Basic quantities in physics. Basic physical quantities in mechanics, their measurement and units
The concept of a physical quantity is common in physics and metrology and is used to describe material systems of objects.
Physical quantity, as mentioned above, this is a characteristic that is common in a qualitative sense for many objects, processes, phenomena, and in a quantitative sense - individual for each of them. For example, all bodies have their own mass and temperature, but the numerical values of these parameters for different bodies are different. The quantitative content of this property in an object is the size of the physical quantity, numerical estimate of its size called the value of a physical quantity.
A physical quantity that expresses the same quality in a qualitative sense is called homogeneous (of the same name ).
Main task of measurements - obtaining information about the values of a physical quantity in the form of a certain number of units accepted for it.
Values physical quantities are divided into true and real.
True meaning - this is the meaning in an ideal way reflecting qualitatively and quantitatively the corresponding properties of the object.
Real value - this is a value found experimentally and so close to the true one that it can be taken instead.
Physical quantities are classified according to a number of characteristics. The following are distinguished: classifications:
1) in relation to measurement information signals, physical quantities are: active - quantities that can be converted into a measurement information signal without the use of auxiliary energy sources; passive new - quantities that require the use of auxiliary energy sources, through which a measurement information signal is created;
2) on the basis of additivity, physical quantities are divided into: additive , or extensive, which can be measured in parts, and also accurately reproduced using a multi-valued measure based on the summation of the sizes of individual measures; Not additive, or intensive, which are not directly measured, but are converted into a measurement of magnitude or measurement by indirect measurements. (Additivity (lat. additivus - added) is a property of quantities, consisting in the fact that the value of a quantity corresponding to the whole object is equal to the sum of the values of quantities corresponding to its parts).
Evolution of development systems of physical units.
Metric system- the first system of units of physical quantities
was adopted in 1791 by the French National Assembly. It included units of length, area, volume, capacity and weight , which were based on two units - meter and kilogram . It was different from the system of units used now, and was not yet a system of units in the modern sense.
Absolute systemunits of physical quantities.
The method for constructing a system of units as a set of basic and derived units was developed and proposed in 1832 by the German mathematician K. Gauss, calling it an absolute system. He took as a basis three quantities independent of each other - mass, length, time .
For the main units of measurement he accepted these quantities milligram, millimeter, second , assuming that the remaining units can be determined using them.
Later, a number of systems of units of physical quantities appeared, built on the principle proposed by Gauss, and based on the metric system of measures, but differing in basic units.
In accordance with the proposed Gauss principle, the main systems of units of physical quantities are:
GHS system, in which the basic units are the centimeter as a unit of length, the gram as a unit of mass and the second as a unit of time; was installed in 1881;
MKGSS system. The use of the kilogram as a unit of weight, and later as a unit of force in general, led at the end of the 19th century. to the formation of a system of units of physical quantities with three basic units: meter - a unit of length, kilogram - force - a unit of force, second - a unit of time;
5. MKSA system- The basic units are meter, kilogram, second and ampere. The foundations of this system were proposed in 1901 by the Italian scientist G. Giorgi.
International relations in the field of science and economics required the unification of units of measurement, the creation unified system units of physical quantities, covering various branches of the measurement area and preserving the principle of coherence, i.e. equality of the coefficient of proportionality to unity in the equations of connection between physical quantities.
SystemSI. In 1954, the commission to develop a unified International
system of units proposed a draft system of units, which was approved in 1960. XI General Conference on Weights and Measures. The International System of Units (abbreviated SI) takes its name from the initial letters of the French name System International.
The International System of Units (SI) includes seven main ones (Table 1), two additional ones and a number of non-systemic units of measurement.
Table 1 - International system of units
|
Physical quantities that have an officially approved standard |
Unit of measurement |
Abbreviated unit designation physical quantity |
|
|
international |
|||
|
kilogram | |||
|
Electric current strength | |||
|
Temperature | |||
|
Illuminance unit | |||
|
Quantity of substance | |||
Source: Tyurin N.I. Introduction to metrology. M.: Standards Publishing House, 1985.
Basic units measurements physical quantities in accordance with the decisions of the General Conference on Weights and Measures are defined as follows:
meter - the length of the path that light travels in a vacuum in 1/299,792,458 of a second;
a kilogram is equal to the mass of the international prototype of the kilogram;
a second is equal to 9,192,631,770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the Cs 133 atom;
An ampere is equal to the strength of a constant current, which, when passing through two parallel straight conductors of infinite length and negligibly small circular cross-sectional area, located at a distance of 1 m from each other in a vacuum, causes an interaction force on each section of the conductor 1 m long;
candela is equal to the luminous intensity in a given direction of a source emitting ion-protective radiation, the energetic luminous intensity of which in this direction is 1/683 W/sr;
a kelvin is equal to 1/273.16 of the thermodynamic temperature of the triple point of water;
mole equals quantity substances of the system, containing the same number of structural elements as there are atoms in C 12 weighing 0.012 kg 2.
Additional units International system of units for measuring plane and solid angles:
radian (rad) - a flat angle between two radii of a circle, the arc between which is equal in length to the radius. In degrees, a radian is equal to 57°17"48"3;
steradian (sr) - a solid angle whose vertex is located at the center of the sphere and which cuts out on the surface of the sphere an area equal to the area of a square with a side length equal to the radius of the sphere.
Additional SI units are used to form the units of angular velocity, angular acceleration and some other quantities. The radian and steradian are used for theoretical constructions and calculations, since most of the practical values of angles in radians are expressed as transcendental numbers.
Non-system units:
A tenth of a white is taken as a logarithmic unit - decibel (dB);
Diopter - luminous intensity for optical instruments;
Reactive power-var (VA);
Astronomical unit (AU) - 149.6 million km;
A light year is the distance a ray of light travels in 1 year;
Capacity - liter (l);
Area - hectare (ha).
Logarithmic units are divided into absolute, which represent decimal logarithm the ratio of a physical quantity to a standardized value, and relative, formed as a decimal logarithm of the ratio of any two homogeneous (same) quantities.
Non-SI units include degrees and minutes. The remaining units are derivatives.
Derived units SI are formed using the simplest equations that relate quantities and in which the numerical coefficients are equal to unity. In this case, the derived unit is called coherent.
Dimension is a qualitative display of measured quantities. The value of a quantity is obtained as a result of its measurement or calculation in accordance with basic equation frommeasurements:Q = q * [ Q]
where Q - quantity value; q- numerical value of the measured quantity in conventional units; [Q] - the unit chosen for measurement.
If the defining equation includes a numerical coefficient, then to form a derived unit, such numerical values of the initial quantities should be substituted into the right side of the Equation so that the numerical value of the derived unit being determined is equal to one.
(For example, 1 ml is taken as a unit of measurement for the mass of a liquid, so on the packaging it is indicated: 250 ml, 750, etc., but if 1 liter is taken as a unit of measurement, then the same amount of liquid will be indicated 0.25 liters. , 075l. respectively).
As one of the ways to form multiples and submultiples, the decimal multiplicity between major and minor units, adopted in the metric system of measures, is used. In table 1.2 provides factors and prefixes for the formation of decimal multiples and submultiples and their names.
Table 2 - Factors and prefixes for the formation of decimal multiples and submultiples and their names
|
Factor |
Prefix |
Prefix designation |
|
|
international |
|||
(Exabyte is a unit of measurement of the amount of information, equal to 1018 or 260 bytes. 1 EeV (exaelectronvolt) = 1018 electronvolt = 0.1602 joule)
It should be taken into account that when forming multiple and submultiple units of area and volume using prefixes, dual reading may arise depending on where the prefix is added. For example, 1 m2 can be used as 1 square meter and as 100 square centimeters, which is far from the same thing, because 1 square meter that's 10,000 square centimeters.
According to international rules, multiples and submultiples of area and volume should be formed by adding prefixes to the original units. Degrees refer to those units that are obtained by attaching prefixes. For example, 1 km 2 = 1 (km) 2 = (10 3 m) 2 == 10 6 m 2.
To ensure the uniformity of measurements, it is necessary to have identical units in which all measuring instruments of the same physical quantity are calibrated. Unity of measurements is achieved by storing, accurately reproducing established units of physical quantities and transferring their sizes to all working measuring instruments using standards and reference measuring instruments.
Reference - a measuring instrument that ensures the storage and reproduction of a legalized unit of physical quantity, as well as the transfer of its size to other measuring instruments.
The creation, storage and use of standards, monitoring their condition are subject to uniform rules established by GOST “GSI. Standards of units of physical quantities. Procedure for development, approval, registration, storage and application.”
By subordination standards are divided into primary and secondary and have the following classification.
Primary standard ensures storage, reproduction of units and transmission of dimensions with the highest accuracy in the country achievable in this field of measurement:
- special primary standards- are intended to reproduce the unit in conditions in which direct transmission of the unit size from the primary standard with the required accuracy is technically infeasible, for example, for low and high voltages, microwave and HF. They are approved as state standards. In view of the special importance of state standards and to give them the force of law, GOST is approved for each state standard. The State Committee for Standards creates, approves, stores and applies state standards.
Secondary standard reproduces the unit in special conditions and replaces the primary standard under these conditions. It is created and approved to ensure the least wear and tear on the state standard. Secondary standards in turn divided according to purpose:
Copy standards - designed to transfer unit sizes to working standards;
Comparison standards - designed to check the safety of the state standard and to replace it in case of damage or loss;
Witness standards - used for comparison of standards that, for one reason or another, cannot be directly compared with each other;
Working standards - reproduce a unit from secondary standards and serve to transfer the size to a standard of a lower rank. Secondary standards are created, approved, stored and used by ministries and departments.
Unit standard - one means or set of measuring instruments that provide storage and reproduction of a unit for the purpose of transmitting its size to subordinate measuring instruments in the verification scheme, made according to a special specification and officially approved in the prescribed manner as a standard.
Reproduction of units, depending on the technical and economic requirements, is carried out by two ways:
- centralized- using a single state standard for the entire country or group of countries. All basic units and most of the derivatives are reproduced centrally;
- decentralized- applicable to derived units, the size of which cannot be conveyed by direct comparison with the standard and provide the necessary accuracy.
The standard establishes a multi-stage procedure for transferring the dimensions of a unit of a physical quantity from the state standard to all working means of measuring a given physical quantity using secondary standards and exemplary means of measuring various categories from the highest first to the lowest and from exemplary means to working ones.
Size transfer is carried out by various verification methods, mainly by well-known measurement methods. Transferring a size in a stepwise manner is accompanied by a loss of accuracy, however, multi-stepping allows you to save standards and transfer the unit size to all working measuring instruments.
In 1875, the International Bureau of Weights and Measures was founded by the Metric Conference; its goal was to create a unified measurement system that would be used throughout the world. It was decided to take as a basis the metric system, which appeared back in the days French Revolution and was based on the meter and kilogram. Later, the standards of the meter and kilogram were approved. Over time, the system of units of measurement has evolved and currently has seven basic units of measurement. In 1960, this system of units received the modern name International System of Units (SI System) (Systeme Internatinal d "Unites (SI)). The SI system is not static; it is developing in accordance with the requirements that are currently imposed on measurements in science and technology.
Basic units of measurement of the International System of Units
The definition of all auxiliary units in the SI system is based on seven basic units of measurement. The main physical quantities in the International System of Units (SI) are: length ($l$); mass ($m$); time ($t$); strength electric current($I$); Kelvin temperature (thermodynamic temperature) ($T$); amount of substance ($\nu $); luminous intensity ($I_v$).
The basic units in the SI system are the units of the above-mentioned quantities:
\[\left=m;;\ \left=kg;;\ \left=s;\ \left=A;;\ \left=K;;\ \ \left[\nu \right]=mol;;\ \left=cd\ (candela).\]
Standards of basic units of measurement in SI
Let us present the definitions of the standards of basic units of measurement as done in the SI system.
Meter (m) is the length of the path that light travels in a vacuum in a time equal to $\frac(1)(299792458)$ s.
Standard mass for SI is a weight in the shape of a straight cylinder, the height and diameter of which is 39 mm, consisting of an alloy of platinum and iridium weighing 1 kg.
One second (s) called a time interval that is equal to 9192631779 periods of radiation, which corresponds to the transition between two hyperfine levels of the ground state of the cesium atom (133).
One ampere (A)- this is the current strength passing in two straight infinitely thin and long conductors located at a distance of 1 meter, located in a vacuum, generating the Ampere force (the force of interaction of conductors) equal to $2\cdot (10)^(-7)N$ for each meter of conductor .
One kelvin (K)- this is the thermodynamic temperature equal to $\frac(1)(273.16)$ part of the triple point temperature of water.
One mole (mole)- this is the amount of a substance that has the same number of atoms as there are in 0.012 kg of carbon (12).
One candela (cd) equal to the intensity of light emitted by a monochromatic source with a frequency of $540\cdot (10)^(12)$Hz with an energy force in the direction of radiation of $\frac(1)(683)\frac(W)(avg).$
Science is developing, measuring technology is being improved, and definitions of units of measurement are being revised. The higher the measurement accuracy, the greater the requirements for determining units of measurement.
SI derived quantities
All other quantities are considered in the SI system as derivatives of the basic ones. The units of measurement of derived quantities are defined as the result of the product (taking into account the degree) of the basic ones. Let us give examples of derived quantities and their units in the SI system.
The SI system also has dimensionless quantities, for example, reflection coefficient or relative dielectric constant. These quantities have dimension one.
The SI system includes derived units with special names. These names are compact forms of representing combinations of basic quantities. Let us give examples of SI units that have their own names (Table 2).
Each SI quantity has only one unit of measurement, but the same unit of measurement can be used for different sizes. Joule is a unit of measurement for the amount of heat and work.
SI system, units of measurement multiples and submultiples
The International System of Units has a set of prefixes to units of measurement that are used if numerical values the quantities under consideration are significantly more or less than the unit of the system, which is used without a prefix. These prefixes are used with any units of measurement; in the SI system they are decimal.
Let us give examples of such prefixes (Table 3).
When writing, the prefix and the name of the unit are written together, so that the prefix and the unit of measurement form a single symbol.
Note that the unit of mass in the SI system (kilogram) has historically already had a prefix. Decimal multiples and submultiples of the kilogram are obtained by connecting the prefix to the gram.
Non-system units
The SI system is universal and convenient in international communication. Almost all units that are not included in the SI system can be defined using SI terms. The use of the SI system is preferred in science education. However, there are some quantities that are not included in the SI, but are widely used. Thus, units of time such as minute, hour, day are part of culture. Some units are used for historical reasons. When using units that do not belong to the SI system, it is necessary to indicate how they are converted to SI units. An example of units is given in Table 4.
In science and technology, units of measurement of physical quantities are used that form certain systems. The set of units established by the standard for mandatory use is based on the units International system(SI). In theoretical sections of physics, units of the SGS systems are widely used: SGSE, SGSM and the symmetric Gaussian system SGS. Units are also used to some extent technical system MKGSS and some non-systemic units.
The International System (SI) is built on 6 basic units (meter, kilogram, second, kelvin, ampere, candela) and 2 additional ones (radian, steradian). The final version of the draft standard “Units of Physical Quantities” contains: SI units; units allowed for use along with SI units, for example: ton, minute, hour, degree Celsius, degree, minute, second, liter, kilowatt-hour, revolutions per second, revolutions per minute; units of the GHS system and other units used in theoretical sections of physics and astronomy: light year, parsec, barn, electronvolt; units temporarily allowed for use such as: angstrom, kilogram-force, kilogram-force-meter, kilogram-force per square centimeter, millimeter of mercury, horsepower, calorie, kilocalorie, roentgen, curie. The most important of these units and the relationships between them are given in Table A1.
Abbreviated designations of units given in the tables are used only after the numerical value of the quantity or in the headings of table columns. Abbreviations cannot be used instead of the full names of units in the text without the numerical value of the quantities. When using both Russian and international symbols of units, a straight font is used; designations (abbreviated) of units whose names are given by the names of scientists (newton, pascal, watt, etc.) should be written with a capital letter (N, Pa, W); In unit designations, a dot is not used as an abbreviation sign. The designations of the units included in the product are separated by dots as multiplication signs; A slash is usually used as a division sign; If the denominator includes a product of units, then it is enclosed in parentheses.
To form multiples and submultiples, decimal prefixes are used (see Table A2). It is especially recommended to use prefixes that represent a power of 10 with an exponent that is a multiple of three. It is advisable to use submultiples and multiples of units derived from SI units and resulting in numerical values lying between 0.1 and 1000 (for example: 17,000 Pa should be written as 17 kPa).
It is not allowed to attach two or more attachments to one unit (for example: 10 –9 m should be written as 1 nm). To form mass units, a prefix is added to the main name “gram” (for example: 10 –6 kg = 10 –3 g = 1 mg). If the complex name of the original unit is a product or fraction, then the prefix is attached to the name of the first unit (for example, kN∙m). In necessary cases, it is allowed to use submultiple units of length, area and volume in the denominator (for example, V/cm).
Table A3 shows the main physical and astronomical constants.
Table P1
UNITS OF MEASUREMENT OF PHYSICAL QUANTITIES IN THE SI SYSTEM
AND THEIR RELATIONSHIP WITH OTHER UNITS
| Name of quantities | Units of measurement | Abbreviation | Size | Coefficient for conversion to SI units | ||
| GHS | MKGSS and non-systemic units | |||||
| Basic units | ||||||
| Length | meter | m | 1 cm=10 –2 m | 1 Å=10 –10 m 1 light year=9.46×10 15 m | ||
| Weight | kilograms | kg | 1g=10 –3 kg | |||
| Time | second | With | 1 hour=3600 s 1 min=60 s | |||
| Temperature | kelvin | TO | 1 0 C=1 K | |||
| Current strength | ampere | A | 1 SGSE I = =1/3×10 –9 A 1 SGSM I =10 A | |||
| The power of light | candela | cd | ||||
| Additional units | ||||||
| Flat angle | radian | glad | 1 0 =p/180 rad 1¢=p/108×10 –2 rad 1²=p/648×10 –3 rad | |||
| Solid angle | steradian | Wed | Full solid angle=4p sr | |||
| Derived units | ||||||
| Frequency | hertz | Hz | s –1 | |||
Continuation of Table P1
| Angular velocity | radians per second | rad/s | s –1 | 1 r/s=2p rad/s 1 rpm= =0.105 rad/s | |
| Volume | cubic meter | m 3 | m 3 | 1cm 2 =10 –6 m 3 | 1 l=10 –3 m 3 |
| Speed | meter per second | m/s | m×s –1 | 1cm/s=10 –2 m/s | 1km/h=0.278 m/s |
| Density | kilogram per cubic meter | kg/m 3 | kg×m –3 | 1 g/cm 3 = =10 3 kg/m 3 | |
| Strength | newton | N | kg×m×s –2 | 1 din=10 –5 N | 1 kg=9.81N |
| Work, energy, amount of heat | joule | J (N×m) | kg×m 2 ×s –2 | 1 erg=10 –7 J | 1 kgf×m=9.81 J 1 eV=1.6×10 –19 J 1 kW×h=3.6×10 6 J 1 cal=4.19 J 1 kcal=4.19×10 3 J |
| Power | watt | W (J/s) | kg×m 2 ×s –3 | 1erg/s=10 –7 W | 1hp=735W |
| Pressure | pascal | Pa (N/m2) | kg∙m –1 ∙s –2 | 1 dyne/cm 2 =0.1 Pa | 1 atm=1 kgf/cm 2 = =0.981∙10 5 Pa 1 mm.Hg.=133 Pa 1 atm= =760 mm.Hg.= =1.013∙10 5 Pa |
| moment of force | newton meter | N∙m | kgm 2 ×s –2 | 1 dyne×cm= =10 –7 N×m | 1 kgf×m=9.81 N×m |
| Moment of inertia | kilogram-meter squared | kg×m 2 | kg×m 2 | 1 g×cm 2 = =10 –7 kg×m 2 | |
| Dynamic viscosity | pascal-second | Pa×s | kg×m –1 ×s –1 | 1P/poise/==0.1Pa×s |
Continuation of Table P1
| Kinematic viscosity | square meter per second | m 2 /s | m 2 ×s –1 | 1St/Stokes/= =10 –4 m 2 /s | |
| Heat capacity of the system | joule per kelvin | J/C | kg×m 2 x x s –2 ×K –1 | 1 cal/ 0 C = 4.19 J/K | |
| Specific heat | joule per kilogram-kelvin | J/ (kg×K) | m 2 ×s –2 ×K –1 | 1 kcal/(kg × 0 C) = =4.19 × 10 3 J/(kg × K) | |
| Electric charge | pendant | Cl | А×с | 1SGSE q = =1/3×10 –9 C 1SGSM q = =10 C | |
| Potential, electrical voltage | volt | V (W/A) | kg×m 2 x x s –3 ×A –1 | 1SGSE u = =300 V 1SGSM u = =10 –8 V | |
| Electric field strength | volt per meter | V/m | kg×m x x s –3 ×A –1 | 1 SGSE E = =3×10 4 V/m | |
| Electrical displacement (electrical induction) | pendant per square meter | C/m 2 | m –2 ×s×A | 1SGSE D = =1/12p x x 10 –5 C/m 2 | |
| Electrical resistance | ohm | Ohm (V/A) | kg×m 2 ×s –3 x x A –2 | 1SGSE R = 9×10 11 Ohm 1SGSM R = 10 –9 Ohm | |
| Electrical capacity | farad | F (Cl/V) | kg –1 ×m –2 x s 4 ×A 2 | 1SGSE S = 1 cm = =1/9×10 –11 F |
End of Table P1
| Magnetic flux | weber | Wb (W×s) | kg×m 2 ×s –2 x x A –1 | 1SGSM f = =1 Mks (maxvel) = =10 –8 Wb | |
| Magnetic induction | tesla | Tl (Wb/m2) | kg×s –2 ×A –1 | 1SGSM V = =1 G (gauss) = =10 –4 T | |
| Tension magnetic field | ampere per meter | Vehicle | m –1 ×A | 1SGSM N = =1E(oersted) = =1/4p×10 3 A/m | |
| Magnetomotive force | ampere | A | A | 1SGSM Fm | |
| Inductance | Henry | Gn (Wb/A) | kg×m 2 x x s –2 ×A –2 | 1SGSM L = 1 cm = =10 –9 Hn | |
| Luminous flux | lumen | lm | cd | ||
| Brightness | candela per square meter | cd/m2 | m –2 ×cd | ||
| Illumination | luxury | OK | m –2 ×cd |
Each measurement is a comparison of the measured quantity with another homogeneous quantity, which is considered unitary. Theoretically, the units for all quantities in physics can be chosen to be independent of each other. But this is extremely inconvenient, since for each value one should enter its own standard. Besides this, in all physical equations, which display the relationship between different quantities, numerical coefficients would arise.
The main feature of the currently used systems of units is that there are certain relationships between units of different quantities. These relationships are established by the physical laws (definitions) that relate the measured quantities to each other. Thus, the unit of speed is chosen in such a way that it is expressed in terms of distance and time units. When selecting speed units, the speed definition is used. The unit of force, for example, is established using Newton's second law.
When building a certain system units, several physical quantities are selected, the units of which are set independently of each other. Units of such quantities are called basic. The units of other quantities are expressed in terms of the basic ones, they are called derivatives.
The number of basic units and the principle of their selection may be different for different unit systems. The main physical quantities in the International System of Units (SI) are: length ($l$); mass ($m$); time ($t$); electric current ($I$); Kelvin temperature (thermodynamic temperature) ($T$); amount of substance ($\nu $); luminous intensity ($I_v$).
Unit tables
The basic units in the SI system are the units of the above-mentioned quantities:
\[\left=m;;\ \left=kg;;\ \left=s;;\ \left=A;;\ \left=K;;\ \ \left[\nu \right]=mol;; \ \left=cd\ (candela).\]
For basic and derived units of measurement in the SI system, submultiples and multiple prefixes are used; Table 1 shows some of them
Table 2 summarizes basic information about the basic units of the SI system.
In Table 3 we present some derived units of measurement of the SI system.
and many others.
In the SI system, there are derived units of measurement that have their own names, which are actually compact forms of combinations of basic quantities. Table 4 shows examples of such SI units.
There is only one SI unit for each physical quantity, but the same unit can be used for several quantities. For example, work and energy are measured in joules. There are dimensionless quantities.
There are some quantities that are not included in the SI, but are widely used. Thus, units of time such as minute, hour, day are part of culture. Some units are used for historical reasons. When using units that do not belong to the SI system, it is necessary to indicate how they are converted to SI units. An example of units is given in Table 5.
Examples of problems with solutions
Example 1.
Exercise. The unit of force in the CGS system (centimeter, gram, second) is taken to be the dyne. Dyna is a force that imparts an acceleration of 1 $\frac(cm)(s^2)$ to a body weighing 1 g. Express the dyne in newtons.
Solution. The unit of force is determined using Newton's second law:
\[\overline(F)=m\overline(a)\left(1.1\right).\]
This means that the units of force are obtained using the units of mass and acceleration:
\[\left=\left\left\ \left(1.2\right).\]
In the SI system, a newton is equal to:
\[Н=kg\cdot \frac(m)(s^2)\ \left(1.3\right).\]
In the GHS system, the unit of force (dyne) is equal to:
\[din=g\cdot \frac(cm)(s^2)\ \left(1.4\right).\]
Let's convert meters into centimeters and kilograms into grams in expression (1.3):
Answer.$1Н=(10)^5din.$
Example 2.
Exercise. The car was moving at a speed of $v_0=72\\frac(km)(h)$. During emergency braking, he was able to stop after $t=5\ c.$ What is the braking distance of the car ($s$)?
Solution.
To solve the problem, we write down the kinematic equations of motion, considering the acceleration with which the car reduced its speed to be constant:
equation for speed:
\[\overline(v)=(\overline(v))_0+\overline(a)t\ \left(2.1\right)\]
equation for displacement:
\[\overline(s)=(\overline(s))_0+(\overline(v))_0t+\frac(\overline(a)t^2)(2)\ \left(2.2\right).\]
In the projection onto the X axis and taking into account the fact that the final speed of the car is zero, and we consider braking the car started from the origin of coordinates, we write expressions (2.1) and (2.2) as:
\ \
From formula (2.3) we express the acceleration and substitute it into (2.4), we obtain:
Before carrying out calculations, we should convert the speed $v_0=72\ \frac(km)(h)$ into speed units in the SI system:
\[\left=\frac(m)(s).\]
To do this, we use Table 1, where we see that the prefix kilo means multiplying 1 meter by 1000, and since 1 hour = 3600 s (Table 4), then in the SI system the initial speed will be equal to:
Let's calculate the braking distance:
Physical quantities
Physical quantity– this is a characteristic of physical objects or phenomena of the material world, common to many objects or phenomena in a qualitative sense, but individual in a quantitative sense for each of them. For example, mass, length, area, temperature, etc.
Each physical quantity has its own qualitative and quantitative characteristics .
Qualitative characteristics is determined by what property of a material object or what feature of the material world this quantity characterizes. Thus, the property “strength” quantitatively characterizes materials such as steel, wood, fabric, glass and many others, while the quantitative value of strength for each of them is completely different
To identify the quantitative difference in the content of a property in any object, reflected by a physical quantity, the concept is introduced physical quantity size . This size is set during the process measurements- a set of operations performed to determine the quantitative value of a quantity (Federal Law “On Ensuring the Uniformity of Measurements”
The purpose of measurements is to determine the value of a physical quantity - a certain number of units accepted for it (for example, the result of measuring the mass of a product is 2 kg, the height of a building is 12 m, etc.). Between the sizes of each physical quantity there are relationships in the form of numerical forms (such as “more”, “less”, “equality”, “sum”, etc.), which can serve as a model of this quantity.
Depending on the degree of approximation to objectivity, they distinguish true, actual and measured values of a physical quantity .
The true value of a physical quantity is this is a value that ideally reflects the corresponding property of an object in qualitative and quantitative terms. Due to the imperfection of measurement tools and methods, it is practically impossible to obtain the true values of quantities. They can only be imagined theoretically. And the values obtained during measurement only approach the true value to a greater or lesser extent.
The actual value of a physical quantity is this is a value of a quantity found experimentally and so close to the true value that it can be used instead for a given purpose.
Measured value of a physical quantity - this is the value obtained by measurement using specific methods and measuring instruments.
When planning measurements, you should strive to ensure that the range of measured quantities meets the requirements of the measurement task (for example, during control, the measured quantities must reflect the corresponding indicators of product quality).
For each product parameter the following requirements must be met:
The correctness of the formulation of the measured value, excluding the possibility different interpretations(for example, it is necessary to clearly define in what cases the “mass” or “weight” of the product, the “volume” or “capacity” of the vessel, etc. is determined);
The certainty of the properties of the object to be measured (for example, “the temperature in the room is not more than ... °C” allows for the possibility of different interpretations. It is necessary to change the wording of the requirement so that it is clear whether this requirement is established for the maximum or for average temperature premises, which will be taken into account later when performing measurements);
Use of standardized terms.
A physical quantity that, by definition, is assigned a numerical value equal to one is called unit of physical quantity.
Many units of physical quantities are reproduced by measures used for measurements (for example, meter, kilogram). In the early stages of the development of material culture (in slave-holding and feudal societies), there were units for a small range of physical quantities - length, mass, time, area, volume. Units of physical quantities were chosen without connection with each other, and, moreover, different in different countries and geographical areas. This is how it arose large number often identical in name, but different in size - elbows, feet, pounds.
As trade relations between peoples expanded and science and technology developed, the number of units of physical quantities increased and the need for unification of units and the creation of systems of units was increasingly felt. Special international agreements began to be concluded on units of physical quantities and their systems. In the 18th century In France, the metric system of measures was proposed, which later received international recognition. On its basis, a number of metric systems of units were built. Currently, further ordering of units of physical quantities is taking place on the basis of the International System of Units (SI).
Units of physical quantities are divided into systemic, i.e., those included in any system of units, and non-systemic units (for example, mmHg, horsepower, electron-volt).
System units physical quantities are divided into basic, chosen arbitrarily (meter, kilogram, second, etc.), and derivatives, formed by equations of connection between quantities (meter per second, kilogram per cubic meter, newton, joule, watt, etc.).
For the convenience of expressing quantities that are many times larger or smaller than units of physical quantities, we use multiples of units (for example, kilometer - 10 3 m, kilowatt - 10 3 W) and submultiples (for example, a millimeter is 10 -3 m, a millisecond is 10-3 s)..
In metric systems of units, multiples and fractional units of physical quantities (except for units of time and angle) are formed by multiplying the system unit by 10 n, where n is a positive or negative integer. Each of these numbers corresponds to one of the decimal prefixes adopted to form multiples and units.
In 1960, at the XI General Conference on Weights and Measures of the International Organization of Weights and Measures (IIOM), the International System of Weights and Measures was adopted units(SI).
Basic units in the international system of units are: meter (m) – length, kilogram (kg) – mass, second (s) – time, ampere (A) – electric current strength, kelvin (K) – thermodynamic temperature, candela (cd) – luminous intensity, mole – amount of substance.
Along with systems of physical quantities, so-called non-systemic units are still used in measurement practice. These include, for example: units of pressure - atmosphere, millimeter of mercury, unit of length - angstrom, unit of heat - calorie, units of acoustic quantities - decibel, background, octave, units of time - minute and hour, etc. However, in Currently, there is a tendency to reduce them to a minimum.
The International System of Units has a number of advantages: universality, unification of units for all types of measurements, coherence (consistency) of the system (proportionality coefficients in physical equations are dimensionless), better mutual understanding between various specialists in the process of scientific, technical and economic relations between countries.
Currently, the use of units of physical quantities in Russia is legalized by the Constitution of the Russian Federation (Article 71) (standards, standards, the metric system and time calculation are under the jurisdiction of Russian Federation) And federal law"On ensuring the uniformity of measurements." Article 6 of the Law determines the use in the Russian Federation of units of quantities of the International System of Units adopted by the General Conference on Weights and Measures and recommended for use by the International Organization of Legal Metrology. At the same time, in the Russian Federation, non-system units of quantities, the name, designation, rules of writing and application of which are established by the Government of the Russian Federation, can be accepted for use on an equal basis with SI units of quantities.
In practical activities, one should be guided by the units of physical quantities regulated by GOST 8.417-2002 “ State system ensuring uniformity of measurements. Units of quantities."
Standard along with mandatory use basic and derivatives units of the International System of Units, as well as decimal multiples and submultiplies of these units, it is allowed to use some units that are not included in SI, their combinations with SI units, as well as some found wide application in practice, decimal multiples and submultiples of the listed units.
The standard defines the rules for the formation of names and designations of decimal multiples and submultiples of SI units using multipliers (from 10 –24 to 10 24) and prefixes, the rules for writing unit designations, the rules for the formation of coherent derived SI units
Factors and prefixes used to form the names and designations of decimal multiples and submultiples of SI units are given in Table.
Factors and prefixes used to form the names and designations of decimal multiples and submultiples of SI units
| Decimal multiplier | Prefix | Prefix designation | Decimal multiplier | Prefix | Prefix designation | ||
| intl. | rus | intl. | russ | ||||
| 10 24 | iotta | Y | AND | 10 –1 | deci | d | d |
| 10 21 | zetta | Z | Z | 10 –2 | centi | c | With |
| 10 18 | exa | E | E | 10 –3 | Milli | m | m |
| 10 15 | peta | P | P | 10 –6 | micro | µ | mk |
| 10 12 | tera | T | T | 10 –9 | nano | n | n |
| 10 9 | giga | G | G | 10 –12 | pico | p | n |
| 10 6 | mega | M | M | 10 –15 | femto | f | f |
| 10 3 | kilo | k | To | 10 –18 | atto | a | A |
| 10 2 | hecto | h | G | 10 –21 | zepto | z | h |
| 10 1 | soundboard | da | Yes | 10 –24 | iocto | y | And |
Coherent derived units The International System of Units, as a rule, is formed using the simplest equations of connections between quantities (defining equations), in which the numerical coefficients are equal to 1. To form derived units, the designations of quantities in the connection equations are replaced by the designations of SI units.
If the coupling equation contains a numerical coefficient different from 1, then to form a coherent derivative of an SI unit, the notation of quantities with values in SI units is substituted into the right side, giving, after multiplication by the coefficient, a total numerical value equal to 1.