Name: finding forces with virtual work in linked bodies
Uploaded: 2023-09-22T11:49:36.000Z
Duration: 1 min 6 s
Channel: JoVE

O princípio do trabalho virtual pode ser aplicado a máquinas com vários corpos rígidos conectados sob cargas para resolver problemas envolvidos.
Considere um torno articulado, onde uma força é aplicada em seu ponto médio, resultando em uma força de reação exercida pelo bloco de madeira no torno.
No diagrama de corpo livre, o atrito é negligenciado e um deslocamento virtual positivo é considerado.
Escolha um sistema de eixos de coordenadas e defina os incrementos positivos e negativos.
As forças de reação no ponto esquerdo e a força normal não funcionam durante esse deslocamento.
Como resultado, apenas o trabalho virtual realizado pelas forças aplicadas e de reação precisa ser computado.
Expressando as coordenadas em termos do ângulo e diferenciando, o trabalho virtual total de ambas as forças pode ser determinado.
Definir o trabalho virtual total como zero fornece a equação para a força de reação exercida pelo bloco de madeira no torno.

<ol>
	<li>Hibbeler, R.C. (2016). Engenharia Mecânica: Estática. Décima quarta edição, Nova Jersey: Pearson. Seção 11.1, pp. 586-587.</li>
	<li>Cerveja, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. e Self, B.P. (2016). Mecânica vetorial para engenheiros. Décima primeira edição, Nova York: McGraw-Hill Education. Pág. 578-579.</li>
</ol>

trabalho virtual para um sistema de corpos rígidos conectados

O trabalho virtual é um método poderoso usado para resolver problemas envolvendo vários corpos rígidos conectados. Quando o sistema está em equilíbrio, o trabalho virtual é zero. Isso permite o cálculo das forças resultantes quando um sistema passa por um deslocamento virtual. Ao tentar analisar tal sistema, primeiro, use um diagrama de corpo livre, onde uma coordenada independente representa a configuração dos elos e marque sua posição defletida resultante do deslocamento virtual positivo.

Em seguida, meça as coordenadas de posição a partir de um ponto fixo no diagrama de corpo livre e direcione-as para as forças que realizam o trabalho. Isso permite que cada deslocamento virtual seja expresso em termos da coordenada independente. O próximo passo é escrever a equação do trabalho virtual, o que ajuda na determinação das forças e momentos resultantes. É também importante observar aqui que se uma força ou momento atua ao longo da direção do deslocamento virtual positivo, então seu trabalho é determinado como trabalho virtual positivo; caso contrário, ét's trabalho virtual negativo.

A principal vantagem de usar esse método é que ele pode ser usado para resolver problemas que envolvem um sistema de vários corpos rígidos conectados. Cada um desses sistemas é considerado ter apenas um grau de liberdade, uma vez que a disposição dos elos pode ser completamente especificada usando apenas uma coordenada. Isso simplifica bastante cálculos complexos e ajuda a entender melhor como diferentes variáveis estão relacionadas entre si dentro de sistemas complexos.

No final das contas, a avaliação analítica de problemas de equilíbrio envolvendo vários corpos rígidos conectados pode ser feita com eficácia usando o trabalho virtual, possibilitando não apenas respostas precisas, mas também uma compreensão clara de seu funcionamento interno.

Trabalho Virtual para um Sistema de Corpos Rígidos Conectados

O trabalho virtual é um método poderoso usado para resolver problemas envolvendo vários corpos rígidos conectados. Quando o sistema está em equilíbrio, o trabalho virtual é ...

virtual-work-for-a-system-of-connected-rigid-bodies

Education

JoVE Core

Mechanical Engineering

Engenharia Mecânica

Unit 1

Unidade 1

Virtual Work

Trabalho Virtual

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

Virtual Work for a System of Connected Rigid Bodies

finding forces with virtual work in linked bodies

Virtual work helps find forces in a system of connected rigid bodies. It is a useful method when several links move together and the system is in equilibrium. In that case, the total virtual work is zero.

To analyze the system, start with a free-body diagram. Use one independent coordinate to describe the link configuration. Then mark the deflected position that comes from a positive virtual displacement. This makes the small change in position clear before any calculations begin.

Next, measure position coordinates from a fixed point on the diagram. Direct those coordinates toward the forces that do work. This lets each virtual displacement be written in terms of the independent coordinate. After that, write the virtual work equation to determine the resulting forces and moments.

The sign of the work depends on the direction of motion. If a force or couple moment acts along the positive virtual displacement, the work is positive. If it acts opposite that direction, the work is negative.

This method is especially helpful for systems with several connected rigid bodies because they often have only one degree of freedom. That means the full link arrangement can be described by one coordinate. Virtual work simplifies the calculations and also shows how the variables in the system are related.

Finding Forces with Virtual Work in Linked Bodies

finding-forces-with-virtual-work-in-linked-bodies

work

Work in Force and Motion

Work connects force, motion, and energy in mechanics. It happens when a force acts on an object and the object moves along the line of action of that force. Work can also be described as energy transfer caused by applying a force, which leads to a change in the object’s motion or position. Work is calculated as the force multiplied by the part of the displacement in the same direction as the force. It can also be written as the dot product of the applied force and the object’s displacement. In...

work of a couple moment

Couple Moment Work in Rotation

Mechanical engineering studies motion, energy, and force, and it uses the idea of a couple moment to describe how two equal and opposite forces act on a rigid body. A couple moment is created when those forces act at two points on the body that are separated by a distance. When a rigid body moves because of a couple, its displacement can be split into two parts. First, the two points move by the same amount to their final positions. Then the body rotates about one of those points. During the...

virtual work

Virtual Work in Force Equilibrium

Virtual work is a mechanics principle used to check equilibrium with imaginary motion. If a body is in static or dynamic equilibrium, the total virtual work from external forces and couple moments must be zero for any virtual displacement. A virtual displacement is an imagined small movement. It can be a shift or a rotation. The virtual work done by a force equals the force dotted with the virtual displacement in the force’s direction. For a couple moment, virtual rotational work is found by...

virtual work for a system of connected rigid bodies

Virtual work helps find forces in a system of connected rigid bodies. It is a useful method when several links move together and the system is in equilibrium. In that case, the total virtual work is zero. To analyze the system, start with a free-body diagram. Use one independent coordinate to describe the link configuration. Then mark the deflected position that comes from a positive virtual displacement. This makes the small change in position clear before any calculations begin. Next,...

principle of virtual work: problem solving

principle-of-virtual-work-problem-solving

Virtual Work for Finding Unknown Forces

The principle of virtual work helps find unknown forces and moments in equilibrium problems. It is an important idea in mechanics and engineering. The method uses a small, hypothetical motion called a virtual displacement. If the system is in equilibrium, the work done by the forces during that displacement is zero. To apply this principle, the positions of the internal and external forces must be written in terms of one common coordinate parameter. That parameter can be an angle, a distance,...

mechanical efficiency of real machines

Friction’s Role in Machine Efficiency

Mechanical efficiency shows how well a machine turns input work into output work. It is calculated as the ratio of output work to input work. An ideal machine has an efficiency of one, which means the input work equals the output work. Real machines are never perfectly ideal because some energy is lost. Friction is one of the main causes of that loss. In a toggle vise used to compress wooden blocks, the sliding block rubs against the horizontal plane and creates friction. To find the...

conservative forces

Conservative Forces and Path-Independent Work

Conservative forces are forces whose work depends only on an object’s starting and ending positions. The path between those positions does not change the amount of work done. This idea is important in mechanical engineering because it helps describe how energy moves through a system. A conservative force also conserves energy in the sense that its work is path independent. Gravity is one example. Electrostatic forces and springs modeled by Hooke’s law are also examples. A ball rolling down a...

potential energy

Gravitational and Elastic Energy Stored

Gravitational and elastic potential energy are forms of stored energy from conservative forces. A conservative force, such as gravity or an elastic force, gives a body the capacity to do work. This capacity is measured as potential energy and depends on the body’s position relative to a fixed reference point, or datum. For gravitational potential energy, the datum is the level where the energy is taken as zero. If a body is above this reference plane, its weight has positive gravitational...

potential-energy criterion for equilibrium

potential-energy-criterion-for-equilibrium

Stable Equilibrium Through Potential Energy

Potential energy helps determine when a mechanical system is stable at equilibrium. When a system is acted on by gravitational and elastic forces, its total potential function is the algebraic sum of gravitational potential energy and elastic potential energy. If the system is already in equilibrium and is given a small displacement, the work done on the system equals the negative of the change in potential energy between the starting and ending positions. For a virtual displacement, which is...

stability of equilibrium configuration

Types of Equilibrium in Mechanical Systems

Types of equilibrium in mechanical systems are stable, neutral, and unstable. These three cases help explain how a structure or object responds when it is pushed slightly away from balance. They are important for predicting whether a system will return to its original position, stay where it is, or move farther away. Stable equilibrium occurs when a system returns toward its original position after a small displacement. In this case, the potential energy is at a minimum. A cantilever beam...

one-degree-of-freedom system

Spring-Mass Motion and Energy Stability

A one-degree-of-freedom system uses a single independent variable to describe its state and behavior. In mechanical engineering, this kind of model helps explain how parts in a larger system respond to force. It also gives engineers a way to predict motion before a design is built in real life. A simple harmonic oscillator is one example of a one-degree-of-freedom system. A mass attached to a spring moves along one axis, and that position determines the system’s state. The spring force makes...

stability of equilibrium configuration: problem solving

stability-of-equilibrium-configuration-problem-solving

Equilibrium Stability Through Potential Energy

Stability of equilibrium in physics and engineering can be studied by using a system’s potential energy. An equilibrium configuration is a state where the system can remain at rest. Stability describes whether the system tends to return to that state after a small disturbance. Problem solving begins by finding the equilibrium points of the system. This is done by setting the derivative of the potential energy function equal to zero and solving for the independent variable values that satisfy...

key terms and concepts

Learn how virtual work is used with connected rigid bodies to find forces and moments using a free-body diagram, one coordinate, and equilibrium.

Finding Forces with Virtual Work in Linked Bodies | 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

Finding Forces with Virtual Work in Linked Bodies

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