حلول التدريبات العملية 3- مسارات رأسية
7. 2.3-
نرسم مخططًا للقوى المؤثرة على الجسم عندما يكون في النقطة B.
نختار هيئة محاور: المحور X في الاتجاه المماسي والمحور Y في الاتجاه نحو مركز الدوران.
نكتب معادلات الحركة:
في الاتجاه المركزي (اتجاه المحور Y) وفي الاتجاه المماسي :
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نعبر من حفظ الطاقة عن السرعة في النقطة B:
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الارتفاع hA يساوي نصف قطر الدوران R. يتحرك الجسم من حالة السكون وسرعته في النقطة A تساوي صفرًا.
نعبر عن السرعة في النقطة B من معادلة حفظ الطاقة:
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للوصول إلى التعبير المطلوب، نعبر عن الارتفاع hB هندسيًا اعتمادًا على الزاوية β ونصف قطر الدوران R.
مجموع الارتفاعات X و hB يساوي نصف قطر الدوران R.
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حسب نسبة cos يتحقق:
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نعبر عن الارتفاع hB من هاتين المعادلتين
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نعوّض الارتفاع hB في تعبير السرعة vB
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نعبر عن القوة العمودية في النقطة B من معادلة الحركة الدائرية ، ونعوّض تعبير السرعة VB:
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