Name: finding a cable force from two points
Uploaded: 2025-05-22T09:06:01.000Z
Duration: 1 min 26 s
Channel: JoVE

Considérons un exemple statique tridimensionnel comme un poteau avec un câble ancré au sol. Ici, une force de tension agit le long du câble.
Maintenant, considérons un système de coordonnées cartésiennes avec une origine arbitraire pour représenter la force comme un vecteur cartésien.
PA et PB représentent les vecteurs de position pour les deux extrémités du câble. Le vecteur force est dirigé du point A vers B dans la même direction que le vecteur position PAB. Le vecteur unitaire spécifie cette direction.
En appliquant la loi triangulaire de l’addition vectorielle, le vecteur position le long des points A et B peut être obtenu en soustrayant PA de PB.
Deuxièmement, sa norme peut être déterminée en utilisant la racine carrée de la somme des carrés de ses composantes.
Maintenant, en divisant le vecteur position par sa norme, on obtient le vecteur unitaire le long du câble AB.
Enfin, le produit de l’intensité du vecteur force et du vecteur unité exprime le vecteur force sous forme cartésienne.

<ol>
	<li>Hibbeler, R.C. (2016). Génie mécanique \u2012 Statique et dynamique. Hoboken, New Jersey : Pearson Prentice Hall. page 59</li>
</ol>

vecteur de force sur une ligne

Très souvent dans les problèmes de statique tridimensionnelle, la direction d'une force est spécifiée par deux points à travers lesquels passe sa ligne d'action. Considérez un poteau statique tridimensionnel avec un câble ancré au sol. <img alt="Equation 1" src="/files/ftp_upload/14237/14237_PT_Fig_1v2.svg" style="text-align: center; height: 350px;"> En considérant un système de coordonnées cartésiennes avec l'origine à la base du poteau, les extrémités du câble peuvent être désignées par A et B. PA et PB représentent les vecteurs de position des deux extrémités du câble. La loi triangulaire de l'addition vectorielle est utilisée pour obtenir le vecteur de position le long des points A et B. Dans ce but, le vecteur de position PA est soustrait de PB. <img alt="Equation 1" src="/files/ftp_upload/14237/14237_PT_Equation_1v2.svg" style="text-align: center; height: 15px;"> La magnitude du vecteur de position peut être obtenue à partir de la racine carrée de la somme des carrés de ses composantes. <img alt="Equation 2" src="/files/ftp_upload/14237/14237_PT_Equation_2v2.svg" style="text-align: center; height: 26px;"> La force de tension agissant sur le câble est dirigée de point A vers point B suivant la même direction que le vecteur de position PAB. Le vecteur unitaire le long du câble spécifie la direction de la force. Il est évalué en divisant le vecteur de position par sa magnitude. <img alt="Equation 3" src="/files/ftp_upload/14237/14237_PT_Equation_3v2.svg" style="text-align: center; height: 39px;"> Enfin, le vecteur de force peut être exprimé sous forme cartésienne en multipliant la magnitude du vecteur de force par le vecteur unitaire. Ce produit donne un vecteur tridimensionnel représentant la force agissant sur le poteau. <img alt="Equation 4" src="/files/ftp_upload/14237/14237_PT_Equation_4v2.svg" style="text-align: center; height: 11px;">

Vecteur de force sur une ligne

Très souvent, dans les problèmes de statique tridimensionnelle, la direction d’une force est spécifiée par deux points par lesquels passe sa ligne d’action. Considérez un ...

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finding a cable force from two points

A cable force can be found from the two points that define its line of action. In three-dimensional statics, this setup often appears with a pole and a cable anchored to the ground. The cable ends are labeled A and B, and their position vectors are written as P_A and P_B.

The position vector from A to B is found using the triangle law of vector addition. First, subtract P_A from P_B to get P_AB. Then find the magnitude of P_AB by taking the square root of the sum of the squares of its components. This gives the length of the vector in Cartesian form.

The tension force in the cable points from A toward B. It has the same direction as the position vector P_AB. To show that direction, divide P_AB by its magnitude to get the unit vector along the cable. A unit vector is a vector with length 1 that gives direction only.

The force vector is written in Cartesian form by multiplying the force magnitude by the unit vector. This product gives a three-dimensional vector for the force acting on the pole. The method connects the geometry of points A and B to the final force vector.

Finding a Cable Force from Two Points

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A cable force can be found from the two points that define its line of action. In three-dimensional statics, this setup often appears with a pole and a cable anchored to the ground. The cable ends are labeled A and B, and their position vectors are written as P_A and P_B. The position vector from A to B is found using the triangle law of vector addition. First, subtract P_A from P_B to get P_AB. Then find the magnitude of P_AB by taking the square root of the sum of the squares of its...

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Learn how to use two position vectors, a unit vector, and force magnitude to express a cable’s tension as a 3D Cartesian force vector.

Finding a Cable Force from Two Points | JoVE K12

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Finding a Cable Force from Two Points

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