Name: vector components for force calculations
Uploaded: 2023-09-22T11:49:19.000Z
Duration: 1 min 28 s
Channel: JoVE
Description: Scalar notation helps simplify vector calculations by breaking a vector into separate x and y parts. When vectors are added or subtracted, each component can be handled on its own using scalar notation. This makes force problems easier to solve.

北東の方向にフックからロープを引っ張っている男性を考えてみましょう。
力ベクトルは F1 で表されます。これは、x 軸に沿って F1x、y 軸に沿って F1y として表されるスカラー成分に分解されます。
この方向は、F1 が正の x 軸を反時計回りに持つ角度であり、y 成分と x 成分の逆タンです。
ここで、F1x と F1y は直角三角形を形成する長方形の成分であり、三角関数を使用して取得できます。
別の力F2が南東方向からフックに作用する場合、F2xは正のx軸に沿っており、F2yは負のy軸に沿っています。
F2 の x 成分と y 成分は三角関数を使用して取得され、合力は x 軸と y 軸に沿った両方の力の成分の代数的和であり、その大きさは、その成分の 2 乗和の平方根を使用して得られます。

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	<li>ビール、FP;ジョンストン、ER;マズレック、D.F;クロムウェル、PJおよびセルフ、BP(2019)。エンジニアのためのベクトル力学 \u2012 静力学と動力学。ニューヨーク:マグロウヒル。29-33ページ</li>
	<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。33 \u2012 35ページ。</li>
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スカラー表記法

スカラー表記法は、ベクトルを用いた計算を簡略化するための有用な方法です。ベクトルの加算や減算の際には、スカラー表記法を使用してそれぞれの成分を個別に加算または減算することができます。例えば、ベクトル量である力は、そのx成分とy成分である直交成分に分解することができ、その成分の大きさと方向を三角関数を使用して求めることができます。

東北方向からフックにロープを引っ張る人物を考えてみましょう。この適用される力のベクトルの大きさはF1と表されます。これは、x軸に沿ったF1xおよびy軸に沿ったF1yというスカラー成分に分解されます。直角三角形を形成するため、直角成分F1xおよびF1yの式は三角関数を使用して求められます。これらの成分とピタゴラスの定理を使用して、力F1の大きさを計算することができます。力の方向は、x成分をy成分で割った逆正接で得られます。同じフックに対して別の力F2が南東方向から作用する場合も、同様の方法を使用してこの力の大きさと方向を求めることができます。

合力は、両方の力の成分の代数的な和です。その大きさは、成分の二乗の和の平方根を使用しても求めることができます。この合力は、オブジェクトに対するネット力または他の力を打ち消すために必要な力を表すこともできます。

スカラー表記法は、異なる方向の力を計算し、オブジェクトに作用する力を理解するために役立ちます。力を直交成分に分解し、三角関数を使用することで、迅速かつ正確に力の大きさと方向を求めることができます。

スカラー表記は、ベクトルを含む計算を簡略化するための便利な方法です。ベクトルが加算または減算されるとき、それらの成分を加算または...

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

Scalar Notation

vector components for force calculations

Scalar notation helps simplify vector calculations by breaking a vector into separate x and y parts. When vectors are added or subtracted, each component can be handled on its own using scalar notation. This makes force problems easier to solve.

Vector Components for Force Calculations

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two-dimensional force system: problem solving

two-dimensional-force-system-problem-solving

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scalar notation

Scalar notation helps simplify vector calculations by breaking a vector into separate x and y parts. When vectors are added or subtracted, each component can be handled on its own using scalar notation. This makes force problems easier to solve.

cartesian vector notation

Vector Components in 3D Space

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three-dimensional force system

Force Components in 3D Space

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three-dimensional force system:problem solving

three-dimensional-force-systemproblem-solving

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cross product

Cross Product Direction and Magnitude

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key terms and concepts

Learn how scalar notation breaks forces into x and y components so students can calculate magnitude, direction, and resultant force with trigonometry.

Vector Components for Force Calculations | 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

Vector Components for Force Calculations

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