Name: resolving forces in a plane
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 20 s
Channel: JoVE

Considere un elemento estructural en un espacio bidimensional donde una fuerza actúa en un ángulo theta con el eje x.
Teniendo en cuenta que la línea de acción de la fuerza pasa por el origen, sus componentes pueden expresarse en la forma cartesiana. La dirección del vector de fuerza siempre viene dada por la tangente inversa de la relación de sus componentes.
Ahora, incluso si la línea de acción del vector de fuerza no pasa a través del origen, sus componentes vectoriales aún se pueden expresar en forma cartesiana. La convención de signos de estos componentes vectoriales se puede elegir en función de su dirección.
Aquí, la fuerza se dirige a un ángulo pi menos theta, medido en sentido contrario a las agujas del reloj desde el eje y positivo.
Ahora, considere una estructura donde la línea de acción de la fuerza forma un ángulo arbitrario alfa menos beta con respecto al eje x positivo del sistema de coordenadas elegido. Los componentes de la fuerza se pueden resolver utilizando un análisis similar.

<ol>
	<li>Meriam, J.L.; Kraige, L.G. y Bolton, J.N. (2020). Ingeniería Mecánica \u2012 Estática. Hoboken, Nueva Jersey: John Wiley. págs. 33</li>
</ol>

sistema de fuerzas bidimensional

Un sistema bidimensional en ingeniería mecánica implica el análisis del movimiento y las fuerzas en un plano. Un vector de fuerza bidimensional se puede descomponer en sus componentes de la siguiente manera: <img alt="Equation 1" src="/files/ftp_upload/14229/14229_Equation_1v2.svg" style="text-align: center; height: 15px;"> donde Fx y Fy son las componentes vectoriales de F en las direcciones x e y, respectivamente. Cada una de estas componentes vectoriales se puede representar como un escalar (Fx y Fy) multiplicado por el vector unitario correspondiente. Para determinar las componentes del vector de fuerza en un sistema de coordenadas cartesianas, primero se debe determinar el ángulo θ que la fuerza forma con el eje x positivo. Suponiendo que la línea de acción de la fuerza pasa a través del origen, sus componentes se pueden expresar en forma cartesiana utilizando trigonometría básica. <img alt="Equation 2" src="/files/ftp_upload/14229/14229_Equation_2v3.svg" style="text-align: center; height: 34px;"> donde F denota la magnitud del vector de fuerza. La dirección del vector de fuerza se obtiene tomando la inversa de la tangente de la razón de sus componentes. <img alt="Equation 3" src="/files/ftp_upload/14229/14229_Equation_3v3.svg" style="text-align: center; height: 34px;"> Sin embargo, en casos en los que la línea de acción del vector de fuerza no pasa a través del origen, sus componentes vectoriales aún se pueden expresar en forma cartesiana utilizando el mismo enfoque. Podemos elegir el signo de cada componente en función de la dirección del vector de fuerza. Al descomponer el vector de fuerza en sus componentes, podemos determinar el efecto neto de la fuerza sobre la estructura en cuestión. Comprender el sistema de fuerzas bidimensional es fundamental para que los ingenieros analicen y diseñen estructuras que sean seguras y sólidas desde el punto de vista estructural. Este conocimiento proporciona la comprensión básica de cómo una estructura reaccionará ante diversas fuerzas y ayuda a identificar cualquier debilidad de diseño, si la hay.

Sistema de fuerzas bidimensional

Un sistema bidimensional en ingeniería mecánica implica el análisis del movimiento y las fuerzas en un plano. Un vector de fuerza bidimensional puede resolverse ...

Education

Educación

JoVE Core

Mechanical Engineering

Ingeniería Mecánica

Unit 1

Unidad 1

Force Vectors

Vectores de fuerza

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

Two-Dimensional Force System

resolving forces in a plane

Resolving forces in a plane is a key part of two-dimensional mechanical analysis. A force vector can be split into x- and y-components, which show how the force acts in each direction. These components are written with the help of unit vectors, one for the x direction and one for the y direction.

To find the components in a Cartesian coordinate system, first identify the angle theta between the force and the positive x-axis. If the line of action passes through the origin, basic trigonometry gives the Cartesian form of the force. The magnitude of the force is F, and the direction can be found from the inverse tangent of the ratio of its components.

The same component method also works when the line of action does not pass through the origin. In that case, the sign of each component is chosen from the direction of the force vector. By breaking a force into parts, engineers can judge its net effect on a structure and look for possible weak points. This skill helps them analyze and design structures that are safe and structurally sound.

Resolving Forces in a Plane

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Resolving forces in a plane is a key part of two-dimensional mechanical analysis. A force vector can be split into x- and y-components, which show how the force acts in each direction. These components are written with the help of unit vectors, one for the x direction and one for the y direction. To find the components in a Cartesian coordinate system, first identify the angle theta between the force and the positive x-axis. If the line of action passes through the origin, basic trigonometry...

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Learn how to break a force into x- and y-components, use trigonometry and angle theta, and understand a structure's net force in a plane.

Resolving Forces in a Plane | 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.

mechanical engineering

Resolving Forces in a Plane

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