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

Problemas envolvendo a estimativa de quantidades físicas são frequentemente chamados de problema de Fermi, em homenagem ao físico Enrico Fermi, conhecido por fazer estimativas rápidas e aproximadas com base em cálculos e suposições simples.
A determinação do número de folhas de grama em um campo de futebol é um exemplo de um problema de Fermi.
A resposta para qualquer problema de Fermi, chamada de estimativa de Fermi, é alcançada dividindo o problema em partes menores e usando as informações disponíveis para estimar aproximadamente as incógnitas.
Agora, o número de folhas de grama em um campo de futebol pode ser estimado considerando as dimensões do campo e estimando que existem 20 folhas de grama em um centímetro quadrado.
A partir do comprimento e largura, a área do campo de futebol é calculada.
Em seguida, convertendo a área do campo em centímetros e multiplicando a área pelo número de folhas de grama por unidade de área, obtém-se a estimativa de Fermi do número total de folhas de grama.

<ol>
	<li>OpenStax. (2019). Física Universitária Vol. 1. [Versão Web]. Obtido de <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>, seção 1.5; pág. 25-27</li>
</ol>

estimativa das grandezas físicas

Em muitas ocasiões, físicos, outros cientistas e engenheiros precisam fazer estimativas de uma quantidade específica. Isso às vezes é chamado de estimativas informais, aproximações de ordem de grandeza, ou cálculos de Fermi. O físico Enrico Fermi era famoso por sua habilidade em estimar vários tipos de dados com uma precisão surpreendente. Estimar não significa adivinhar um número ou uma fórmula aleatoriamente. Em vez disso, estimar significa usar experiência prévia e raciocínio físico sólido para ter uma ideia aproximada do valor de uma quantidade. Como determinar uma aproximação confiável geralmente envolve a identificação de princípios físicos corretos e uma boa suposição a respeito das variáveis relevantes, a estimativa é muito útil para desenvolver intuição física. As estimativas também nos permitem realizar "testes de sanidade" em cálculos ou propostas de políticas, ajudando a descartar certos cenários ou números irreais.

Muitas estimativas são baseadas em fórmulas nas quais as quantidades de entrada são conhecidas apenas com um nível limitado de precisão. Para fazer algum progresso na estimativa, é necessário ter algumas ideias definidas sobre como as variáveis podem estar relacionadas. As seguintes estratégias podem ajudar a praticar a arte da estimativa:

<ol style="list-style-type: circle;">
	<li>Obter grandes comprimentos a partir de comprimentos menores - Ao estimar comprimentos, lembre-se de que qualquer coisa pode ser usada como régua. Imagine dividir algo grande em coisas menores, estimar o comprimento de uma das coisas menores e, em seguida, multiplicar para obter o comprimento da coisa grande.</li>
	<li>Obter áreas e volumes a partir de comprimentos - Ao lidar com a área ou o volume de um objeto complexo, introduza um modelo simples do objeto, como uma esfera ou uma caixa. Em seguida, estime as dimensões lineares primeiro e use as estimativas para obter o volume ou a área por meio de fórmulas geométricas padrão.</li>
	<li>Obter massas a partir de volumes e densidades - Ao estimar as massas dos objetos, pode ser útil estimar primeiro o volume e, em seguida, estimar a massa a partir de uma estimativa aproximada de sua densidade média.</li>
	<li>Se tudo mais falhar, estabeleça limites - Para quantidades físicas completamente desconhecidas, pense em algo que ela deve ser maior que e menor que.</li>
	<li>Um algarismo significativo já está bom - Não há necessidade de ir além de um algarismo significativo, ou um dígito no coeficiente de uma expressão em notação científica, ao fazer cálculos para obter uma estimativa.</li>
	<li>Faça a seguinte pergunta - Isso faz algum sentido? Verifique se a resposta é razoável. Como ela se compara com os valores de outras quantidades conhecidas com as mesmas dimensões?</li>
</ol>

Estimativa das Grandezas Físicas

Em muitas ocasiões, físicos, outros cientistas e engenheiros precisam fazer estimativas de uma determinada quantidade. Às vezes, eles são chamados de ...

/files/media/science-education/science-education-thumbs/14734.jpg

Education

JoVE Core

Physics

Física

Unit 1

Unidade 1

Units, Dimensions, and Measurements

Unidades, Dimensões e Medidas

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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 - Fisica apresenta a teoria e a aplicação de tópicos fundamentais da física, incluindo cinemática, dinâmica, mecânica dos fluidos, estática, ondas e acústica, com vídeos animados concisos e de fácil compreensão. Além disso, os vídeos de cientistas em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássica e original realizados nos laboratórios de todo o mundo hoje em dia.

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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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

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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
• 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

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Relative Frequency Histogram

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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
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• apply mathematical concepts and processes to scientific questions
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PS.1.c

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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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