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

考虑一个受到多个力作用的物体。当这些力的作用线位于同一平面内时，该系统称为共面力系。
所有这些力都可以用笛卡尔矢量形式分解为各自的分量。
当共面力系的合力在各个方向上的分量均为零，且作用在该系统上的合力为零时，该共面力系将处于平衡状态。这些条件称为共面力系的平衡方程。
考虑一个由三根绳子悬挂并处于平衡状态的箱子。由于这些力作用于同一平面内，该系统被称为共面力系。
两根绳子与木板成 Theta 角。这两根绳子中的张力已知。
通过应用平衡方程可以确定第三根绳子中张力的大小。将已知的张力分解为分量后可知，水平分量相互平衡。
现在，可以通过重新整理垂直分量的方程来确定第三根绳子中的张力。

<ol>
	<li>希伯勒，RC（2016 年）。工程力学 \u2012 静力学和动力学。新泽西州霍博肯:Pearson Prentice Hall。第 91-92 页</li>
	<li>梅里亚姆，JL;Kraige， LG 和 Bolton， JN （2020）。工程力学 \u2012 静力学。新泽西州霍博肯:约翰·威利。第 58 页</li>
</ol>

共面力

思考作用在物体上的多个力。如果每个力的作用线都在同一个平面内，那么该系统能够被认为是共面的。可以使用笛卡尔向量的形式将每个力分解为它们各自的分量。对于共面系统来说，如果合力的每个分量都等于零并且系统上的合力为零，那么系统将处于平衡状态。如果合力的值不等于零，那么物体将不会处于平衡状态，并且会沿着净力的方向进行加速。 要解决涉及到共面力和平衡的问题，则必须要确定作用在物体上的所有力以及它们的大小和方向。然后可以使用向量来将这些力分解为它们在x和y方向上的分量。使用平衡方程可以计算出未知的力并以此来检查物体是否处于平衡状态。 如图所示，假设有一个被三根绳子悬挂且处于平衡状态的盒子。 <img alt="Equation 1" src="/files/ftp_upload/14244/14244_PT_Fig_1v2.svg" style="text-align: center; height: 350px;"> 这是一个共面系统，因为力会作用在一个单一的平面上。与平板所连接的两根对角的绳子与平面成等角，并且这两根绳子的张力是已知的。为了能够确定第三根垂直于绳子的张力大小，则可以使用平衡方程。将两根已知的张力分解为它们的分量后，可以发现水平的分量是相互平衡的。因此，可以通过对垂直分量的方程进行重新排列来确定第三根绳子的张力。一旦确定了第三根绳子的张力，可以使用平衡方程来检查系统是否确实处于平衡状态。

考虑一个受到多个力作用的物体。如果每个力的作用线均位于同一平面内，则该力系可被视为……

Education

教育

JoVE Core

Mechanical Engineering

机械工程

Unit 1

第一单元

Equilibrium of a Particle

质点平衡

KEY TERMS AND CONCEPTS

关键术语与概念

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.

mechanical engineering

Resolving Coplanar Force Components

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