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

Considere um elemento estrutural em um espaço bidimensional onde uma força atua em um ângulo com o eixo x.
Considerando que a linha de ação da força passa pela origem, seus componentes podem ser expressos na forma cartesiana. A direção do vetor de força é sempre dada por tan inverso da razão de seus componentes.
Agora, mesmo que a linha de ação do vetor de força não passe pela origem, seus componentes vetoriais ainda podem ser expressos na forma cartesiana. A convenção de sinal desses componentes vetoriais pode ser escolhida dependendo de sua direção.
Aqui, a força é direcionada em um ângulo pi menos, medido no sentido anti-horário a partir do eixo y positivo.
Agora, considere uma estrutura em que a linha de ação da força faz um ângulo arbitrário alfa menos beta para o eixo x positivo do sistema de coordenadas escolhido. Os componentes da força podem ser resolvidos usando uma análise semelhante.

<ol>
	<li>Oliveira, J.L.; Kraige, L.G. e Bolton, J.N. (2020). Engenharia Mecânica \u2012 Estática. Hoboken, Nova Jersey: John Wiley. pág. 33</li>
</ol>

sistema de forças bidimensionais

Um sistema bidimensional na engenharia mecânica envolve a análise de movimento e forças em um plano. Um vetor de força bidimensional pode ser resolvido em seus componentes como:

onde Fx e Fy são os componentes do vetor F nas direções x e y, respectivamente. Cada um desses componentes do vetor pode ser representado como um escalar (Fx e em>Fy) multiplicado pelo vetor unitário apropriado.

Para determinar os componentes do vetor de força em um sistema de coordenadas cartesianas, é necessário primeiro determinar o ângulo θ que a força faz com o eixo x positivo. Presumindo que a linha de ação da força passa pela origem, seus componentes podem ser expressos na forma cartesiana usando trigonometria básica.

onde F denota a magnitude do vetor de força. A direção do vetor de força é dada pelo inverso da tangente da razão de seus componentes.

No entanto, nos casos em que a linha de ação do vetor de força não passa pela origem, seus componentes vetoriais ainda podem ser expressos na forma cartesiana usando a mesma abordagem. Podemos escolher o sinal de cada componente com base na direção do vetor de força. Ao resolver o vetor de força em seus componentes, podemos determinar o efeito líquido da força na estrutura em questão.

Compreender o sistema de forças bidimensional é fundamental para os engenheiros analisarem e projetarem estruturas que sejam seguras e sólidas. Esse conhecimento fornece a compreensão fundamental de como uma estrutura reagirá a várias forças e ajuda a identificar eventuais fraquezas de projeto.

Sistema de forças bidimensionais

Um sistema bidimensional em engenharia mecânica envolve a análise de movimento e forças em um plano. Um vetor de força bidimensional pode ser resolvido ...

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Force Vectors

Vetores de Força

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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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two-dimensional force system

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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key terms and concepts

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

O JoVE Core Mechanical Engineering oferece vídeos animados concisos e de fácil compreensão que abrangem tópicos-chave como equilíbrio, forças, análise de treliças e mecânica estrutural. Explore suas aplicações no mundo real e observe esses conceitos em ação por meio de experimentos conduzidos por cientistas.

mechanical engineering

Resolving Forces in a Plane

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