Name: resolving forces in 3d coordinates
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 30 s
Channel: JoVE

Considérons une tente attachée au sol, à l’aide de boulons à œil, soumise à trois forces.
Considérons un système de coordonnées cartésiennes, avec l’origine au niveau de l’œillet. La force F1 agit le long d’un plan x-y bidimensionnel, tandis que la force F2 agit dans un espace tridimensionnel. La force F3 se trouve le long de l’axe des x négatif.
L’intensité des composantes x et y de F1 peut être obtenue à l’aide d’un triplet de Pythagore. En utilisant les grandeurs obtenues, F1 peut être exprimé sous forme cartésienne.
De même, F2 est résolu en composantes verticales et horizontales. En résolvant davantage les composantes horizontales, F2 peut être exprimé en termes de vecteurs unitaires i, j et k le long des trois axes.
Comme la troisième force se trouve le long de l’axe des x négatif, ses composantes y et z sont nulles.
La force résultante est ensuite obtenue sous sa forme cartésienne en additionnant les composantes respectives des trois forces de manière vectorielle.
L’intensité de la force résultante est calculée comme la racine carrée de la somme des carrés des trois forces agissant le long des directions respectives.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. p. 47 à 49.</li>
</ol>

un système de force tridimensionnel : résolution de problèmes

Un système de force tridimensionnel fait référence à un scénario dans lequel trois forces agissent simultanément dans trois directions différentes. Ce type de problème est couramment rencontré en physique et en ingénierie, où il est nécessaire de calculer la force résultante sur le système, qui peut ensuite être utilisée pour prédire ou analyser le comportement de l'objet ou de la structure en question. Pour résoudre un système de force tridimensionnel, d'abord décomposez chaque force en ses composantes scalaires respectives. Faites cela en utilisant des fonctions trigonométriques et les principes de l'addition vectorielle. Une fois que chaque force est décomposée en ses composantes, ajoutez les composantes respectives des trois forces vectoriellement pour obtenir la force résultante. Un autre aspect important à prendre en compte lors de la résolution d'un système de force tridimensionnel est le choix d'un système de coordonnées. Un système de coordonnées cartésiennes est un système de référence fréquemment utilisé, qui nous permet de déterminer la direction et la magnitude de chaque force par rapport aux axes x, y et z. Parfois, il est également nécessaire d'utiliser des systèmes de coordonnées sphériques ou cylindriques en fonction de la nature du problème. La magnitude de la force résultante est calculée comme la racine carrée de la somme des carrés des trois forces agissant le long de leurs directions respectives. Cela donne la force globale agissant sur le système.

Un système de force tridimensionnel : résolution de problèmes

Un système de forces tridimensionnel fait référence à un scénario dans lequel trois forces agissent simultanément dans trois directions différentes. Ce type de problème est...

three-dimensional-force-systemproblem-solving

Education

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Force Vectors

Vecteurs de force

KEY TERMS AND CONCEPTS

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Three-Dimensional Force System:Problem Solving

resolving forces in 3d coordinates

Three-dimensional force systems involve forces acting in three different directions at the same time. These problems are common in physics and engineering. They are used to find the resultant force, which helps predict or analyze how an object or structure will behave.

The first step is to resolve each force into scalar components. A scalar component is the amount of force along one axis. Trigonometric functions and vector addition are used to break the force into parts and then combine those parts correctly.

After each force is split into components, the matching x, y, and z components are added vectorially. A Cartesian coordinate system is often used for this step because it shows each force relative to the x, y, and z axes. In some problems, spherical or cylindrical coordinate systems are a better fit, depending on the shape of the situation.

The resultant force is then found from the combined components. Its magnitude is calculated as the square root of the sum of the squares of the three directional parts. This value gives the overall strength of the force acting on the system.

Resolving Forces in 3D Coordinates

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three-dimensional force system:problem solving

Three-dimensional force systems involve forces acting in three different directions at the same time. These problems are common in physics and engineering. They are used to find the resultant force, which helps predict or analyze how an object or structure will behave. The first step is to resolve each force into scalar components. A scalar component is the amount of force along one axis. Trigonometric functions and vector addition are used to break the force into parts and then combine those...

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key terms and concepts

Learn how to break 3D forces into x, y, and z components, choose a coordinate system, and calculate the resultant force for physics problem solving.

Resolving Forces in 3D Coordinates | 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 3D Coordinates

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