Name: equilibrium stability through potential energy
Uploaded: 2023-09-22T11:49:38.000Z
Duration: 1 min 13 s
Channel: JoVE

K12 Standards

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Physics

PHYS.1

IPC.1.G

stability-of-equilibrium-configuration-problem-solving

Stability of Equilibrium Configuration: Problem Solving

Si consideri un disco collegato a un sistema di pulegge a molla con una sfera attaccata al suo bordo.
Il disco viene ruotato e viene disegnato il diagramma di corpo libero delle sole forze che funzionano. Le deflessioni sulle rotazioni sono mostrate rispetto all'asse delle coordinate.
Per determinare le posizioni di equilibrio del sistema e la loro stabilità, si ottiene la somma delle funzioni di energia potenziale elastica e gravitazionale.
La deflessione verticale della molla e della sfera viene determinata e sostituita nella funzione di energia potenziale.
All'equilibrio, la derivata prima della funzione di energia potenziale è zero. Risolvendo e sostituendo i valori numerici si ottengono le posizioni di equilibrio in termini di angolo di rotazione.
La stabilità degli angoli di equilibrio è determinata dalla derivata seconda dell'energia potenziale.
Se la derivata seconda è negativa, l'equilibrio è instabile. A questa angolazione, un leggero movimento mette in rotazione il sistema.
Se è positivo, l'equilibrio è stabile, il che implica che, sotto rotazione, il sistema si ferma a questo angolo.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica: Statica. Quattordicesima edizione, New Jersey: Pearson. Sezione 11.7, pp. 603-606.</li>
	<li>Birra, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. e Self, B.P. (2016). Meccanica vettoriale per ingegneri. Undicesima edizione, New York: McGraw-Hill Education. Pagine 601.</li>
</ol>

stabilità della configurazione di equilibrio: risoluzione dei problemi

La stabilità delle configurazioni di equilibrio è un concetto importante in fisica, ingegneria e altri campi correlati. In termini semplici, si riferisce alla tendenza di un oggetto o un sistema a tornare alla sua posizione di equilibrio, dopo essere stato disturbato. La stabilità di una configurazione di equilibrio può essere analizzata considerando la funzione di energia potenziale del sistema e osservando il suo comportamento vicino al punto di equilibrio.

La risoluzione dei problemi nel contesto della stabilità della configurazione di equilibrio, comporta diversi passaggi. In primo luogo, è necessario identificare i punti di equilibrio del sistema. Questo può essere fatto ponendo la derivata della funzione di energia potenziale a zero e risolvendo per i valori delle variabili indipendenti che soddisfano l'equazione.

Una volta determinati i punti di equilibrio, il passo successivo è esaminare la loro stabilità. Per fare ciò, si valuta la seconda derivata della funzione di energia potenziale, in ciascun punto di equilibrio. Se la seconda derivata è positiva, l'equilibrio è stabile, indicando che il sistema tornerà alla posizione di equilibrio quando disturbato. Al contrario, se la seconda derivata è negativa, l'equilibrio è instabile, il che significa che il sistema si allontanerà dalla posizione di equilibrio quando disturbato.

È importante notare che un sistema può avere più punti di equilibrio e ognuno deve essere analizzato separatamente per determinarne la stabilità. Inoltre, la stabilità di una configurazione di equilibrio può essere influenzata da vari fattori, come la presenza di smorzamento o forze esterne.

Stabilità della configurazione di equilibrio: Risoluzione dei problemi

La stabilità delle configurazioni di equilibrio è un concetto importante in fisica, ingegneria e altri campi correlati. In parole povere, si riferisce al ...

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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 the equation. A system may have more than one equilibrium point, so each point must be checked on its own.

The next step is to test stability at each equilibrium point. For this, the second derivative of the potential energy function is evaluated at the equilibrium point. If the second derivative is positive, the equilibrium is stable. If it is negative, the equilibrium is unstable and the system moves away after being disturbed.

Other factors can also affect stability. Damping and external forces may change how a system behaves near equilibrium. Because of this, equilibrium analysis is an important problem-solving tool in physics, engineering, and related fields.

Equilibrium Stability Through Potential Energy

equilibrium-stability-through-potential-energy

work

Work in Force and Motion

Work connects force, motion, and energy in mechanics. It happens when a force acts on an object and the object moves along the line of action of that force. Work can also be described as energy transfer caused by applying a force, which leads to a change in the object’s motion or position. Work is calculated as the force multiplied by the part of the displacement in the same direction as the force. It can also be written as the dot product of the applied force and the object’s displacement. In...

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virtual work for a system of connected rigid bodies

virtual-work-for-a-system-of-connected-rigid-bodies

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potential-energy criterion for equilibrium

potential-energy-criterion-for-equilibrium

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...

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stability of equilibrium configuration: problem solving

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

Learn how to find equilibrium points and test stability with potential energy, first and second derivatives, and signs of stable or unstable motion.

Equilibrium Stability Through Potential Energy | JoVE K12

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Equilibrium Stability Through Potential Energy

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