Name: conservative forces and path independence
Uploaded: 2023-04-30T10:56:52.000Z
Duration: 1 min 14 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

Energy

PS.PSc.7.2

Conservative Forces

Kräfte können in konservative und nicht-konservative Kräfte eingeteilt werden.
Gravitationskräfte, elektrostatische und elastische Rückstellkräfte sind einige Beispiele für konservative Kräfte.
Zum Beispiel besitzt ein Auto im Ruhezustand potentielle Energie, während seine kinetische Energie Null ist. Wenn sich das Auto in Bewegung setzt, wird seine potentielle Energie in kinetische Energie umgewandelt, und wenn es anhält, wird seine kinetische Energie wieder in potentielle Energie umgewandelt, sofern keine Reibung vorliegt.
Da sich diese Energien von einer Form in eine andere umwandeln, bleibt die Summe aus kinetischer und potentieller Energie auf dem gesamten Weg gleich. Diese Umwandlung der Energien wird von konservativen Kräften beherrscht.
Die Arbeit der konservativen Kräfte ist konsequent reversibel und hängt nicht vom Weg ab, den das Objekt nimmt. Sie hängt nur vom Start- und Endpunkt ab und kann als Differenz der potentiellen Energien an diesen Punkten ausgedrückt werden.
Bei einem geschlossenen Pfad ist die geleistete Arbeit jedoch null.

konservative kräfte

Gemäß dem Energieerhaltungssatz bleibt die Gesamtenergie des Systems bei jedem Übergang zwischen kinetischer und potenzieller Energie erhalten. Daher ist die von einer konservativen Kraft verrichtete Arbeit vollständig umkehrbar. Sie ist wegsunabhängig, was bedeutet, dass wir an beliebigen zwei Punkten des Übergangs beginnen und stoppen können und die Gesamtenergie des Systems (kinetische plus potenzielle Energie an diesen Punkten) erhalten bleibt. Dies ist charakteristisch für eine konservative Kraft. Einige wichtige Beispiele für konservative Kräfte sind Gravitation, elastische und statische elektrische Kraft.

Die von einer konservativen Kraft verrichtete Arbeit hängt nicht vom zurückgelegten Weg ab, sie ist also für jede Verbindung zweier Punkte gleich. Wir können daraus schließen, dass die verrichtete Arbeit unabhängig vom Weg ist, indem wir prüfen, ob die infinitesimale Arbeit eine exakte Differentialform ist. Bei einem geschlossenen Weg, bei dem der Anfangs- und Endpunkt identisch sind, beträgt die von einer konservativen Kraft auf einen Gegenstand verrichtete Arbeit null.

Dieser Text ist angepasst von <a href="https://openstax.org/books/university-physics-volume-1/pages/8-2-conservative-and-non-conservative-forces">Openstax, University Physics Volume 1, Abschnitt 8.2: Konservative und nicht-konservative Kräfte.</a>

Konservative Kräfte

Nach dem Gesetz der Energieerhaltung erhält jeder Übergang zwischen kinetischer und potentieller Energie die Gesamtenergie des Systems. Daher ist die ...

Education

Lehre

JoVE Core

Physics

Physik

Unit 1

Einheit 1

Potential Energy and Energy Conservation

Potenzielle Energie und Energieerhaltung

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

conservative forces and path independence

Conservative forces are forces for which the work done depends only on the starting and ending points. In this case, the work is path independent. That means the total energy of the system, including kinetic energy and potential energy, stays conserved during the change.

This idea follows the law of conservation of energy. When energy shifts between kinetic and potential forms, the total amount remains the same. Because the work is completely reversible, an object can start and stop at any two points without changing the total energy of the system.

Common examples of conservative forces include gravity, elastic force, and static electric force. A key test is that the work done along any path between two points is the same. For a closed path, where the starting point and ending point are the same, the work done by a conservative force is zero.

Conservative Forces and Path Independence

conservative-forces-and-path-independence

gravitational potential energy

Gravitational Energy from Height and Weight

Gravitational potential energy depends on an object’s weight and its height above the ground. It is one part of the total potential energy of a system, which comes from the interactions between objects. In a system, the total potential energy is the sum of the potential energies for all the objects. Potential energy is usually grouped into two main categories: gravitational potential energy and elastic potential energy. Gravitational potential energy describes the energy tied to a body’s...

elastic potential energy

Spring Force and Stored Energy

Elastic potential energy is stored when an elastic object is deformed, such as when a spring is stretched. An object is elastic if it returns to its original shape and size after the force is removed. This stored energy is part of a system’s potential energy. An ideal spring also exerts an elastic force. The work done by this force can be described as a change in the spring’s elastic potential energy. For a perfectly elastic spring in one dimension, that work depends only on the spring...

conservation of mechanical energy

Mechanical Energy in Isolated Systems

Mechanical energy in an isolated system is the total of kinetic energy and potential energy. Kinetic energy is the energy of motion, and potential energy is stored energy. The transcript focuses on what happens when energy shifts within a system without outside influence. In this case, only conservative forces act on the objects in the system. Conservative forces can transfer energy between kinetic energy and potential energy. Friction and drag do not act here, and no external force from...

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work done on a system by external force

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conservative forces

Conservative forces are forces for which the work done depends only on the starting and ending points. In this case, the work is path independent. That means the total energy of the system, including kinetic energy and potential energy, stays conserved during the change. This idea follows the law of conservation of energy. When energy shifts between kinetic and potential forms, the total amount remains the same. Because the work is completely reversible, an object can start and stop at any two...

non-conservative forces

Friction and Energy Loss in Motion

Non-conservative forces, such as friction and air resistance, remove energy from a system as it moves. The energy is not stored as potential energy. Instead, it is lost from the system and cannot be used later for useful work. These forces are path-dependent, which means the route matters. Where an object starts and stops can change the work done. A grinding wheel is one example, because the work depends on how many rotations the wheel makes. Non-conservative forces also turn large-scale...

conservation of energy

Energy Changes in a Closed System

Energy changes in a closed system follow a conservation law in physics. A conserved quantity is not the same as the everyday use of the word "conserved." In science, a conserved quantity stays constant, or it changes by a definite amount that is transferred to another system and converted into another form of the same quantity. This means a conserved quantity can change form, but it cannot be created or destroyed in a strict physical sense. For that reason, physics does not have a law of...

conservation of energy: application

Energy Conservation Problem-Solving Steps

Energy conservation problem-solving uses a clear set of steps. First, identify the system you want to study. In many cases, that system includes more than one body at the same time. Next, identify the forces acting on the object and decide whether each force is conservative. A conservative force is one whose work can be described with potential energy. If a non-conservative force such as friction does work, then mechanical energy is not conserved, and the system must be analyzed with...

force and potential energy in one dimension

force-and-potential-energy-in-one-dimension

Finding Force from Potential Energy

Force can be found from potential energy when the energy is written as a function of position. For a conservative force, the force component in a given direction equals the negative derivative of the matching potential energy with respect to displacement. This means force and the slope of potential energy have opposite signs. Where potential energy changes quickly with displacement, the force and the work done are largest. When a force acts along the positive coordinate axis, potential energy...

force and potential energy in three dimensions

force-and-potential-energy-in-three-dimensions

Gradient Force from 3D Potential Energy

Gradient force from 3D potential energy shows how a conservative force changes along the x, y, and z axes. The potential energy function U depends on all three spatial coordinates. Each force component is linked to how U changes with position along one coordinate. In one dimension, force can be written as the negative ratio of the change in potential energy to the displacement along that axis. For very small displacements, these ratios become derivatives. When a function has several variables,...

energy diagrams - i

Potential Energy Diagrams and Stability

Potential energy diagrams help describe how a mechanical system moves. Because energy is a scalar quantity, the system’s behavior is easier to interpret from the diagram. A skater on a parabolic ramp is a clear example. The ramp height changes with horizontal position, so the potential energy changes as well. As the skater moves down from the highest point, potential energy changes into kinetic energy. Kinetic energy is the energy of motion. The net force on the skater is gravitational force,...

energy diagrams - ii

Stability in Potential Energy Diagrams

Potential energy diagrams show how stable a system is at different positions. Their shape, or topology, helps identify equilibrium points. An equilibrium point is a place where the system can stay in balance because the net force is zero. At a local minimum, the potential energy is lowest. The system tends to remain there unless a net force acts on it. The slope at the minimum is zero. The slope is positive on both sides, so the force acts as a restoring force and pushes the system back. A...

key terms and concepts

Learn how conservative forces make work path independent, conserve kinetic and potential energy, and produce zero work over a closed path.

Conservative Forces and Path Independence | 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.

PS.Phy.6.1

Tennessee Academic Standards

High School

PHYS.PS3.8

Chemistry

CHEM1.PS3.4

Virginia  Standards of Learning

HIgh School

PH.4

PH.4.b

Next Generation Science Standards

HS-PS3-5

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South Carolina College and Career Ready Science Standards

C-PS3-4

Energy Basics

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Use models to explain thermal energy and its transfer.

PS.PSc.7.1

The universe is composed of matter in different forms, and all forms of matter contain energy.&#160; The different forms of energy on Earth originate from ...

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Types of Kinetic Energy

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According to the law of conservation of energy, any transition between kinetic and potential energy conserves the total energy of the system. Hence, the ...

Non-conservative Forces

Non-conservative forces are dissipative forces such as friction or air resistance. These forces take energy away from a system as it progresses. Unlike ...

Conservation of Energy

The terms &#39;conserved quantity&#39;&#160;and &#39;conservation law&#39;&#160;have specific scientific meanings in physics, which differ from the ...

Conservation of Energy: Application

When solving problems using the energy conservation law, the object (system) to be studied should first be identified. Often, in applications of energy ...

Use mathematics and computational thinking to explain the Law of Conservation of Energy in a mechanical system in terms of kinetic and potential energy.

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Work is done when energy is transferred from one object to another. In other words, work is when a force acts on something that undergoes a displacement ...

Positive, Negative, and Zero Work

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work-energy-theorem-for-motion-along-a-curve

Work-Energy Theorem for Motion Along a Curve

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Work Done Over an Inclined Plane

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Work Done by Many Forces

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Work Done by Gravity

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Like other forces, ...

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Use mathematics and computational thinking to explain work in terms of the relationship among the applied force to an object, the resulting displacement of the object, and the energy transferred to an object.

PS.PSc.7.3

Power

The concept of work involves force and displacement; meanwhile, the work-energy theorem relates the net work done on a body to the difference in its ...

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The relationship between work done and the time taken to do it can be explained using the concept of power. For example, several sprinters in a race may ...

Construct an explanation to infer the relationship between work and power, both quantitatively and qualitatively.

PS.PSc.7.4

Analyze energy transfers and transformations within a mechanical system.

Conservative Forces and Path Independence

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