For a long time, people have been seriously interested in the question of how it is most convenient to compare values expressed in different values. And it is not only a matter of natural curiosity. The man of the most ancient civilizations of the earth attached this rather difficult task to purely applied significance. Correctly measure the land, determine the weight of the product on the market, calculate the necessary ratio of goods during barter, determine the correct rate of grapes during the harvesting of wine - these are just a fraction of the tasks that often surfaced in the already difficult life of our ancestors. Therefore, poorly educated and illiterate people, if necessary, to compare the values, went for advice to their more experienced comrades, and they often took the corresponding bribe for such a service, and quite good, by the way.
What can be compared
In our time, this occupation also plays a significant role in the process of studying the exact sciences. Everyone, of course, knows that it is necessary to compare homogeneous quantities, that is, apples - with apples, and beets - with beets. It would never occur to anyone to try to express degrees Celsius in kilometers or kilograms in decibels, but we have known the length of a boa in a parrot since childhood (for those who do not remember: 38 parrots in one boa). Although the parrots are also different, and in fact the length of the boa constrictor will vary depending on the subspecies of the parrot, but these are the details that we will try to understand.
Dimensions
When the task states: “Compare the values of the quantities”, it is necessary to bring these very values to the same denominator, that is, express them in the same values for ease of comparison. It is clear that comparing the value expressed in kilograms with the value expressed in centners or tons will not be difficult for many of us. However, there are homogeneous quantities, which can be expressed in different dimensions and, moreover, in different measurement systems. Try, for example, comparing kinematic viscosity values and determining which fluid is more viscous in centistokes and square meters per second. Does not work? And it will not work. To do this, you need to reflect both values in the same quantities, and already by the numerical value to determine which one is superior to the opponent.
Measuring system
In order to understand what quantities can be compared, we will try to recall the existing measurement systems. To optimize and speed up the settlement processes in 1875, seventeen countries (including Russia, the USA, Germany, etc.) signed the metric convention and determined the metric system of measures. To develop and consolidate the standards of meter and kilogram, the International Committee of Weights and Measures was founded, and the International Bureau of Weights and Measures was set up in Paris. This system has evolved over time into the International System of Units, SI. Currently, this system is adopted by most countries in the field of technical calculations, including those countries where traditionally physical quantities are used in everyday life (for example, the USA and England).
GHS
However, in parallel with the generally accepted standard of standards, another, less convenient GHS system (centimeter-gram-second) developed. It was proposed in 1832 by the German physicist Gauss, and in 1874 it was modernized by Maxwell and Thompson, mainly in the field of electrodynamics. In 1889, a more convenient ISS system (meter-kilogram-second) was proposed. Comparison of objects in terms of the standard values of a meter and a kilogram is much more convenient for engineers than using their derivatives (centi, milli, deci, etc.). However, this concept also did not find a mass response in the hearts of those for whom it was intended. The metric system of measures was actively developed and used throughout the world , therefore, calculations in the GHS were carried out less and less, and after 1960, with the introduction of the SI system, the GHS was almost completely out of use. At present, GHSs are actually applied in practice only in calculations in theoretical mechanics and astrophysics, and this is due to a simpler form of writing down the laws of electromagnetism.
Step-by-step instruction
Let us examine an example in detail. Let’s say the task is: “Compare the values of 25 t and 19570 kg. Which of the larger?” What you need to do first things first is to determine in which quantities we have given values. So, the first value is given in tons, and the second in kilograms. In the second step, we check whether the drafters of the problem are trying to mislead us, trying to force us to compare heterogeneous quantities. There are also such tasks-traps, especially in quick tests, where the answer to each question is given 20-30 seconds. As we can see, the values are uniform: in kilograms and tons we measure body weight and weight, so the second test was passed with a positive result. The third step is to convert kilograms to tons or, conversely, tons to kilograms for easy comparison. In the first version, 25 and 19.57 tons are obtained, and in the second: 25 000 and 19 570 kilograms. And now you can compare the values of these values with a calm soul. As can be clearly seen, the first value (25 t) in both cases is greater than the second (19 570 kg).
Traps
As mentioned above, modern tests contain a lot of tricks. These are not necessarily the tasks we have examined, a trap can turn out to be a rather innocuous-looking question, especially one where a logical answer suggests itself. However, insidiousness, as a rule, lies in the details or in a small nuance that the drafters of the task try to disguise in every possible way. For example, instead of the question already familiar to you with the question posed: “Compare the values where possible” - the compilers of the test may simply ask you to compare the indicated values, and choose the values that are strikingly similar to each other. For example, kg * m / s 2 and m / s 2 . In the first case, this is the force acting on the object (newtons), and in the second - the acceleration of the body, or m / s 2 and m / s, where you are asked to compare the acceleration with the speed of the body, that is, completely dissimilar values.
Complicated Comparisons
However, very often in tasks two values are given, expressed not only in different units of measurement and in different calculus systems, but also different from each other in the specificity of physical meaning. For example, the statement of the problem says: "Compare the values of the dynamic and kinematic viscosities and determine which fluid is more viscous." In this case, the kinematic viscosity values are indicated in SI units, that is, in m 2 / s, and dynamic values in GHS, that is, in poises. What to do in this case?
To solve such problems, you can use the above instruction with a small addition to it. We determine which system we will work on: let it be a SI system, generally accepted among engineers. As a second step, we also check if this is a trap? But in this example, too, everything is clean. We compare two fluids by the parameter of internal friction (viscosity), therefore both quantities are homogeneous. The third step is to translate the dynamic viscosity from poise to pascal-second, that is, to the generally accepted units of the SI system. Next, we translate the kinematic viscosity into dynamic, multiplying it by the corresponding value of the density of the liquid (tabular value), and compare the results.
Out of system
There are also non-systemic units of measurement, that is, units that are not included in the SI, but according to the results of the decisions of the convocation of the General Conferences on Weights and Measures (GKVM), acceptable for sharing with SI. Such values can be compared with each other only when they are brought to their general appearance in the SI standard. Non-systemic units include units such as minute, hour, day, liter, electron-volt, unit, hectare, bar, angstrom and many others.