Name: finding force from potential energy
Uploaded: 2023-04-30T10:57:22.000Z
Duration: 1 min 13 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Physics

Energy

PS.Phy.6.2

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

Force and Potential Energy in One Dimension

Les forces conservatrices peuvent être exprimées en termes d’énergie potentielle.
Considérons un corps se déplaçant le long d’une ligne droite en raison d’une force conservatrice qui est fonction de la position.
Or, le travail effectué par la force conservatrice est égal au négatif de la variation de son énergie potentielle.
Le travail effectué est également égal au produit de la force et du déplacement causé par la force.
Ainsi, la force exercée sur le corps est égale au négatif de la variation de l’énergie potentielle divisée par le déplacement. 
Le signe négatif indique que la force conservatrice entraîne le système vers une énergie potentielle plus faible.
Pour de très petits déplacements, l’expression de la force et de l’énergie potentielle dans une dimension peut être établie.
Pour vérifier la relation entre la force et l’énergie potentielle, considérons l’exemple de l’énergie potentielle élastique. Lorsqu'elle est substituée dans la relation entre la force et l'énergie, la formule de la loi de Hooke est établie.

force and potential energy in one dimension

La force peut être calculée à partir de l'expression de l'énergie potentielle, qui est une fonction de la position. La composante d'une force conservatrice, dans une direction particulière, est égale à l'opposé de la dérivée de l'énergie potentielle correspondante par rapport au déplacement dans cette direction. Pour les régions où l'énergie potentielle change rapidement avec le déplacement, le travail effectué et la force sont maximums. De plus, lorsque la force est appliquée le long de l'axe des coordonnées positives, l'énergie potentielle diminue avec une augmentation du déplacement. Par conséquent, la force et la dérivée de l'énergie potentielle par rapport au déplacement ont des signes opposés.

Par exemple, si l'énergie potentielle d'une particule en mouvement unidimensionnel le long de l'axe x est

<img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_1.png" style="height: 32px;" />

où c = 8 N/m3, quelle sera la force pour l'énergie potentielle donnée? Ici, la quantité connue est l'énergie potentielle. La quantité inconnue, la force, doit être calculée.

<img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_2.png" style="height: 32px;" />

En incorporant la valeur de l'énergie potentielle dans l'expression ci-dessus, la force le long de la direction x est calculée pour être -cx3. En substituant la valeur de c, la force est calculée pour être -8x3.

La fonction d'énergie potentielle pour la force entre deux atomes dans une molécule diatomique est approximativement donnée par

<img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_3.png" style="height: 32px;" />

où a et b sont des constantes et x est la distance entre les atomes. Si l'énergie de dissociation de la molécule est

<img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_4.png" style="height: 14px;" />

quelle est la valeur de D? Ici, la quantité connue est l'énergie potentielle. La quantité inconnue est l'énergie de dissociation de la molécule. En substituant la fonction d'énergie potentielle, nous obtenons l'expression de la force. Puisque la force nette est nulle à l'équilibre, nous obtenons

<img alt="Equation1" src="/files/ftp_upload/12677/12677_Equation_5.png" style="height: 32px;" />

Maintenant, la valeur de x6 est substituée dans l'expression de l'énergie potentielle. Puisque l'énergie potentielle à l'infini est nulle, l'énergie de dissociation de la molécule est calculée pour être b2/4a.

Ce texte est adapté de <a href="https://openstax.org/books/university-physics-volume-1/pages/8-4-potential-energy-diagrams-and-stability">Openstax, University Physics Volume 1, Section 8.4: Potential Energy Diagrams and Stability</a>.

La force peut être calculée à partir de l’expression de l’énergie potentielle, qui est fonction de la position. La composante d’une force conservatrice, dans un ...

Education

Enseignement

JoVE Core

Physique

Unit 1

Unité 1

Potential Energy and Energy Conservation

Énergie potentielle et conservation de l'énergie

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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 decreases as displacement increases. In one-dimensional motion, this relationship is often used to move from a known potential energy function to the force it produces.

For example, if a particle moves along the x-axis and its potential energy is given with c = 8 N/m^3, the force can be calculated from that expression. The potential energy is the known quantity, and the force is the unknown quantity. Differentiating the energy function gives the x-direction force as -cx^3, which becomes -8x^3 after substituting the value of c.

The same idea also applies to the force between two atoms in a diatomic molecule. Their potential energy can be written approximately as a function of distance x, with a and b as constants. If the dissociation energy is needed, the force is first found from the potential energy, and the equilibrium point is used because the net force is zero there. Then the value of x^6 is substituted into the energy expression, and since the potential energy at infinity is zero, the dissociation energy is b^2/4a.

Finding Force from Potential Energy

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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

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energy diagrams - i

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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 to calculate force from potential energy in one dimension, including the sign rule, a particle example, and dissociation energy for atoms.

Finding Force from Potential Energy | JoVE K12

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JoVE Core Physique présente plusieurs branches de la physique fondamentale grâce à des vidéos animées concises et faciles à comprendre ; cela inclut: la cinématique, la dynamique, la mécanique des fluides, la mécanique statique, les ondes et l'acoustique. En parallèle, les vidéos de scientifiques à l'action démontrent l'application de concepts associés à ces domaines dans des expériences de recherche classiques et originales réalisées dans des laboratoires modernes du monde entier.

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Finding Force from Potential Energy

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