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

Considere um exemplo estático tridimensional como um poste com um cabo ancorado ao solo. Aqui, uma força de tensão está agindo ao longo do cabo.
Agora, considere um sistema de coordenadas cartesianas com uma origem arbitrária para representar a força como um vetor cartesiano.
PA e PB representam os vetores de posição para as duas extremidades do cabo. O vetor de força é direcionado do ponto A para B na mesma direção que o vetor de posição PAB. O vetor unitário especifica essa direção.
Aplicando a lei do triângulo da adição de vetores, o vetor de posição ao longo dos pontos A e B pode ser obtido subtraindo PA de PB.
Em segundo lugar, sua magnitude pode ser encontrada usando a raiz quadrada da soma dos quadrados de seus componentes.
Agora, dividir o vetor de posição por sua magnitude fornece o vetor unitário ao longo do cabo AB.
Finalmente, o produto da magnitude do vetor de força e do vetor unitário expressa o vetor de força na forma cartesiana.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pág. 59</li>
</ol>

vetor de força ao longo de uma linha

Muitas vezes, em problemas estáticos em três dimensões, a direção de uma força é especificada por dois pontos pelos quais sua linha de ação passa. Considere um poste estático tridimensional com um cabo ancorado ao solo.

<img alt="Equation 1" src="/files/ftp_upload/14237/14237_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

Considerando um sistema de coordenadas cartesianas com a origem na base do poste, as extremidades do cabo podem ser denotadas como A e B. PA e PB representam os vetores posição para as duas extremidades do cabo. A lei do triângulo de adição de vetores é usada para obter o vetor posição entre os pontos A and B. Para isso, o vetor posição PA é subtraído de PB.


<img alt="Equation 1" src="/files/ftp_upload/14237/14237_PT_Equation_1v2.svg" style="text-align: center; height: 15px;" />

A magnitude do vetor posição pode ser obtida a partir da raiz quadrada da soma dos quadrados de seus componentes.

<img alt="Equation 2" src="/files/ftp_upload/14237/14237_PT_Equation_2v2.svg" style="text-align: center; height: 26px;" />

A força de tensão atuando no cabo é direcionada do ponto A para o ponto B, seguindo a mesma direção do vetor posição PAB. O vetor unitário ao longo do cabo especifica a direção da força. Ele é avaliado dividindo o vetor posição pela sua magnitude.

<img alt="Equation 3" src="/files/ftp_upload/14237/14237_PT_Equation_3v2.svg" style="text-align: center; height: 39px;" />

Por fim, o vetor de força pode ser expresso na forma cartesiana multiplicando a magnitude do vetor de força pelo vetor unitário. Esse produto resulta em um vetor tridimensional representando a força atuante no poste.

<img alt="Equation 4" src="/files/ftp_upload/14237/14237_PT_Equation_4v2.svg" style="text-align: center; height: 11px;" />

Vetor de força ao longo de uma linha

Muitas vezes, em problemas de estática tridimensional, a direção de uma força é especificada por dois pontos através dos quais sua linha de ação passa. Considere um ...

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Force Vectors

Vetores de Força

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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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