Name: finding a cable force from two points
Uploaded: 2025-05-22T09:06:01.000Z
Duration: 1 min 26 s
Channel: JoVE

ケーブルが地面に固定されたポールのような 3 次元の静的な例を考えてみましょう。ここでは、ケーブルに沿って張力が作用しています。
ここで、力をデカルトベクトルとして表すために、任意の原点を持つデカルト座標系を考えてみます。
P A と PB は、ケーブルの両端の位置ベクトルを表します。力ベクトルは、位置ベクトルPABと同じ方向に沿って点AからBに向けられます。単位ベクトルは、この方向を指定します。
ベクトル加算の三角形の法則を適用すると、PBからPA Aを引くことで、点AとBに沿った位置ベクトルを求めることができます。
第二に、その大きさは、その成分の二乗の合計の平方根を使用して見つけることができます。
ここで、位置ベクトルをその大きさで割ると、ケーブルABに沿った単位ベクトルが得られます。
最後に、力ベクトルと単位ベクトルの大きさの積は、力ベクトルをデカルト形式で表します。

<ol>
	<li>ヒベラー、RC(2016)。エンジニアリングメカニクス \u2012 静力学と力学。ニュージャージー州ホーボーケン:ピアソンプレンティスホール。59ページ</li>
</ol>

線に沿った力ベクトル

三次元静力学の問題では、力の方向は作用線が通る2つの点で指定されることがよくあります。地面に固定されたケーブルを持つ三次元静力ポールを考えてみましょう。

<img alt="Equation 1" src="/files/ftp_upload/14237/14237_PT_Fig_1v2.svg" style="text-align: center; height: 350px;" />

ポールの底辺に原点を持つ直交座標系を考慮すると、ケーブルの端点はAとBとして示すことができます。PAとPBはケーブルの2つの端点の位置ベクトルを表します。

<img alt="Equation 1" src="/files/ftp_upload/14237/14237_PT_Equation_1v2.svg" style="text-align: center; height: 15px;" />

ベクトルの三角法則を用いて、点Aと点Bに沿った位置ベクトルを得るために、位置ベクトルPAを位置ベクトルPBから引きます。

<img alt="Equation 2" src="/files/ftp_upload/14237/14237_PT_Equation_2v2.svg" style="text-align: center; height: 26px;" />

 位置ベクトルの大きさは、成分の二乗の和の平方根から得ることができます。

 ケーブルに作用する張力は、位置ベクトルPAから点Aから点Bに向かう方向と同じ方向を持ちます。ケーブルの方向を指定するために、位置ベクトルをその大きさで割ることで単位ベクトルを評価します。

<img alt="Equation 3" src="/files/ftp_upload/14237/14237_PT_Equation_3v2.svg" style="text-align: center; height: 39px;" />

最後に、力ベクトルは力ベクトルの大きさと単位ベクトルを掛けることによって直交座標形式で表されます。この積は、ポールに作用する力を表す三次元ベクトルを与えます。

<img alt="Equation 4" src="/files/ftp_upload/14237/14237_PT_Equation_4v2.svg" style="text-align: center; height: 11px;" />

3次元の静力学問題では、力の方向は、その作用線が通過する2つの点によって指定されることがよくあります。考えてみてください...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Force Vectors

力のベクトル

KEY TERMS AND CONCEPTS

主要用語と概念

Force Vector along a Line

finding a cable force from two points

A cable force can be found from the two points that define its line of action. In three-dimensional statics, this setup often appears with a pole and a cable anchored to the ground. The cable ends are labeled A and B, and their position vectors are written as P_A and P_B.

The position vector from A to B is found using the triangle law of vector addition. First, subtract P_A from P_B to get P_AB. Then find the magnitude of P_AB by taking the square root of the sum of the squares of its components. This gives the length of the vector in Cartesian form.

The tension force in the cable points from A toward B. It has the same direction as the position vector P_AB. To show that direction, divide P_AB by its magnitude to get the unit vector along the cable. A unit vector is a vector with length 1 that gives direction only.

The force vector is written in Cartesian form by multiplying the force magnitude by the unit vector. This product gives a three-dimensional vector for the force acting on the pole. The method connects the geometry of points A and B to the final force vector.

Finding a Cable Force from Two Points

scalar and vectors

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force vector along a line

A cable force can be found from the two points that define its line of action. In three-dimensional statics, this setup often appears with a pole and a cable anchored to the ground. The cable ends are labeled A and B, and their position vectors are written as P_A and P_B. The position vector from A to B is found using the triangle law of vector addition. First, subtract P_A from P_B to get P_AB. Then find the magnitude of P_AB by taking the square root of the sum of the squares of its...

dot product

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key terms and concepts

Learn how to use two position vectors, a unit vector, and force magnitude to express a cable’s tension as a 3D Cartesian force vector.

Finding a Cable Force from Two Points | JoVE K12

JoVE Core 機械工学は、平衡、力、トラス解析、構造力学などの重要なトピックをカバーする簡潔でわかりやすいアニメーション ビデオを提供します。実際のアプリケーションを探索し、科学者主導の実験を通じてこれらのコンセプトが実際に動作しているのを目撃してください。

mechanical engineering

Finding a Cable Force from Two Points

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