Name: virtual work for finding unknown forces
Uploaded: 2023-09-22T11:49:20.000Z
Duration: 1 min 13 s
Channel: JoVE

Considere un sistema de enlace de tijera conectado a un resorte, que no está estirado en un cierto ángulo.
En presencia de una fuerza externa, el resorte se estira y el sistema experimenta un desplazamiento virtual. En esta condición, solo la fuerza del resorte y la fuerza externa contribuyen al trabajo.
Para determinar el ángulo de deflexión para mantener el equilibrio del sistema, se determinan las coordenadas de posición de las dos fuerzas con respecto a un punto fijo.
Luego, se evalúa la cantidad en la que se comprime el resorte y la fuerza del resorte correspondiente.
La diferenciación de las coordenadas de posición da los desplazamientos virtuales correspondientes a las dos fuerzas.
La fuerza externa actúa en la dirección del desplazamiento virtual, por lo que realiza un trabajo positivo. Mientras tanto, la fuerza del resorte actúa de manera opuesta al desplazamiento virtual y hace un trabajo negativo.
A continuación, se utiliza el principio del trabajo virtual para escribir la ecuación del trabajo virtual para el sistema.
Resolviendo la ecuación de trabajo virtual para la fuerza dada, se puede obtener el ángulo necesario para mantener el equilibrio del sistema de enlace de las tijeras.

<ol>
	<li>Hibbeler, R.C. (2016). Ingeniería Mecánica: Estática. Decimocuarta edición, Nueva Jersey: Pearson. Sección 11.3, págs. 587 y 588.</li>
	<li>Beer, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. y Self, B.P. (2016). Mecánica vectorial para ingenieros. Undécima Edición, Nueva York: McGraw-Hill Education. Págs. 582.</li>
</ol>

principio del trabajo virtual: resolución de problemas

El principio del trabajo virtual es un concepto esencial en el campo de la mecánica e ingeniería. Se utiliza para resolver problemas relacionados con el equilibrio de una estructura o sistema. Se basa en la suposición de que si un sistema está en equilibrio, el trabajo realizado por todas las fuerzas durante un desplazamiento virtual es cero. Este principio se aplica considerando los desplazamientos virtuales del sistema y el trabajo correspondiente realizado por las fuerzas internas y externas. Para aplicar el principio del trabajo virtual, es necesario expresar las coordenadas de posición de las fuerzas internas y externas en términos de un parámetro de coordenadas común. Este parámetro es típicamente un ángulo, distancia o desplazamiento relevante para el problema en cuestión. Una vez que se han expresado las coordenadas, se encuentran los desplazamientos virtuales correspondientes a cada una de las fuerzas mediante la diferenciación de las expresiones de coordenadas. Los desplazamientos virtuales representan desplazamientos hipotéticos que el sistema podría experimentar, y nos permiten calcular el trabajo virtual realizado por cada fuerza que actúa sobre el sistema. La fuerza externa que actúa sobre el sistema realiza un trabajo positivo cuando se mueve en la dirección de su desplazamiento virtual, mientras que las fuerzas internas realizan un trabajo negativo cuando se oponen a sus desplazamientos virtuales. Para resolver un problema utilizando el principio del trabajo virtual, primero, identifique las fuerzas y momentos desconocidos que existen dentro del sistema. Luego evaluar el trabajo realizado por estas fuerzas y momentos durante un desplazamiento virtual hipotético del sistema. El desplazamiento virtual es muy pequeño y representa un desplazamiento hipotético que el sistema experimenta. Esto permite la determinación de cada fuerza y momento que actúa sobre el sistema y el trabajo realizado por ellos durante este desplazamiento virtual. A continuación, escriba la ecuación del trabajo virtual para el sistema utilizando el principio del trabajo virtual. Esta ecuación considera los desplazamientos virtuales y el trabajo correspondiente realizado por cada fuerza y momento que actúa sobre el sistema. Finalmente, resolver la ecuación del trabajo virtual da los valores de las fuerzas y momentos desconocidos en el sistema. El principio del trabajo virtual es beneficioso para resolver problemas relacionados con sistemas complejos que involucran muchas partes interconectadas. Se utiliza ampliamente en ingeniería y mecánica para calcular las fuerzas y momentos desconocidos de una estructura o sistema.

Principio del trabajo virtual: Resolución de problemas

El principio del trabajo virtual es un concepto esencial en el campo de la mecánica y la ingeniería. Esto se utiliza para resolver problemas relacionados con el equilibrio ...

principle-of-virtual-work-problem-solving

Education

Educación

JoVE Core

Mechanical Engineering

Ingeniería Mecánica

Unit 1

Unidad 1

Virtual Work

Trabajo virtual

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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, or another displacement that fits the problem. After the coordinates are written this way, the virtual displacements are found by differentiating the coordinate expressions. These displacements are hypothetical, but they show how the system could move.

Virtual work is then found from the forces acting on the system. An external force does positive work when it moves in the same direction as its virtual displacement. Internal forces do negative work when they oppose their virtual displacements. This sign difference is part of the virtual-work equation.

To solve a problem, first identify the unknown forces and moments in the system. Next, evaluate the work done during a virtual displacement. Then write the virtual-work equation for the whole system. Solving that equation gives the values of the unknown forces and moments. This approach is useful for complex systems with many connected parts.

Virtual Work for Finding Unknown Forces

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...

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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

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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,...

principle of virtual work: problem solving

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

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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...

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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...

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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...

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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 the principle of virtual work uses a small virtual displacement to find unknown forces and moments in equilibrium problems with connected systems.

Virtual Work for Finding Unknown Forces | 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

Virtual Work for Finding Unknown Forces

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