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

특정 각도로 늘어나지 않는 스프링에 연결된 가위 연결 시스템을 고려하십시오.
외부 힘이 존재하면 스프링이 늘어나고 시스템이 가상 변위를 겪습니다. 이 상태에서는 스프링 힘과 외부 힘만 작업에 기여합니다.
시스템의 평형을 유지하기 위한 편향 각도를 결정하기 위해 고정점에 대한 두 힘의 위치 좌표가 결정됩니다.
그런 다음 스프링이 압축되는 양과 해당 스프링 힘이 평가됩니다.
위치 좌표를 차별화하면 두 힘에 해당하는 가상 변위가 제공됩니다.
외력은 가상 변위의 방향으로 작용하므로 긍정적인 작용을 합니다. 한편, 스프링 힘은 가상 변위와 반대로 작용하여 음의 작업을 수행합니다.
다음으로, 가상 작업의 원리를 사용하여 시스템의 가상 작업 방정식을 작성합니다.
주어진 힘에 대한 가상 작업 방정식을 풀면 가위 연결 시스템의 평형을 유지하는 데 필요한 각도를 얻을 수 있습니다.

<ol>
	<li>히벨러, R.C. (2016). 엔지니어링 역학: 정적. 14판, 뉴저지: 피어슨. 섹션 11.3, pp. 587-588.</li>
	<li>Beer, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. 및 Self, B.P. (2016). 엔지니어를 위한 벡터 역학. 제 11 판, 뉴욕 : McGraw-Hill Education. 582쪽.</li>
</ol>

가상 작업의 원리: 문제 해결

가상 일의 원리는 역학 및 공학 분야에서 필수적인 개념입니다. 이것은 구조나 시스템의 평형과 관련된 문제를 해결하는 데 사용됩니다. 시스템이 평형 상태에 있을 때 가상 변위 동안 모든 힘이 수행하는 일은 0이라는 가정에 기초합니다. 이 원리는 시스템의 가상 변위와 내부 및 외부 힘에 의해 수행되는 해당 작업을 고려하여 적용됩니다.

가상 작업의 원리를 적용하기 위해서는 내력과 외력의 위치 좌표를 공통의 좌표 매개변수로 표현할 필요가 있습니다. 이 매개변수는 일반적으로 당면한 문제와 관련된 각도, 거리 또는 변위입니다.

일단 좌표가 표현되면, 각 힘에 대응하는 가상의 변위는 좌표식을 미분함으로써 구할 수 있습니다. 가상의 변위는 시스템이 겪을 수 있는 가상의 변위를 나타내며, 이는 시스템에 작용하는 각 힘이 수행하는 가상의 일을 계산할 수 있게 해줍니다.

시스템에 작용하는 외력은 가상 변위 방향으로 이동할 때 양의 일을 하고, 내력은 가상 변위에 반대할 때 음의 일을 합니다.

가상의 일의 원리를 이용하여 문제를 해결하려면 먼저 시스템 내에 존재하는 알려지지 않은 힘과 모멘트를 확인해야 합니다. 그런 다음 가상의 시스템이 가상으로 변위하는 동안 이 힘과 모멘트에 의해 수행된 작업을 평가합니다. 가상의 변위는 매우 작고 시스템이 겪는 가상의 변위를 나타냅니다. 이를 통해 시스템에 작용하는 각 힘과 모멘트와 이 가상의 변위 동안 시스템에 의해 수행된 작업을 결정할 수 있습니다.

다음으로, 가상 일의 원리를 이용하여 시스템에 대한 가상 일 방정식을 작성합니다. 이 방정식은 시스템에 작용하는 각 힘과 모멘트에 의해 이루어지는 가상 변위와 해당 일을 고려합니다. 마지막으로, 가상 일 방정식을 푸는 것은 시스템에서 알려지지 않은 힘과 모멘트의 값을 제공합니다. 

가상 작업의 원리는 상호 연결된 많은 부분을 포함하는 복잡한 시스템과 관련된 문제를 해결하는 데 유용합니다. 구조나 시스템의 알려지지 않은 힘과 모멘트를 계산하기 위해 공학과 역학에서 널리 사용됩니다.

가상 작업의 원리는 기계 및 엔지니어링 분야에서 필수적인 개념입니다. 이것은 평형과 관련된 문제를 해결하는 데 사용됩니다 ...

principle-of-virtual-work-problem-solving

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Virtual Work

가상일

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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...

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-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,...

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

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 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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