Name: couple moment work in rotation
Uploaded: 2023-09-22T11:49:20.000Z
Duration: 1 min 12 s
Channel: JoVE

Stellen Sie sich einen starren Körper mit zwei gleichen und entgegengesetzten Kräften vor, die an zwei Punkten wirken, die durch einen Abstand voneinander getrennt sind.
Dieses Paar erzeugt ein Moment, das der Kraft multipliziert mit dem Abstand zwischen ihnen ist. Infolgedessen erfährt der starre Körper sowohl eine Translation als auch eine Rotation, um die endgültige Position zu erreichen.
Während der Übersetzung ist die Arbeit einer Kraft gleich und der Arbeit einer anderen Kraft entgegengesetzt. Die Netzwerkarbeit, die von den beiden Kräften während der Übersetzung geleistet wird, ist also Null.
Während der Drehung ergibt jedoch die Winkelverschiebung aufgrund einer der Kräfte eine äquivalente lineare Verschiebung, die zu Arbeit führt.
Wenn man die Arbeit in Form einer Winkelverschiebung ausdrückt und den Ausdruck für die Größe des Moments des Paares verwendet, erhält man die endgültige Menge der geleisteten Arbeit, die vom Moment des Paares und dem Drehwinkel abhängt.
Wenn der Paarmoment und der Drehwinkel den gleichen Sinn haben, ist die Arbeit, die der Paarmoment leistet, positiv.
Wenn sie dagegen den gegenteiligen Sinn haben, ist die geleistete Arbeit negativ.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik: Statik. Vierzehnte Auflage, New Jersey: Pearson. Abschnitt 11.1, S. 582.</li>
	<li>Meriam, J.L., Kraige, L.G. und Bolton, J.N. (2016). Technische Mechanik: Statik und Dynamik. Achte Auflage, Singapur: John Wiley & Sons. S. 393-394.</li>
	<li>Bier, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. und Self, B.P. (2016). Vektormechanik für Ingenieure. Elfte Auflage, New York: McGraw-Hill Education. Abschnitt 10.1A, S. 577</li>
</ol>

die arbeit eines momentenpaares

Die mechanische Ingenieurwissenschaft befasst sich mit der Untersuchung von Bewegung, Energie und Kraft und beschäftigt sich mit dem Entwurf, der Herstellung und der Wartung mechanischer Systeme. Ein wichtiger Begriff in diesem Bereich ist das Momentenpaar, das durch zwei gleiche und entgegengesetzte Kräfte erzeugt wird, die an zwei Punkten in einem starren Körper wirken, die durch einen bestimmten Abstand voneinander getrennt sind. Wenn der starre Körper aufgrund eines Momentenpaares eine differentielle Verdrängung erfährt, kann seine Bewegung in zwei Teile aufgeteilt werden: die gleichmäßige Verschiebung der beiden Punkte in ihre Endpositionen und die Drehung um einen von ihnen. Während der Verschiebung unterliegen die beiden Kräfte der gleichen Verschiebung, jedoch in entgegengesetzten Richtungen. Die Arbeit, die von den Kräften geleistet wird, ergibt daher aufgrund ihrer entgegengesetzten Vorzeichen, aber gleichen Betrags, eine Nullarbeit. Während der Rotation verursacht die Kraft jedoch eine Winkelverdrängung, die zu einer von Null verschiedenen Arbeit führt. Die bei der Rotation geleistete Arbeit kann als das Produkt aus dem Betrag des Momentenpaares und dem Rotationswinkel berechnet werden. Wenn das Momentenpaar und der Rotationswinkel die gleiche Richtung haben, ist die vom Momentenpaar geleistete Arbeit positiv. Wenn das Momentenpaar und der Rotationswinkel jedoch entgegengesetzte Richtungen haben, ist die geleistete Arbeit negativ. Die vom Momentenpaar geleistete Arbeit ist ein wesentlicher Faktor, der bei der Konstruktion von mechanischen Systemen berücksichtigt werden muss. Ingenieure berücksichtigen die aufgewendete Arbeit während der Rotation sowie den Betrag und die Richtung des Momentenpaares, um sicherzustellen, dass das System ordnungsgemäß funktioniert.

Die Arbeit eines Momentenpaares

Der Maschinenbau befasst sich mit der Untersuchung von Bewegung, Energie und Kraft und befasst sich mit der Entwicklung, Herstellung und Wartung mechanischer ...

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JoVE Core

Mechanical Engineering

Maschinenbau

Unit 1

Einheit 1

Virtual Work

Virtuelle Arbeit

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

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 translation part, each force moves the same distance but in the opposite direction. Because the forces are equal in magnitude and opposite in sign, the work done in this step is zero.

The rotation part is different. Here, the force produces an angular displacement, so the work is not zero. The work done by the couple moment equals the magnitude of the couple moment times the angle of rotation.

The sign of the work depends on direction. If the couple moment and the rotation angle have the same sense, the work is positive. If they have opposite senses, the work is negative. Engineers use this idea when they design mechanical systems, since the amount of work during rotation matters, along with the size and direction of the couple moment.

Couple Moment Work in Rotation

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

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...

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Finding Forces with Virtual Work in Linked Bodies

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Virtual Work for Finding Unknown Forces

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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...

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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...

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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...

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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...

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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...

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key terms and concepts

Learn how a couple moment does zero work during translation but non-zero work during rotation, and how sign depends on the direction of rotation.

Couple Moment Work in Rotation | 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

Couple Moment Work in Rotation

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