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

Si consideri un esempio statico tridimensionale come un palo con un cavo ancorato al suolo. Qui, una forza di tensione agisce lungo il cavo.
Ora, si consideri un sistema di coordinate cartesiane con un'origine arbitraria per rappresentare la forza come un vettore cartesiano.
PA e PB rappresentano i vettori di posizione per le due estremità del cavo. Il vettore di forza è diretto dal punto A al punto B lungo la stessa direzione del vettore di posizione PAB. Il vettore unitario specifica questa direzione.
Applicando la legge triangolare dell'addizione vettoriale, il vettore di posizione lungo i punti A e B può essere ottenuto sottraendo PA da PB.
In secondo luogo, la sua grandezza può essere trovata utilizzando la radice quadrata della somma dei quadrati dei suoi componenti.
Ora, dividendo il vettore di posizione per la sua grandezza si ottiene il vettore unitario lungo il cavo AB.
Infine, il prodotto della grandezza del vettore forza e del vettore unitario esprime il vettore forza nella forma cartesiana.

<ol>
	<li>Hibbeler, R.C. (2016). Ingegneria Meccanica \u2012 Statica e Dinamica. Hoboken, New Jersey: Pearson Prentice Hall. pagine 59</li>
</ol>

vettore di forza lungo una linea

Spesso, nei problemi di statica tridimensionale, la direzione di una forza è specificata da due punti attraverso i quali passa la sua linea d'azione. Consideriamo un palo statico tridimensionale con un cavo ancorato a terra.

<img alt="Equation 1" src="/files/ftp_upload/14237/14237_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

Considerando un sistema di coordinate cartesiane con l'origine alla base del palo, le estremità del cavo possono essere indicate come A e B. PA e PB rappresentano i vettori posizione delle due estremità del cavo. Viene utilizzata la regola del triangolo per la somma dei vettori per ottenere il vettore posizione lungo i punti A e B. A questo scopo, il vettore posizione PA viene sottratto a PB.

<img alt="Equation 1" src="/files/ftp_upload/14237/14237_PT_Equation_1v2.svg" style="text-align: center; height: 15px;" />

La magnitudine del vettore posizione può essere ottenuta dalla radice quadrata della somma dei quadrati dei suoi componenti.

<img alt="Equation 2" src="/files/ftp_upload/14237/14237_PT_Equation_2v2.svg" style="text-align: center; height: 26px;" />

La forza di tensione agente sul cavo è diretta dal punto A al punto B seguendo la stessa direzione del vettore posizione PAB. Il vettore unitario lungo il cavo specifica la direzione della forza. Viene valutato dividendo il vettore posizione per la sua magnitudine.

<img alt="Equation 3" src="/files/ftp_upload/14237/14237_PT_Equation_3v2.svg" style="text-align: center; height: 39px;" />

Infine, il vettore di forza può essere espresso nella forma cartesiana moltiplicando la magnitudine del vettore di forza per il vettore unitario. Questo prodotto produce un vettore tridimensionale che rappresenta la forza che agisce sul palo.

<img alt="Equation 4" src="/files/ftp_upload/14237/14237_PT_Equation_4v2.svg" style="text-align: center; height: 11px;" />

Vettore di forza lungo una linea

Molto spesso nei problemi di statica tridimensionale, la direzione di una forza è specificata da due punti attraverso i quali passa la sua linea d'azione. Considera un ...

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Force Vector along a Line

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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