There are devices with digital display, in which information about the measured value is provided in the form of a number displayed through a special display.

For each device, you can select an interval of the measured value, within which it can operate safely and give reliable results. This interval is called working measurement range. If the value to be determined is less than lower limit operating range, the measurement result will be too rough or the instrument reading cannot be distinguished from zero at all. If the measured value exceeds upper limit, then the device may be damaged.

Sensitivity a measuring instrument is characterized by its ability to respond to small changes in the measured quantity. Sensitivity  is determined by the formula:

 =S / x ,

where S is the movement of the reading device pointer when the measured value changes by x.

If the sensitivity remains constant throughout the entire operating range, then the same changes in the value x both at the beginning and at the end of the scale correspond to the same movements of the S pointer. In this case, the device has scale with the same divisions, called uniform. If the sensitivity of the device is not constant, then in different parts of the range equal changes in the measured value correspond to unequal movements of the pointer. The scales in these cases turn out to be uneven.

At the cost of a scale division WITH X called a change in the measured quantity that causes the pointer to move one division. Moving the pointer by n such divisions indicates that the measured value has changed by x = nС Х.

this implies rule for determining the division price: the difference in the values of the measured quantity x, which corresponds to the nearest digitized marks, should be divided by the number of divisions n between these marks, that is

C X = x / n.

For example, the numbers 7 and 8 on a student ruler correspond to distances of 7 cm and 8 cm from its origin. The difference between these distances is x = 8 cm –7 cm = 1 cm = 10 mm. The number of divisions between the indicated marks is n = 10. Therefore,

C X = x / n = 10 mm /10 = 1 mm.

There are instruments with uneven scales, in which the value of the divisions changes when moving from one section of the scale to another. As an example, Figure 1 shows an ohmmeter scale. The division price in the area up to 0.5 Ohm is 0.05 Ohm, in the area from 0.5 Ohm to 2 Ohm it is 0.1 Ohm. Determine the value of the divisions in other areas yourself and read the reading of the ohmmeter shown in Fig. 1.

At reading countdown instruments, you should determine the value of the instrument divisions at the point on the scale where the pointer is located.

For correct reading, the line of sight should be perpendicular to the plane of the scale. To ensure this condition, electrical measuring instruments are equipped with a mirror scale. The line of sight is perpendicular to the scale if the stroke of the reading device coincides with its image in the mirror.

The sequence of placement of instruments and their connection with each other should be such as to ensure maximum accuracy and convenience of the experiment. In this case, setting their zero values on a scale or digital display is of paramount importance to obtain an accurate result. Working on faulty devices is not allowed! If the equipment malfunctions, you should immediately report it to your teacher or laboratory assistant! Before turning on the devices, you must make sure that they are connected correctly and obtain permission to turn them on from the teacher.

Observations of instrument readings should be carried out so that the scale or display of the instrument is clearly visible

The form for recording experimental results should be clear and compact. For this purpose, the tables given in the guidelines for each laboratory work are used, and it is in these tables, copied by students onto the work form, that the results should be recorded, taking into account the units of measurement and the division value of the device. Moreover, if the required accuracy of the result is not specified in advance, then one must try to write down the measurement result with the highest possible accuracy that the device provides (i.e., write down the maximum possible number of significant digits). To reduce the number of zeros in the obtained values of the measured quantity (those zeros that are not significant figures), it is convenient to indicate the decimal factor 10 n for the entire row or column of the table. For example, it is necessary to record the density values of bodies (in kg/m3) with an accuracy of two significant figures. In order not to write extra zeros, for the entire row (or column) of the table in which the values of the density of bodies are entered, a multiplier of 10 3 is placed before the unit of measurement. Then for the density of water in the corresponding cell of the table, instead of 1000 there will be 1.0. We note, however, that when making measurements, you should not, at any cost, achieve greater accuracy than is necessary for the task at hand. For example, if you need to know the length of boards prepared for the production of containers, then you do not need to take measurements with an accuracy of, say, a micron. Or, if, when carrying out indirect measurements, the value of any of the measured quantities is limited to a certain accuracy (expressed in a certain number of significant figures), then it makes no sense to try to measure other quantities with much greater accuracy than this.

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1. Basic concepts and definitions in information and measurement processes

What is measurement, control, testing, how do they differ from each other in content and what do they have in common?

By measuring is called experimentally finding the value of a physical quantity (PV) using special technical means. The purpose of measurement is to extract information about the input (measured) quantity from the output signal of the measuring instrument (MI), taking into account its properties and characteristics.

The information flow diagram is shown in Figure 1.

Picture 1.

Tests according to GOST 16504-81, experimental determination of quantitative and/or qualitative characteristics of the properties of the test object as a result of the impact on it during its operation, when modeling the object and/or impacts. During testing. As a rule, measuring instruments, other technical devices, substances and/or materials are used.

Control is the verification of the conformity of a product, process or service to specified requirements. Control is usually carried out in two stages. At the first stage, the value of the controlled characteristic is determined (quantitative - by measurement), at the second stage, the obtained value is compared with the norm. Sometimes both stages are combined in one action. For example, when controlling the dimensions of parts using gauges. Thus, control is a check of compliance with the norm. The norm is established in advance, and verification of compliance with it ends with a decision: “complies, does not comply”; “defective product”, etc.

The presence of a norm presupposes a gradation of the quantitative characteristics of any property and determines the possibility of making a decision.

By analyzing the procedures and tasks of “measurement”, “control” and “testing”, it is possible to establish their relationship, which is shown in Figure 2.

Figure 2. Relationship between the concepts of “measurement”, “control” and “testing”

Measurement can be either part of an intermediate transformation in the control process or the final stage of obtaining information during testing. Testing is the stage of obtaining primary information in the process of control using measuring operations.

What is “unity of measurement”?

In almost all spheres of human activity one has to deal with measuring physical quantities and ensuring their unity. The importance of the uniformity of measurement is so high that a special law “On ensuring the uniformity of measurements” /1/ was issued in Russia.

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

Unity of measurements is necessary in order to be able to compare the results of measurements taken in different places, at different times, using different measuring instruments. It is important both within the country and in interactions between countries. An example of this is that the quality indicators of imported goods are checked in the countries where they are sold.

What quantities are to be measured?

The quantities that a person operates in reality can be divided into two types, as shown in Figure 3.

Figure 3. Classification of quantities

In the course being studied, “Methods and means of measurement, testing and control,” we deal with physical quantities inherent in specific objects, phenomena, processes, that is, quantities that are limited in size and are measurable. A measurable physical quantity is a quantity for which a unit of measurement can be selected and this unit can be embodied in a measuring instrument.

What is a “physical quantity” and “physical parameter”?

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

PV size - quantitative content in a given object of a property corresponding to the concept of “physical quantity”. Considering objects A and B, different in one of their physical properties (for example, weight), we can say about them that they are of different sizes (weights) and differ from each other (A>B or A<Б).

PV value - expression of the size of the PV in the form of a certain number of units accepted for it. The PV value is obtained as a result of its measurement or calculation in accordance with the basic measurement equation.

Q change = AU,

Where Qchange- PV value;

A- the numerical value of the measured physical quantity, expressed in the accepted unit;

U- selected PV unit.

The numerical value of the PV is an abstract number included in the value of the PV value. For example: L=20 mm, where 20 is a numerical value.

In measurement practice, very often it is not the PV that is measured, but physical parameters.

Physical parameter (briefly - parameter) - PV, considered when measuring another physical quantity as an auxiliary one. A physical parameter characterizes a particular feature of the measured physical quantity. For example, when measuring AC voltage, the amplitude and frequency of this current are considered as voltage parameters.

What is called the “true” and “actual” values of a physical quantity?

True value of PV - PV value, which would ideally reflect the existing PV in qualitative and quantitative terms. This concept is correlated with the concept of “absolute truth,” which is impossible in reality.

Actual PV value - the PV value found experimentally and so close to the true value that for the given measurement task it can replace it. In case of repeated measurements, the arithmetic mean value from a number of measured values of a quantity is taken as the actual value. For single measurements - the value of the quantity obtained as a result of measurements with the most accurate SI.

What is the dimension of a physical quantity and how is it determined?

Dimension - a formalized reflection of the qualitative difference in physical quantities is their . The dimension is indicated by the symbol dim, originating from the word dimension, which, depending on the context, can be translated as both size and dimension.

The dimensions of basic physical quantities are indicated by the corresponding capital letters. For length, mass and time, e.g.

dim l = L; dim m = M; dim t = T.

When determining the dimension derivatives quantities are guided by the following rules:

1. The dimensions of the right and left sides of the equation cannot but coincide, because Only identical properties can be compared with each other. Thus, only quantities having the same dimensions can be summed algebraically.

2. The algebra of dimensions is multiplicative, i.e. consists of one single multiplication action.

2.1. The dimension of the product of several quantities is equal to the product of their dimensions. So, if the relationship between the values of quantities Q, A, B, C has the form Q = ABC, then

dim Q = dim AChdim HFdim C.

2.2. The dimension of a quotient when dividing one quantity by another is equal to the ratio of their dimensions, i.e. if Q=A/B then

dim Q = dim A / dim B.

2.3. The dimension of any quantity raised to a certain power is equal to its dimension to the same power. So, if Q=A n , then

dim Q = dim A = dim n A.

For example, if the speed is determined by the formula V = S/t, then

dim V = dim S/dim t = L/T=LT -1 .

If the force according to Newton’s second law is F = ma, where a = V/t is the acceleration of the body, then

dim F = dim m dim a = ML/T 2 = MLT -2 .

Thus, it is always possible to express the dimension of a derivative physical quantity in terms of the dimensions of the basic physical quantities using a power monomial:

where L, M, T, are the dimensions of the corresponding basic physical quantities; , - exponents of dimension. Each of the exponents of the degrees of dimension can be positive or negative, an integer or fractional number, or zero.

If all dimension indicators are equal to zero, then such a quantity is called dimensionless. She may be relative, defined as the ratio of quantities of the same name (for example, relative dielectric constant), and logarithmic defined as the logarithm of a relative quantity (for example, the logarithm of a power or voltage ratio).

Dimension theory is widely used to quickly check the correctness of formulas (according to rule 1). The formal application of dimensional algebra sometimes makes it possible to determine an unknown relationship between physical quantities.

What is a unit of measurement of a physical quantity?

Unit of measurement of physical quantity a physical quantity of a fixed size, which is conventionally assigned a numerical value equal to one, and used for the quantitative expression of physical quantities similar to it. Units of measurement of a certain quantity may differ in size, for example, meter, foot and inch, being units of length, have different sizes: 1 foot = 0.3048 m, 1 inch = 0.254 m.

What is a system of units of physical quantities?

To ensure the uniformity of measurements, from January 1, 1982, GOST 8.417-81 GSI “Units of Physical Quantities” was introduced in our country. The standard meets the requirements of the International System of Units (SI) and contains:

SI units (basic, minor, derivative);

Non-system units allowed on a par with SI units and in combination with them;

The rule for the formation of multiples and submultiples;

Name of units, their designations and other provisions.

The standard does not apply to units used in scientific research works and in publications of their results, as well as to units of quantities assessed on conventional scales (scales of metal hardness, earthquakes, sea waves, photosensitivity, etc.).

Thus, Withsystem of units of physical quantities a set of basic and derived units of physical quantities, formed in accordance with the principles for a given system of physical quantities. For example, the International System of Units (SI), adopted in 1960.

What are the SI base units?

Basic unit of the system of units of physical quantities a unit of a basic physical quantity in a given system of units.

The main units of the International SI System are: meter, kilogram, second, ampere, degree Kelvin, candella, mole. When choosing these units, we were guided only by practical expediency, i.e. ease of use of units in human activities.

A meter is a unit of length equal to the path traveled in a vacuum by light in 1/299792458 of a second. The meter was originally defined as the length of 1/40,000,000 of the length of the Parisian meridian and was reproduced as the distance between the marks marked on a platinum and later platinum-iridium bar of X-shaped cross-section. But this value turned out to be unstable, so the meter began to be expressed using the wavelength of the red line of cadmium, and currently - the orange line of the krypton-86 atom. 1 meter corresponds to 1650763.73 wavelengths of radiation in vacuum, corresponding to the transition between the 2p 10 and 5d 5 levels of the Kr-86 atom.

The meter is determined by indirect methods on radiometric bridges. They consist of a series of radio generators and lasers arranged in series with frequency multiplication between them. A reference frequency of 5 MHz is supplied to the input from a generator synchronized through a system of frequency multipliers with hydrogen time and frequency reference generators, calibrated against a cesium frequency reference. The bridge multiplies this frequency to a value of about 1*10 14 Hz. Its task is to measure the frequencies of stabilized lasers. Knowing them, the wavelengths of their radiation are calculated and, using optical interferometers, various measures of length are certified and verified.

A kilogram is a unit of mass equal to the mass of 1.000028 dm 3 of water at a temperature of its highest density of 4 °C.

The standard kilogram in Russia is a cylinder with a height and a diameter of 39 mm with rounded ribs. Work is underway to determine the kilogram in terms of Volts and Ohms using inverted ampere balances.

A second is a unit of time equal to 9192631770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom. The standard second was established in 1967. It is based on the ability of atoms to emit and absorb energy during the transition between two energy states in the radio frequency region. A reference point, or quantum frequency standard, is a device for accurately reproducing the frequency of electromagnetic oscillations in ultra-high-frequency and optical spectra, based on measuring the frequency of quantum transitions of atoms, ions or molecules. Passive quantum standards use the frequencies of spectral absorption lines, while active ones use the stimulated emission of photons by particles. Active quantum frequency standards are used on a beam of ammonia molecules (so-called molecular generators) and hydrogen atoms (hydrogen generators). Passive frequency standards - on a beam of cesium atoms (cesium frequency benchmarks)

To reproduce the second, cesium frequency generators (standards) are used - these are highly stable generators of monochromatic radiation (signal) with a frequency of 9192631770 Hz; the frequency error does not exceed 1.5*10 -13. The Russian state standard uses hydrogen generators periodically compared with cesium generators; their long-term frequency is not postulated, but the instability is less than 3*10 -14. In addition, the standard contains equipment for generating and storing time scales. The main scale of TA is uniform atomic time with a fixed zero, not related to the rotation and position in space of the Earth. Other scales: UT0 - universal time (mean solar “s”); UT1 corrected for pole fluctuations; UT2 - adjusted for seasonal unevenness of the Earth's rotation. These are worldwide scales, gradually diverging from TA due to the slowing speed of the Earth's rotation. To harmonize them, the UTC scale was introduced, in which 1s utc = 1s ta, and the beginning of counting can change to 1s from the 1st day of each month (1.01 or 1.06). In Russia, time signals are transmitted on TV or radio using the UTC scale.

Ampere is a unit of electric current. An ampere is equal to the strength of a constant current, which, passing through two parallel straight conductors of infinite length and a negligibly small circular cross-sectional area, located in a vacuum at a distance of 1 m from each other, would cause on each section of the conductor 1 m long an interaction force equal to 2 10 -7 N.

As Ampere standards, ampere scales are used, which realize A by measuring force, or by measuring the moment of force acting on a coil with current placed in the magnetic field of another coil. This is a precision equal-arm scale made of non-magnetic materials. A cup is suspended at one end of the rocker to accommodate permanent and additional balancing weights. A moving coil is suspended from the other end of the rocker arm and enters coaxially into a stationary coil of larger diameter. The coil windings (in the simplest case) are connected in series. In de-energized mode, the scales are balanced. When electric current passes through the coils, the moving coil is pulled into (or pushed out of) the stationary coil. An additional balancing weight is used to restore balance. Based on the results of the metrological study, the value of the mass of this load is calculated, corresponding, for example, to an electric current of 1A. By connecting a reference resistor to the coil circuit, you can calibrate the EMF reference measures (current standards are not yet used).

More accurate standards based on magnetic induction measurements using nuclear magnetic resonance are currently used only as secondary standards. In 1992, Russia approved the national standard A, the size of which is reproduced using Volt and Ohm elements. The standard deviation (RMSD) is no more than 1·10 -8, systematic errors (NSE) cannot be excluded more than 1·10 -7 (for ampere scales CKO?4·10 -6, NSP?8·10 -6).

Kelvin is a unit of thermodynamic temperature equal to 1/273.16 of the thermodynamic temperature of the triple point of water. The triple point of water is the state of water in a sealed glass vessel in which ice, water and its vapor are in equilibrium: water does not freeze, does not evaporate, ice does not melt, and steam does not condense.

State primary standards of Russia reproduce the international degree scale MGSh-90 in two subranges: 0.8...273.16 K and 373.16...2773 K. The low-temperature standard includes two groups of iron-rhodium and platinum resistance thermometers as its main part , the calibration dependencies of which were determined based on the results of comparisons of results obtained in laboratories in Russia, England, the USA, Australia and Holland. Each group contains two platinum and two iron-rhodium thermometers, permanently located in a comparison block - a massive cylinder with four longitudinal channels for thermometers. The transfer of the scale to thermometers - secondary and working standards - is carried out by bringing them into thermal contact with a reference comparison unit and comparison in a cryostat. In addition to devices for precise resistance measurements, the set of standard control equipment includes a set of installations for realizing temperatures of reference points, a gas interpolating thermometer with a unique mercury manometer and a comparison cryostat. Standard deviation of the standard is 0.3…1.0 mK, NSP 0.4…1.5 mK, the lowest value of the reproducible temperature is 0.8 K.

The second standard includes platinum resistance thermometers, temperature lamps, equipment for reproducing reference points in the range 273.16...1355.77 K, (RMS?5·10 -5 ...1·10 -2; NSP?1·10 - 45...10 -3). The following relationships have been established for various temperature scales:

Celsius scale: C=K=t C +273.16

Reaumur scale: 1R=1.25 C; t C =1.25 t R ; T=1.25 t R +273.16

Fahrenheit scale: 1F=5/9C=5/9K; t C =5/9(t F -32); T=5/9(t F -32)+273.16

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

A mole is a unit of quantity of a substance equal to the amount of substance containing the same number of structural elements (atoms, molecules) as are contained in 0.012 kg of carbon-12. Mole standards have never been created, since the mass of one mole of various substances or structures is numerically equal to Avogadro’s number - 6.025·10 23 particles; Measuring instruments calibrated in moles are not available. There are reasonable proposals to exclude the mole from the basic SI units and allow it to be used on a par with SI units as a special unit of mass convenient for chemical calculations.

The Russian standard base has 114 state standards and more than 250 secondary standards of PV units. Of these, 52 are located at VNIIM named after. D.I. Mendeleev (S.-Pb.), incl. standards m, kg, A, K, rad; 25 - in VNIIFTRI (physical-technical and radio-technical measurements, Moscow, including standards of time and frequency units; 13 - in the VNIIFTRI of optical-physical measurements, including candelas; respectively 5 and 6 - in the Ural and Siberian Research Institute of Metrology.

What are derived SI units?

Derived unit of the system of units of physical quantities - a unit of a derivative of a physical quantity of a system of units, formed in accordance with an equation connecting it with the basic units or with the basic and already defined derivatives.

Derived SI units are formed from basic, additional and previously formed derived SI units using equations of connection between physical quantities in which the numerical coefficients are equal to unity. For this, the quantities on the right and left sides of the coupling equation are taken to be equal to SI units. For example, for the derivative unit of speed, determined from the equation v = L/T, write the equation of units [v] = [L] / [T], and instead of the symbols L and T, substitute their units (1 m and 1 s) and get [V ]=1 m/1 s = 1 m/s. This means that the SI unit of speed is meters per second. Derived units may be named after famous scientists. Thus, the equation for the relationship between quantities to determine the unit of pressure is p=F/S, the equation for the relationship between the units of pressure, force and area is [p]= [F]/[S]. Substituting instead F and S units of these quantities in SI (1 N and 1 m 2), we obtain [p] = 1 N/ 1 m 2 = 1 N/m 2. This unit was given the name pascal (Pa) after the French mathematician and physicist Blaise Pascal.

What are multiples and submultiples? and what are the rules for their formation?

At the XI General Conference on Weights and Measures, together with the adoption of SI, 12 multiple and submultiple prefixes were adopted, to which new ones were added at subsequent conferences. Prefixes made it possible to form decimal multiples and submultiples of SI units.

Multiple unit of physical quantity a unit of physical quantity that is an integer number of times larger than a systemic or non-systemic unit. For example, a unit of length 1 km (kilometer) = 10 3 m, i.e., a multiple of the meter; frequency unit 1 MHz (megahertz) = 10 6 Hz, multiple of hertz; unit of radionuclide activity 1 MBq (megabecquerel) = 10 6 Vk, multiple becquerel.

Submultiple unit of physical quantity - a unit of physical quantity that is an integer number of times smaller than a systemic or non-systemic unit.

The names of multiple and submultiple units are formed using the prefixes given in Table 3.

Table 3 - Factors and prefixes for SI units

What is a “non-system unit of physical quantity”?

Non-systemic unit of physical quantity - a unit of physical activity that is not included in any of the accepted systems of units. In relation to SI units, non-system units of physical quantities are divided into four types: acceptable on a par with basic units; approved for use in special areas; obsolete (invalid); temporarily allowed.

To non-systemic units allowed on a par with SI units , relate: ton - unit of mass; degree, minute, second - unit of plane angle; liter - unit of capacity; minute, day, week, month, year, century - units of time.

Non-systemic units allowed for use in special fields include: in physics - electron-volt; in agriculture - a hectare; in astronomy - light year; in optics - diopter.

Non-systemic units, temporarily used along with SI units, include: in maritime navigation: - nautical mile - a unit of length; knot - unit of speed; for precious stones the unit of mass is the carat; in other areas: revolution per minute (rpm) - unit of rotational speed; bar (bar) is a unit of pressure.

Temporarily used units must be (and are) withdrawn from use in accordance with international agreements.

Non-systemic units withdrawn from use include: kilogram-force - a unit of force, weight; centner - unit of mass; horsepower - a unit of power, etc.

What is measurement?

Measurement physical quantities is a set of operations for the use of a technical means that stores a unit of a physical quantity, ensuring that the relationship (explicit and implicit) of the measured quantity with its unit is found and the value of this quantity is obtained.

The measurement result is written in the form of a general measurement equation:

Q meas = n [Q],

where Q meas - measured physical quantity; P - number of units; [Q] - unit of physical quantity.

Note. Since not only physical quantities are measured, there is another interpretation of the concept of “measurement”. Measurement is a set of operations performed to determine the value of a quantity. Here, the definition of the concept of “measurement” is not limited to finding the value of a physical quantity; there is no mention of technical means. This interpretation of the concept is suitable for both physical and non-physical quantities. Consequently, various types of quantitative assessment of quantities can also be classified as measurements.

How are measurements classified?

With all the variety of measurements, they can be classified according to six criteria.

Based on criterion 1 of the dependence of the measured value on time, measurements are divided into static and dynamic.

Static measurement measurement of PV, which is taken in accordance with a specific measurement task to be constant throughout the measurement time. For example, measuring DC voltage of electric current. Measuring the size of a land plot.

Dynamic measurement - measurement of a physical quantity that varies in size. For example, measuring the height of a descending aircraft, that is, with a continuous change in the size of the measured value; measurement of alternating voltage of electric current.

Based on criterion 2 - accuracy of measurement results, measurements are divided into equally accurate and unequally accurate.

Equal precision measurements - measurements of quantities performed by measuring instruments of equal accuracy, under the same conditions, by the same operator, with the same care and the same number of measurements.

Unequal measurements - measurements of a quantity performed by measuring instruments that differ in accuracy, under different conditions, by different operators, with a different number of measurements. In order for the measurement results to be unequal, the presence of one of the listed factors is often sufficient.

Based on 3 conditions that determine the accuracy of the result, measurements are divided into technical and metrological.

Technical measurements measurements using working measuring instruments. Technical measurements are performed for the purpose of monitoring and managing technological processes, scientific experiments, diagnosing diseases, and so on. An example of technical measurements is measuring the speed of a bus, an airplane, that is, any moving body.

Metrological measurements These are measurements performed using standards and standard measuring instruments in order to reproduce units of physical quantities or transfer their size to working measuring instruments. For example, verification or calibration of working weights of the 2nd accuracy class according to the verification scheme is carried out with standard weights of the 1st category on scales of the 1st category. Such measurements are made to establish the accuracy of standards and working measuring instruments, that is, they are metrological. Metrological measurements are divided into measurements of the highest possible accuracy and control and verification measurements.

Based on criterion 4, the number of measurements performed to obtain the result, measurements are divided into single (ordinary) and multiple (statistical).

Single measurement This is a measurement taken once. For example, measuring a specific moment in time using a clock.

Multiple measurements This is a measurement of the same physical quantity of constant size, the result of which is obtained from several successive measurements, that is, a measurement consisting of a number of single measurements. The result of multiple measurements is usually taken as the arithmetic mean value from the results of single measurements included in the series. A measurement is considered multiple if the number of individual measurements is n > 4.

Based on criterion 5 - the method of obtaining the result (by type), measurements are divided into direct, indirect, cumulative and joint.

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

Indirect measurement is a determination of a physical quantity based on the results of direct measurements of other physical quantities that are functionally related to the desired quantity. For example, the length of the hypotenuse of a right triangle (c) can be determined by direct measurements of the two legs (a and b), which are mathematically related to the hypotenuse by the formula:

Aggregate Measurements These are measurements of several quantities of the same name carried out simultaneously. In this case, the required values of quantities are determined by solving a system of equations obtained by measuring these quantities in various states.

Joint measurements These are measurements of two or more non-identical quantities carried out simultaneously to determine the relationship between them.

The basic equations for cumulative and joint measurements have the form:

Where at 1 ...y n- required quantities;

x 1 ...X m- parameters or quantities established on the basis of direct or indirect measurement;

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

a functional relationship of the form is known:

that is, the relationship between the resistance R t at any temperature, the components R 0 at t = 0 and the constant coefficients and is known.

With three known values t1, t2, t3 measured R tl , R t 2 , R t 3 .

Let's make up the equations:

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

According to characteristic 6, the method of expressing measurement results, measurements are divided into absolute and relative.

Absolute measurement is a measurement based on direct measurements of one or more quantities in its units.

The concept of absolute measurement is used as the opposite of the concept of relative measurement.

Relative dimension measurement of the ratio of a quantity to a quantity of the same name, which plays the role of a unit, or measurement of a change in a quantity in relation to a quantity of the same name, taken as the initial one.

For example, measuring the strength of an electric current with an ammeter, when the measurement result is expressed in a unit of the measured value (in amperes), is a direct measurement.

Measuring a mass on a two-pan scale, the value of which is greater than the measurement limit on the scale, is relative. On the scale scale there will be a reading corresponding to the difference between the measured mass and the mass of the original weight, which is smaller than the weight being weighed, installed on the weight platform.

What is the relationship between the concepts of “technique”, “method” and “principle” of measurements?

Each measuring process, regardless of the purpose of its implementation and the final result, consists of the following main stages: preparation for measurements, performing measurements, processing measurement results. In order to ensure proper measurement quality, each stage of the measurement process must be performed in accordance with established rules, which are determined by the measurement methodology.

Measurement procedure this is an established set of operations and rules during measurement, the implementation of which ensures that the necessary measurement results are obtained in accordance with a given method.

The measurement technique includes: analysis of the measurement task; choice of principle, method and measuring instrument; preparing the measuring instrument for work; requirements for measurement conditions; taking measurements indicating their number; processing of measurement results, including calculation, introduction of corrections and methods of expressing errors.

Typically, the measurement technique is regulated by some regulatory and technical document. Many measurement techniques are unified, since their unification is important in ensuring the uniformity of measurements.

The choice of the principle and method of measurement is carried out on the basis of an analysis of the measurement task, in which the following questions are resolved: what physical quantities and parameters of the object are to be measured; what accuracy should the measurement result be; in what form it should be presented so that it corresponds to the purpose of the measurement task.

Measuring principle This is a physical phenomenon or effect that forms the basis for measurements using one or another type of measuring instrument.

For example, according to the Seebeck phenomenon, a thermo-emf arises in a closed electrical circuit formed by two dissimilar conductors. direct current, proportional to the temperature difference between the ends of the soldered conductors. The magnitude of this thermo-emf. can be represented by the function E ab= f(t a- t b) , Where t a And t b temperature of the ends of soldered conductors A And IN. This physical phenomenon is the basis for temperature measurements with thermocouples.

Measurement method th a technique or set of techniques for comparing a measured physical quantity with its unit in accordance with the implemented measurement principle. Measurement methods are methods for solving measurement problems, characterized by their theoretical justification and the development of basic techniques for using measuring instruments. Measurement methods are very diverse. Their appearance is due to scientific and technological progress.

The classification of the main measurement methods is shown in Figure 5. The classification feature in this division of measurement methods is the presence or absence of a measure during measurement. In this regard, measurement methods are divided into the method of direct assessment and the method of comparison with a measure.

Method of direct assessment (counting) a measurement method in which the PV value is determined directly from the reading device of the measuring instrument (Figure 6).

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

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

Zero measurement method a method of comparison with a measure, in which the resulting effect of the influence of the measured quantity and measure on the comparison device is brought to zero (Figure 7).

Differential measurement method a method of measurement in which the quantity being measured is compared with a homogeneous quantity having a known value that is initially different from the quantity being measured, and in which the difference between these two quantities is measured.

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

Contrasting method a method of comparison with a measure, in which the measured value and the value reproduced by the measure simultaneously influence the means of comparison, with the help of which the relationship between these values is established (Figure 8, a).

Substitution method - a method of comparison with a measure, in which the measured quantity is replaced by a measure of a known quantity (Figures 7, b and 8, b).

Coincidence method (vernier method) - a method of comparison with a measure, in which the difference between the measured value and the value of the reproduced measure is measured using the coincidence of scale marks or periodic signals.

Direct assessment method.

The weight of the load X is determined on the basis of a measurement transformation based on the value - the deformation of the spring.

Figure 6. Direct assessment measurement scheme.

Methods of comparison with a measure.

A load X is balanced by weights.

Figure 7. Zero method measurement schemes:

a) method of opposition; b) substitution method.

Figure 8. Differential measurement schemes:

From the diagrams shown in Figures 7 and 8 it follows that a distinctive feature of these methods is the simultaneous influence of the measured quantity and measure. With the substitution method, the measured quantity (object of measurement) and the measure act on the measuring instrument alternately.

2 . Measurement conditions

For what purpose and how are measurement conditions standardized?

During measurements, along with the measured physical quantity, other physical factors are involved, the action of which can distort the measurement result. These accompanying quantities are called influencing quantities and primarily include: ambient temperature, atmospheric pressure, humidity, amplitude and frequency of oscillations during vibration, voltage and frequency of alternating current, magnetic induction, etc. During the measurement process, changing the values of influencing quantities is extremely undesirable, since this leads to a decrease in the measurement accuracy.

To increase the accuracy of measurements, the values of influencing quantities are normalized. In this case, for each type of measurement, a set of influencing quantities and their values are established.

The following are accepted as normal values of some influencing quantities:

Ambient air temperature (20±2) °C;

Barometric pressure (101.325+3.3) kPa;

Supply voltage (22010) V,

AC frequency (505) Hz, etc.

The basic (marginal) error of measuring instruments is usually calculated for the normal values of influencing quantities; the results of measurements performed under different conditions are given to them.

The limits of normal values of influencing quantities are determined by GOST 8.395-80 “Normal conditions for verification”.

Normal conditions for using measuring instruments are not operating conditions. For each type of measuring instrument, standards or technical specifications establish an extended (working) range of values of influencing quantities, within which the value of the additional error is normalized.

The working range of influencing quantities is taken, for example:

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

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

Supply voltage from 187 to 242V, etc.

In working conditions, external phenomena may occur, influence
which does not directly affect the readings of the device (output signal of the converter), but can cause damage and malfunction of measuring instrument units (aggressive gases, dust, water, etc.). Measuring instruments are protected from the effects of these factors using protective cases, covers, etc. In addition, external mechanical forces (vibration, shaking, shock) can affect measuring instruments, leading to distortion of their readings and the impossibility of reporting. Measuring instruments operating under mechanical influence are protected by special devices from destructive effects or increase their strength.

Depending on the degree of protection from external influences and resistance to them, devices and converters are divided into ordinary, vibration-proof, dust-proof, splash-proof, hermetic, gas-proof, explosion-proof, etc. This makes it possible to select SI in relation to operating conditions.

What are measuring instruments?

Measuring instrument - this is a technical means (or a set of technical means) intended for measurements, having standardized technical characteristics that reproduce and/or store one or more physical quantities, the dimensions of which are assumed unchanged over a known period of time (inter-verification interval).

When talking about measuring instruments, they use the following concepts: SI type, SI type.

View measuring instruments - a set of measuring instruments designed to measure a given type of PV.

Type measuring instruments - a set of measuring instruments for the same purpose, based on the same principle of operation, having the same design, manufactured according to the same technical documentation, but having different modifications (for example, differing measurement limits). A type of measuring instrument may include several types, a type may include several modifications.

Classification of measuring instruments can be carried out according to various criteria. In metrology, measuring instruments are usually classified according to type, principle of operation and metrological purpose (Figure 10).

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

Measure - a measuring instrument designed to reproduce and/or store PV of one or more specified sizes, the values of which are expressed in conventional units and are known with the required accuracy. The following types of measures are distinguished:

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

- multivalued measure- a measure that reproduces a physical quantity of different sizes (for example, a line measure of length - a ruler);

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

- store measures- a set of measures structurally combined into a single device, which contains devices for connecting them in various combinations (for example, a store of electrical resistances).

Transducer - a measuring instrument used to convert a measured quantity into another quantity or a measured signal, convenient for processing, storage, further transformations, display or transmission, but not amenable to direct perception by the observer.

Measuring device - a measuring instrument designed to generate a signal about the value of a measured physical quantity in a specified range in a form accessible to direct perception by an observer.

Measuring setup - a set of functionally combined measures, measuring instruments, measuring transducers and other devices designed to measure one or more physical quantities and located in one place.

Measuring installations are usually used in scientific research carried out in laboratories, in quality control and in metrological services to determine the metrological characteristics of measuring instruments. They are designed to display measurement information in a form convenient for direct perception by the operator.

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

Depending on the purpose, measuring systems are divided into measuring information, measuring control, measuring control, measuring computing, etc. An example is the measuring system of a thermal power plant, containing a large number of measuring channels, the sensors of which are spaced in space at a considerable distance from each other.

What are the main parts of measuring devices?

Measuring devices (MD) consist of elements that perform the functions of converting the input signal according to the form or type of energy, calming oscillations, protecting against interference fields, switching circuits, presenting, processing information, etc.

The measuring devices include:

- conversion element, in which one of a number of quantity transformations occurs;

- measuring circuit- a set of elements of a measuring instrument that form a continuous path of the measuring signal of one PV from input to output; (for the measuring system it was called the measuring channel);

- sensing element- part of the measuring transducer in the measuring circuit that perceives the input measuring signal;

- measuring mechanism- a set of elements of a measuring instrument that provide the necessary movement of the pointer (arrow, light spot, etc.). For example, for a millivoltmeter, the measuring mechanism consists of a permanent magnet and a movable frame;

- indicating device- a set of elements of a measuring instrument that provide visual perception of the values of the measured quantity or quantities associated with it;

- pointer- part of the indicating device, the position of which relative to the scale marks determines the readings of the measuring instrument. The pointer can be an arrow, a light beam, the surface of a liquid column in a thermometer, etc.

- recording device- a set of elements of a measuring instrument that record the value of the quantity being measured or associated with it.

What are the block diagrams of measuring devices?

For the convenience of analyzing various connections of measuring devices with each other and with autonomous control means, any measuring device is considered as a converter for converting the input signal (input action) X into the output signal (response) Y.

Figure 10 shows block diagrams of measuring instruments based on the method of direct transformation (a) - direct action, and inverse transformation (comparison) (b) - balancing or compensating transformation. The block diagram of a particular device is completely determined by the conversion method.

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

A measuring device based on the direct conversion method works as follows. The measured quantity X enters the sensitive element 1, where it is converted into another physical quantity convenient for further use (current, voltage, pressure, displacement, force), and enters the intermediate element 2, which usually either amplifies the incoming signal or converts it according to form. Sometimes element 2 may be missing. The output signal of element 2 is supplied to the measuring mechanism 3, the movement of the elements of which is determined using a reading device 4. The output signal Y (reading), generated by the measuring mechanism, can be perceived by the human senses.

A distinctive feature of comparison devices is the presence of negative feedback (Figure 10, b). The Z signal arising from the output of the sensing element is supplied to the comparison conversion element 5 (comparing element), which is capable of comparing two quantities received at its input. In addition to Z, a balancing signal Z level is supplied to the input of element 5 with the opposite sign, which is generated at the output of the inverse converting element 6. At the output of element 5 a signal is generated that is proportional to the difference in the values of Z Z level. It enters the intermediate transforming element 2, the output signal of which is sent simultaneously to the measuring mechanism 3 and to the input of element 6. Depending on the type of intermediate transformations of element 2, for each value of the measured parameter and the corresponding value Z, the difference (Z Z ur) received at the input element 5, can be reduced to 0 or have some small value proportional to the measured value.

What elements of reading devices are used to obtain readings from measuring instruments?

An indication is the value of a quantity or a number on the indicating device of a measuring instrument, expressed in the accepted units of this quantity. The reading device is a digital display, or more often a scale with a pointer. For scale reading devices, it is customary to use a number of concepts illustrated in Figure 11.

Scalemeasuring instruments- part of the indicating device, which is an ordered series of marks along with the numbering associated with them. The marks may be applied evenly or unevenly depending on the type of scale.

Scale mark- a sign on the scale of a measuring instrument (dash, tooth, dot, etc.), constituting a certain value of a physical quantity.

How to measure a physical quantity

Definition 1

A physical quantity is a characteristic that is common to many material objects or phenomena in a qualitative sense, but can acquire individual meaning for each of them.

The measurement of physical quantities is a sequence of experimental operations to find a physical quantity that characterizes an object or phenomenon. To measure means to compare the measured quantity with another homogeneous quantity, taken as a standard.

The measurement ends with determining the degree of approximation of the found value to the true value or to the true average. The true average is characterized by values that are statistical in nature, for example, the average height of a person, the average energy of gas molecules, and the like. Parameters such as body weight or volume are characterized by a true value. In this case, we can talk about the degree of approximation of the found average value of a physical quantity to its true value.

Measurements can be either direct, when the desired quantity is found directly from experimental data, or indirect, when the final answer to the question is found through known relationships between a physical quantity. We are also interested in quantities that can be obtained experimentally using direct measurements.

Path, mass, time, force, stress, density, pressure, temperature, illumination - these are not all examples of physical quantities that many have become acquainted with while studying physics. To measure a physical quantity means to compare it with a homogeneous quantity taken as a unit.

Measurements can be direct or indirect. In the case of direct measurements, a quantity is compared with its unit (meter, second, kilogram, ampere, etc.) using a measuring device calibrated in the appropriate units.

The main experimentally measured quantities are distance, time and mass. They are measured, for example, using a tape measure, a clock, and a scale (or scale), respectively. There are also instruments for measuring complex quantities: speedometers are used to measure the speed of bodies, ammeters are used to determine the strength of electric current, etc.

Main types of measurement errors

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

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

The main types of measurement errors include:

Gross errors (misses) that arise as a result of the negligence or inattention of the experimenter. For example, a reading of a measured value was accidentally carried out without the necessary instruments, a number on a scale was read incorrectly, and the like. These errors are easy to avoid.
Random errors arise for various reasons, the effect of which is different in each experiment; they cannot be foreseen in advance. These errors are subject to statistical laws and are calculated using mathematical statistics methods.
Systematic errors arise as a result of an incorrect measurement method, malfunction of instruments, etc. One of the types of systematic errors is the errors of instruments that determine the measurement accuracy of instruments. When reading, the measurement result is inevitably rounded, taking into account the division value and, accordingly, the accuracy of the device. These types of errors cannot be avoided and must be taken into account along with random errors.

The proposed guidelines provide the final formulas of the theory of errors necessary for mathematical processing of measurement results.

Area in SI system

Area, volume and velocity are derived units; their dimensions come from basic units of measurement.

In calculations, multiple units are also used; a whole power of ten exceeds the basic unit of measurement. For example: 1 km = 1000 m, 1 dm = 10 cm (centimeters), 1 m = 100 cm, 1 kg = 1000 g. Or private units, a whole degree of ten less than the established unit of measurement: 1 cm = 0.01 m , 1 mm = 0.1 cm.

Time units are a little different: 1 minute. = 60 s, 1 hour = 3600 s. The quotients are only 1 ms (millisecond) = 0.001 s and 1 μs (microsecond) = 10-6s.

Figure 1. List of physical quantities. Author24 - online exchange of student works

Measurements and measuring instruments

Measurements and measuring instruments includes:

Measuring instruments are devices with which physical quantities are measured.
Scalar physical quantities are physical quantities that are specified only by numerical values.
Physical quantity is a physical property of a material object, physical phenomenon, process that can be characterized quantitatively.
Vector physical quantities are physical quantities characterized by numerical value and direction. The value of a vector quantity is called its modulus.
Length is the distance from point to point.
Area is a quantity that determines the size of a surface, one of the main properties of geometric shapes.
Volume is the capacity of a geometric body, or a part of space limited by closed surfaces.
The displacement of a body is a directed segment drawn from the initial position of the body to its final position.
Mass is a physical quantity, which is one of the main characteristics of a body, usually denoted by the Latin letter m.
Gravity is the force with which the Earth attracts objects.

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