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

力は、その仕事がたどる道に関係なく、初期位置と最終位置のみに依存する場合、保守的と呼ばれます。
保存力の 2 つの例は、ボディの重量とばね力です。
重量は、重力によって物体が受ける力です。
クレーンからぶら下がっているブロックがdrの垂直変位によって重力に逆らって変位する場合、行われる作業は力と垂直変位の内積です。
重量が変位の反対方向に作用するため、行われる作業は負です。
行われる作業は経路に依存せず、垂直方向の変位にのみ依存するため、重量は控えめな力になります。
同様に、線形弾性スプリングの場合、ブロックが水平方向に変位すると、仕事はスプリングの初期位置と最終位置にのみ依存し、たどる経路とは無関係です。そのため、バネが加える力も保守的です。

<ol>
	<li>ヒベラー、RC(2016)。エンジニアリングメカニクス:静力学。第14版、ニュージャージー州:ピアソン。597ページ。</li>
	<li>ビール、FP、ジョンストン、ER、マズレック、DF、コーンウェル、PJおよびセルフ、BP(2016)。エンジニアのためのベクトル力学。第11版、ニューヨーク:マグロウヒル教育。595-597ページ。</li>
</ol>

保守力

保守力は、機械工学の分野における重要な概念です。これらの力の特性と特性を理解することは、機械システムの設計と解析において重要です。

保守力は、物体の初期位置と最終位置にのみ依存し、物体がこれらの位置間で取る経路には依存しない力です。これらの力はエネルギーを保存し、つまり力による仕事は経路に依存しません。保守力の例には、重力、静電力、フックの法則によってモデル化されるバネなどがあります。

丘を転がるボールを考えてみましょう。ボールが丘の頂上から下まで移動する際の重力による仕事は、ボールが丘を下る経路に関係なく同じです。保守力はまた、機械システムの設計にも役立ちます。エンジニアはこれらの力を使用して、システムに対する力の仕事量を計算し、オブジェクトを1つの位置から別の位置に移動するために必要なエネルギーを決定することができます。この情報は、より効率的なシステムの設計および摩擦などの非保守力によるエネルギー損失を最小化するために使用することができます。

保守力のもう1つの重要な側面は、ポテンシャルエネルギー関数によって表されることです。この関数は、力と物体の位置との関係によって定義される位置エネルギーを記述します。

保守的な力は、機械工学の分野では不可欠な概念です。これらの力の特性と特性を理解することは...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Virtual Work

仮想仕事

KEY TERMS AND CONCEPTS

主要用語と概念

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 機械工学は、平衡、力、トラス解析、構造力学などの重要なトピックをカバーする簡潔でわかりやすいアニメーション ビデオを提供します。実際のアプリケーションを探索し、科学者主導の実験を通じてこれらのコンセプトが実際に動作しているのを目撃してください。

mechanical engineering

Conservative Forces and Path-Independent Work

Description

Transcript