Name: conservative forces and path-independent work
Uploaded: 2025-05-22T09:06:05.000Z
Duration: 1 min 3 s
Channel: JoVE

힘은 따라간 경로에 관계없이 초기 및 최종 위치에만 작업이 의존하는 경우 보수적이라고 합니다.
보존력의 두 가지 예는 물체의 무게와 스프링 힘입니다.
무게는 중력으로 인해 물체가 받는 힘입니다.
크레인에 매달려 있는 블록이 dr의 수직 변위에 의해 중력에 반하여 변위되는 경우, 완료된 작업은 힘과 수직 변위의 내적입니다.
수행된 작업은 무게가 변위의 반대 방향으로 작용하기 때문에 음수입니다.
수행된 작업은 이동한 경로와 무관하고 수직 변위에만 의존하기 때문에 무게는 보수적인 힘입니다.
마찬가지로, 선형 탄성 스프링의 경우 블록이 수평으로 변위되면 작업은 스프링의 초기 및 최종 위치에만 의존하며 선택한 경로와 무관합니다. 따라서 스프링이 가하는 힘도 보수적입니다.

<ol>
	<li>히벨러, R.C. (2016). 엔지니어링 역학: 정적. 14판, 뉴저지: 피어슨. 597쪽.</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. 595-597쪽.</li>
</ol>

보존력

보존력은 기계공학 분야에서 필수적인 개념입니다. 이러한 힘의 특성과 특성을 이해하는 것은 기계 시스템의 설계 및 분석에 매우 중요합니다.
보존력은 물체의 초기 위치와 최종 위치에만 의존하고 물체가 이 위치들 사이에서 취하는 경로와는 독립적인 힘입니다. 이 힘들은 에너지를 보존하는데, 이는 힘에 의해 행해진 일이 경로와 무관하다는 것을 의미합니다. 보존력의 예로는 중력, 정전기력, 후크의 법칙으로 모델링된 용수철 등이 있습니다.
언덕 아래로 굴러 내려가는 공을 생각해 보겠습니다. 공이 언덕 위에서 아래로 이동할 때 중력에 의해 만들어지는 일은 공이 언덕을 내려가는 경로에 관계없이 동일합니다. 보존력은 또한 기계 시스템의 설계에 유용합니다. 공학자들은 이 힘을 사용하여 시스템에 작용하는 힘의 양을 계산하고 물체가 한 위치에서 다른 위치로 이동하는 데 필요한 에너지를 결정할 수 있습니다. 이 정보는 더 효율적인 시스템을 설계하고 마찰과 같은 비보존력에 의한 에너지 손실을 최소화하는 데 사용될 수 있습니다.
보존력의 또 다른 중요한 측면은 물체의 위치와 힘 사이의 관계로 정의되는 퍼텐샬에너지 함수로 나타낼 수 있다는 것입니다. 이 함수는 물체의 위치 때문에 시스템에 저장된 힘을 나타냅니다.

보수력은 기계 공학 분야에서 필수적인 개념입니다. 이러한 힘의 속성과 특성을 이해하는 것은 ...

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Virtual Work

가상일

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 hill shows this idea clearly. The work done by gravity is the same whether the ball takes a straight path or a longer route to the bottom.

Because conservative forces are tied to position, they can be represented by a potential energy function. This function describes the energy stored in a system based on where an object is located. Engineers use this relationship to calculate the work done on a system and the energy needed to move an object from one position to another. That information helps them design more efficient systems and reduce energy loss from non-conservative forces such as friction.

Conservative Forces and Path-Independent Work

conservative-forces-and-path-independent-work

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

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 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 conservative forces depend on start and end positions, not path, and how gravity, electrostatic forces, and springs relate to potential energy.

Conservative Forces and Path-Independent Work | 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

Conservative Forces and Path-Independent Work

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