Name: resolving coplanar force components
Uploaded: 2025-05-22T09:06:02.000Z
Duration: 1 min 25 s
Channel: JoVE

Consider an object on which multiple forces act. When the lines of action of these forces lie within the same plane, the system is known as a coplanar force system.
All these forces can be resolved into their respective components using cartesian vector form.
A coplanar system will be in equilibrium if each component of the resultant force equals zero and the resultant force on the system is zero. These are called equations of equilibrium for a coplanar force system.
Consider a box in equilibrium held by three strings. The system is said to be a coplanar force system because the forces act in a single plane.
Two strings make an angle Theta with the plank. The tension force in these two strings is known.
The magnitude of the tension force in the third string can be determined by applying the equilibrium equations. Resolving the known tension forces into its components show that the horizontal components counterbalance each other.
Now, the tension in the third string can be determined by rearranging the equation for vertical components.

coplanaire krachten

Beschouw een object waarop meerdere krachten werken. Als de werklijnen van elke kracht binnen hetzelfde vlak liggen, kan het systeem als coplanaire worden beschouwd. De cartesiaanse vectorvorm kan worden gebruikt om elke kracht op te lossen in zijn respectievelijke componenten. Voor een coplanaire systeem is het systeem in evenwicht als elke component van de resultante kracht nul is en de resultante kracht op het systeem ook nul is. Als de som van de krachten niet gelijk is aan nul, dan zal het object niet in evenwicht zijn en zal het versnellen in de richting van de nettokracht. Om problemen op te lossen die coplanair krachten en evenwicht betreffen, moeten alle krachten die op het object werken, samen met hun magnitudes en richtingen, geïdentificeerd worden. Deze krachten kunnen dan worden opgelost in hun x- en y-componenten met behulp van vectoralgebra. De evenwichtsvergelijkingen worden gebruikt om de onbekende krachten te berekenen en te controleren of het object in evenwicht is of niet. Beschouw een doos in een toestand van evenwicht die wordt opgehangen door drie touwen zoals getoond in de figuur <img alt="Equation 1" src="/files/ftp_upload/14244/14244_PT_Fig_1v2.svg" style="text-align: center; height: 350px;"> Dit is een coplanaire systeem omdat de krachten in een enkel vlak werken. Twee van de diagonale touwen, verbonden met het platform, hebben gelijke hoeken met het platform, en de spanning in deze twee touwen is bekend. Om de grootte van de spanning in het derde verticale touw te bepalen, kunnen de evenwichtsvergelijkingen worden toegepast. Het oplossen van de bekende spanningen van de twee touwen in hun componenten laat zien dat de horizontale componenten elkaar in evenwicht houden. Daarom kan de spanning in het derde touw worden bepaald door de vergelijking voor de verticale componenten te herschikken. Als de spanning in het derde touw eenmaal is bepaald, kunnen de evenwichtsvergelijkingen worden gebruikt om te controleren of het systeem inderdaad in een evenwichtstoestand is.

Coplanaire krachten

Consider an object upon which multiple forces are acting. If the lines of action of each force lie within the same plane, the system can be considered ...

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JoVE Core

Mechanical Engineering

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Unit 1

Equilibrium of a Particle

Evenwicht van een deeltje

KEY TERMS AND CONCEPTS

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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 force.

Solving these problems starts with identifying every force on the object, including its size and direction. The known forces are then broken into horizontal and vertical parts. The equations of equilibrium are used to find unknown forces and to check whether the system is balanced.

One example is a box suspended by three strings in equilibrium. The two diagonal strings make equal angles with the plank, and their tensions are known. Their horizontal components cancel each other, so the third vertical string can be found from the vertical component equation. After the tension is calculated, the equilibrium equations can confirm that the box is still in balance.

Resolving Coplanar Force Components

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 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...

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

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 coplanar forces are split into x and y components, how equilibrium is tested, and how string tension is found in a three-string system.

Resolving Coplanar Force Components | 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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Resolving Coplanar Force Components

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