Name: resultant force from tugboats
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 23 s
Channel: JoVE

两个或多个力矢量的矢量加法可使用平行四边形法则来求得合力。
考虑一艘船被两艘小型拖船牵引。两个力 F1 和 F2 同时作用于该船。
使用平行四边形法则求合力时，需分别沿两个力矢量的方向作平行线，从而形成一个平行四边形。
现在，平行四边形的对角线表示两艘拖船对船舶施加的合力 FN &#160;，该合力可表示为力 F1 和 F2 的矢量和。
假设现在另一艘拖船施加的第三个力作用在船上。
利用 FN &#160;和第三个力 F3 构成另一个平行四边形。该新平行四边形的对角线表示三艘拖船共同作用于船体的合力。
此处，作用在船上的合力表示为所有三个力的矢量和。

<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 18-22 页</li>
	<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 页</li>
</ol>

力的矢量叠加

Vector Addition of Forces

在理解多个力对物体所产生的影响时，矢量的叠加是一个需要掌握的重要概念。这个数学概念用于计算两个及以上力的情况下作用在物体上的净力。 为了理解矢量叠加的概念，可以设想一艘船被两艘小拖船拉动的情景。其中有两个力F1和F2，这两个力以不同方向同时作用于船上。可以使用平行四边形法则来计算作用在船上的净力。 平行四边形法则在矢量叠加中很有帮助，因为它提供了一种几何方法来将两个矢量进行相加。根据平行四边形法则，将这两个力分别作为平行四边形的相邻边，在原点放置它们的起点，并画出与各自力平行的边，最后画出平行四边形的对角线，该对角线即为F1和F2的合成力。其大小和方向可通过测量对角线的长度和角度确定。 如果引入第三个力F3，则需要再次绘制一个平行四边形。将先前的净力F1 + F2作为新的平行四边形的一条边，而第三个力F3则作为另一条边。同样的，这个平行四边形的对角线代表由所有三艘拖船来引起船上的合力或净力。这个船上的净力可以表示为所有三个力的矢量和，即F1 + F2 + F3。 矢量叠加是通过理解多个力对物体产生影响的有力工具。它在物理学、工程学和数学中的各个领域非常重要。通过理解平行四边形法则和矢量叠加的概念，可以精确计算和预测作用在物体上的净力。

当理解多个力作用于物体所产生的效应时，矢量加法是一个必须掌握的关键概念。这一数学概念可以……

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

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, the two force vectors form adjacent sides of a parallelogram. The diagonal through their intersection shows the resultant, or net force.

To use the law for the tugboat example, parallel lines are drawn to both force vectors to complete the parallelogram. Then a diagonal is drawn across the shape. That diagonal represents the net force acting on the ship from the two tugboats.

A third force, F3, can be added in the same way. A new parallelogram is drawn using the previous resultant, F1 + F2, as one side and F3 as the other. The diagonal of this second parallelogram gives the total resultant force, written as F1 + F2 + F3.

Vector addition is useful in physics, engineering, and mathematics. It helps scientists and engineers calculate and predict the net force on an object. The parallelogram law makes that prediction easier to picture and measure.

Resultant Force from Tugboats

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vector addition of forces

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key terms and concepts

Learn how vector addition uses the parallelogram law to find the resultant force on a ship pulled by two or three tugboats in physics.

Resultant Force from Tugboats | 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

Resultant Force from Tugboats

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