Name: vector components for force calculations
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 28 s
Channel: JoVE
Description: Scalar notation helps simplify vector calculations by breaking a vector into separate x and y parts. When vectors are added or subtracted, each component can be handled on its own using scalar notation. This makes force problems easier to solve.

Imaginons un homme tirant une corde à un crochet dans la direction nord-est.
Le vecteur force est noté F1. Il est résolu en composantes scalaires, représentées par F1x le long de l’axe des x et F1y le long de l’axe des y.
La direction, qui est l’angle formé par F1 avec l’axe des x positif dans le sens inverse des aiguilles d’une montre, est l’inverse de la composante y sur la composante x.
Ici, F1x et F1y sont des composantes rectangulaires formant un triangle rectangle et peuvent être obtenues à l’aide de fonctions trigonométriques.
Si une autre force F2 agit sur le crochet depuis la direction sud-est, alors F2x est le long de l’axe des x positif et F2y est le long de l’axe des y négatif.
Les composantes x et y de F2 sont obtenues à l’aide de la fonction trigonométrique, et la force résultante est la somme algébrique des composantes des forces le long des axes x et y, tandis que sa norme est obtenue en utilisant la racine carrée de la somme des carrés de ses composantes.

<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>

notation scalaire

La notation scalaire est une méthode utile pour simplifier les calculs impliquant des vecteurs. Lorsque des vecteurs sont ajoutés ou soustraits, leurs composantes peuvent être ajoutées ou soustraites séparément en utilisant la notation scalaire. Par exemple, la force, une quantité vectorielle, peut être décomposée en ses x et y composantes, appelées composantes rectangulaires, puis la magnitude et la direction de ces composantes peuvent être déterminées à l’aide de fonctions trigonométriques. Considérons un homme tirant sur une corde depuis un crochet en direction du nord–est. La magnitude de ce vecteur force appliquée est désignée par F1. Elle est décomposée en composantes scalaires, représentées par F1x le long de l’x-axe et F1y le long de l’y-axe. Les expressions pour les composantes rectangulaires F1x et F1y sont obtenues à l’aide de fonctions trigonométriques, car elles forment un triangle rectangle. En utilisant ces composantes et le théorème de Pythagore, la magnitude de la force F1 peut être calculée. L’arc tangente de la composante y sur la composante x donne la direction de la force. Si une autre force F2 agit sur le même crochet depuis la direction du sud–est, en utilisant une méthode similaire, on peut trouver la magnitude et la direction de cette force également. La force résultante est la somme algébrique des composantes des deux forces le long des axes x et y. Sa magnitude peut également être obtenue en utilisant la racine carrée de la somme des carrés de ses composantes. Cette force résultante peut représenter soit la force nette sur un objet, soit la force nécessaire pour contrecarrer les autres forces. La notation scalaire est utile pour calculer les forces dans différentes directions et comprendre les forces agissant sur un objet. En décomposant les forces en leurs composantes rectangulaires, puis en utilisant des fonctions trigonométriques, on peut déterminer rapidement et précisément la magnitude de la force et sa direction.

Notation scalaire

La notation scalaire est une méthode utile pour simplifier les calculs impliquant des vecteurs. Lorsque des vecteurs sont ajoutés ou soustraits, leurs composantes peuvent être ajoutées ou ...

Education

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Génie mécanique

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Force Vectors

Vecteurs de force

KEY TERMS AND CONCEPTS

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Scalar Notation

vector components for force calculations

Scalar notation helps simplify vector calculations by breaking a vector into separate x and y parts. When vectors are added or subtracted, each component can be handled on its own using scalar notation. This makes force problems easier to solve.

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key terms and concepts

Learn how scalar notation breaks forces into x and y components so students can calculate magnitude, direction, and resultant force with trigonometry.

Vector Components for Force Calculations | JoVE K12

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Vector Components for Force Calculations

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