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

Probleme, bei denen es um die Schätzung physikalischer Größen geht, werden oft als Fermi-Problem bezeichnet, benannt nach dem Physiker Enrico Fermi, der dafür bekannt ist, schnelle, grobe Schätzungen auf der Grundlage einfacher Berechnungen und Annahmen vorzunehmen.
Die Bestimmung der Anzahl der Grashalme auf einem Fußballfeld ist ein Beispiel für ein Fermi-Problem.
Die Antwort auf jedes Fermi-Problem, die sogenannte Fermi-Schätzung, wird erreicht, indem das Problem in kleinere Teile zerlegt und die verfügbaren Informationen verwendet werden, um die Unbekannten grob zu schätzen.
Nun kann die Anzahl der Grashalme auf einem Fußballfeld geschätzt werden, indem man die Abmessungen des Feldes berücksichtigt und schätzt, dass sich 20 Grashalme auf einem Quadratzentimeter befinden.
Aus der Länge und Breite wird die Fläche des Fußballfeldes berechnet.
Wenn man dann die Fläche des Feldes in Zentimeter umrechnet und die Fläche mit der Anzahl der Grashalme pro Flächeneinheit multipliziert, erhält man die Fermi-Schätzung der Gesamtzahl der Grashalme.

<ol>
	<li>OpenStax. (2019). Universitätsphysik Vol. 1. [Webversion]. Abgerufen von <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>, Abschnitt 1.5; Seiten 25-27</li>
</ol>

schätzung der physikalischen größen

Auf An vielen Gelegenheiten müssen Physiker, andere Wissenschaftler und Ingenieure Schätzungen einer bestimmten Größe vornehmen. Diese werden manchmal als Schätzungen, Größenordnungsabschätzungen, Schnellrechnungen oder Fermi-Berechnungen bezeichnet. Der Physiker Enrico Fermi war berühmt für seine Fähigkeit, verschiedene Arten von Daten mit erstaunlicher Genauigkeit abzuschätzen. Schätzen bedeutet nicht, eine Zahl oder eine Formel willkürlich zu raten. Stattdessen bedeutet Schätzen, auf frühere Erfahrungen und vernünftige physikalische Überlegungen zurückzugreifen, um eine grobe Vorstellung vom Wert einer Größe zu geben. Da eine zuverlässige Annäherung in der Regel die Identifizierung korrekter physikalischer Prinzipien und eine gute Vermutung über die relevanten Variablen erfordert, ist Schätzen sehr nützlich, um physikalisches Verständnis zu entwickeln. Schätzungen ermöglichen es uns auch, "Gesundheitschecks" bei Berechnungen oder Vorschlägen für politische Maßnahmen durchzuführen, indem bestimmte Szenarien oder unrealistische Zahlen ausgeschlossen werden.

Viele Schätzungen basieren auf Formeln, bei denen die Eingangsgrößen nur auf begrenztem Niveau bekannt sind. Um Fortschritte bei der Schätzung zu erzielen, muss man einige klare Vorstellungen darüber haben, wie die Variablen miteinander in Beziehung stehen könnten. Die folgenden Strategien könnten helfen, die Kunst der Schätzung zu üben:

<ol style="list-style-type: disc;">
	<li>Große Längen aus kleineren Längen ableiten - Beim Schätzen von Längen sollte man bedenken, dass alles als Lineal dienen kann. Man stellt sich vor, dass man etwas Großes in kleinere Teile aufteilt, schätzt die Länge eines der kleineren Teile und multipliziert dann, um die Länge des großen Teils zu erhalten.</li>
	<li>Flächen und Volumen aus Längen ableiten - Beim Umgang mit der Fläche oder dem Volumen eines komplexen Objektes führt man am besten ein einfaches Modell des Objektes ein, wie zum Beispiel eine Kugel oder eine Box. Dann schätzt man zuerst die linearen Dimensionen ab und verwendet die Schätzungen, um das Volumen oder die Fläche anhand von Standardgeometrieformeln zu berechnen.</li>
	<li>Massen aus Volumina und Dichten ableiten - Beim Schätzen von Massen von Objekten kann es hilfreich sein, zuerst ihr Volumen abzuschätzen und dann die Masse anhand einer groben Schätzung ihrer durchschnittlichen Dichte zu berechnen.</li>
	<li>Wenn alle Stricke reißen, begrenzen - Für völlig unbekannte physikalische Größen überlegt man, was sie größer alsoder und kleiner als sein müssen.muss.</li>
	<li>Eine signifikante Ziffer ist in Ordnung - Es ist nicht notwendig, über eine signifikante Ziffer oder eine Ziffer im Koeffizienten eines Ausdrucks in wissenschaftlicher Notation hinauszugehen, wenn man Berechnungen durchführt, um eine Schätzung zu erhalten.</li>
	<li>Stellen Sie die folgenden Fragen - Ergibt dies einen Sinn? Überprüfen Sie, ob die Antwort sinnvoll ist. Wie vergleicht sie sich mit den Werten anderer bekannter Größen mit den gleichen Dimensionen?</li>
</ol>

Schätzung der physikalischen Größen

In vielen Fällen müssen Physiker, andere Wissenschaftler und Ingenieure Schätzungen einer bestimmten Größe vornehmen. Diese werden manchmal auch als ...

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Education

Lehre

JoVE Core

Physics

Physik

Unit 1

Einheit 1

Units, Dimensions, and Measurements

Einheiten, Dimensionen und Messungen

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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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• 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
• 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

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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

Fermi Estimation for Physical Quantities

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