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

물체에 작용하는 힘이 물체를 전위시킬 때 작업이 수행됩니다. 이는 변위 방향을 따라 힘의 스칼라 성분의 곱과 같습니다.
수학적으로 작업은 적용된 힘과 물체의 변위의 내적으로 주어질 수 있습니다.
SI 작업 단위는 줄입니다. 1줄은 1뉴턴의 힘이 물체를 1미터 변위시킬 때 수행되는 작업입니다.
작업은 스칼라 양이기 때문에 그 크기는 변위에 상대적인 힘의 방향에 따라 양수, 음수 또는 0이 될 수 있습니다.

짐을 위로 들어 올리는 크레인의 예를 생각해 보십시오. 여기서 적용된 힘과 변위 벡터는 같은 방향으로 정렬되므로 수행된 작업은 긍정적입니다.

또 다른 예로, 움직이는 자동차에 브레이크가 가해지면 제동력은 자동차의 움직임과 반대 방향으로 작용합니다. 여기서 수행 된 작업은 부정적입니다.

질량이 없고 팽창할 수 없는 끈을 통해 하중을 들어 올리는 마찰 없는 풀리는 힘과 변위가 수직이기 때문에 작동하지 않습니다.

<ol>
	<li>히벨러, R.C. (2016). 엔지니어링 역학: 정적. 14판, 뉴저지: 피어슨. 섹션 11.1, pp. 581-582.</li>
	<li>Meriam, J.L., Kraige, L.G. 및 Bolton, J.N. (2016). Engineering Mechanics: Statics and Dynamics(정역학 및 동역학). 여덟 번째 판, 싱가포르 : John Wiley & Sons. 섹션 7.2 pp. 392-393.</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. 섹션 10.1A, 575쪽.</li>
</ol>

일은 기계 공학의 기본 개념이며 많은 응용 분야를 가지고 있습니다. 일이 계산되는 방식과 다양한 일 유형을 이해하는 것은 물리적 프로세스를 더 잘 이해하고 복잡한 문제에 대한 통찰력을 제공하는 데 도움이 될 수 있습니다.
일은 힘이 물체에 작용하여 물체가 힘의 작용선을 따라 움직이게 한 결과로 정의됩니다. 또한 물체에 힘을 가하여 에너지를 전달하여 물체의 변위를 가져오는 과정으로 정의됩니다. 이 에너지 전달은 물체의 운동이나 위치 변화에 영향을 미칩니다. 일은 같은 방향으로 힘과 변위의 성분의 곱으로 쓰여질 수도 있고, 물체에 가해지는 힘과 변위의 점의 곱으로 쓰여질 수도 있습니다. SI 시스템은 1줄을 단위로 간주하는데, 이것은 변위 1미터에 걸쳐 1 뉴턴의 힘을 수행하는 것과 같습니다.
물체에 가해지는 일의 종류는 변위에 대한 힘의 방향에 따라 달라집니다. 가해진 힘과 변위가 서로 평행하면 수행된 일은 양수이고 반 평행하면 수행된 일은 음수입니다. 가해진 힘과 변위가 서로 수직이면 수행된 일은 0입니다. 긍정적인 일의 예는 크레인이 무거운 하중을 들어올릴 때 하중에 대해 위 방향의 힘을 가하여 지면에 대해 위로 이동하는 것입니다. 예를 들어 움직이는 자동차에 브레이크를 걸 때 바퀴가 운동에 반대하는 힘을 가하여 부정적인 일이 발생합니다. 
고정된 점이나 변위에 수직으로 작용하는 힘과 같은 일부 힘은 작용하지 않습니다. 예를 들어, 지지체가 회전할 때 마찰이 없는 핀에서의 반응, 마찰이 없는 표면에서 움직이는 물체에 작용하는 반력 등을 들 수 있습니다. 그러나 작용하는 힘에는 물체의 무게와 거친 표면에서 움직이는 물체에 작용하는 마찰력 등이 포함됩니다. 
어떤 경우에는 여러 힘으로 한 일의 합이 0이 되기도 합니다. 예를 들어 마찰이 없는 핀으로 연결된 두 강체는 운동에 대해 동일하지만 반대되는 힘을 필요로 하므로 이들의 결합된 일은 0이 됩니다. 마찬가지로 확장 가능한 코드로 연결된 두 블록은 크기는 같지만 부호는 반대이므로 일이 0이 됩니다.
전반적으로 어떤 힘이 일을 생성하고 일을 계산하는 방법을 이해하면 복잡한 물리적 문제에 대한 유용한 통찰력을 얻을 수 있으며 원하는 결과를 얻기 위해 이러한 프로세스를 효과적으로 관리할 수 있습니다.

작업은 기계 공학의 기본 개념이며 많은 응용 분야가 있습니다. 작업 계산 방법과 다양한 작업 유형 이해 ...

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Virtual Work

가상일

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 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

Work in Force and Motion

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