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

Rozważmy ciało sztywne z dwiema równymi i przeciwstawnymi siłami działającymi w dwóch punktach oddalonych od siebie odległością.
Ta para wytwarza moment równy sile pomnożonej przez odległość między nimi. W rezultacie, sztywne ciało ulega translacji, a także rotacji, aby osiągnąć ostateczną pozycję.
Podczas translacji praca jednej siły jest równa i przeciwna do pracy innej siły. Tak więc praca netto wykonana przez te dwie siły podczas translacji wynosi zero.
Jednak podczas obrotu przemieszczenie kątowe spowodowane jedną z sił daje równoważne przemieszczenie liniowe, które skutkuje pracą.
Wyrażenie pracy w kategoriach przemieszczenia kątowego i użycie wyrażenia na wielkość momentu pary daje ostateczną ilość wykonanej pracy, która zależy od momentu pary i kąta obrotu.
Jeśli moment pary i kąt obrotu mają ten sam sens, praca wykonana przez moment pary jest dodatnia.
W przeciwieństwie do tego, jeśli mają przeciwny sens, wykonana praca jest negatywna.

<ol>
	<li>Hibbeler, R.C. (2016). Mechanika inżynierska: Statyka. Czternasta edycja, New Jersey: Pearson. Sekcja 11.1, s. 582.</li>
	<li>Meriam, J.L., Kraige, L.G. i Bolton, J.N. (2016). Mechanika inżynierska: statyka i dynamika. Ósma edycja, Singapur: John Wiley & Sons. Strony 393-394.</li>
	<li>Beer, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. i Self, B.P. (2016). Mechanika wektorowa dla inżynierów. Jedenasta edycja, Nowy Jork: McGraw-Hill Education. Sekcja 10.1A, str. 577</li>
</ol>

praca pary sił

Inżynieria mechaniczna polega na badaniu ruchu, energii i siły oraz zajmuje się projektowaniem, produkcją i utrzymaniem układów mechanicznych. Jednym z ważnych pojęć w tej dziedzinie jest para momentów, generowana przez dwa równe i przeciwne siły działające w dwóch punktach sztywnego ciała oddalonych od siebie o określoną odległość.

Kiedy sztywne ciało ulega różnicowemu przemieszczeniu spowodowanemu parą momentów, jego ruch można podzielić na dwie części: równoległe przesunięcie obu punktów do ich ostatecznej pozycji i obrót wokół jednego z nich. Podczas przesunięcia obie siły przechodzą przez ten sam odległy przesunięcie, ale w przeciwnych kierunkach. Dlatego praca wykonana przez siły, będąc przeciwna znaku, ale równa co do wartości, daje wynik zerowy.

Jednak podczas obrotu siła powoduje przemieszczenie kątowe, co prowadzi do pracy nierównej zeru. Wykonana praca podczas obrotu może być obliczona jako iloczyn modułu momentu pary i kąta obrotu.

Jeśli moment pary i kąt obrotu mają ten sam kierunek, wykonana praca przez parę momentów jest dodatnia. W przeciwnym razie, jeśli moment pary i kąt obrotu mają przeciwne kierunki, wykonana praca będzie ujemna.

Wykonana praca przez parę momentów jest istotnym czynnikiem, który należy uwzględnić podczas projektowania układów mechanicznych. Inżynierowie brali pod uwagę ilość pracy, która zostanie wykonana podczas obrotu, a także wielkość i kierunek momentu pary, aby zapewnić prawidłowe funkcjonowanie systemu.

Praca pary sił

Inżynieria mechaniczna obejmuje badanie ruchu, energii i siły i zajmuje się projektowaniem, produkcją i konserwacją ...

Education

JoVE Core

Mechanical Engineering

Inżynieria mechaniczna

Unit 1

Jednostka 1

Virtual Work

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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...

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 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

Description

Transcript

Tags