Name: resolving forces in a plane
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 20 s
Channel: JoVE

Considérons un élément structurel dans un espace bidimensionnel où une force agit à un angle thêta avec l’axe x.
Considérant que la ligne d’action de la force passe par l’origine, ses composantes peuvent être exprimées sous la forme cartésienne. La direction du vecteur force est toujours donnée par l’inverse du rapport de ses composantes.
Maintenant, même si la ligne d’action du vecteur force ne passe pas par l’origine, ses composantes vectorielles peuvent toujours être exprimées sous forme cartésienne. La convention de signe de ces composantes vectorielles peut être choisie en fonction de leur direction.
Ici, la force est dirigée vers un angle pi moins thêta, mesuré dans le sens inverse des aiguilles d’une montre à partir de l’axe des y positifs.
Considérons maintenant une structure où la ligne d’action de la force forme un angle arbitraire alpha moins bêta à l’axe x positif du système de coordonnées choisi. Les composantes de la force peuvent être résolues à l’aide d’une analyse similaire.

<ol>
	<li>Meriam, J.L. ; Kraige, L.G. et Bolton, J.N. (2020). Génie mécanique \u2012 Statique. Hoboken, New Jersey : John Wiley. page 33</li>
</ol>

système de force bidimensionnel

Un système bidimensionnel en génie mécanique implique l'analyse du mouvement et des forces dans un plan. Un vecteur de force bidimensionnel peut être décomposé en ses composantes de la manière suivante : <img alt="Equation 1" src="/files/ftp_upload/14229/14229_Equation_1v2.svg" style="text-align: center; height: 15px;"> Où Fx et Fy sont les composantes vectorielles de F dans les directions x et y, respectivement. Chacune de ces composantes vectorielles peut être représentée par un scalaire (Fx et Fy) multiplié par le vecteur unitaire approprié. Pour déterminer les composantes du vecteur de force dans un système de coordonnées cartésiennes, il faut d'abord déterminer l'angle θ que la force forme avec l'axe x positif. En supposant que la ligne d'action de la force passe par l'origine, ses composantes peuvent être exprimées sous une forme cartésienne en utilisant la trigonométrie de base. <img alt="Equation 2" src="/files/ftp_upload/14229/14229_Equation_2v3.svg" style="text-align: center; height: 34px;"> où F représente la magnitude du vecteur de force. La direction du vecteur de force est donnée par l'inverse de la tangente du rapport de ses composantes. <img alt="Equation 3" src="/files/ftp_upload/14229/14229_Equation_3v3.svg" style="text-align: center; height: 34px;"> Cependant, dans les cas où la ligne d'action du vecteur de force ne passe pas par l'origine, ses composantes vectorielles peuvent toujours être exprimées sous une forme cartésienne en utilisant la même approche. Nous pouvons choisir le signe de chaque composante en fonction de la direction du vecteur de force. En décomposant le vecteur de force en ses composantes, nous pouvons déterminer l'effet net de la force sur la structure en question. Comprendre le système de force bidimensionnel est essentiel pour les ingénieurs afin d'analyser et de concevoir des structures qui sont sûres et solides sur le plan structurel. Cette connaissance fournit une compréhension fondamentale de la réaction d'une structure à diverses forces et permet de repérer les faiblesses de conception, le cas échéant.

Système de force bidimensionnel

Un système bidimensionnel en génie mécanique implique l’analyse du mouvement et des forces dans un plan. Un vecteur de force bidimensionnel peut être résolu ...

Education

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Mechanical Engineering

Génie mécanique

Unit 1

Unité 1

Force Vectors

Vecteurs de force

KEY TERMS AND CONCEPTS

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Two-Dimensional Force System

resolving forces in a plane

Resolving forces in a plane is a key part of two-dimensional mechanical analysis. A force vector can be split into x- and y-components, which show how the force acts in each direction. These components are written with the help of unit vectors, one for the x direction and one for the y direction.

To find the components in a Cartesian coordinate system, first identify the angle theta between the force and the positive x-axis. If the line of action passes through the origin, basic trigonometry gives the Cartesian form of the force. The magnitude of the force is F, and the direction can be found from the inverse tangent of the ratio of its components.

The same component method also works when the line of action does not pass through the origin. In that case, the sign of each component is chosen from the direction of the force vector. By breaking a force into parts, engineers can judge its net effect on a structure and look for possible weak points. This skill helps them analyze and design structures that are safe and structurally sound.

Resolving Forces in a Plane

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Resolving forces in a plane is a key part of two-dimensional mechanical analysis. A force vector can be split into x- and y-components, which show how the force acts in each direction. These components are written with the help of unit vectors, one for the x direction and one for the y direction. To find the components in a Cartesian coordinate system, first identify the angle theta between the force and the positive x-axis. If the line of action passes through the origin, basic trigonometry...

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key terms and concepts

Learn how to break a force into x- and y-components, use trigonometry and angle theta, and understand a structure's net force in a plane.

Resolving Forces in a Plane | 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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Resolving Forces in a Plane

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