Name: couple moment in force systems
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 29 s
Channel: JoVE

Um par é um par de forças paralelas com magnitudes iguais, mas agindo em direções opostas, separadas por uma distância perpendicular.
O casal causa uma força de rotação que gira o corpo em torno de um eixo perpendicular ao plano das forças, e o momento resultante é conhecido como momento do casal.
Considere apertar um parafuso com uma chave inglesa. Um par de forças é formado quando duas forças iguais e opostas são aplicadas na chave nos pontos A e B, separadas por uma distância perpendicular.
Os vetores de posição rA e rB são direcionados da origem de um sistema de coordenadas para os pontos de aplicação.
O momento de casal sobre a origem é a soma do produto cruzado dos vetores de posição e das forças.
A diferença entre os vetores de posição rA e rB é o vetor de posição r, que é a distância entre as duas forças opostas.
O momento do par depende apenas do vetor de posição r entre as forças e não dos vetores de posição rA e rB. Portanto, é considerado um vetor livre.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pág. 154</li>
	<li>Cerveja, F.P.; Johnston, E.R.; Mazurek, D.F; Cromwell, PJ e Self, BP (2019). Mecânica vetorial para engenheiros \u2012 estática e dinâmica. Nova Iorque: McGraw-Hill. pág. - 120.</li>
</ol>

acoplamento

Um acoplamento é um par de forças paralelas, de igual magnitude, mas em direções opostas. As forças são separadas por uma distância perpendicular, conhecida como braço do acoplamento. O acoplamento causa uma força de rotação ou momento que gira o corpo em torno de um eixo perpendicular ao plano das forças. O momento resultante é chamado de momento do acoplamento. A unidade SI de momento do acoplamento é o Newton-metro (N-m).

Um exemplo típico para entender esse conceito é apertar um parafuso com uma chave de roda. Um acoplamento de forças é formado quando duas forças iguais e opostas são aplicadas na chave nos pontos A e B, separados por uma distância perpendicular. Os vetores de posição respectivos são direcionados do ponto de aplicação até a origem de um sistema de coordenadas. O momento do acoplamento em relação à origem é a soma do produto cruzado dos vetores de posição e das forças. A diferença entre os vetores de posição das duas forças opostas dá o vetor de posição r, que é a distância entre as forças opostas.

Curiosamente, o momento do acoplamento depende apenas do vetor de posição r entre as forças, e não dos vetores de posição individuais das duas forças. O vetor de posição r é independente da origem. Isso implica que calcular os momentos das mesmas forças em torno de um ponto diferente produzirá o mesmo resultado. O momento do acoplamento é um vetor livre. Ao contrário de um momento do acoplamento, o momento de uma força depende da posição em que é medido. Se dois casais produzem um momento de magnitude e direção iguais, então esses dois casais são equivalentes. Casais equivalentes têm o mesmo torque ou efeitos de torção, independentemente de suas posições, direções ou magnitudes.

Calcular o momento do acoplamento e entender seus efeitos é crucial para o projeto de sistemas estáveis e robustos que possam suportar forças externas.

Acoplamento

Um par é um par de forças paralelas iguais em magnitude, mas em direções opostas. As forças são separadas por uma distância perpendicular, conhecida como ...

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Force System Resultants

Resultantes de Sistemas de Forças

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

Couple

couple moment in force systems

A couple is a pair of parallel forces that are equal in magnitude and opposite in direction. The two forces are separated by a perpendicular distance called the couple arm. Together, they create a turning effect on a body instead of a net push.

This turning effect is called the couple moment. It rotates the body about an axis that is perpendicular to the plane of the forces. The SI unit for a couple moment is the Newton-meter (N-m).

A common example is tightening a bolt with a lug wrench. In that case, two equal and opposite forces act at points A and B on the wrench. These points are separated by a perpendicular distance, so they form a force couple.

The couple moment about the origin is found by adding the cross products of the position vectors and the forces. The position vector between the two opposing forces is r, which is the distance between them. The couple moment depends only on this vector r, not on the separate position vectors of the forces.

Because r does not depend on the origin, the same couple moment is obtained even if the moments are taken about a different point. This is why a couple moment is a free vector. A moment of a single force is different because it depends on where it is measured.

If two couples create moments with the same magnitude and direction, they are equivalent couples. Equivalent couples have the same torque, or turning effect, even if their positions, directions, or magnitudes differ. Understanding couple moments helps in designing stable systems that can resist external forces.

Couple Moment in Force Systems

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couple

A couple is a pair of parallel forces that are equal in magnitude and opposite in direction. The two forces are separated by a perpendicular distance called the couple arm. Together, they create a turning effect on a body instead of a net push. This turning effect is called the couple moment. It rotates the body about an axis that is perpendicular to the plane of the forces. The SI unit for a couple moment is the Newton-meter (N-m). A common example is tightening a bolt with a lug wrench. In...

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Equivalent Couples in Mechanical Systems

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Equivalent Force and Moment Systems

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key terms and concepts

Learn how a couple creates rotation, why couple moment depends on the distance between forces, and how equivalent couples are identified in force systems.

Couple Moment in Force Systems | 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

Couple Moment in Force Systems

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