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

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HS-PS3-5

Stability of Equilibrium Configuration

Un système en équilibre peut être neutre, stable ou instable.
En équilibre neutre, si le système est légèrement déplacé, il reste en équilibre à sa nouvelle position. Son énergie potentielle reste constante à ce stade.
En équilibre stable, lorsque le système est légèrement déplacé, il revient à sa position d’origine. Un tel système est à son énergie potentielle minimale.
En équilibre instable, après un petit déplacement, le système s’éloigne de sa position d’équilibre d’origine et son énergie potentielle est maximale.
Considérons une poutre schématique dans un laboratoire chargée d’un petit poids qui la déforme légèrement. Une fois le poids retiré, la poutre revient à sa position d’origine. Ce système est en équilibre stable.
Si la poutre est chargée de manière égale des deux côtés, elle se déplace légèrement et reste dans sa nouvelle position. Il est donc en équilibre neutre.
Si la charge et le support à une extrémité sont retirés, le système s’éloigne de sa position d’origine et se trouve en équilibre instable.
La détermination de la stabilité à l’équilibre est essentielle pour la conception de structures stables.

<ol>
	<li>Hibbeler, R.C. (2016). Mécanique du génie : Statique. Quatorzième édition, New Jersey : Pearson. P. 601.</li>
	<li>Meriam, J.L., Kraige, L.G. et Bolten, J.N. (2016). Mécanique de l’ingénierie : statique et dynamique. Huitième édition, Singapour : John Wiley & Sons. p. 415.</li>
</ol>

stabilité de la configuration d'équilibre

Comprendre la stabilité des configurations d'équilibre est une partie fondamentale du génie mécanique. Dans tout système, il existe trois types distincts d'équilibre : stable, neutre et instable. Un équilibre stable se produit lorsque le système a tendance à revenir à sa position d'origine lorsqu'il est soumis à un léger déplacement, et que l'énergie potentielle est à son minimum. Un exemple d'équilibre stable est lorsqu'une poutre en porte–à–faux est fixée à une extrémité et qu'un poids est attaché à l'autre extrémité. Si le poids est centré directement sous l'extrémité libre, la poutre sera en position d'équilibre stable. L'énergie potentielle du système est à son minimum, et tout léger déplacement du poids fera osciller la poutre. Cependant, chaque fois que le poids est déplacé loin du centre, la poutre subira une force de rappel due aux contraintes internes dans la poutre, qui la ramène à sa position d'origine. Dans un équilibre neutre, le système reste en équilibre même après avoir été soumis à un léger déplacement par rapport à sa position d'origine, et l'énergie potentielle reste constante. Un exemple d'équilibre neutre est une balle placée sur une surface plate et horizontale. Si la balle est légèrement déplacée vers un côté, elle restera toujours en équilibre et l'énergie potentielle du système restera constante. Un équilibre instable se produit lorsque le système a tendance à s'éloigner davantage de son état d'origine lorsqu'il est soumis à un léger déplacement. À ce stade, l'énergie potentielle du système est à son maximum. Une poutre en porte–à–faux déformée au–delà de sa limite élastique est un exemple de ce phénomène ; une fois qu'elle dépasse sa limite élastique, une déformation supplémentaire conduit à l'instabilité et à l'effondrement final. Dans l'ensemble, comprendre ces trois types d'équilibre est essentiel en génie mécanique pour prédire comment les systèmes réagiront dans différentes conditions ou perturbations. En comprenant leurs propriétés et leurs limites, les ingénieurs peuvent planifier un fonctionnement sûr et garantir l'efficacité de leurs conceptions.

Stabilité de la configuration d'équilibre

La compréhension de la stabilité des configurations d’équilibre est un élément fondamental de l’ingénierie mécanique. Dans tout système, il y a trois types distincts ...

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KEY TERMS AND CONCEPTS

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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

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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Couple Moment Work in Rotation

Mechanical engineering studies motion, energy, and force, and it uses the idea of a couple moment to describe how two equal and opposite forces act on a rigid body. A couple moment is created when those forces act at two points on the body that are separated by a distance. When a rigid body moves because of a couple, its displacement can be split into two parts. First, the two points move by the same amount to their final positions. Then the body rotates about one of those points. During the...

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

Virtual work helps find forces in a system of connected rigid bodies. It is a useful method when several links move together and the system is in equilibrium. In that case, the total virtual work is zero. To analyze the system, start with a free-body diagram. Use one independent coordinate to describe the link configuration. Then mark the deflected position that comes from a positive virtual displacement. This makes the small change in position clear before any calculations begin. Next,...

principle of virtual work: problem solving

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Virtual Work for Finding Unknown Forces

The principle of virtual work helps find unknown forces and moments in equilibrium problems. It is an important idea in mechanics and engineering. The method uses a small, hypothetical motion called a virtual displacement. If the system is in equilibrium, the work done by the forces during that displacement is zero. To apply this principle, the positions of the internal and external forces must be written in terms of one common coordinate parameter. That parameter can be an angle, a distance,...

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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...

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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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