حلول التدريبات العملية الديناميكا لجسمين

9.1. ايجاد التسارع

يتحرك الجسم 1 عموديًا بينما يتحرك الجسم 2 على طول السطح المائل.

نظرًا لأن الجسمان موصولان بخيط مثالي مشدود ، فإن تسارعهما متساوٍ في المقدار.

لضمان أن يكون لتسارع كل منهما نفس الإشارة،، نحدّد المحاور على النحو التالي:

للجسم 1: نختار المحور Y لأسفل.

بالنسبة للجسم 2: نختار المحور X لأعلى السطح المائل والمحور Y العمودي على السطح لأعلى.

تؤثر قوتان على الجسم 1:  قوة الجاذبية W₁ وقوة التوتر T.

نرسم مخططًا للقوى المؤثرة على الجسم 1: 

نكتب معادلة الحركة للجسم بالاتجاه العمودي:

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تعمل أربع قوى على الجسم 2:  قوة الجاذبية W₂، والقوة العمودية N، وقوة التوتر T وقوة الاحتكاك f_k. .

نرسم مخططًا للقوى المؤثرة على الجسم 2: 

نحلل القوة W₂ لمركّبيها:

الجسم 2 في حالة سكون في اتجاه المحور Y ويتسارع في اتجاه المحور X.

الجسم 1 يتسارع في اتجاه المحور Y.

نكتب معادلات الحركة للجسم 2 في اتجاه عمودي على المستوى:

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نعوّض القوة العمودية في تعبير الاحتكاك الحركي :

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نجمع المعادلتين المشار لهما ونعبر عن التسارع:

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