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

K12 Standards

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

Energy

PS.PSc.7.2

Conservative Forces

Le forze possono essere classificate come forze conservative e non conservative.
Le forze di ripristino gravitazionali, elettrostatiche ed elastiche sono alcuni esempi di forze conservative.
Ad esempio, un'auto a riposo possiede energia potenziale mentre la sua energia cinetica è zero. Quando l'auto inizia a muoversi, la sua energia potenziale viene convertita in energia cinetica e quando si ferma, la sua energia cinetica si riconverte in energia potenziale a condizione che non vi sia attrito.
Poiché queste energie si interconvertono da una forma all'altra, la somma dell'energia cinetica e potenziale rimane la stessa lungo tutto il percorso. Questa interconversione delle energie è governata da forze conservatrici.
Il lavoro svolto dalle forze conservative è coerentemente reversibile e non dipende dal percorso intrapreso dall'oggetto. Dipende solo dai punti di inizio e fine, e può essere espresso come la differenza nelle energie potenziali in questi punti.
Tuttavia, per un percorso chiuso, il lavoro svolto sarà pari a zero.

forza conservativa

Secondo la legge della conservazione dell'energia, ogni transizione fra l'energia cinetica e l'energia potenziale conserva l'energia totale del sistema. Quindi, il lavoro svolto da una forza conservativa è completamente reversibile. Esso è indipendente dal percorso, il che significa che possiamo iniziare e fermarci in due punti qualsiasi della transizione, e l'energia totale del sistema (energia cinetica più potenziale in questi punti) verrà conservata. Questa è la caratteristica di una forza conservativa. Alcuni importanti esempi di forza conservativa includono la forza di gravità, quella elastica e quella elettrostatica.

Il lavoro svolto da una forza conservativa è indipendente dal percorso preso; in altre parole, è lo stesso per ogni percorso che collega due punti. Possiamo concludere che il lavoro svolto è indipendente dal percorso controllando che il lavoro infinitesimale sia un differenziale esatto. In un percorso chiuso, dove i punti di inizio e fine sono identici, il lavoro svolto da una forza conservativa su un oggetto è zero.

Questo testo è adattato da <a href="https://openstax.org/books/university-physics-volume-1/pages/8-2-conservative-and-non-conservative-forces">Openstax, University Physics Volume 1, Section 8.2: Conservative and Non-Conservative Forces.</a>

Forza conservativa

Secondo la legge di conservazione dell'energia, qualsiasi transizione tra energia cinetica e energia potenziale conserva l'energia totale del sistema. Quindi, il ...

Education

Didattica

JoVE Core

Physics

Fisica

Unit 1

Unità 1

Potential Energy and Energy Conservation

Energia Potenziale e Conservazione dell'Energia

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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

External Work, Energy, and Thermal Loss

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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

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

C-PS3-4

Energy Basics

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Mechanisms of Heat Transfer I

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Mechanisms of Heat Transfer II

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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 ...

Types of Potential Energy

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Types of Kinetic Energy

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Conservation of Mechanical Energy

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Non-conservative Forces

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Conservation of Energy

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Conservation of Energy: Application

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

Work

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

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

Work-Energy Theorem for Motion Along a Curve

The work-energy theorem can be generalized to the motion of a particle along any curved path. The simple argument here is that the curved path can be ...

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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

Gravitation is one of the four fundamental forces in nature. The force between objects on Earth and Earth itself is called gravity.
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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

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Power Expended by a Constant Force

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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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