Name: two-dimensional forces: free-body analysis
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 29 s
Channel: JoVE

Considere um limpador inclinado em um ângulo de 25 graus em relação à linha de base 's' em um sistema bidimensional. Uma força que atua na alça, girada para o centro do limpador, faz um ângulo de 20 graus com a linha de referência 'c', que é paralela à linha de base 's'.
Se a componente de força ao longo do eixo a for de 65 Newtons, determine a magnitude da força e sua componente ao longo do eixo b.
Aqui, considerando ângulos alternados, coa' torna-se 25 graus, enquanto o ângulo Foc é 20 graus. Assim, o ângulo feito pelo vetor de força com o eixo a é determinado pela soma dos dois ângulos e é igual a 45 graus.
Como a componente de força ao longo do eixo a é conhecida, a magnitude de uma força é estimada pela razão entre a componente a da força e o cosseno de 45 graus.
Agora, o componente b da força é expresso como o produto da magnitude da força e do seno de 45 graus. É negativo, pois está ao longo do eixo b negativo.

<ol>
	<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. 29-33</li>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica \u2012 Estática e Dinâmica. Hoboken, Nova Jersey: Pearson Prentice Hall. pág. 33 a 35.</li>
</ol>

sistema de forças bidimensionais: resolução de problemas

Resolver problemas relacionados a sistemas de forças bidimensionais é um aspecto essencial da mecânica e engenharia. Ao aplicar os princípios da análise vetorial e equilíbrio de forças, é possível determinar o efeito de múltiplas forças atuando em um objeto em um espaço bidimensional.

O primeiro passo para resolver um problema de sistema de forças bidimensionais é desenhar um diagrama de corpo livre do objeto em consideração. Esse diagrama ajuda a identificar todas as forças externas atuando no objeto, incluindo suas magnitudes, direções e ponto de aplicação.

Em seguida, é necessário decompor as forças em suas componentes nas direções x e y usando os princípios da análise vetorial. Essa etapa ajuda a converter as forças dadas em sua forma vetorial cartesiana, permitindo uma representação e análise mais fácil. As componentes podem ser decompostas usando funções trigonométricas, como o seno e o cosseno dos ângulos dados.

Após a decomposição das forças em componentes, o próximo passo é determinar a força resultante em cada direção. Isso é feito somando todas as forças em cada direção. Em seguida, a força resultante e sua direção são determinadas usando o teorema de Pitágoras e trigonometria. Se a força resultante for zero, o objeto está em equilíbrio e não está acelerando. Se a força resultante for diferente de zero, então o objeto está acelerando na direção da força resultante. O princípio do equilíbrio de forças afirma que a soma de todas as forças externas atuando no elemento deve ser igual a zero tanto nas direções x e y. Isso nos permite determinar as forças desconhecidas atuando no objeto, como tensão ou compressão em um membro.

Em alguns casos, o princípio do equilíbrio de momentos também é utilizado para determinar o efeito de forças externas no objeto. Esse princípio afirma que a soma de todos os momentos externos atuando no elemento deve ser igual a zero. Essa etapa ajuda a determinar os valores e direções dos momentos atuando no objeto.

Sistema de Forças Bidimensionais: Resolução de Problemas

Resolver problemas relacionados a sistemas de força bidimensionais é um aspecto essencial da mecânica e da engenharia. Ao aplicar os princípios do vetor ...

two-dimensional-force-system-problem-solving

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: Problem Solving

two-dimensional forces: free-body analysis

Two-dimensional force analysis starts with a free-body diagram. A free-body diagram shows the object and every external force acting on it. It includes each force’s size, direction, and point of application.

After the diagram is drawn, each force is broken into x- and y-components. This uses vector analysis and trigonometry, especially sine and cosine. The forces can then be written in Cartesian vector form, which makes them easier to work with.

Next, the components in each direction are added to find the net force in x and y. The resultant force is then found with the Pythagorean theorem and trigonometry. If the net force is zero, the object is in equilibrium and does not accelerate. If the net force is not zero, the object accelerates in the direction of the net force.

Force equilibrium means the sum of external forces is zero in both the x and y directions. This helps solve for unknown forces such as tension or compression in a member. In some problems, moment equilibrium is also used. Moment equilibrium means the sum of external moments is zero, which helps determine the size and direction of moments acting on the object.

Two-Dimensional Forces: Free-Body Analysis

two-dimensional-forces-free-body-analysis

scalar and vectors

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two-dimensional force system

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two-dimensional force system: problem solving

Two-dimensional force analysis starts with a free-body diagram. A free-body diagram shows the object and every external force acting on it. It includes each force’s size, direction, and point of application. After the diagram is drawn, each force is broken into x- and y-components. This uses vector analysis and trigonometry, especially sine and cosine. The forces can then be written in Cartesian vector form, which makes them easier to work with. Next, the components in each direction are...

scalar notation

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three-dimensional force system

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three-dimensional-force-systemproblem-solving

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dot product

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The dot product connects vectors, work, and direction in mathematics and physics. In engineering, it is found by multiplying the magnitudes of two vectors and the cosine of the angle between them. It is shown with a dot symbol between the vectors. A real-world example is a vehicle pulling an object along the ground with a rope. If the rope is angled above the horizontal axis, the work done can be calculated with the dot product of the applied force and the object’s displacement. This makes the...

dot product: problem solving

Using the Dot Product to Solve Vector Questions

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cross product

Cross Product Direction and Magnitude

The cross product is a vector operation in vector algebra that creates a third vector from two input vectors. Unlike the scalar product, it does not give a single number. The result is a vector perpendicular to both original vectors. The size, or magnitude, of the cross product depends on the magnitudes of both vectors and the sine of the angle between them. A larger angle between the vectors gives a larger cross product magnitude. The direction is found with the right-hand rule. If the...

key terms and concepts

Learn how to use free-body diagrams, force components, and equilibrium to solve two-dimensional force problems and find resultant forces and moments.

Two-Dimensional Forces: Free-Body Analysis | 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

Two-Dimensional Forces: Free-Body Analysis

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