Name: force, motion, and mechanical effects
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 25 s
Channel: JoVE

Wenn ein Mann an einer Kiste zieht oder sie schiebt, bewegt sie sich in horizontaler Richtung. Der Zug oder Druck, der auf die Box ausgeübt wird und zu ihrer Bewegung führt, wird als Kraft bezeichnet. Es handelt sich um eine Vektorgröße, die in Newton ausgedrückt wird.
Kräfte, die auf Körper wirken, können als äußere und innere Kräfte kategorisiert werden. Wenn die Kraft, die von außen auf einen Körper ausgeübt wird, eine Wirkung erzeugt, wird sie als äußere Kraft bezeichnet, während die im Körper vorhandenen Reaktionskräfte als innere Kräfte bezeichnet werden.
Das Prinzip der Übertragbarkeit besagt, dass, wenn sich der Punkt einer Krafteinwirkung auf einen Körper ändert, aber in der gleichen Wirkungsrichtung bleibt, sich die resultierende Kraft auf den Körper nicht ändert.
Stellen Sie sich zwei Kräfte vor, die auf einen starren Körper wirken. Nach dem Prinzip der Übertragbarkeit bleibt der Körper unverändert, wenn die auf den Körper wirkenden Kräfte in der gleichen Wirkungsrichtung wirken, auch wenn sie an unterschiedlichen Punkten wirken.
Da diese Kräfte gleich und entgegengesetzt sind, ist ihre Summe gleich Null, und die resultierende Kraft auf den Körper bleibt unverändert.

<ol>
	<li>Meriam, J.L., Kraige, L.G., Bolton, J.N. (2018). Technische Mechanik \u2012 Statik, New Jersey: John Wiley & Sons. S. 23-24.</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. S. 85 \u2012 86.</li>
</ol>

einführung in die kraft

Betrachten Sie Wasser, das aus einer Düse auf ein Turbinenblatt strömt. Wenn das Wasser auf das Turbinenblatt trifft, wirkt es eine Kraft aus, die es in Richtung des Flusses bewegt. Kraft ist ein Einfluss, der die Bewegung, Form oder Ausrichtung eines Objekts verändert. Kräfte können durch physischen Kontakt, wie Druck oder Zug, oder durch nicht-kontaktive Wechselwirkungen wie magnetische oder gravitationelle Kräfte verursacht werden. Kraft ist eine Vektorgröße mit sowohl Betrag als auch Richtung und wird im SI-Einheitensystem in Newton (N) gemessen. Betrachten Sie ein Objekt mit einer Masse von 1 kg, das sich mit einer Beschleunigung von 1m/s2 nach vorne bewegt. In diesem Fall beträgt die auf das Objekt ausgeübte Kraft 1 N. In der Mechanik gibt es zwei Arten von Kräften, die auf einen starren Körper einwirken: externe Kräfte und interne Kräfte. Diese verursachen externe und interne Effekte. Die externen Effekte sind die Reaktionskräfte, die der Körper auf seine Umgebung ausübt, aufgrund externer Kräfte wie dem Körpergewicht, von Menschen ausgeübte Kräfte und Reibungskräfte. Die internen Effekte sind die internen Kräfte und Verformungen, die im Material des Körpers auftreten. Nehmen Sie als Beispiel eine Halterung, die einer externen Kraft ausgesetzt ist. Die externen Effekte dieser Kraft auf die Halterung sind die Reaktionskräfte, die das Fundament und die Bolzen auf die Halterung ausüben. Die internen Effekte dieser Kraft auf die Halterung sind die daraus resultierenden internen Spannungen und Verformungen im Material der Halterung. Diese internen Kräfte und Verformungen verteilen sich im Material der Halterung und hängen von den Materialeigenschaften und Geometrien des Körpers ab. Das Transmissibilitäts-Prinzip ist ein Konzept, das die Effekte erklärt, wenn der Angriffspunkt einer angewendeten Kraft entlang der gleichen Wirkungslinie bewegt wird. Es besagt, dass sich die resultierende Kraft, die auf einen starren Körper wirkt, nicht ändert, wenn eine Kraft auf den Körper angewendet wird und der Angriffspunkt dieser Kraft sich entlang der gleichen Wirkungslinie ändert, aber in derselben Linie bleibt. Betrachten Sie zwei gleiche Kräfte, die auf einen starren Körper von verschiedenen Punkten aus wirken. Gemäß dem Transmissibilitäts-Prinzip sind die auf den Körper wirkenden Kräfte in derselben Wirkungslinie, was sie zu einer einzelnen Kraft an einem bestimmten Punkt äquivalent macht. Wenn der Angriffspunkt dieser Kräfte verändert wird oder sich entlang der gleichen Wirkungslinie bewegt, bleibt die resultierende Kraft auf den Körper gleich, da es sich um dieselbe Kraft handelt, die entlang derselben Wirkungslinie wirkt.

Einführung in die Kraft

Stellen Sie sich vor, Wasser fließt von einer Düse zu einer Turbinenschaufel. Wenn das Wasser auf die Turbinenschaufel trifft, übt es eine Kraft aus, die sie dazu bringt, sich entlang der Strömung des Turbinenflügels zu bewegen.

Education

Lehre

JoVE Core

Mechanical Engineering

Maschinenbau

Unit 1

Einheit 1

Force Vectors

Kraftvektoren

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

Introduction to force

force, motion, and mechanical effects

Force changes the motion, shape, or orientation of an object. A flowing stream of water can push on a turbine vane and make it move in the direction of the flow. In mechanics, force is treated as a vector quantity, which means it has both magnitude and direction. It is measured in newtons, or N, in the SI unit system.

Forces can act through direct contact or without contact. A push or pull is a contact force. Magnetic and gravitational forces are examples of non-contact interactions. For an object with a mass of 1 kg that accelerates at 1 m/s2, the applied force is 1 N.

When a rigid body is under load, mechanics separates the effects into external forces and internal forces. External forces produce the reactive forces that the body exerts on its surroundings. These can include body weight, forces applied by people, and frictional forces. Internal effects are the stresses and deformations that develop inside the material.

A bracket loaded by an external force shows both kinds of effects. The foundation and bolts react to the force on the bracket. At the same time, internal stresses and deformations spread through the bracket material. These internal forces depend on the material properties and the shape of the body.

The principle of transmissibility explains what happens when the point of application of a force moves along the same line of action. If the force stays on that line, the resultant force on a rigid body does not change. Two equal forces on a rigid body can therefore be treated as a single equivalent force when they act along the same line of action.

Force, Motion, and Mechanical Effects

scalar and vectors

Scalar vs Vector Quantities in Mechanics

Scalar and vector quantities are two main ways to describe physical quantities in mechanics. Common examples include force, speed, velocity, and work. Some of these are scalars, and others are vectors. A scalar is a quantity that has magnitude only. It does not need direction. Mass, area, and length are examples of scalar quantities. Scalars with the same units can be added or subtracted like ordinary numbers. A class that ends 10 min earlier than 50 min lasts 50 min minus 10 min, which is 40...

vector operations

Adding and Multiplying Vectors

Vectors are quantities with both magnitude and direction, and their operations include addition, subtraction, and scalar multiplication. Scalar multiplication means a vector is multiplied by a scalar value, which creates a new vector with a different magnitude. If the scalar is positive, the direction stays the same. If the scalar is negative, the direction reverses. A common example is momentum, which comes from multiplying mass by velocity. In this case, mass is the scalar quantity and...

introduction to force

Force changes the motion, shape, or orientation of an object. A flowing stream of water can push on a turbine vane and make it move in the direction of the flow. In mechanics, force is treated as a vector quantity, which means it has both magnitude and direction. It is measured in newtons, or N, in the SI unit system. Forces can act through direct contact or without contact. A push or pull is a contact force. Magnetic and gravitational forces are examples of non-contact interactions. For an...

force classification

Types of Forces in Physics

Forces in physics can be grouped by how they act and where they come from. These groups help describe motion, behavior, and equilibrium in the physical world. They are also useful in physics and engineering. One common way to classify forces is by whether they need contact. Contact forces act only when two objects touch. Frictional force, tension, and normal force are all contact forces that come from surface contact. Forces can also act without physical touch. These are called non-contact...

vector addition of forces

Resultant Force from Tugboats

Resultant force can be found with vector addition when two or more forces act on the same object. This idea helps explain how multiple pulls combine to create one net force. It is a key tool for understanding motion in physics. A clear example is a ship pulled by two small tugboats. The forces, F1 and F2, act at the same time but in different directions. The net force on the ship is the vector sum of those two forces. The parallelogram law gives a geometric way to add vectors. In this method,...

two-dimensional force system

Resolving Forces in a Plane

Resolving forces in a plane is a key part of two-dimensional mechanical analysis. A force vector can be split into x- and y-components, which show how the force acts in each direction. These components are written with the help of unit vectors, one for the x direction and one for the y direction. To find the components in a Cartesian coordinate system, first identify the angle theta between the force and the positive x-axis. If the line of action passes through the origin, basic trigonometry...

two-dimensional force system: problem solving

two-dimensional-force-system-problem-solving

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...

scalar notation

Vector Components for Force Calculations

Scalar notation helps simplify vector calculations by breaking a vector into separate x and y parts. When vectors are added or subtracted, each component can be handled on its own using scalar notation. This makes force problems easier to solve.

cartesian vector notation

Vector Components in 3D Space

Cartesian vector notation shows how to write vectors in three-dimensional space using x, y, and z components. It gives a clear way to represent direction and size for quantities used in mechanical engineering. The notation uses the unit vectors i, j, and k for the x, y, and z axes. A vector pointing in the direction (3, −4, 5) can be written as A = 3i - 4j + 5k. The unit vectors are i = (1, 0, 0), j = (0, 1, 0), and k = (0, 0, 1). This form is useful for describing displacement, velocity,...

direction cosines of a vector

Vector Orientation with Direction Cosines

Direction cosines describe how a vector is oriented relative to the x, y, and z axes. For a vector A written in Cartesian form with i, j, and k unit vectors, this idea helps connect the vector’s components to its direction in space. The magnitude of vector A is the square root of the sum of the squares of its components. Its direction is described by the coordinate direction angles α, β, and γ with the x, y, and z axes. These angles can be found by projecting vector A onto each axis. The...

three-dimensional force system

Force Components in 3D Space

A three-dimensional force system describes forces acting in x, y, and z directions. In mechanical engineering, this framework helps students and engineers study how objects and structures behave in three-dimensional space. One common example is a force acting on a particle in space. That force can be split into three parts: the x-component, the y-component, and the z-component. Vector mathematics is used to calculate each component, and together they make up the full three-dimensional force...

three-dimensional force system:problem solving

three-dimensional-force-systemproblem-solving

Resolving Forces in 3D Coordinates

Three-dimensional force systems involve forces acting in three different directions at the same time. These problems are common in physics and engineering. They are used to find the resultant force, which helps predict or analyze how an object or structure will behave. The first step is to resolve each force into scalar components. A scalar component is the amount of force along one axis. Trigonometric functions and vector addition are used to break the force into parts and then combine those...

position vectors

Using Position Vectors to Locate Points

Position vectors are used to locate points in space and show the direction and distance between two points. In math and science, they help describe spatial relationships and make calculations easier. A position vector can connect one point to another point or show a point’s location relative to the origin of coordinates. For a point P(x, y, z) relative to the origin O, the position vector r runs from O to P. In Cartesian vector form, it is written as r = x i + y j + z k. Here, i, j, and k are...

force vector along a line

Finding a Cable Force from Two Points

A cable force can be found from the two points that define its line of action. In three-dimensional statics, this setup often appears with a pole and a cable anchored to the ground. The cable ends are labeled A and B, and their position vectors are written as P_A and P_B. The position vector from A to B is found using the triangle law of vector addition. First, subtract P_A from P_B to get P_AB. Then find the magnitude of P_AB by taking the square root of the sum of the squares of its...

dot product

Using Dot Product to Find Work and Angle

The dot product connects vectors, work, and direction in mathematics and physics. In engineering, it is found by multiplying the magnitudes of two vectors and the cosine of the angle between them. It is shown with a dot symbol between the vectors. A real-world example is a vehicle pulling an object along the ground with a rope. If the rope is angled above the horizontal axis, the work done can be calculated with the dot product of the applied force and the object’s displacement. This makes the...

dot product: problem solving

Using the Dot Product to Solve Vector Questions

The dot product helps solve vector questions by combining vector size and the cosine of the angle between them. It is useful when the angle is measured anti-clockwise and when a problem asks for a vector relationship in component form. A good first step is to identify the question being asked. Then list the given vectors and write them in Cartesian form, also called component form. This makes the data easier to use in a calculation. Next, decide whether the dot product is the right operation.

cross product

Cross Product Direction and Magnitude

The cross product is a vector operation in vector algebra that creates a third vector from two input vectors. Unlike the scalar product, it does not give a single number. The result is a vector perpendicular to both original vectors. The size, or magnitude, of the cross product depends on the magnitudes of both vectors and the sine of the angle between them. A larger angle between the vectors gives a larger cross product magnitude. The direction is found with the right-hand rule. If the...

key terms and concepts

Learn how force changes motion, shape, and orientation, plus the difference between contact and non-contact forces, internal effects, and transmissibility.

Force, Motion, and Mechanical Effects | 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

Force, Motion, and Mechanical Effects

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