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

ضع في اعتبارك مثالا ثابتا ثلاثي الأبعاد مثل عمود بكابل مثبت على الأرض. هنا ، تعمل قوة التوتر على طول الكابل.
الآن ، ضع في اعتبارك نظام إحداثيات ديكارتي له أصل عشوائي لتمثيل القوة كمتجه ديكارتي.
يمثل PA و PB متجهات الموضع لطرفي الكابل. يتم توجيه متجه القوة من النقطة A إلى B على نفس اتجاه متجه الموضع PAB. يحدد متجه الوحدة هذا الاتجاه.
بتطبيق قانون المثلث لجمع المتجه ، يمكن الحصول على متجه الموضع على طول النقطتين A و B عن طريق طرح PA من PB.
ثانيا ، يمكن العثور على حجمه باستخدام الجذر التربيعي لمجموع مربعات مكوناته.
الآن، بقسمة متجه الموضع على حجمه يوفر متجه الوحدة على طول الكبل AB.
أخيرا ، يعبر حاصل ضرب حجم متجه القوة ومتجه الوحدة عن متجه القوة في الشكل الديكارتي.

<ol>
	<li>هيبلر ، آر سي (2016). الميكانيكا الهندسية - الإحصاء والديناميكيات. هوبوكين ، نيو جيرسي: قاعة بيرسون برنتيس. ص 59</li>
</ol>

متجه القوة على خط مستقيم.

<div style="direction:rtl">في كثير من الأحيان، في مسائل الإستاتيكا ثلاثية الأبعاد، يتم تحديد اتجاه القوة من خلال نقطتين يمر عبرهما خط تأثيرها. لنفترض وجود عمود ثابت في الفضاء ثلاثي الأبعاد، ومثبت به كابل ممتد إلى نقطة ارتكازه على الأرض. <img alt="Equation 1" src="/files/ftp_upload/14237/14237_PT_Fig_1v2.svg" style="text-align: center; height: 350px;"> باعتبار نظام إحداثيات ديكارتي يكون فيه الأصل عند قاعدة العمود، يمكن تمثيل نقطتي نهاية الكابل بالرمزين A وB. تمثل PA وPB متجهات الموضع لنهايتي الكابل. يتم استخدام قانون مثلث جمع المتجهات للحصول على متجه الموضع الممتد بين النقطتين A وB. لتحقيق ذلك، يتم طرح متجه الموضع PA من PB. <img alt="Equation 1" src="/files/ftp_upload/14237/14237_PT_Equation_1v2.svg" style="text-align: center; height: 15px;"> يمكن الحصول على مقدار متجه الموضع من الجذر التربيعي لمجموع مربعات مكوناته. <img alt="Equation 2" src="/files/ftp_upload/14237/14237_PT_Equation_2v2.svg" style="text-align: center; height: 26px;"> تكون قوة الشد المؤثرة على الكابل موجهة من النقطة A نحو النقطة B، متبعةً نفس اتجاه متجه الموضع PAB. يحدد المتجه الأحادي على طول الكابل اتجاه القوة، ويتم حسابه بقسمة متجه الموضع على مقداره. <img alt="Equation 3" src="/files/ftp_upload/14237/14237_PT_Equation_3v2.svg" style="text-align: center; height: 39px;">

أخيرًا، يمكن التعبير عن متجه القوة في الصورة الكارتيزية من خلال ضرب مقدار متجه القوة في المتجه الأحادي. ينتج عن هذا الضرب متجه ثلاثي الأبعاد يمثل القوة المؤثرة على العمود 

<img alt="Equation 4" src="/files/ftp_upload/14237/14237_PT_Equation_4v2.svg" style="text-align: center; height: 11px;"></div>

في كثير من الأحيان في مشاكل الإتاتيكا ثلاثية الأبعاد ، يتم تحديد اتجاه القوة بنقطتين يمر من خلالهما خط عملها. النظر في ...

Education

JoVE Core

Mechanical Engineering

الهندسة الميكانيكية

Unit 1

الوحدة الأولى

Force Vectors

متجهات القوة

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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

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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...

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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 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

Finding a Cable Force from Two Points

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