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.

ضع في اعتبارك رجلا يسحب حبلا من خطاف في الاتجاه الشمالي الشرقي.
يشار إلى متجه القوة على أنه F1. يتم حلها إلى مكونات عددية ، ممثلة في F1x على طول المحور x و F1y على طول المحور y.
الاتجاه ، وهو الزاوية التي يصنعها F1 مع المحور x الموجب في الاتجاه عكس اتجاه عقارب الساعة ، هو معكوس تان للمكون y فوق المكون x.
هنا ، F1x و F1y عبارة عن مكونات مستطيلة تشكل مثلثا قائما الزاوية ويمكن الحصول عليها باستخدام الدوال المثلثية.
إذا كانت هناك قوة أخرى F2 تعمل على الخطاف من الاتجاه الجنوبي الشرقي، فإن F2x على طول المحور x الموجب، و F2y على طول المحور y السالب.
يتم الحصول على مركبتي x و y ل F2 باستخدام الدالة المثلثية ، والقوة الناتجة هي المجموع الجبري لمكونات كل من القوى على طول المحورين x و y ، بينما يتم الحصول على حجمها باستخدام الجذر التربيعي لمجموع مربعات مكوناتها.

<ol>
	<li>بير ، إف بي ؛ جونستون ، إي آر ؛ مازوريك ، د. إف. كرومويل ، بي جيه وسيلف ، ب. (2019). ميكانيكا المتجهات للمهندسين - الإحصاء والديناميكيات. نيويورك: ماكجرو هيل. ص 29-33</li>
	<li>هيبلر ، آر سي (2016). الميكانيكا الهندسية - الإحصاء والديناميكيات. هوبوكين ، نيو جيرسي: قاعة بيرسون برنتيس. ص 33 - 35.</li>
</ol>

التمثيل البياني للكميات القياسية

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التمثيل البياني للكميات القياسية هو طريقة مفيدة تستخدم لتبسيط الحسابات التي تتضمن المتجهات. عند جمع أو طرح المتجهات، يمكن جمع أو طرح مركباتها بشكل منفصل من خلال التمثيل البياني للكميات القياسية. على سبيل المثال، يمكن تحليل القوة، التي تعد كمية متجهة، إلى مركباتها في الاتجاهين x و y، والتي تُعرف بالمركبات المستطيلة، ثم يمكن تحديد مقدار واتجاه هذه المركبات باستخدام الدوال المثلثية.

تخيل رجل يسحب حبلًا من خطاف في الاتجاه الشمالي الشرقي. يتم تمثيل مقدار هذا المتجه للقوة المؤثرة بالرمز F1. يتم تحليل هذه القوة إلى مكوناتها العددية، والتي يتم تمثيلها بـ F1x على طول المحور x و F1y على طول المحورy يتم الحصول على التعبيرات الخاصة بالمكونات المستطيلة F1x و F1y باستخدام الدوال المثلثية، حيث تشكل هذه المركبات مثلثًا قائم الزاوية. باستخدام هذه المكونات ونظرية فيثاغورس، يمكن حساب مقدار القوة F1 . أما اتجاه القوة فيتم تحديده باستخدام الدالة العكسية للظل tan-1 لنسبة المكون y إلى المكون x. وإذا أثرت قوة أخرى F2 على نفس الخطاف من الاتجاه الجنوبي الشرقي، يمكن استخدام نفس الطريقة لحساب مقدار واتجاه هذه القوة أيضًا.

القوة المحصلة هي المجموع الجبري لمركبات كلتا القوتين على المحورين x وy. يمكن أيضًا حساب مقدارها باستخدام الجذر التربيعي لمجموع مربعات مركباتها. تمثل هذه القوة المحصلة إما القوة الصافية المؤثرة على الجسم أو القوة المطلوبة لمعادلة القوى الأخرى.

يعد التمثيل البياني للكميات القياسية أداة مفيدة لحساب القوى في اتجاهات مختلفة وفهم تأثير القوى على الجسم. من خلال تحليل القوى إلى مركباتها المستطيلة واستخدام الدوال المثلثية، يمكن تحديد مقدار القوة واتجاهها بسرعة ودقة.</div>

التدوين العددي هو طريقة مفيدة لتبسيط العمليات الحسابية التي تتضمن المتجهات. عند إضافة المتجهات أو طرحها ، يمكن إضافة مكوناتها أو ...

Education

JoVE Core

Mechanical Engineering

الهندسة الميكانيكية

Unit 1

الوحدة الأولى

Force Vectors

متجهات القوة

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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

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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

Cartesian vector notation shows how to write vectors in three-dimensional space using x, y, and z components. It gives a clear way to represent direction and size for quantities used in mechanical engineering. The notation uses the unit vectors i, j, and k for the x, y, and z axes. A vector pointing in the direction (3, −4, 5) can be written as A = 3i - 4j + 5k. The unit vectors are i = (1, 0, 0), j = (0, 1, 0), and k = (0, 0, 1). This form is useful for describing displacement, velocity,...

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three-dimensional force system:problem solving

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Resolving Forces in 3D Coordinates

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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 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

Vector Components for Force Calculations

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