Name: two-dimensional forces: free-body analysis
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 29 s
Channel: JoVE

Considérons un essuie-glace incliné à un angle de 25 degrés par rapport au « s » de base dans un système bidimensionnel. Une force agissant sur la poignée, pivotée vers le centre de l'essuie-glace, fait un angle de 20 degrés avec la ligne de référence « c », qui est parallèle à la ligne de base « s ».
Si la composante de force le long de l’axe a est de 65 Newtons, déterminez l’intensité de la force et sa composante le long de l’axe b.
Ici, en considérant des angles alternés, coa' devient 25 degrés, tandis que l’angle Foc est de 20 degrés. Ainsi, l’angle formé par le vecteur force avec l’axe a est déterminé en additionnant les deux angles et est égal à 45 degrés.
Comme la composante de la force le long de l’axe a est connue, l’intensité d’une force est estimée par le rapport de la composante a de la force au cosinus de 45 degrés.
Maintenant, la composante b de la force est exprimée comme le produit de l’intensité de la force et du sinus de 45 degrés. Il est négatif puisqu’il se trouve le long de l’axe B négatif.

<ol>
	<li>Bière, F.P. ; Johnston, E.R. ; Mazurek, D.F ; Cromwell, P.J. et Self, B.P. (2019). Mécanique vectorielle pour les ingénieurs \u2012 Statique et dynamique. New York : McGraw-Hill. pages 29 à 33</li>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. pp 33 à 35.</li>
</ol>

système de forces bidimensionnelles : résolution de problèmes

La résolution de problèmes liés aux systèmes de forces bidimensionnelles est un aspect essentiel de la mécanique et de l'ingénierie. En appliquant les principes de l'analyse vectorielle et de l'équilibre des forces, on peut déterminer l'effet de multiples forces agissant sur un objet dans un espace bidimensionnel. La première étape pour résoudre un problème de système de forces bidimensionnelles est de dessiner un diagramme des forces libres de l'objet en question. Ce diagramme aide à identifier toutes les forces externes agissant sur l'objet, y compris leurs grandeurs, directions et points d'application. Ensuite, il faut résoudre les forces en leurs composantes dans les directions x et y en utilisant les principes de l'analyse vectorielle. Cette étape aide à convertir les forces données en leur forme de vecteur cartésien, permettant une représentation et une analyse faciles. Les composantes peuvent être résolues à l'aide de fonctions trigonométriques, telles que le sinus et le cosinus des angles donnés. Après avoir décomposé les forces en composantes, l'étape suivante consiste à déterminer la force nette dans chaque direction. Cela se fait en additionnant toutes les forces dans chaque direction. Ensuite, la force résultante et sa direction sont déterminées en utilisant le théorème de Pythagore et la trigonométrie. Si la force nette est nulle, l'objet est en équilibre et n'accélère pas. Si la force nette est non nulle, alors l'objet accélère dans la direction de la force nette. Le principe d'équilibre des forces stipule que la somme de toutes les forces externes agissant sur l'élément doit être égale à zéro dans les directions x et y. Cela nous permet de déterminer les forces inconnues agissant sur l'objet, telles que la tension ou la compression dans un élément. Dans certains cas, le principe de l'équilibre des moments est également utilisé pour déterminer l'effet des forces externes sur l'objet. Ce principe stipule que la somme de tous les moments externes agissant sur l'élément doit être égale à zéro. Cette étape aide à déterminer les valeurs et les directions des moments agissant sur l'objet.

Système de forces bidimensionnelles : Résolution de problèmes

La résolution de problèmes liés aux systèmes de forces bidimensionnels est un aspect essentiel de la mécanique et de l’ingénierie. En appliquant les principes de la vectorielle ...

two-dimensional-force-system-problem-solving

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two-dimensional forces: free-body analysis

Two-dimensional force analysis starts with a free-body diagram. A free-body diagram shows the object and every external force acting on it. It includes each force’s size, direction, and point of application.

After the diagram is drawn, each force is broken into x- and y-components. This uses vector analysis and trigonometry, especially sine and cosine. The forces can then be written in Cartesian vector form, which makes them easier to work with.

Next, the components in each direction are added to find the net force in x and y. The resultant force is then found with the Pythagorean theorem and trigonometry. If the net force is zero, the object is in equilibrium and does not accelerate. If the net force is not zero, the object accelerates in the direction of the net force.

Force equilibrium means the sum of external forces is zero in both the x and y directions. This helps solve for unknown forces such as tension or compression in a member. In some problems, moment equilibrium is also used. Moment equilibrium means the sum of external moments is zero, which helps determine the size and direction of moments acting on the object.

Two-Dimensional Forces: Free-Body Analysis

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Learn how to use free-body diagrams, force components, and equilibrium to solve two-dimensional force problems and find resultant forces and moments.

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Two-Dimensional Forces: Free-Body Analysis

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