Name: couple moment in force systems
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 29 s
Channel: JoVE

Para to para równoległych sił o równych wielkościach, ale działających w przeciwnych kierunkach, oddzielonych prostopadłą odległością.
Para powoduje siłę obrotową, która obraca ciało wokół osi prostopadłej do płaszczyzny sił, a wynikowy moment jest znany jako moment pary.
Rozważ dokręcenie za pomocą klucza oczkowego. Para sił powstaje, gdy dwie równe i przeciwstawne siły są przyłożone do klucza w punktach A i B, oddzielonych prostopadłą odległością.
Wektory położenia rA i rB są kierowane od początku układu współrzędnych do punktów zastosowania.
Moment pary wokół początku układu współrzędnych jest sumą iloczynu wektorów położenia i sił.
Różnica między wektorami położenia rA i rB to wektor położenia r, który jest odległością między dwiema przeciwstawnymi siłami.
Moment pary zależy tylko od wektora położenia r między siłami, a nie od wektorów położenia rA i rB. Jest więc uważany za darmowy wektor.

<ol>
	<li>Hibbeler, R.C. (2016). Mechanika inżynierska \u2012 Statyka i dynamika. Hoboken, New Jersey: Pearson Prentice Hall. Strona 154</li>
	<li>Piwo, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, PJ i Self, BP (2019). Mechanika wektorowa dla inżynierów \u2012 Statyka i dynamika. Nowy Jork: McGraw-Hill. Strony – 120.</li>
</ol>

para sił

Para sił to dwie siły równoległe, o tej samej wartości, ale o przeciwnych kierunkach. Siły są oddzielone od siebie przez odległość prostopadłą, znaną jako ramię pary. Para sił wywołuje moment obrotowy, który obraca ciało wokół osi prostopadłej do płaszczyzny sił. Otrzymany moment nazywa się momentem pary. Jednostką SI momentu pary jest niutonometr (N-m).

Typowym przykładem do zrozumienia tego konceptu jest dokręcanie śruby kluczem płaskim. Para sił powstaje, gdy dwie równe i przeciwległe siły są przyłożone do klucza w punktach A i B oddalonych od siebie o odległość prostopadłą. Odpowiednie wektory położenia skierowane są od początku układu współrzędnych do punktu przyłożenia. Moment pary względem początku układu jest sumą iloczynu wektorowego wektorów położenia i sił. Różnica między wektorami położenia dla obu przeciwnych sił daje wektor położenia r, który jest odległością między siłami przeciwnymi.

Co ciekawe, moment pary sił zależy tylko od wektora położenia r między siłami, a nie od indywidualnych wektorów położenia dla obu sił. Wektor położenia r jest niezależny od początku układu współrzędnych. Oznacza to, że obliczanie momentów tych samych sił względem różnych punktów prowadzi do tego samego wyniku. Moment pary sił jest wektorem swobodnym. W przeciwieństwie do momentu pary sił, moment siły zależy od położenia, w którym jest mierzony. Jeśli dwie pary sił powodują moment o równych wartościach i kierunkach, to te dwie pary sił są równoważne. Równoważne pary sił mają równy moment obrotowy bez względu na swoje położenie, kierunki lub wartości.

Obliczanie momentu pary sił i zrozumienie jego efektów jest kluczowe przy projektowaniu stabilnych i wytrzymałych systemów, które mogą wytrzymać zewnętrzne siły.

Para sił

Para to para równoległych sił o równej wielkości, ale w przeciwnych kierunkach. Siły są oddzielone prostopadłą odległością, znaną jako ...

Education

JoVE Core

Mechanical Engineering

Inżynieria mechaniczna

Unit 1

Jednostka 1

Force System Resultants

wypadkowe układu sił

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

Couple

couple moment in force systems

A couple is a pair of parallel forces that are equal in magnitude and opposite in direction. The two forces are separated by a perpendicular distance called the couple arm. Together, they create a turning effect on a body instead of a net push.

This turning effect is called the couple moment. It rotates the body about an axis that is perpendicular to the plane of the forces. The SI unit for a couple moment is the Newton-meter (N-m).

A common example is tightening a bolt with a lug wrench. In that case, two equal and opposite forces act at points A and B on the wrench. These points are separated by a perpendicular distance, so they form a force couple.

The couple moment about the origin is found by adding the cross products of the position vectors and the forces. The position vector between the two opposing forces is r, which is the distance between them. The couple moment depends only on this vector r, not on the separate position vectors of the forces.

Because r does not depend on the origin, the same couple moment is obtained even if the moments are taken about a different point. This is why a couple moment is a free vector. A moment of a single force is different because it depends on where it is measured.

If two couples create moments with the same magnitude and direction, they are equivalent couples. Equivalent couples have the same torque, or turning effect, even if their positions, directions, or magnitudes differ. Understanding couple moments helps in designing stable systems that can resist external forces.

Couple Moment in Force Systems

moment of a force: scalar formulation

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cartesian form for vector formulation

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resultant moment: vector formulation

Calculating Torque from Multiple Forces

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principle of moments

Resolving Forces in Moment Calculations

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principle of moments: problem solving

Torque About an Axis in 3D Systems

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moment of a force about an axis: scalar

Bicycle Torque and Moment About an Axis

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moment of a force about an axis: vector

Torque on a Bicycle Wheel: Vector Method

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couple

A couple is a pair of parallel forces that are equal in magnitude and opposite in direction. The two forces are separated by a perpendicular distance called the couple arm. Together, they create a turning effect on a body instead of a net push. This turning effect is called the couple moment. It rotates the body about an axis that is perpendicular to the plane of the forces. The SI unit for a couple moment is the Newton-meter (N-m). A common example is tightening a bolt with a lug wrench. In...

couples: scalar and vector formulation

Couple Moments and the Right-Hand Rule

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equivalent couples

Equivalent Couples in Mechanical Systems

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moment of a couple: problem solving

Torque from a Couple: Solving Forces

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system of forces and couples

Equivalent Force and Moment Systems

Structural systems often experience several forces and couple moments at the same time. Engineers simplify these loading cases by replacing them with an equivalent force and moment system at a chosen point O. This makes the analysis easier while keeping the same external effects on the member. A key idea in this process is the principle of transmissibility. A force is a sliding vector, which means it can be moved anywhere along its line of action without changing how the body behaves...

simplification of a force and couple system i

simplification-of-a-force-and-couple-system-i

Resultant Forces in Force and Couple Systems

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simplification of a force and couple system: ii

simplification-of-a-force-and-couple-system-ii

Resultant Force and Wrench Motion

Resultant force and resultant couple moment describe how several forces and moments act together on a rigid body in three dimensions. When many forces act on an object, they can be replaced by one equivalent force. The moments from those forces can also be combined into one equivalent couple moment. In some cases, the resultant force and the resultant couple moment are not mutually perpendicular. That means the angle between them is not 90 degrees. To study this situation, the couple moment is...

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key terms and concepts

Learn how a couple creates rotation, why couple moment depends on the distance between forces, and how equivalent couples are identified in force systems.

Couple Moment in Force Systems | JoVE K12

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mechanical engineering

Couple Moment in Force Systems

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