الحلول والمنتديات لـ"ألبوم الحلول" في موضوع كمية الحركة والطاقة

1. نرسم مخطّط للقوى المؤثرة على الجسم عندما يكون في النقطة A . 

نكتب معادلات الحركة. يتم اختيار المحور X للاتجاه المماسي ، والمحور Y للاتجاه المركزي: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#931;F«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mspace linebreak=¨newline¨»«/mspace»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»W«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»X«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mspace linebreak=¨newline¨»«/mspace»«menclose mathcolor=¨#0000FF¨ notation=¨downdiagonalstrike¨»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«menclose mathcolor=¨#0000FF¨ notation=¨downdiagonalstrike¨»«mi mathvariant=¨bold¨»m«/mi»«/menclose»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mspace linebreak=¨newline¨»«/mspace»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»=«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»sin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«/menclose»«mspace linebreak=¨newline¨»«/mspace»«/math»                                              «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#931;F«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»y«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mspace linebreak=¨newline¨»«/mspace»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»W«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»y«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»T«/mi»«mspace linebreak=¨newline¨»«/mspace»«menclose mathcolor=¨#0000FF¨ notation=¨box¨»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»cos«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»=«/mo»«mi mathvariant=¨bold¨»T«/mi»«/menclose»«mspace linebreak=¨newline¨»«/mspace»«mspace linebreak=¨newline¨»«/mspace»«/math»

نجد التسارع من معادلة الحركة المماسية:

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مقدار التسارع في النقطة A هو 8.66m/s².

2. نرسم مخطط للقوى المؤثرة على الجسم عندما يكون في نقطة  B:

لا توجد قوى تعمل في الاتجاه المماسي ، في النقطة B لا يوجد تسارع مماسي. تسارع الجسم في النقطة  B يساوي تسارعه المركزي.

نستخدم تعبير التسارع المركزي:

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وجدنا السرعة في النقطة B في القسم A ، وسنعوضها في تعبير التسارع المركزي:

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مقدار التسارع في النقطة B هو 10m/s².

نرسم مخطّط للقوى المؤثرة على الجسم عندما تكون زاوية ميل الخيط 30 درجة: 

تعمل قوة الشد في اتجاه مركزي ، لكتابة معادلة الحركة الدائرية، نقوم بتحليل قائم الزاوية لقوة الجاذبية.

نختار هيئة المحاور حيث يكون المحور X مماسًا للمسار ، والمحور Y هو محور نصف قطري (راديالي). 

نكتب معادلات الحركة في الاتجاه المماسي وفي الاتجاه المركزي (الراديالي): 

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نعبّر عن قوة الشد من معادلة الحركة المركزية (الراديالي):

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لحساب قوة الشد في النقطة D ، نحسب السرعة في النقطة D باستخدام حفظ الطاقة.

تعمل قوة الشد بشكل عمودي على الحركة ، وبالتالي فهي لا تؤدي شغل، فقط قوة الجاذبية هي التي تؤدي شغل، وبالتالي يتم حفظ الطاقة الميكانيكية.

نقارن الطاقة الميكانيكية في النقطة D بالطاقة الميكانيكية في النقطة A:

يتم اختيار مستوى الانتساب على ارتفاع النقطة B.

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نعوّض V_D وبقية المعطيات في تعبير الشد T_D:

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نجد اتجاه قوة الشد هندسيًا:

إذن ، مقدار قوة الشد 1.6 نيوتن ، واتجاهها 60 درجة فوق الأفق.