Name: free-body diagrams for force analysis
Uploaded: 2023-09-22T11:49:20.000Z
Duration: 1 min 28 s
Channel: JoVE

K12 Standards

Next Generation Science Standards

High School

Physical Science

motion-and-stability-forces-and-interactions

Motion and Stability: Forces and Interactions

HS-PS2-3

Free-body Diagram

Die visuelle Darstellung aller Kräfte, die auf das Teilchen wirken, wird als Freikörperdiagramm oder Kraftdiagramm bezeichnet. Es verwandelt komplexe Probleme in einfache Darstellungen.
In einem Freikörperdiagramm gibt die Richtung der Pfeile die Richtung der Kräfte an, während die Länge der Pfeile die Größe der Kräfte darstellt.
Stellen Sie sich einen stationären Wagen vor, auf dem zwei Kartons gestapelt sind.
Dabei kann man davon ausgehen, dass es sich bei den beiden interessierenden Systemen Kasten eins und zwei um isolierte Systeme handelt, die mit Hilfe eines Freikörperdiagramms in Form eines einfachen Umrisses oder eines Punktes dargestellt werden können.
Die Kräfte, die auf Box eins wirken, sind die Gravitationskraft, die ihr Gewicht definiert, und die ausgleichende Normalkraft aufgrund von Box zwei.
In ähnlicher Weise sind die Kräfte auf Box zwei sein eigenes Gewicht, die Normalkraft aufgrund des Wagens und das Gewicht von Box eins.
Freikörperdiagramme spielen eine integrale Rolle im Problemlösungsprozess als Übergang von einer spezifischen physikalischen Situation zu einer abstrakten mathematischen Gleichung in der Mechanik.

<ol>
	<li>Hibbeler, R.C. (2016). Technische Mechanik \u2012 Statik und Dynamik. Hoboken, New Jersey: Pearson Prentice Hall. Seite 88</li>
	<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 170-171</li>
</ol>

freikörperdiagramm

In der Mechanik ist das Verständnis der Bewegung von Objekten von entscheidender Bedeutung, und ein Werkzeug, das bei der Lösung dieses Problems hilft, ist das Freikörperdiagramm. Es handelt sich um eine einfache, aber leistungsstarke grafische Darstellung, die alle auf ein Objekt wirkenden Kräfte prägnant darstellt. Ein Freikörperdiagramm kann ein stationäres oder bewegtes Objekt darstellen und wird in der Mechanik verwendet, um die Ursache der Bewegung eines Objekts zu erklären. Ein Freikörperdiagramm verwandelt ein komplexes Problem in eine einfache Darstellung, die es ermöglicht, die entscheidenden auf ein Objekt wirkenden Kräfte zu verstehen, was zu einer mathematischen Gleichung führt. In vielen Fällen wäre es extrem schwierig, die Gleichung abzuleiten, ohne Freikörperdiagramme zu verwenden. Um ein Freikörperdiagramm zu erstellen, wählen Sie zuerst das zu untersuchende Objekt oder System aus, isolieren Sie es von seiner Umgebung und zeichnen Sie es als Punkt oder einfache Kontur. Stellen Sie dann alle wesentlichen externen Kräfte dar, die auf das Objekt oder das interessierende System einwirken, mit Pfeilen. Die Richtung der Pfeile repräsentiert die Richtung der Kraft, während die Länge der Pfeile die Stärke der Kraft darstellt. Es ist wichtig zu beachten, dass in einem Freikörperdiagramm Geschwindigkeit und Beschleunigung nicht dargestellt werden, aber aus den auf das Objekt ausgeübten Kräften abgeleitet werden können. Einige häufige Arten von Kräften, die in einem Freikörperdiagramm dargestellt werden können, sind Gewicht, Normalkraft, Spannung, Reibung und äußere Kraft. Gewicht bezieht sich auf die Schwerkraft, die auf das Objekt wirkt und normalerweise durch einen nach unten zeigenden Pfeil dargestellt wird. Die Normalkraft ist die Kraft zwischen zwei Objekten, wenn sie miteinander in Kontakt kommen. Diese Kraft wirkt in entgegengesetzter Richtung zur Gewichtskraft des Objekts. Spannung wird in der Regel durch einen Pfeil dargestellt, der vom Objekt weg in Richtung der Kraft zeigt, und Reibung ist die Kraft, die dem Gleiten zwischen Oberflächen widersteht. Schließlich bezeichnet die äußere Kraft die auf das Objekt durch einen externen Agenten ausgeübte Kraft, wie zum Beispiel ein Schub oder ein Zug. Äußere Kräfte werden durch einen Pfeil dargestellt, der in Richtung der Kraft zeigt. Betrachten Sie einen stationären Handwagen, auf dem zwei Pappkartons gestapelt sind. Die beiden interessierenden Systeme, Kasten eins und Kasten zwei, können als abgeschlossene Systeme betrachtet werden und lassen sich mithilfe eines Freikörperdiagramms darstellen. Die Kräfte, die auf Kasten eins wirken, sind die Gewichtskraft, die sein Gewicht definiert, und die gegenwirkende Normalkraft aufgrund von Kasten zwei. Ähnlich verhält es sich mit den Kräften auf Kasten zwei: seinem Gewicht, der Normalkraft aufgrund des Handwagens und dem Gewicht von Kasten eins.

Freikörperdiagramm

In der Mechanik ist es wichtig, die Bewegung von Objekten zu verstehen, und ein Werkzeug, das hilft, dieses Problem zu lösen, ist das Freikörperdiagramm. Es ist ein einfaches, aber ...

Education

Lehre

JoVE Core

Mechanical Engineering

Maschinenbau

Unit 1

Einheit 1

Equilibrium of a Particle

Gleichgewicht eines Teilchens

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

free-body diagrams for force analysis

Free-body diagrams help analyze the forces acting on an object in mechanics. They give a simple picture of a stationary or moving object and show why it moves the way it does. By turning a complex situation into a clear sketch, they make it easier to write the equation needed to solve the problem.

To draw a free-body diagram, first choose the object or system you want to study. Then isolate it from its surroundings and draw it as a dot or a simple outline. Add arrows for every important external force. The direction of each arrow shows the direction of the force, and the length shows its size.

A free-body diagram does not show velocity or acceleration. Those quantities are not drawn on the diagram, but they can be inferred from the forces acting on the object. Common forces include weight, normal force, tension, friction, and applied force. Weight is the force of gravity and is usually shown with an arrow pointing downward.

Normal force is the contact force between two objects touching each other. It acts in the direction opposite to the object's weight in many situations. Tension is usually drawn as an arrow away from the object and along the direction of the pull. Friction resists sliding between surfaces. Applied force is an outside push or pull, and it is shown with an arrow in the direction of that force.

A stationary trolley with two cardboard boxes stacked on it gives a clear example. Box one and box two can each be treated as separate isolated systems and shown with their own free-body diagrams. For box one, the forces are gravitational force and the balancing normal force from box two. For box two, the forces are its weight, the normal force from the trolley, and the weight of box one.

Free-Body Diagrams for Force Analysis

equilibrium conditions for a particle

Balanced Forces and Torque in Equilibrium

Equilibrium depends on balanced forces and balanced torque. An object in equilibrium is either at rest or moving with a constant velocity. These two cases are called static equilibrium and dynamic equilibrium. Static equilibrium means the object is not moving. Dynamic equilibrium means the object is moving, but its velocity stays constant. In both cases, the forces acting on the object must balance each other. Different forces can add, subtract, or cancel each other out. When the vector sum...

free-body diagram

Free-body diagrams help analyze the forces acting on an object in mechanics. They give a simple picture of a stationary or moving object and show why it moves the way it does. By turning a complex situation into a clear sketch, they make it easier to write the equation needed to solve the problem. To draw a free-body diagram, first choose the object or system you want to study. Then isolate it from its surroundings and draw it as a dot or a simple outline. Add arrows for every important...

steps for free-body diagram

Free-Body Diagram for Two-Block Motion

A free-body diagram helps analyze two-block motion in mechanics. It shows the forces acting on a system so the net force can be found and the acceleration can be calculated. The example in this lesson uses two blocks linked by a massless string over a frictionless pulley. Block 1 moves across a table while block 2 falls under gravity. The two blocks are treated as one isolated system. External forces are then identified and drawn as vector arrows on the diagram. For block 1, the forces...

free-body diagrams: problem solving

Free-Body Diagrams on Inclined Planes

Free-body diagrams help show the forces acting on an object on an inclined plane. A free-body diagram is a simple drawing that focuses only on the object or system being studied. It leaves out extra details so the force problem is easier to analyze and solve. For an example, a 10 kg block is released on a ramp that is 30° to the horizontal. The coefficient of friction is 0.2. The diagram for this block includes the weight from gravity, the normal force, and the frictional force. These are the...

coplanar forces

Resolving Coplanar Force Components

Coplanar forces act on an object in the same plane. To analyze this kind of system, each force is resolved into x and y components using Cartesian vector form and vector algebra. This makes it possible to test whether the object is in equilibrium. A coplanar system is in equilibrium when the resultant force is zero. That means the sum of the forces in each direction must also be zero. If the forces do not balance, the object is not in equilibrium and will accelerate in the direction of the net...

categories of equilibrium

Types of Equilibrium in Forces

Equilibrium in physics describes how forces act on a body so it stays still or moves at a constant speed. In two-dimensional force systems, equilibrium can be grouped into several categories based on how the forces are arranged. Collinear equilibrium is the simplest case. The forces act along one straight line, so only one force equation is needed in the direction of those forces. The other equations are already satisfied. Coplanar concurrent equilibrium is another category. In this case, all...

key terms and concepts

Learn how free-body diagrams show weight, normal force, tension, friction, and applied force. See how isolating an object simplifies force analysis in mechanics.

Free-Body Diagrams for Force 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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HS-PS2-6

Free-Body Diagrams for Force Analysis

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