Name: two-dimensional forces: free-body analysis
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 29 s
Channel: JoVE

Stellen Sie sich einen Wischer vor, der in einem zweidimensionalen System in einem Winkel von 25 Grad zur Grundlinie "s" geneigt ist. Eine Kraft, die auf den Griff wirkt, der zur Mitte des Wischers geschwenkt ist, bildet einen Winkel von 20 Grad mit der Referenzlinie 'c', die parallel zur Grundlinie 's' verläuft.
Wenn die Kraftkomponente entlang der a-Achse 65 Newton beträgt, bestimmen Sie die Größe der Kraft und ihre Komponente entlang der b-Achse.
Hier wird unter Berücksichtigung alternativer Winkel coa' zu 25 Grad, während der Winkel Foc 20 Grad beträgt. Der Winkel, den der Kraftvektor mit der a-Achse bildet, wird also durch Addition der beiden Winkel bestimmt und ist gleich 45 Grad.
Da die Kraftkomponente entlang der a-Achse bekannt ist, wird die Größe einer Kraft durch das Verhältnis der a-Komponente der Kraft zum Kosinus von 45 Grad geschätzt.
Nun wird die b-Komponente der Kraft als Produkt aus der Größe der Kraft und dem Sinus von 45 Grad ausgedrückt. Sie ist negativ, da sie sich entlang der negativen b-Achse befindet.

<ol>
	<li>Bier, F.P.; Johnston, E.R.; Mazurek, D.F.; Cromwell, P.J. und Self, B.P. (2019). Vektormechanik für Ingenieure \u2012 Statik und Dynamik. New York: McGraw-Hill. Seiten 29-33</li>
	<li>Hibbeler, R.C. (2016). Technische Mechanik \u2012 Statik und Dynamik. Hoboken, New Jersey: Pearson Prentice Hall. S. 33 \u2012 35.</li>
</ol>

zweidimensionales kraftsystem: problemlösung

Das Lösen von Problemen im Zusammenhang mit zweidimensionalen Kraftsystemen ist ein wesentlicher Aspekt der Mechanik und des Ingenieurwesens. Durch die Anwendung der Prinzipien der Vektoranalyse und des Kräftegleichgewichts kann man die Auswirkungen mehrerer Kräfte auf einen Gegenstand in einem zweidimensionalen Raum bestimmen. Der erste Schritt zur Lösung eines Problems mit einem zweidimensionalen Kraftsystem besteht darin, ein Freikörperdiagramm des zu betrachtenden Objekts zu zeichnen. Dieses Diagramm hilft dabei, alle externen Kräfte zu identifizieren, die auf den Gegenstand wirken, einschließlich ihrer Größen, Richtungen und Angriffspunkte. Als Nächstes müssen die Kräfte mithilfe der Prinzipien der Vektoranalyse in ihre Komponenten in den Richtungen x und y aufgelöst werden. Dieser Schritt hilft dabei, die gegebenen Kräfte in ihre kartesische Vektorform umzuwandeln, was eine einfache Darstellung und Analyse ermöglicht. Die Komponenten können mithilfe trigonometrischer Funktionen, wie dem Sinus und dem Kosinus der gegebenen Winkel, aufgelöst werden. Nach der Aufteilung der Kräfte in Komponenten besteht der nächste Schritt darin, die resultierende Kraft in jeder Richtung zu bestimmen. Dies wird erreicht, indem alle Kräfte in jeder Richtung addiert werden. Anschließend wird die resultierende Kraft und ihre Richtung mithilfe des Satzes des Pythagoras und der Trigonometrie bestimmt. Wenn die resultierende Kraft Null ist, befindet sich der Gegenstand im Gleichgewicht und beschleunigt nicht. Wenn die resultierende Kraft ungleich Null ist, beschleunigt der Gegenstand in Richtung der resultierenden Kraft. Das Prinzip des Kräftegleichgewichts besagt, dass die Summe aller externen Kräfte, die auf das Element wirken, in beiden Richtungen x und y gleich Null sein muss. Dies ermöglicht es uns, die unbekannten Kräfte zu bestimmen, die auf den Gegenstand wirken, wie Spannung oder Druck in einem Bauteil. In einigen Fällen wird auch das Momentengleichgewichtsprinzip verwendet, um die Auswirkungen externer Kräfte auf den Gegenstand zu bestimmen. Dieses Prinzip besagt, dass die Summe aller externen Momente, die auf das Element wirken, gleich Null sein muss. Dieser Schritt hilft dabei, die Werte und Richtungen der Momente zu bestimmen, die auf den Gegenstand wirken.

Zweidimensionales Kraftsystem: Problemlösung

Die Lösung von Problemen im Zusammenhang mit zweidimensionalen Kraftsystemen ist ein wesentlicher Aspekt der Mechanik und des Ingenieurwesens. Durch die Anwendung der Prinzipien des Vektors ...

two-dimensional-force-system-problem-solving

Education

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JoVE Core

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two-dimensional forces: free-body analysis

Two-dimensional force analysis starts with a free-body diagram. A free-body diagram shows the object and every external force acting on it. It includes each force’s size, direction, and point of application.

After the diagram is drawn, each force is broken into x- and y-components. This uses vector analysis and trigonometry, especially sine and cosine. The forces can then be written in Cartesian vector form, which makes them easier to work with.

Next, the components in each direction are added to find the net force in x and y. The resultant force is then found with the Pythagorean theorem and trigonometry. If the net force is zero, the object is in equilibrium and does not accelerate. If the net force is not zero, the object accelerates in the direction of the net force.

Force equilibrium means the sum of external forces is zero in both the x and y directions. This helps solve for unknown forces such as tension or compression in a member. In some problems, moment equilibrium is also used. Moment equilibrium means the sum of external moments is zero, which helps determine the size and direction of moments acting on the object.

Two-Dimensional Forces: Free-Body Analysis

two-dimensional-forces-free-body-analysis

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two-dimensional force system: problem solving

Two-dimensional force analysis starts with a free-body diagram. A free-body diagram shows the object and every external force acting on it. It includes each force’s size, direction, and point of application. After the diagram is drawn, each force is broken into x- and y-components. This uses vector analysis and trigonometry, especially sine and cosine. The forces can then be written in Cartesian vector form, which makes them easier to work with. Next, the components in each direction are...

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key terms and concepts

Learn how to use free-body diagrams, force components, and equilibrium to solve two-dimensional force problems and find resultant forces and moments.

Two-Dimensional Forces: Free-Body Analysis | 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.

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Two-Dimensional Forces: Free-Body Analysis

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