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

Considere un ejemplo estático tridimensional como un poste con un cable anclado al suelo. Aquí, una fuerza de tensión actúa a lo largo del cable.
Ahora, considere un sistema de coordenadas cartesiano con un origen arbitrario para representar la fuerza como un vector cartesiano.
PA y PB representan los vectores de posición de los dos extremos del cable. El vector de fuerza se dirige del punto A al B a lo largo de la misma dirección que el vector de posición PAB. El vector unitario especifica esta dirección.
Aplicando la ley del triángulo de la suma de vectores, el vector de posición a lo largo de los puntos A y B se puede obtener restando PA de PB.
En segundo lugar, su magnitud se puede encontrar usando la raíz cuadrada de la suma de los cuadrados de sus componentes.
Ahora, dividiendo el vector de posición por su magnitud se obtiene el vector unitario a lo largo del cable AB.
Finalmente, el producto de la magnitud del vector de fuerza y el vector unitario expresa el vector de fuerza en la forma cartesiana.

<ol>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica \u2012 Estática y Dinámica. Hoboken, Nueva Jersey: Pearson Prentice Hall. págs. 59</li>
</ol>

vector de fuerza a lo largo de una línea

A menudo, en problemas estáticos tridimensionales, la dirección de una fuerza se especifica mediante dos puntos por los cuales pasa su línea de acción. Considera un poste estático tridimensional con un cable anclado al suelo.

<img alt="Equation 1" src="/files/ftp_upload/14237/14237_PT_Fig_1v2.svg" style="text-align: center; height: 350px;">

Considerando un sistema de coordenadas cartesianas con el origen en la base del poste, los extremos del cable pueden ser denotados como A y B. PA y PB representan los vectores de posición para los dos extremos del cable. La ley del triángulo de suma de vectores se utiliza para obtener el vector de posición a lo largo de los puntos A y B. Para este propósito, se resta el vector de posición PA de PB.

<img alt="Equation 1" src="/files/ftp_upload/14237/14237_PT_Equation_1v2.svg" style="text-align: center; height: 15px;"> 

La magnitud del vector de posición se puede obtener a partir de la raíz cuadrada de la suma de los cuadrados de sus componentes.

<img alt="Equation 2" src="/files/ftp_upload/14237/14237_PT_Equation_2v2.svg" style="text-align: center; height: 26px;">

La fuerza de tensión actuando sobre el cable se dirige desde el punto A hacia el punto B siguiendo la misma dirección que el vector de posición PB. El vector unitario a lo largo del cable especifica la dirección de la fuerza. Se evalúa dividiendo el vector de posición por su magnitud.

<img alt="Equation 3" src="/files/ftp_upload/14237/14237_PT_Equation_3v2.svg" style="text-align: center; height: 39px;">

Finalmente, el vector de fuerza se puede expresar en forma cartesiana multiplicando la magnitud del vector de fuerza por el vector unitario. Este producto da como resultado un vector tridimensional que representa la fuerza actuando sobre el poste.

<img alt="Equation 4" src="/files/ftp_upload/14237/14237_PT_Equation_4v2.svg" style="text-align: center; height: 11px;">

Vector de fuerza a lo largo de una línea

Muy a menudo, en los problemas de estática tridimensional, la dirección de una fuerza está especificada por dos puntos a través de los cuales pasa su línea de acción. Considere 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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Finding a Cable Force from Two Points | JoVE K12

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Finding a Cable Force from Two Points

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