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

يمكن إجراء إضافة متجهات أو أكثر من متجهات القوة باستخدام قانون متوازي الأضلاع للحصول على القوة الناتجة.
ضع في اعتبارك سفينة يتم سحبها بواسطة زورقين صغيرين. تعمل القوتان ، F1 و F2 ، على السفينة بشكل متزامن.
لإيجاد القوة الكلية باستخدام قانون متوازي الأضلاع، ارسم خطوطا متوازية لكل متجهين للقوة بحيث يتكون متوازي الأضلاع.
الآن ، يمثل قطر متوازي الأضلاع القوة الكلية FN على السفينة بسبب زورقي القاطرة. يتم التعبير عنه كمجموع متجه القوى F1 و F2.
لنفترض الآن أن قوة ثالثة من زورق قطر آخر تعمل على السفينة.
يتم تشكيل متوازي أضلاع آخر ، باستخدام FN والقوة الثالثة F3. يعطي قطر هذا متوازي الأضلاع الجديد القوة الناتجة على السفينة بسبب جميع زوارق القطر الثلاثة.
هنا يتم التعبير عن القوة الناتجة على السفينة كمجموع متجه للقوى الثلاث.

<ol>
	<li>هيبلر ، آر سي (2016). الميكانيكا الهندسية - الإحصاء والديناميكيات. هوبوكين ، نيو جيرسي: قاعة بيرسون برنتيس. ص 18-22</li>
	<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</li>
</ol>

الجمع المتجهي للقوى.

<div style="direction:rtl">يعد جمع المتجهات مفهومًا أساسيًا في فهم تأثيرات القوى المتعددة المؤثرة على جسم ما. يمكن استخدام هذا المفهوم الرياضي لحساب محصلة القوى المؤثرة على الجسم عندما تؤثر عليه قوتين أو أكثر. لاستيعاب مفهوم جمع المتجهات، تخيل سيناريو يتم فيه سحب سفينة بواسطة زورقين صغيرين. تؤثر القوتان F1 و F2 على السفينة في نفس الوقت في اتجاهين مختلفين. يمكن استخدام قانون متوازي الأضلاع لحساب القوة المحصلة المؤثرة على السفينة. يعد قانون متوازي الأضلاع مفيدًا في جمع المتجهات لأنه يوفر طريقة هندسية لإضافة متجهين معًا. وينص على أنه عندما يمثل الضلعان المتجاوران في متوازي الأضلاع متجهين، فإن القطر المار عبر نقطة تقاطعهما يمثل مجموع المتجهين. لتطبيق هذا القانون في سياق سحب السفينة بواسطة زورقين، يتم رسم خطوط موازية لكلا من متجهي القوة لتشكيل متوازي أضلاع. ثم يتم رسم قطر يمر عبر نقطة تقاطع المتجهين، ويمثل هذا القطر القوة المحصلة أو الصافية المؤثرة على السفينة بسبب الزورقين. يتم التعبير عن هذه القوة المحصلة كمجموع متجهي للقوتين. ومع ذلك، إذا تم التأثير بقوة ثالثة F3، يتم رسم متوازي أضلاع جديد. في هذه الحالة، يتم استخدام القوة المحصلة السابقة F1 + F2 كأحد أضلاع متوازي الأضلاع الجديد، بينما تكون القوة الثالثة F3 هي الضلع الآخر. مرة أخرى، يمثل القطر في هذا المتوازي القوة المحصلة أو الصافية المؤثرة على السفينة بسبب الزوارق الثلاثة. يتم التعبير عن هذه القوة المحصلة كمجموع متجهي لجميع القوى الثلاث، أي F1+ F2 + F3. يُعد جمع المتجهات أداة قوية لفهم تأثير محصلة القوى المتعددة المؤثرة على جسم ما، وهو أمر ضروري في مجالات مختلفة، بما في ذلك الفيزياء والهندسة والرياضيات. يمكن إجراء حسابات دقيقة والتنبؤ بالقوة المحصلة المؤثرة على الجسم بدقة من خلال فهم قانون متوازي الأضلاع ومفهوم جمع المتجهات.</div>

عند فهم تأثيرات القوى المتعددة المؤثرة على جسم ما ، تعد إضافة المتجه مفهوما حاسما يجب فهمه. يمكن أن يكون هذا المفهوم الرياضي ...

Education

JoVE Core

Mechanical Engineering

الهندسة الميكانيكية

Unit 1

الوحدة الأولى

Force Vectors

متجهات القوة

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

Vector Addition of Forces

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

scalar and vectors

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vector addition of forces

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,...

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Resolving Forces in a Plane

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Vector Components in 3D Space

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three-dimensional force system:problem solving

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dot product

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Cross Product Direction and Magnitude

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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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