EntrancePresentation on the topic of physical quantities. Measurements
Description of the presentation by individual slides:
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Man was faced with the need for measurements in ancient times, at an early stage of his development - in practical life, when it was necessary to measure distances, areas, volumes, weights, and, of course, time. Where did measurement methods begin?
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Measurement is one of the ways of knowing. The development of science and technology is closely related to measurements. Scientific research are accompanied by measurements that make it possible to establish quantitative relationships and patterns of properties of the phenomena being studied. Measurement is a comparison of a quantity with a homogeneous quantity taken as a unit of measure.
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DI. Mendeleev wrote: “Science begins as soon as they begin to measure: exact science is unthinkable without measure.” Measurement of a physical quantity - length, area, volume, weight, temperature - is carried out experimentally using various means measurements, for example, scales, thermometer.
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During the measurement process, the numerical value of the measured quantity, for example, length, weight, temperature, is found experimentally in accepted units of measurement. A comparison of the results of measuring a quantity and points on a number line is made using a scale (Latin scala - ladder).
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Metrology is the science of measurements and methods of ensuring their unity. With the development of human society and metrology, in particular, the specific concept of measure was gradually supplemented abstract concept"unit of measurement". The first national systems of measures arose a very long time ago: at least four thousand years ago, in Ancient Babylon. The next “object” was Ancient Egypt.
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The experience of Babylon and especially Egypt was adopted by Ancient Republican and Imperial Rome, and by Russia and its predecessor, Kievan Rus. Since ancient times, the measure of length and weight has always been a person: how far he can stretch his arm, how much he can lift on his shoulders, etc. IN Kievan Rus The measures of length were the proportions (measures) of the human body. The system of Old Russian measures of length included four main measures; verst, fathom, elbow, span.
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“day” is the distance covered by a person on foot per day; “harness” - the distance between the points where horses were re-harnessed; “stone’s unease” - the distance that a thrown stone flies; “shoot” – the distance that an arrow fired from a bow flies (60-70 m). Gradually, such a measure as verst (from the verb “to lay out”, “to equalize”) was developed. It has been mentioned in ancient Russian sources since the end of the 11th century. One verst was equal to 750 fathoms or 1,140 meters. Thus, the Old Russian system of length measures had the following form: 1 verst = 750 fathoms = 2250 cubits = 4500 spans. To measure large distances, approximate everyday measures were initially used: sections of the path covered over certain time intervals:
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There were a number of measures of mass: spool, pound (hryvnia), pood. The largest of the known standard weights had a mass equal to two pounds. There was a whole range of volume measures from a bottle to a bucket (12.29904 l) to a barrel equal to 40 buckets.
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TO XVIII century there were up to 400 units of measures of different sizes used in different countries. The variety of measures made trading operations difficult. Therefore, each state sought to establish uniform measures for its country. For the unity of measurements in Kievan Rus, there were samples of measures that were kept by the princes or in the church, for example, the “golden belt of Svyatoslav” Yaroslavich (1073-1076) or “Ivansky Elbow” (1334) - a measure transferred to the disposal of the bishop and merchants corporation at the Church of John the Baptist in Novgorod.
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The system of measures is one of the signs of statehood; it develops together with the state and is protected by it. In Russia, back in the 16th and 17th centuries. uniform systems of measures were determined for the entire country. In the 18th century in connection with economic development and the need for strict accounting in foreign trade, in Russia the question arose of the accuracy of measurements, the creation of standards on the basis of which verification work ("metrology") could be organized.
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In 1736, the Senate decided to form a Commission of Weights and Measures, headed by the chief director of the Monetary Board, Count Mikhail Gavrilovich Golovkin. The commission created exemplary measures - standards. Under Paul I, by decree of April 29, 1797, on the “Establishment throughout Russian Empire correct scales, drink and grain measures" a lot of work was begun on streamlining measures and weights. Its completion dates back to the 30s of the 19th century. The decree of 1797 was drawn up in the form of desirable recommendations. The decree concerned four issues of measurement: weighing instruments, measures weights, measures of liquid and granular bodies.
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In 1841, in accordance with the adopted Decree “On the System of Russian Weights and Measures”, which legalized a number of measures of length, volume and weight, the Depot of Model Weights and Measures was organized at the St. Petersburg Mint - the first state verification institution. On May 20, 1875, Russia signed the metric convention. In the same year, the International Organization of Weights and Measures (IOIM) was created. The seat of this organization is France (Sèvres). In 1889 Standards of the kilogram and meter arrived at the Depot of Standard Weights and Measures.
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In 1893, the Main Chamber of Weights and Measures was formed in St. Petersburg on the basis of the Depot, which it headed until 1907. great Russian scientist D.I. Mendeleev. In 1900, the Moscow District Assay Office opened a verification tent for trade weights and measures. This was the beginning of the organization of a metrological institute in Moscow (currently the All-Russian Scientific Research Institute of Metrological Service - VINIMS).
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On the threshold of the 19th century. A significant event in the history of metrology occurred: by decree of the French revolutionary government of December 10, 1799, the metric system of measures was legalized and introduced as mandatory in France. On May 20, 1875, seventeen countries signed the Meter Convention. kg
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The metric system of measures was approved for use in Russia by the law of June 4, 1899, the draft of which was developed by D. I. Mendeleev, and introduced as mandatory by the decree of the Provisional Government of April 30, 1917, and for the USSR - by the resolution of the Council of People's Commissars of the USSR of July 21 1925. In 1930 there was a unification of metrology and standardization. In 1954 The Committee on Standards, Measures and measuring instruments under the Council of Ministers of the USSR (hereinafter Gosstandart of the USSR).
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Based on the metric system, the International System of Units (SI) was developed and adopted in 1960 by the XI General Conference on Weights and Measures. During the second half of the 20th century, most countries in the world switched to the SI system.
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To date, the metric system has been officially adopted in all countries of the world, except the USA, Liberia and Myanmar (Burma). The last country to have already completed the transition to metric system became Ireland (2005). In the UK and Saint Lucia, the process of transition to SI is still not completed. China, which has completed this transition, nevertheless uses ancient Chinese names for metric units. In the USA, the SI system is adopted for use in science and the manufacture of scientific instruments; for all other areas, the American version of the British system of units is adopted.
Physical quantity This quantitative characteristic properties physical body or physical phenomenon . For each physical quantity there are corresponding units .
Values physical quantities are obtained in the process measurements .
Measure physical quantity means compare her with homogeneous the value taken as unit this value.
As a result measurements physical quantity, a numerical value is obtained - some number V units of measurement .
Values physical quantities are obtained in the process of their measurements by using measuring instruments .
Length measurement
Ruler
Calipers
Micrometer
Measuring angles
Protractor
Measuring time
Watch
Stopwatch
Volume measurement
Beaker
Temperature measurement
Thermometer
Measurement atmospheric pressure
Barometer
Pressure measurement
Pressure gauge
Instrument scale this is a part of the reading device, which is a set of strokes, corresponding to a series of sequential values measurable physical quantity.
Measurement limit - maximum value on the scale.
Scale division price - meaning least divisions on the instrument scale.
Hatch this is the sign of the corresponding quantity.
Scale division it's the space between two neighboring strokes scales.
Measurements
Direct
Indirect
The result is obtained directly using the measuring device.
The result is obtained using calculations using special formulas that connect the results of direct measurements with the measured value.
V=a b c
Direct
measurements
Measurable
magnitude
V= 5cm 2 c m·5cm=50cm 3
Indirect measurement
a=5 cm
b=2 cm
c=5 cm
Any measurement gives an approximate value of the measured quantity.
The degree of accuracy varies.
The degree of accuracy depends on:
-Device sensitivity
- Sensitivity of the senses
-Measurement methods
Box length:
4 cm with a deficiency
5 cm in excess
The error should not exceed the division value of the measuring device.
L= 4.5 cm - approximate value of the measured value
Δ L= 0.5 cm - absolute error in length measurement
The approximate value of the measured quantity is equal to the arithmetic mean of two values between which the true value lies.
The absolute error is equal to half the division value of the measuring device.
Denoted by the Greek letter Δ “delta”, measured in units of the measured value.
The absolute error shows the interval in which the true value of the measured value lies.
What is measured more accurately?
L= 8 cm
t=6 0 C
Relative error measurement is the ratio of the absolute measurement error to the approximate value of the measured quantity.
Relative error measurement shows what part the absolute measurement error is from the approximate value of the measured value.
Slide 1
Quantities Physical
Slide 2
D.I.Mendeleev
Science begins as soon as they begin to measure
Portrait of Mendeleev in a professor's robe, 1885
Slide 3
1. What is quantity? 2. What quantities are called physical? 3. What does it mean to measure a physical quantity? 4. What is division price? How to determine it? 5. Basic and derived units of measurement of physical quantities. 6. Units of length, area, volume and mass. 7. Accuracy of measurement of physical quantities. Absolute and relative error. 8. Order of physical quantities. 9. Methods of presenting experimental results. 10. Approximate calculations
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Anything that can be measured is called a quantity
1.What is quantity?
Slide 5
If quantities characterize physical phenomena from a quantitative perspective, then they are called physical quantities.
2. What quantities are called physical?
Physical quantities are volume (V), temperature (T), distance traveled (s), mass (m), weight (P).
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Measurements of physical quantities are divided into direct and indirect. If the value under study itself is measured using physical instruments, these are direct measurements. For example, measuring the length of a beam using a ruler, and measuring body weight by weighing on a scale. In indirect measurements, the physical quantity of interest to us is calculated using a formula from other quantities that are measured using physical instruments. Measuring the speed of a body based on time and distance traveled.
3. Measurements of physical quantities
To measure a physical quantity means to compare it with a homogeneous quantity taken as the unit of this quantity.
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Plan for a story about measuring instruments
1. Name of the device. 2. What quantity is it intended to measure? 3. Unit of measurement of a given quantity. 4. What is the lower limit of measurement of the device? 5. What is the upper limit of measurement of the device? 6. What is the price of the instrument scale division? 7. How to use this device correctly?
micrometer beaker vernier caliper
Slide 8
The scale division is the gap between two adjacent marks on the scale.
Value of division- smallest value measuring instrument scales
To determine the division price, you need to find the two closest lines of the scale, near which are written numeric values. Then subtract the smaller number from the larger value and divide the resulting number by the number of divisions between them.
0.5 (ml) = 0.5 (cm3) Division value =
4. What is division price?
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The figure shows three stopwatches. Determine the division price of these devices.
Stopwatches 2 s 5 s 1 s
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1. Determine the price of dividing the beaker
5 ml 2.5 ml 5 mm 10 ml
2. Determine the volume of water in the beaker before the body is immersed
50 ml 45 ml 70 ml Beaker
3. Determine the volume of water in the beaker after the body is immersed
30 ml 40 ml 60 ml
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5. Units of measurement of physical quantities
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6. Units of length, area, volume, mass
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7. Absolute measurement error
The accuracy of measurements is characterized by an error, or, as they also say, measurement error. There is no difference between the terms “error” and “error”, and both can be used. Measurement error is the difference between the measured and true value of a physical quantity. ∆Χ = Χmeas – Χist It is called the absolute error (∆ is the capital Greek letter “delta”). The true value is the arithmetic mean of repeatedly performed measurements, determined as follows: Χav=(Χ1+Χ2+Χ3+…+Χn) /n The absolute error of an individual measurement ∆xi is the deviation of the measured value from the arithmetic mean: ∆xi = xi – xav
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Relative measurement error
To estimate the limits of error when measuring a quantity, it was agreed to use the average absolute error ∆x, obtained by dividing the sum absolute values errors of an individual measurement ∆xi per number of measurements n: ∆ xav = (| ∆x1|+| ∆x2|+| ∆x3|+ … +| ∆xn|) ⁄ n Average absolute value is simply called the absolute error of the measured physical quantity, and the measurement result is written in the form: x= xср ± ∆ xср
Therefore, the relative error is also important
Absolute error does not fully characterize the accuracy of measurements. The quality of measurements with an absolute error of 1 mm is different when measuring, for example, bolt diameter (d = 20 mm), sleeve length (l = 200 mm) and table length (L = 2000 mm).
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Calculation of error
Let's consider the calculation of errors using the example of measuring the length of a bolt
1) l1= 10.6 cm; 2) l2 = 10.8 cm;
3) lav.= (10.6 +10.8)/ 2 =10.7(cm);
4) l 1= 10.6-10.7= -0.1 (cm); 5) l2 =10.8-10.7=0.1 (cm);
6) lav.= (0.1+0.1)/2=0.1 (cm);
7) δ = 0.1/10.7*100%=0.9%
Therefore, the relative error (lowercase letter “delta”) is also important, which is determined by the ratio of the absolute error of the measured value to its average value, and is usually calculated in %: δ = ∆ xav ⁄ xav ∙ 100%
0.13% - high accuracy 1.3% - satisfactory 13% - very rough
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Bar length
The length of the bar is measured using a ruler. Write down the measurement result, taking into account that the measurement error is equal to half the division value
7.5 cm (7.0±0.5) cm (7.5±0.5) cm (7.50±0.25) cm
If a relative error of more than 10% is obtained during a measurement, then they say that only an estimate of the measured value has been made. In physics workshop laboratories, it is recommended to carry out measurements with a relative error of up to 10%.
Slide 17
I. Determine the thermometer division price
II. Determine the absolute error of the thermometer
III. What temperature does the thermometer show taking into account the measurement error?
0.1 C. 0.2 C. 1 C. 10 C. ±0.05 C. ±0.5 C. ±0.25 C. . 36.9±0.05C. ±0.01 C. 37±0.01C. 36.8±0.2 5C. 36.9±0.2C. Thermometer
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Water is poured into the beaker. Write down the value of the volume of water, taking into account that the measurement error is equal to half the division value
(60 ±15) ml (70 ±15) ml (60 ±5) ml
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8. Order of physical quantity
In practice physical measurements situations arise when you have to deal with very large numbers, or with very small numbers. Such numbers are very inconvenient for calculations. To overcome this difficulty, they use raising 10 to the power to write numbers. Multiplying the number 10 by itself several times, we get: 10 ∙ 10 = 100 = 102 10 ∙ 10 ∙ 10 = 1000 = 103 10 ∙ 10 ∙ 10 ∙ 10 = 10000 = 104 A number that shows how many times 10 is multiplied by itself , is the superscript of 10 and is called the exponent of 10, or the power to which 10 is raised. Obviously, 101 = 10, and by definition 100 = 1: 10n ∙ 10m = 10(n+m) 10n/10m = 10n ∙ 1/10m = 10n ∙ 10-m = 10(n-m) Then any number can be written as the product of a number lying between 0.1 and 10 and a number representing a power of ten. For example, the distance from the earth to the Sun can be written as 1.5 ∙ 1011 m,
2 Each physical quantity has its own unit. For example, in the International System of Units (abbreviated SI, which means: international system) adopted by many countries, the basic unit of length is the meter (1 m), the unit of time is the second (1 s). meter second
3
4 Physical quantities: height h, mass m, path s, speed v, time t, temperature t, volume V, etc. To measure a physical quantity means to compare it with a homogeneous quantity taken as a unit. Units of measurement of physical quantities: Basic Length - 1 m - (meter) Time - 1 s - (second) Mass - 1 kg - (kilogram) Derivatives Volume - 1 m³ - (cubic meter) Speed - 1 m/s - (meter per second)
5 Prefixes to the names of units: Multiple prefixes - increase by 10, 100, 1000, etc. times g - hecto (×100) k – kilo (× 1000) M – mega (×) 1 km (kilometer) 1 kg (kilogram) 1 km = 1000 m = 10³ m 1 kg = 1000 g = 10³ g Sub-sections – decrease by 10, 100, 1000, etc. times d – deci (×0.1) s – centi (× 0.01) m – milli (× 0.001) 1 dm (decimeter) 1 dm = 0.1 m 1 cm (centimeter) 1cm = 0.01 m 1 mm (millimeter) 1mm = 0.001 m Multiple attachments are used when measuring large distances, masses, volumes, velocities, etc. Multiple attachments are used when measuring small distances, velocities, masses, volumes, etc.
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13 Physical measuring instruments: each device is designed to measure a certain physical quantity; each device, as a rule, has a scale; scales of instruments designed to measure one physical quantity may differ in division value. Beakers for measuring volumes of liquids Ammeters and voltmeters for measuring force electric current and voltage in the circuit Clock and stopwatch for measuring time Rulers for measuring lengths of segments Thermometers for measuring temperature
14 Most measuring instruments have division lines and the values of quantities corresponding to the divisions are written. The intervals between the strokes, around which numerical values are written, can be further divided into several divisions not indicated by numbers.
16 Instrument division: The instrument division value shows to which value the smallest scale division corresponds. To determine the price of a scale division, you need to: find the two nearest scale lines, next to which the values of the quantities are written; subtract the smaller value from the larger value and divide the subtraction result by the number of divisions located between the selected strokes. Example (see Fig. 1 below): (80 – 60) : 4 = 5 ml, i.e. the division price of beaker 1 is 5 ml. Task: Determine the division price of the devices shown in the figures.
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25 Which of the following instruments is used for research plant cell? A) Compass. B) Microscope. C) Speedometer. D) Telescope. E) Roulette. Which of the following statements is most true? A measuring tape allows you to determine: A) The length of the room. B) Room area. C) Length and area of the room. D) Length, area and volume of the room. E) Volume of the room.
28 What is the maximum temperature shown by the thermometer shown in the figure, taking into account the measurement error? A. The thermometer division value is 1 C. B. The thermometer division value is 0.1 C. C. The thermometer reading is greater than 37 C. D. The thermometer reading is less than 36.6 C.
30 A. The beaker division value is 2 ml. B. The volume of liquid in the beaker is more than 25 ml. B. The division value of the beaker is 0.5 ml. G. Beaker is a device for measuring the volume of liquid and granular bodies. What is the maximum volume that can be measured, taking into account measurement error?
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32 Which of the following statements is true for the beaker shown in the figure? A) The lower limit of measurement of this device is 50 ml, the upper limit is 150 ml. B) The lower limit of measurement of this device is 10 ml, the upper limit is 150 ml. C) lower limit measurements of this device are 0, upper 150 ml. D) The lower limit of measurement of this device is 5 ml, the upper limit is 10 ml E) The lower limit of measurement of this device is 5 ml, the upper is 150 ml.
