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

Bir mesafe ile ayrılmış iki noktada hareket eden iki eşit ve zıt kuvvete sahip katı bir cisim düşünün.
Bu çift, aralarındaki mesafenin kuvvet çarpımına eşit bir moment üretir. Sonuç olarak, rijit cisim, son konuma ulaşmak için translasyonun yanı sıra rotasyona da uğrar.
Çeviri sırasında, bir kuvvetin işi başka bir kuvvetin işine eşit ve zıttır. Dolayısıyla, çeviri sırasında iki kuvvetin yaptığı net iş sıfırdır.
Bununla birlikte, dönme sırasında, kuvvetlerden birine bağlı açısal yer değiştirme, işle sonuçlanan eşdeğer bir doğrusal yer değiştirme verir.
İşi açısal yer değiştirme cinsinden ifade etmek ve ifadeyi çiftin anının büyüklüğü için kullanmak, çift momentine ve dönme açısına bağlı olarak yapılan son iş miktarını verir.
Çift momenti ve dönme açısı aynı anlama sahipse, çift momentinin yaptığı iş pozitiftir.
Buna karşılık, eğer tam tersi bir anlayışa sahiplerse, yapılan iş olumsuzdur.

<ol>
	<li>Hibbeler, R.C. (2016). Mühendislik Mekaniği: Statik. On Dördüncü Baskı, New Jersey: Pearson. Bölüm 11.1, s. 582.</li>
	<li>Meriam, J.L., Kraige, L.G. ve Bolton, J.N. (2016). Mühendislik Mekaniği: Statik ve Dinamik. Sekizinci Baskı, Singapur: John Wiley & Sons. Sayfa 393-394.</li>
	<li>Bira, F.P., Johnston, E.R., Mazurek, D.F., Cornwell, P.J. ve Öz, B.P. (2016). Mühendisler için Vektör Mekaniği. On Birinci Baskı, New York: McGraw-Hill Eğitimi. Bölüm 10.1A, s. 577</li>
</ol>

bir Çift momentin İşi

Work of a Couple Moment

Mekanik mühendislik, hareketin, enerjinin ve kuvvetin incelenmesini içerir ve mekanik sistemlerin tasarımı, imalatı ve bakımı ile ilgilenir. Bu alandaki önemli bir kavram çift momentidir, belirli bir mesafe ile birbirine zıt iki noktada etkili olan iki eşit ve zıt kuvvet tarafından oluşturulur.

Rijit bir cisim çiftin etkisiyle farklı bir yer değiştirme geçirdiğinde, hareketi iki bölüme ayrılabilir: iki noktanın eşit şekilde hareket ederek son pozisyonlarına ulaşması ve bunlardan biri etrafındaki dönme. Çeviri sırasında, iki kuvvet aynı miktarda yer değiştirir, ancak zıt yönlere doğru. Bu nedenle, kuvvetler tarafından yapılan iş, işaret bakımından zıt olmasına rağmen büyüklük olarak eşit olduğu için sıfır iş sonucunu verir.

Ancak dönüş sırasında, kuvvet açısal bir yer değiştirmeye neden olur ve bunun sonucunda sıfır olmayan bir iş yapılır. Dönme sırasında yapılan iş, çift momentinin büyüklüğü ile dönme açısının çarpımı olarak hesaplanabilir.

Eğer çift momenti ve dönme açısı aynı yönde ise, çift momenti tarafından yapılan iş pozitiftir. Aksine, çift momenti ve dönme açısı farklı yönlere sahipse, yapılan iş negatif olacaktır.

Bir çift momenti tarafından yapılan iş, mekanik sistemlerin tasarımında dikkate alınması gereken önemli bir faktördür. Mühendisler, dönme sırasında yapılacak işin miktarını, çift momentinin büyüklüğünü ve yönünü göz önünde bulundurarak sistemnin düzgün şekilde çalışmasını sağlar.

Bir Çift Momentin İşi

Makine mühendisliği, hareket, enerji ve kuvvet çalışmalarını içerir ve mekanik mühendisliğin tasarımı, üretimi ve bakımı ile ilgilenir.

Education

JoVE Core

Mechanical Engineering

Makine Mühendisliği

Unit 1

Ünite 1

Virtual Work

Sanal İş

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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

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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

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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

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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...

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...

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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 Makine Mühendisliği, denge, kuvvetler, kafes kiriş analizi ve yapısal mekanik gibi temel konuları kapsayan kısa, anlaşılması kolay animasyonlu videolar sunar. Gerçek dünyadaki uygulamalarını keşfedin ve bilim insanlarının önderlik ettiği deneylerle bu kavramların uygulanmasına tanık olun.

mechanical engineering

Couple Moment Work in Rotation

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