Name: types of equilibrium in mechanical systems
Uploaded: 2023-09-22T11:49:37.000Z
Duration: 1 min 23 s
Channel: JoVE

K12 Standards

Next Generation Science Standards

High School

Physical Science

Energy

HS-PS3-5

Stability of Equilibrium Configuration

Un sistema in equilibrio può essere neutro, stabile o instabile.
In equilibrio neutro, se il sistema è leggermente spostato, rimane in equilibrio nella sua nuova posizione. La sua energia potenziale rimane costante a questo punto.
In equilibrio stabile, quando il sistema viene spostato leggermente, ritorna alla sua posizione originale. Un tale sistema è al minimo dell'energia potenziale.
In equilibrio instabile, dopo un piccolo spostamento, il sistema si allontana dalla sua posizione di equilibrio originale e la sua energia potenziale è massima.
Si consideri un traliccio schematico in un laboratorio caricato con un peso ridotto che lo deforma leggermente. Dopo aver rimosso il peso, il traliccio ritorna nella sua posizione originale. Questo sistema è in equilibrio stabile.
Se il traliccio è caricato allo stesso modo su entrambi i lati, si sposta leggermente e rimane nella sua nuova posizione. Quindi, è in equilibrio neutro.
Se il carico e il supporto a un'estremità vengono rimossi, il sistema si allontana dalla sua posizione originale e si trova in equilibrio instabile.
La determinazione della stabilità all'equilibrio è essenziale per la progettazione di strutture stabili.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica: Statica. Quattordicesima edizione, New Jersey: Pearson. Pagine 601.</li>
	<li>Meriam, J.L., Kraige, L.G. e Bolten, J.N. (2016). Meccanica ingegneristica: statica e dinamica. Ottava edizione, Singapore: John Wiley & Sons. Pagine 415.</li>
</ol>

stabilità della configurazione di equilibrio

La comprensione della stabilità delle configurazioni di equilibrio, è una parte fondamentale dell'ingegneria meccanica. In qualsiasi sistema, ci sono tre tipi distinti di equilibrio: stabile, neutrale e instabile.

Un equilibrio stabile si verifica quando un sistema tende a tornare alla sua posizione originale se sottoposto a un piccolo spostamento, e l'energia potenziale è al minimo. Un esempio di equilibrio stabile è quando una trave a sbalzo è fissata ad un'estremità e un peso è attaccato all'altra estremità. Se il peso è centrato direttamente sotto l'estremità libera, la trave sarà in una posizione di equilibrio stabile. L'energia potenziale del sistema è al minimo, e qualsiasi piccolo spostamento del peso farà oscillare la trave. Tuttavia, ogni volta che il peso viene spostato lontano dal centro, la trave esperimenterà una forza di ripristino dovuta agli sforzi interni all'interno della trave, che la riporterà alla sua posizione originale.

In un equilibrio neutrale, il sistema rimane in equilibrio anche dopo essere stato sottoposto ad un piccolo spostamento dalla sua posizione originale, e l'energia potenziale rimane costante. Un esempio di equilibrio neutrale è una palla posta su una superficie piana e livellata. Se la palla viene spostata leggermente da un lato, rimarrà comunque nello stato di equilibrio, e l'energia potenziale del sistema rimarrà costante.

Un equilibrio instabile si verifica quando il sistema, tende a spostarsi ulteriormente dalla sua condizione originale quando sottoposto ad un piccolo spostamento. A questo punto, l'energia potenziale del sistema è al massimo. Una trave a sbalzo deviata al di là del suo limite elastico è un esempio di questo fenomeno; una volta superato il limite elastico, ulteriori deviazioni portano all'instabilità e al collasso finale.

In generale, la comprensione di questi tre tipi di equilibrio, è essenziale nell'ingegneria meccanica per prevedere come i sistemi risponderanno in diverse condizioni o disturbi. Comprendendo le loro proprietà e limitazioni, gli ingegneri possono pianificare un funzionamento sicuro e garantire il corretto funzionamento dei loro progetti.

Stabilità della configurazione di equilibrio

Comprendere la stabilità delle configurazioni di equilibrio è una parte fondamentale dell'ingegneria meccanica. In ogni sistema, ci sono tre tipi distinti ...

Education

Didattica

JoVE Core

Mechanical Engineering

Ingegneria Meccanica

Unit 1

Unità 1

Virtual Work

Lavoro virtuale

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

types of equilibrium in mechanical systems

Types of equilibrium in mechanical systems are stable, neutral, and unstable. These three cases help explain how a structure or object responds when it is pushed slightly away from balance. They are important for predicting whether a system will return to its original position, stay where it is, or move farther away.

Stable equilibrium occurs when a system returns toward its original position after a small displacement. In this case, the potential energy is at a minimum. A cantilever beam fixed at one end with a weight at the free end is one example. When the weight is centered directly below the free end, the beam is in stable equilibrium, and a small displacement makes it oscillate back.

The beam also shows a restoring force when the weight moves away from the center. This force comes from internal stresses within the beam. It pulls the system back to its original position. That behavior is a key feature of stable equilibrium.

Neutral equilibrium means the system stays balanced after a small displacement. The position changes, but the potential energy remains constant. A ball on a flat, level surface is a simple example. If the ball is nudged to one side, it still remains in equilibrium.

Unstable equilibrium is the opposite case. After a small displacement, the system tends to move farther from its original state. Here, the potential energy is at a maximum. A cantilever beam deflected beyond its elastic limit shows this behavior. Once it passes that limit, further deflection leads to instability and can end in collapse.

Knowing stable, neutral, and unstable equilibrium helps engineers judge how a design will respond under different conditions or disturbances. This makes it easier to plan for safe operation and reliable performance. Understanding these limits is a basic part of mechanical engineering.

Types of Equilibrium in Mechanical Systems

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work

Work in Force and Motion

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virtual work

Virtual Work in Force Equilibrium

Virtual work is a mechanics principle used to check equilibrium with imaginary motion. If a body is in static or dynamic equilibrium, the total virtual work from external forces and couple moments must be zero for any virtual displacement. A virtual displacement is an imagined small movement. It can be a shift or a rotation. The virtual work done by a force equals the force dotted with the virtual displacement in the force’s direction. For a couple moment, virtual rotational work is found by...

virtual work for a system of connected rigid bodies

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Finding Forces with Virtual Work in Linked Bodies

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Virtual Work for Finding Unknown Forces

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conservative forces

Conservative Forces and Path-Independent Work

Conservative forces are forces whose work depends only on an object’s starting and ending positions. The path between those positions does not change the amount of work done. This idea is important in mechanical engineering because it helps describe how energy moves through a system. A conservative force also conserves energy in the sense that its work is path independent. Gravity is one example. Electrostatic forces and springs modeled by Hooke’s law are also examples. A ball rolling down a...

potential energy

Gravitational and Elastic Energy Stored

Gravitational and elastic potential energy are forms of stored energy from conservative forces. A conservative force, such as gravity or an elastic force, gives a body the capacity to do work. This capacity is measured as potential energy and depends on the body’s position relative to a fixed reference point, or datum. For gravitational potential energy, the datum is the level where the energy is taken as zero. If a body is above this reference plane, its weight has positive gravitational...

potential-energy criterion for equilibrium

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Stable Equilibrium Through Potential Energy

Potential energy helps determine when a mechanical system is stable at equilibrium. When a system is acted on by gravitational and elastic forces, its total potential function is the algebraic sum of gravitational potential energy and elastic potential energy. If the system is already in equilibrium and is given a small displacement, the work done on the system equals the negative of the change in potential energy between the starting and ending positions. For a virtual displacement, which is...

stability of equilibrium configuration

Types of equilibrium in mechanical systems are stable, neutral, and unstable. These three cases help explain how a structure or object responds when it is pushed slightly away from balance. They are important for predicting whether a system will return to its original position, stay where it is, or move farther away. Stable equilibrium occurs when a system returns toward its original position after a small displacement. In this case, the potential energy is at a minimum. A cantilever beam...

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Spring-Mass Motion and Energy Stability

A one-degree-of-freedom system uses a single independent variable to describe its state and behavior. In mechanical engineering, this kind of model helps explain how parts in a larger system respond to force. It also gives engineers a way to predict motion before a design is built in real life. A simple harmonic oscillator is one example of a one-degree-of-freedom system. A mass attached to a spring moves along one axis, and that position determines the system’s state. The spring force makes...

stability of equilibrium configuration: problem solving

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Equilibrium Stability Through Potential Energy

Stability of equilibrium in physics and engineering can be studied by using a system’s potential energy. An equilibrium configuration is a state where the system can remain at rest. Stability describes whether the system tends to return to that state after a small disturbance. Problem solving begins by finding the equilibrium points of the system. This is done by setting the derivative of the potential energy function equal to zero and solving for the independent variable values that satisfy...

key terms and concepts

Explore stable, neutral, and unstable equilibrium in mechanical systems with beam and ball examples. Learn how small displacements affect balance and energy.

Types of Equilibrium in Mechanical Systems | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

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Types of Equilibrium in Mechanical Systems

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