Name: fermi estimation for physical quantities
Uploaded: 2023-05-16T08:18:41.000Z
Duration: 1 min 5 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Physical Science

PS.1

PS.1.b

Estimation of the Physical Quantities

Problemy związane z szacowaniem wielkości fizycznych są często określane jako problem Fermiego, nazwany tak na cześć fizyka Enrico Fermiego, który jest znany z dokonywania szybkich, zgrubnych oszacowań na podstawie prostych obliczeń i założeń.
Określenie liczby źdźbeł trawy na boisku do piłki nożnej jest przykładem problemu Fermiego.
Odpowiedź na każdy problem Fermiego, zwany oszacowaniem Fermiego, jest osiągana poprzez podzielenie problemu na mniejsze części i wykorzystanie dostępnych informacji do przybliżonego oszacowania niewiadomych.
Teraz liczbę źdźbeł trawy na boisku do piłki nożnej można oszacować, biorąc pod uwagę wymiary boiska i szacując, że w jednym centymetrze kwadratowym znajduje się 20 źdźbeł trawy.
Na podstawie długości i szerokości obliczana jest powierzchnia boiska do piłki nożnej.
Następnie przeliczenie powierzchni pola na centymetry i pomnożenie powierzchni przez liczbę źdźbeł trawy na jednostkę powierzchni daje oszacowanie Fermiego całkowitej liczby źdźbeł trawy.

<ol>
	<li>Protokół OpenStax. (2019). Fizyka uniwersytecka Vol. 1. [Wersja internetowa]. Źródło: <a href="https://openstax.org/books/university-physics-volume-1/pages/1-5-estimates-and-fermi-calculations">https://openstax.org/books/university-physics-volume-1/pages/1-5-estimates-and-fermi-calculations</a>, sekcja 1.5; Strony 25-27</li>
</ol>

szacowanie wielkości fizycznych

W wielu przypadkach fizycy, inni naukowcy i inżynierowie muszą dokonać szacunków określonej wielkości. Nazywa się je czasem szacunkami, przybliżeniami rzędu wielkości, obliczeniami od tyłu koperty lub obliczeniami Fermiego. Fizyk Enrico Fermi słynął ze swojej umiejętności szacowania różnego rodzaju danych z zaskakującą precyzją. Szacowanie nie oznacza losowego odgadywania liczby lub wzoru. Zamiast tego szacowanie oznacza wykorzystanie wcześniejszego doświadczenia i zdrowego rozumowania fizycznego w celu uzyskania przybliżonego wyobrażenia o wartości wielkości. Ponieważ określenie wiarygodnego przybliżenia zwykle wiąże się z identyfikacją prawidłowych zasad fizycznych i dobrym przypuszczeniem co do odpowiednich zmiennych, szacowanie jest bardzo przydatne w rozwijaniu intuicji fizycznej. Szacunki pozwalają nam również przeprowadzać „kontrole zdrowego rozsądku”. na obliczeniach lub propozycjach polityki, pomagając wykluczyć pewne scenariusze lub nierealistyczne liczby.

Wiele szacunków opiera się na wzorach, w których wielkości wejściowe są znane jedynie z ograniczonym poziomem precyzji. Aby poczynić pewne postępy w szacowaniu, trzeba mieć pewne określone wyobrażenia o tym, w jaki sposób zmienne mogą być powiązane. Poniższe strategie mogą pomóc w ćwiczeniu sztuki szacowania:

<ol style="list-style-type: circle;">
	<li>Uzyskaj duże długości z mniejszych długości – Szacując długości, pamiętaj, że linijką może być wszystko. Wyobraź sobie, że dzielisz dużą rzecz na mniejsze, szacujesz długość jednej z mniejszych i mnożysz, aby otrzymać długość dużej rzeczy.</li>
	<li>Uzyskiwanie pól i objętości na podstawie długości — gdy mamy do czynienia z polem lub objętością złożonego obiektu, wprowadź prosty model obiektu, taki jak kula lub pudełko. Następnie oszacuj najpierw wymiary liniowe i na podstawie tych szacunków uzyskaj objętość lub powierzchnię ze standardowych wzorów geometrycznych.</li>
	<li>Uzyskaj masy na podstawie objętości i gęstości – Przy szacowaniu mas obiektów pomocne może być najpierw oszacowanie ich objętości, a następnie oszacowanie ich masy na podstawie przybliżonego oszacowania ich średniej gęstości.</li>
	<li>Jeśli wszystko inne zawiedzie, zwiąż go – Dla zupełnie nieznanych wielkości fizycznych zastanów się, od czego musi być większa, a od czego mniejsza.</li>
	<li>Jedna znacząca cyfra jest w porządku – Podczas wykonywania obliczeń w celu uzyskania oszacowania nie ma potrzeby przekraczania jednej cyfry znaczącej lub jednej cyfry współczynnika wyrażenia w notacji naukowej.</li>
	<li>Zadaj następujące pytanie: – Czy to ma jakiś sens? Sprawdź, czy odpowiedź jest rozsądna. Jak wypada w porównaniu z wartościami innych znanych wielkości o tych samych wymiarach?</li>
</ol>

Szacowanie wielkości fizycznych

W wielu przypadkach fizycy, inni naukowcy i inżynierowie muszą oszacować określoną wielkość. Są one czasami określane jako ...

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Education

JoVE Core

Physics

Fizyka

Unit 1

Jednostka 1

Units, Dimensions, and Measurements

Jednostki, wymiary i pomiary

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

fermi estimation for physical quantities

Fermi estimation helps physicists, scientists, and engineers make rough calculations for physical quantities. These estimates are also called guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. Enrico Fermi was known for making these kinds of estimates with surprising precision.

Estimation is not random guessing. It uses prior experience and sound physical reasoning to get a rough value for a quantity. This kind of reasoning helps build physical intuition. It also gives a useful sanity check by showing when a result or policy idea seems unrealistic.

Many estimates start with formulas that use input values known only to limited precision. To move forward, it helps to decide how the variables are related. One way to estimate length is to break a large object into smaller parts. Another way is to remember that almost anything can serve as a ruler.

Area and volume estimates often begin with a simple model of the object. A sphere or a box can stand in for a more complex shape. Estimate the linear dimensions first, then use standard geometry formulas to find the area or volume. Mass estimates can then follow from volume and a rough average density.

If a quantity is hard to figure out, it is still useful to bound it. That means deciding what it must be bigger than and smaller than. When doing the math, one significant figure is usually enough. Afterward, check whether the answer makes sense and compare it with other known quantities that have the same dimensions.

Fermi Estimation for Physical Quantities

the scope of physics

How Physics Shapes Science and Technology

Physics studies the interactions of energy, matter, space, and time. It looks for the basic mechanisms that explain natural phenomena. The word physics comes from the Greek word physis, which means nature. Physics helps us understand the natural world at its most fundamental level. It relies on quantitative laws, or rules written in numbers and measurements, to describe how things behave. That approach can also help other fields improve the limits of current technology. Physics matters in...

orders of magnitude

Estimating Scale with Powers of 10

Orders of magnitude help estimate the scale of a number using powers of 10. It is a simple way to round values to the nearest power of 10. This makes it easier to compare very large and very small numbers. To find the order of magnitude of a number, take its base-10 logarithm and round to the nearest integer. The result gives the power of 10 that most closely matches the original value. This method gives a consistent estimate of size without using exact digits. Orders of magnitude are useful...

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models, theories, and laws

Scientific Models, Theories, and Laws

Scientific models, theories, and laws help physicists describe natural phenomena. A model is a simplified version of a physical system that is too complex to study in full. It acts as a rough mental or visual picture of what may be happening. Good models keep the important parts and simplify the rest so the problem becomes workable. The light wave model is one example. Light waves are usually invisible, so they cannot be seen in the same way as water waves. Even so, it is useful to think of...

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units and standards of measurement

SI Units for Physical Quantities

SI units give a standard way to measure physical quantities. A physical quantity can be defined by how it is measured or by how it is calculated from other measurements. For example, the mass and dimensions of a metallic cube can be found with a weighing machine and a meter scale. Some quantities are built from others. The volume of a cube is the cube of its side length. The density of the cube is then found by dividing mass by volume. Measurements are written in units, which are standardized...

estimation of the physical quantities

Fermi estimation helps physicists, scientists, and engineers make rough calculations for physical quantities. These estimates are also called guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. Enrico Fermi was known for making these kinds of estimates with surprising precision. Estimation is not random guessing. It uses prior experience and sound physical reasoning to get a rough value for a quantity. This kind of reasoning helps build...

base quantities and derived quantities

SI Base Units Behind Measured Quantities

SI base units are the starting point for measuring physical quantities. In any system of units, some quantities must be defined through direct measurement. These are called base quantities, and their units are base units. Other physical quantities are built from these base values by algebraic combinations. These are called derived quantities, and their units are derived units. For example, area comes from two lengths multiplied together. It is a derived quantity and is written in SI base units...

conversion of units

Unit Conversion Steps and Real-World Errors

Unit conversion lets you change a measurement from one unit to another. It is useful in everyday life, such as when a cookbook gives amounts in liters or ounces and you need cups instead. It also helps when directions use feet or meters, but you want to know the distance in miles. The first step is to list the given unit and the unit you need. The second step is to choose a conversion factor, which is a ratio that shows how many of one unit equal another unit. For example, 1,000 meters equal 1...

accuracy and precision

Repeated Measurements in Science

Repeated measurements help scientists check the quality of their results. They are used to judge both precision and accuracy. These two ideas are related, but they do not mean the same thing. Measurements are precise when repeated trials give very similar results. Precision shows how closely the values agree with one another. Measurements are accurate when the result is very close to the true value or the accepted value. Accuracy shows how closely the values agree with the real target. High...

random and systematic errors

How Measurement Errors Affect Results

Measurement errors can change how accurate and precise a result appears. Scientists try to record measurements as carefully as possible, but errors can still happen. These errors are usually random or systematic. Random errors come from inconsistency or fluctuation in the measuring process. They can also come from changes in the quantity being measured. In repeated measurements, random error may make a value appear greater than the true value one time and less than it the next. A simple...

rules for significant figures

Measurement Precision and Significant Figures

Measurement precision depends on the tool used, and significant figures show that precision. A ruler can measure length to the closest millimeter. A caliper can measure length to the nearest 0.01 mm, so it gives a more precise measurement because it can detect very small changes in length. When a value is written from a measurement, the last digit is not exact. The person making the measurement must estimate that digit. For example, a stick that seems to fall between 13.2 cm and 13.3 cm must...

significant figures in calculations

Rounding Rules for Significant Figures

Rounding rules for significant figures help show the right level of certainty in measured results. When a calculation is reported with the correct number of significant figures, it better matches the uncertainty in the measurements. The rounding rule depends on the type of math being done. For addition and subtraction, the result should have the same number of decimal places as the number with the fewest decimal places. For multiplication and division, the result should have the same number of...

dimensional analysis

Dimensional Checks in Physics Equations

Dimensional consistency is a key check in physics equations. It means the dimensions on both sides of an equation must match. The idea helps show whether an equation can represent a real physical law. The first rule is simple: expressions on each side of the equal sign must have the same dimensions. That makes sense because you can only add or subtract quantities of the same type. The second rule says that the input to a standard mathematical function, such as a trigonometric function, a...

problem solving: dimensional analysis

Dimensional Checks for Physics Equations

Dimensional analysis helps check whether physics equations make sense. It compares the dimensions on each side of an equation and shows whether the units are consistent. This method is useful for spotting algebra errors, typos, and for remembering physical laws. A valid equation must follow two rules. First, both sides of an equality must have the same dimension, so only quantities with matching dimensions can be added or subtracted. Second, common math functions such as exponential,...

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solving problems in physics

Physics Problem Solving: Strategy to Check

Physics problem solving uses general physical principles to work out specific situations. It is a key skill in physics, and it can also help with everyday life. The same analytical skills can be used in new situations, while a list of facts can never cover every possible case. Solving physics problems also takes creativity and insight. These skills grow with experience and practice. There is no simple step-by-step method that works for every problem, but a three-stage process can guide the...

key terms and concepts

Learn Fermi estimation for physical quantities using rough calculations, bounds, density, and sanity checks to build strong physics intuition.

Fermi Estimation for Physical Quantities | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

PH.1

PH.1.b

Texas Essential Knowledge and Skills

High School

Chemistry

CHEM.1

CHEM.1.E

Specialised Topic in Science

112.51.c.1.

112.51.c.2.C.

PHYS.2

PHYS.2.A

PHYS.2.C

Chemistry and Physics

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IPC.2.A

IPC.2.C

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The student will demonstrate an understanding of scientific and engineering practices by asking questions and defining problems
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• offer simple solutions to design problems

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• independently and collaboratively plan and conduct observational and experimental investigations; identify variables, constants, and controls where appropriate and include the safe use of chemicals and equipment
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• take metric measurements using appropriate tools and technologies
• apply scientific ideas or principles to design, construct, and/or test a design of an object, tool, process or system

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The student will demonstrate an understanding of scientific and engineering practices by pnterpreting, analyzing, and evaluating data
• construct and interpret data tables showing independent and dependent variables, repeated trials, and means
• construct, analyze, and interpret graphical displays of data and consider limitations of data analysis
• apply mathematical concepts and processes to scientific questions
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PS.1.c

Models, Theories, and Laws

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Deductive Reasoning

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The student will demonstrate an understanding of scientific and engineering practices by constructing and critiquing conclusions and explanations
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• generate and compare multiple solutions to problems based on how well they meet the criteria and constraints
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PS.1.d

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• evaluate limitations of models

PS.1.e

Fermi Estimation for Physical Quantities

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