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.

coplanar forces

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 coplanar. The Cartesian vector form can be used to resolve each force into its respective components. For a coplanar system, the system will be in equilibrium if each component of the resultant force equals zero and the resultant force on the system is zero. If the sum of the forces is not equal to zero, then the object will not be in equilibrium and will accelerate in the direction of the net force.
To solve problems involving coplanar forces and equilibrium, all the forces acting on the object, along with their magnitudes and directions, must be identified. These forces can then be resolved into their x and y components using vector algebra. The equations of equilibrium are used to calculate the unknown forces and check whether the object is in equilibrium or not.
Consider a box in a state of equilibrium suspended by three strings as shown in the figure
<img alt="Static equilibrium diagram; forces F1, F2, F3 at angles θ; vector components; physics concept." src="/files/ftp_upload/14244/14244_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" data-altupdatedat="1754904545000" data-alt="Static equilibrium concept; force diagram with ΣF=0, pulley system, crate suspended by cables.">
This is a coplanar system because the forces are acting in a single plane. Two of the diagonal strings, connected to the plank, have equal angles with the plank, and the tension force in these two strings is known. In order to determine the magnitude of the tension force in the third vertical string, the equilibrium equations can be applied. Resolving the known tension forces of the two strings into their components shows that the horizontal components counterbalance each other. Therefore, the tension in the third string can be determined by rearranging the equation for the vertical components. Once the tension in the third string has been determined, the equilibrium equations can be used to check that the system is, indeed, in a state of equilibrium.

Coplanar Forces

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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Mechanical Engineering

Unit 1

Equilibrium of a Particle

KEY TERMS AND CONCEPTS

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

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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

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steps for free-body diagram

Free-Body Diagram for Two-Block Motion

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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

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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

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Resolving Coplanar Force Components

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