Name: two-dimensional forces: free-body analysis
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 29 s
Channel: JoVE

考虑一个在二维系统中与基线's'成25度角倾斜的雨刷。作用在手柄上的力围绕雨刷中心旋转，该力与参考线'c'成20度角，参考线'c'与基线's'平行。
如果沿 a 轴方向的力分量为 65 牛顿，请确定该力的大小及其沿 b 轴方向的分量。
此处，考虑不同的角度，coa‘ 变为 25 度，而角 Foc 为 20 度。因此，力矢量与 a 轴所成的角度通过将这两个角度相加确定，等于 45 度。
由于沿a轴的力分量已知，因此可通过将力的a轴分量与45度的余弦值之比来估算该力的大小。
现在，力的 b 分量表示为力的大小与 45 度角正弦值的乘积。由于该分量沿负 b 轴方向，因此为负值。

<ol>
	<li>比尔，F.P.;约翰斯顿，ER;马祖克，DF;克伦威尔，PJ 和塞尔夫，BP（2019 年）。工程师的矢量力学 \u2012 静力学和动力学。纽约:麦格劳-希尔。第 29-33 页</li>
	<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 33 \u2012 35 页。</li>
</ol>

二维力系统：问题解决

通过使用应用向量的分析和力的平衡原理，能够确定作用于二维空间物体上多个力的效果，解决与二维力系统相关的问题是力学和工程学的一个重要方面。 解决二维力系统问题的第一步是绘制其中所考虑对象的力图。该图有助于用来确定作用在对象上的所有外力，其中包括它们的大小、方向和作用点。 接下来，使用向量分析的原理可以将力分解为x和y两个方向上的分量。这一步可以将给定的力转换为它们笛卡尔向量的表示形式，以便于对其进行表示和分析。可以使用三角函数（如正弦和余弦）来对这些分量进行分解。 将力分解为分量之后，下一步则是确定每个方向上的净力。可以通过将每个方向上的所有力进行相加来完成。然后，使用勾股定理和三角函数来确定力的大小及其方向。如果净力为零，则物体处于平衡状态且不会加速。如果净力不为零，则物体会朝着净力的方向进行加速。力的平衡原理指出，作用在元素上的所有外力在x和y两个方向上的和必须为零。这使得我们能够确定作用在物体上的未知力，例如成员中的张力或压缩力。 在某些情况下，还可以使用力矩平衡原理来确定外力对物体的影响。该原理指出，作用于元素上所有外力矩的和必须为零。这一步有助于用来确定作用在物体上力矩的值和方向。

解决与二维力系相关的问题是力学与工程学中的基本内容。通过应用矢量原理……

two-dimensional-force-system-problem-solving

Education

教育

JoVE Core

Mechanical Engineering

机械工程

Unit 1

第一单元

Force Vectors

力矢量

KEY TERMS AND CONCEPTS

关键术语与概念

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 added to find the net force in x and y. The resultant force is then found with the Pythagorean theorem and trigonometry. If the net force is zero, the object is in equilibrium and does not accelerate. If the net force is not zero, the object accelerates in the direction of the net force.

Force equilibrium means the sum of external forces is zero in both the x and y directions. This helps solve for unknown forces such as tension or compression in a member. In some problems, moment equilibrium is also used. Moment equilibrium means the sum of external moments is zero, which helps determine the size and direction of moments acting on the object.

Two-Dimensional Forces: Free-Body Analysis

two-dimensional-forces-free-body-analysis

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...

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introduction to force

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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...

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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 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

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cartesian vector notation

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three-dimensional force system

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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

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dot product

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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...

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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 to use free-body diagrams, force components, and equilibrium to solve two-dimensional force problems and find resultant forces and moments.

Two-Dimensional Forces: Free-Body 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.

mechanical engineering

Two-Dimensional Forces: Free-Body Analysis

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