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

Задачи, связанные с оценкой физических величин, часто называют проблемой Ферми, названной в честь физика Энрико Ферми, который известен тем, что делает быстрые и грубые оценки, основанные на простых вычислениях и предположениях.
Определение количества травинок на футбольном поле является примером задачи Ферми.
Ответ на любую задачу Ферми, называемую оценкой Ферми, достигается путем разбивки задачи на более мелкие части и использования доступной информации для грубой оценки неизвестных.
Теперь количество травинок на футбольном поле можно оценить, рассмотрев размеры поля и оценив, что на одном квадратном сантиметре приходится 20 травинок.
Исходя из длины и ширины, рассчитывается площадь футбольного поля.
Затем, переведя площадь поля в сантиметры и умножив площадь на количество травинок на единицу площади, мы получим оценку Ферми общего количества травинок.

<ol>
	<li>OpenStax. (2019). Университетская физика Том 1. [Веб-версия]. Получено из <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>, раздел 1.5; страницы 25-27</li>
</ol>

Оценка физических величин

Во многих случаях физики, другие учёные и инженеры должны делать оценки определённой величины. Их иногда называют предположениями, оценками порядка величины, грубыми расчётами или расчётами Ферми. Физик Энрико Ферми был известен своей способностью оценивать различные виды данных с удивительной точностью. Оценка не означает угадывание числа или формулы наугад. Вместо этого оценка означает использование предыдущего опыта и здравого физического рассуждения, чтобы дать примерное представление о значении величины. Поскольку определение надёжной аппроксимации обычно включает определение правильных физических принципов и хорошее предположение о соответствующих переменных, оценка очень полезна для развития физической интуиции. Оценки также позволяют проводить "проверку здравого смысла" расчётов или предложений политики, помогая исключить определённые сценарии или нереалистичные числа.

Многие оценки основаны на формулах, в которых входные величины известны только с ограниченной точностью. Чтобы продвинуться в оценке, нужно иметь определённые представления о том, как между собой могут быть связаны переменные. Следующие стратегии могут помочь освоить искусство оценки:

<ol style="list-style-type: circle;">
	<li>Получайте большие длины из меньших длин - При оценке длин помните, что всё может быть линейкой. Представьте, что разбиваете большой предмет на маленькие предметы, оценивая длину одного из маленьких предметов, и умножайте, чтобы получить длину большого предмета.</li>
	<li>Получайте площади и объёмы из длин - При работе с площадью или объёмом сложного объекта, введите простую модель объекта, такую как сфера или коробка. Затем сначала оцените линейные размеры и используйте эти оценки для получения объёма или площади из стандартных геометрических формул.</li>
	<li>Получайте массы из объемов и плотностей - При оценке масс объектов может помочь сначала оценить их объём, а затем оценить их массу на основе грубой оценки их средней плотности.</li>
	<li>Если всё остальное не помогает, ограничьте это - Для полностью неизвестных физических величин подумайте, чем она должна быть больше и меньше.</li>
	<li>Одна значащая цифра в порядке - Нет необходимости идти дальше одной значащей цифры или одной цифры в коэффициенте выражения в научной нотации при проведении расчетов для получения оценки.</li>
	<li>Задайте следующий вопрос - Это имеет смысл? Проверьте, разумно ли это. Как он сравнивается со значениями других известных величин с тем же размером?</li>
</ol>

Во многих случаях физикам, другим ученым и инженерам необходимо произвести оценку определенной величины. Иногда их называют ...

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Education

JoVE Core

Physics

Физика

Unit 1

Раздел 1

Units, Dimensions, and Measurements

Единицы, размерности и измерения

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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

IPC.2

IPC.2.A

IPC.2.C

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When the null and alternative hypotheses are stated, it is observed ...

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Hypothesis Test for Test of Independence

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Decision Making: P-value Method

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Solving Problems in Physics

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The student will demonstrate an understanding of scientific and engineering practices by asking questions and defining problems
• ask questions that require empirical evidence to answer
• develop hypotheses indicating relationships between independent and dependent variables
• offer simple solutions to design problems

PS.1.a

What is an Experiment?

An experiment is a planned activity carried out under controlled conditions. The purpose of an experiment is to investigate the relationship between two ...

Study Design in Statistics

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Observational Studies

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Experimental Designs

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Randomized Experiments

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Crossover Experiments

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Controls in Experiments

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Bias

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Blinding

Blinding is a commonly used method of not telling participants which treatment a subject is receiving. Blinding is a critical part of a randomized control ...

Clinical Trials

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Data Collection by Observations

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Data Collection by Survey

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Units and Standards of Measurement

A physical quantity is defined either by specifying its measurement method or by stating how it is calculated from other measurements. For example, ...

On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as ...

Base Quantities and Derived Quantities

In any system of units, the units for some physical quantities must be specified through a measurement process. These measurements are the base quantities ...

Conversion of Units

Sometimes, there is a need to convert from one unit to another one. For instance, reading a cookbook in which quantities are expressed in units of liters ...

The student will demonstrate an understanding of scientific and engineering practices by planning and carrying out investigations
• 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
• evaluate the accuracy of various methods for collecting data
• 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

Review and Preview

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What is a Frequency Distribution

A frequency is the number of times a value of the data occurs. The sum of all the frequency values represents the total number of students included in the ...

Ogive Graph

An ogive graph is sometimes called a cumulative frequency polygon. It is one type of frequency polygon that shows cumulative frequency. In other words, ...

Histogram

The histogram is a graphical representation in the x-y form of data distribution in a data set. The horizontal x-axis is labeled with what the data ...

Relative Frequency Histogram

The relative frequency depicts the proportion of data points that have each value. The frequency tells the number of data points that have each value. ...

Scatter Plot

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Time-Series Graph

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Bar Graph

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Multiple Bar Graph

As the name suggests, a multiple bar graph is the same as a bar graph but has multiple bars to depict relationships between different data values. One can ...

Pareto Chart

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Pie Chart

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What is Central Tendency?

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What is Variation?

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Range

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Standard Deviation

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Calculating Standard Deviation

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Variance

&#160;The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative ...

Coefficient of Variation

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Contingency Table

A contingency table provides a way of portraying data that can facilitate calculating probabilities. It is a method of displaying a frequency distribution ...

Statistical Analysis: Overview

An analysis is usually conducted by replicated sampling or repeated measurements on the same sample. This leads to scattered results rather than a single ...

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
• use data to evaluate and refine design solutions to best meet criteria

PS.1.c

Models, Theories, and Laws

Scientists frequently use models to help them comprehend a specific collection of phenomena. In physics, a model is a condensed version of a physical ...

Inductive Reasoning

Inductive reasoning is a form of logical thinking that uses related observations to arrive at a general conclusion. It is uncertain and operates in ...

Deductive Reasoning

Deductive reasoning, or deduction, is the type of logic used in hypothesis-based science. In deductive reasoning, the pattern of thinking moves in the ...

The student will demonstrate an understanding of scientific and engineering practices by constructing and critiquing conclusions and explanations
• construct scientific explanations based on valid and reliable evidence obtained from sources (including the students' own investigations)
• construct arguments supported by empirical evidence and scientific reasoning
• generate and compare multiple solutions to problems based on how well they meet the criteria and constraints
• differentiate between a scientific hypothesis, theory, and law

PS.1.d

The student will demonstrate an understanding of scientific and engineering practices by developing and using models
• construct, develop, and use models and simulations to illustrate and/or explain observable and unobservable phenomena
• evaluate limitations of models

PS.1.e

Fermi Estimation for Physical Quantities

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