Name: work in force and motion
Uploaded: 2023-09-22T11:49:36.000Z
Duration: 1 min 14 s
Channel: JoVE

仕事は、物体に作用する力が物体を変位させることで生じます。これは、変位方向に沿った力のスカラー成分の積に等しくなります。
数学的には、仕事は加えられた力と物体の変位の内積として与えることができます。
SIの仕事単位はジュールです。1ジュールは、1ニュートンの力が物体を1メートル移動させたときに行われる作業です。
仕事はスカラー量であるため、その大きさは、変位に対する力の方向に応じて、正、負、またはゼロになります。

クレーンが荷物を上に持ち上げる例を考えてみましょう。ここでは、加えられた力と変位ベクトルが同じ方向に整列しているため、行われた作業は正です。

別の例では、移動中の車にブレーキがかかると、ブレーキ力は車の動きとは逆方向に作用します。ここでは、行われた作業は否定的です。

質量のない伸びないストリングを介して荷重を持ち上げる摩擦のないプーリーは、力と変位が垂直であるため、ゼロの仕事をします。

<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。セクション11.1、581-582ページ。</li>
	<li>メリアム、JL、クレイジ、LGおよびボルトン、JN(2016)。エンジニアリングメカニクス:静力学とダイナミクス。第8版、シンガポール:John Wiley & Sons。セクション7.2、392-393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。セクション10.1A、575ページ。</li>
</ol>

仕事

仕事は機械工学の基本的な概念であり、多くの応用があります。仕事の計算方法や異なる種類の仕事を理解することは、物理的なプロセスをより良く理解し、複雑な問題に対する洞察を提供するのに役立ちます。

仕事は、物体に作用する力の結果として定義され、物体を力の作用線に沿って移動させることを引き起こします。また、物体に力を加えることによってエネルギーを転送するプロセスとしても定義され、それによって物体の変位が生じます。このエネルギー転送によって、物体の運動や位置の変化が起こります。仕事は、力と変位の成分が同じ方向である場合のそれらの積として書かれることもあり、また物体に加えられた力と変位のドット積としても書かれることがあります。国際単位系では、1ジュールがその単位とされており、これは1メートルの変位に対して1ニュートンの力を行使することに相当します。

物体に対して行われる仕事の種類は、力の方向に対する変位によって異なります。もし適用された力と変位が互いに平行であれば、行われる仕事は正であり、反平行であれば行われる仕事は負です。適用された力と変位が互いに直行している場合、行われる仕事はゼロです。例えば、クレーンが重い荷物を持ち上げる際には正の仕事が行われます-荷物に上向きの力を加えることにより、地面と比較して上に移動します。逆に、動いている車にブレーキをかける場合は負の仕事が行われます-タイヤが運動に逆らう力を加え、それにより負の仕事が行われます。

固定点にかかる力や変位に垂直な力など、一部の力は仕事をしない場合もあります。例えば、摩擦のないピンが回転するときの支持体にかかる反作用、摩擦のない表面上で動く物体にかかる反作用力などが挙げられます。しかし、仕事をする力には物体の重量やザラついた表面上で動く物体にかかる摩擦力などが含まれます。

場合によっては、複数の力によって行われる仕事の合計がゼロになることがあります。例えば、摩擦のないピンで接続された2つの剛体は、移動に対して等しい大きさで逆向きの力が必要であり、その合計仕事はゼロです。同様に、伸縮性のあるコードで接続された2つのブロックのテンション力も等しい大きさで逆の符号を持ち、結果としてゼロの仕事が行われます。

全体として、どの力が仕事を生み出し、どのように仕事を計算するかを理解することは、複雑な物理的問題に対する有益な洞察を提供し、望ましい結果に対してこれらのプロセスを効果的に管理することを可能にします。

仕事は機械工学の基本的な概念であり、多くの用途があります。仕事の計算方法とさまざまな種類の仕事を理解する...

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

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 the SI system, the unit of work is the joule. One joule is equal to one newton of force acting over one meter of displacement.

The direction of the force compared with the displacement tells us the type of work done. When the force and displacement are parallel, the work is positive. When they are anti-parallel, the work is negative. When the force and displacement are perpendicular, the work is zero.

A crane lifting a heavy load is an example of positive work. The crane applies an upward force, and the load moves upward. Brakes on a moving car show negative work. The wheels exert a force that opposes motion, so work is done against the car’s movement.

Some forces do no work. This includes forces acting at fixed points or forces perpendicular to displacement. Examples include the reaction at a frictionless pin when a body rotates about it, and the reaction force on a body moving on a frictionless surface. Forces that do work include the weight of a body and friction acting on a body moving on a rough surface.

In some systems, the total work done by multiple forces is zero. Two rigid bodies connected by a frictionless pin need equal and opposite forces for motion, so their combined work is zero. The same idea applies to two blocks connected by an extensible cord, where the tension forces have equal magnitude but opposite signs. Knowing which forces produce work helps explain physical processes and solve mechanical problems.

Work in Force and Motion

work

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 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 work is calculated from force and displacement, why it can be positive, negative, or zero, and see real examples from cranes and brakes.

Work in Force and Motion | 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

Work in Force and Motion

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