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حلول التدريبات العملية حفظ كمية الحركة

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المقرر: התנע ושימורו - ערבית
كتاب: حلول التدريبات العملية حفظ كمية الحركة
طبع بواسطة: משתמש אורח
التاريخ: الأربعاء، 4 فبراير 2026، 2:36 AM

جدول المحتويات

1. א.1





حسب تعريف كمية الحركة:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»p«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/math»

مقدار كمية الحركة يساوي حاصل ضرب الكتلة في مقدار سرعة الجسم، واتجاه كمية الحركة هو باتجاه السرعة (اتجاه الحركة).

نحسب مقدار كمية الحركة:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»p«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»100«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«/math»

اتجاه  كمية الحركة في اتجاه الحركة ، إلى اليمين 




2. א.2



حسب تعريف كمية الحركة:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»p«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/math»

مقدار  كمية الحركة يساوي حاصل ضرب الكتلة في مقدار سرعة الجسم، واتجاه كمية الحركة باتجاه السرعة (اتجاه السرعة). 

نجد مقدار كمية الحركة:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»p«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»100«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«/math»

اتجاه كمية الحركة في اتجاه الحركة، وفي هذه الحالة تكون كمية الحركة إلى اليسار، ويمكن القول أن كمية الحركة سالبة بالنسبة للمحور.


3. ב.1


القوة المؤثرة على الجسم ثابتة، وبالتالي فإن مقدار الدفع المؤثر على الجسم لمدة أربع ثوانٍ يساوي حاصل ضرب القوة في زمن تأثيرها: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»40«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«/math»

اتجاه متجه الدفع إلى اليمين ، في اتجاه القوة.

4. ב.2



القوة المؤثرة على الجسم ثابتة المقدار، وبالتالي فإن الدفع المؤثر على الجسم لمدة أربع ثوانٍ يساوي حاصل ضرب القوة في زمن تأثيرها: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»40«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«/math»

اتجاه متجه الدفع إلى اليمين، في اتجاه القوة.


5. ב.3


القوة المؤثرة على الجسم ثابتة المقدار، وبالتالي فإن الدفع المؤثر على الجسم لمدة أربع ثوانٍ يساوي حاصل ضرب القوة في زمن تأثيرها: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»40«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«/math»

اتجاه متجه الدفع إلى اليمين، في اتجاه القوة.


6. ב.4



قوة الاحتكاك ثابتة، مقدار الدفع الذي تشغّله قوة الاحتكاك على الجسم، لمدة أربع ثوان. 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»f«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»12«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«/math»

اتجاه متجه الدفع الذي تشغّله قوة الاحتكاك هو نحو اليسار. 

7. ב.5

الدفع المحصّل المؤثر على الجسم يساوي مجموع متجه الدفع للقوى المؤثرة على الجسم.

لذلك الدفع المحصل المؤثرة على الجسم. لمدة أربع ثوان: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle displaystyle=¨false¨»«munder»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8721;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»J«/mi»«mi mathvariant=¨bold¨»F«/mi»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»f«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»40«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mstyle mathvariant=¨bold¨ mathcolor=¨#0000FF¨»«mo stretchy=¨true¨»(«/mo»«mrow»«mo»-«/mo»«mn»12«/mn»«/mrow»«mo stretchy=¨true¨»)«/mo»«/mstyle»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»28«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«/mrow»«mrow/»«/munder»«/mstyle»«/math»

يكون اتجاه متجه محصلة الدفع إلى اليمين، وهو نفس اتجاه متجه الدفع الأكبر. 

8. ב.6



مقدار الدفع للقوة المحصّلة. لمدة أربع ثوان:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munder mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»§#8721;«/mo»«mrow/»«/munder»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»f«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»7«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mrow mathcolor=¨#0000FF¨»«munder»«mo mathvariant=¨bold¨»§#8721;«/mo»«mrow/»«/munder»«mi mathvariant=¨bold¨»F«/mi»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«munder mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»§#8721;«/mo»«mrow/»«/munder»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»28«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«/math»

اتجاه متجه محصلة الدفع إلى اليمين، بنفس اتجاه القوة المحصلة. 

9. ג.1.א-


نجد تسارع الجسم وفقًا للقانون الثاني:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mover»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mi mathvariant=¨bold¨»m«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»10«/mn»«mn mathvariant=¨bold¨»20«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«msup»«mi mathvariant=¨bold¨»s«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mfrac»«mspace linebreak=¨newline¨/»«/math»

وفقًا لصيغة السرعة كدالة للزمن لجسم يتحرك بتسارع ثابت: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨/»«/math»

نعوّض معطيات السؤال في التعبير عن السرعة كدالة للزمن: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»/«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«/math»

10. ג.1.ב-


نجد مقدار سرعة الجسم V في نهاية تأثير القوة F. حسب تعبير الدفع وكمية الحركة: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«/math»

نعوّض معطيات السؤال ونعبر عن السرعة النهائية من تعبير V:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»p«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»V«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»V«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mover»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mi mathvariant=¨bold¨»m«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»40«/mn»«mn mathvariant=¨bold¨»20«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»V«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mspace linebreak=¨newline¨/»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»V«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»/«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/math»

11. ג.2.א-


نستخدم مبادئ الديناميكا ونحسب تسارع الجسم: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mrow»«munder»«mo mathvariant=¨bold¨»§#8721;«/mo»«mrow/»«/munder»«mi mathvariant=¨bold¨»F«/mi»«/mrow»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mover»«mrow»«munderover»«mo mathvariant=¨bold¨»§#8721;«/mo»«mrow/»«mrow/»«/munderover»«mi mathvariant=¨bold¨»F«/mi»«/mrow»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mi mathvariant=¨bold¨»m«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»-«/mo»«msub»«mi mathvariant=¨bold¨»f«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«/mrow»«mi mathvariant=¨bold¨»m«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»10«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«mn mathvariant=¨bold¨»20«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»35«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨ bevelled=¨true¨»«mi mathvariant=¨bold¨»m«/mi»«msup»«mi mathvariant=¨bold¨»s«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mfrac»«/math»


نستخدم مبادئ الكينماتيكا ونحسب سرعة الجسم في نهاية تأثير القوة F، أي في اللحظة t = 4s: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»35«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨ bevelled=¨true¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/math»

اتجاه متجه السرعة نحو اليمين

12. ג.2.ב-


نستخدم قانون الدفع وكمية الحركة لحساب سرعة الجسم في اللحظة t = 4s:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mstyle displaystyle=¨false¨»«munderover mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»§#8721;«/mo»«mrow/»«mrow/»«/munderover»«/mstyle»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨/»«mstyle displaystyle=¨false¨»«munderover mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨»§#8721;«/mo»«mrow/»«mrow/»«/munderover»«/mstyle»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»f«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»k«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mspace linebreak=¨newline¨/»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»28«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mrow mathcolor=¨#0000FF¨»«mo stretchy=¨true¨ mathvariant=¨bold¨»(«/mo»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨»-«/mo»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo stretchy=¨true¨ mathvariant=¨bold¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mover»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mi mathvariant=¨bold¨»m«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mover»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mi mathvariant=¨bold¨»m«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»28«/mn»«mn mathvariant=¨bold¨»20«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨ bevelled=¨true¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/math»

اتجاه متجه السرعة نحو اليمين في الاتجاه الموجب.


13. ג.3.א-


نقسم الحركة إلى مرحلتين:

المرحلة الأولى من لحظة الصفر إلى نهاية عمل القوة F1 (حتى اللحظة t = 4s):

نحسب التسارع في هذه المرحلة ونحسب السرعة في اللحظة t = 4s: 


«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mrow»«munder»«mo mathvariant=¨bold¨»§#8721;«/mo»«mrow/»«/munder»«mover»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mrow»«mrow/»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mover»«mrow»«munderover»«mo mathvariant=¨bold¨»§#8721;«/mo»«mrow/»«mrow/»«/munderover»«mover»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mrow»«mrow/»«/mover»«mi mathvariant=¨bold¨»m«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«msub»«mi mathvariant=¨bold¨»F«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»-«/mo»«msub»«mi mathvariant=¨bold¨»F«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/mrow»«mi mathvariant=¨bold¨»m«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»10«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»6«/mn»«/mrow»«mn mathvariant=¨bold¨»20«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨ bevelled=¨true¨»«mi mathvariant=¨bold¨»m«/mi»«msup»«mi mathvariant=¨bold¨»s«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mfrac»«mspace linebreak=¨newline¨/»«/math»

نستخدم مبادئ الكينماتيكا ونحسب سرعة الجسم في نهاية تأثير القوة F1 ، أي في اللحظة t = 4s:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨ bevelled=¨true¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/math»

نتطرّق إلى مقطع الحركة الثاني من اللحظة t = 4s حتى لحظة نهاية عمل القوة F2 (حتى اللحظة t = 12s):

نحسب التسارع في هذا القسم ونحسب السرعة في اللحظة t = 12s: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mrow»«munder»«mo mathvariant=¨bold¨»§#8721;«/mo»«mrow/»«/munder»«mover»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mrow»«mrow/»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mover»«mrow»«munderover»«mo mathvariant=¨bold¨»§#8721;«/mo»«mrow/»«mrow/»«/munderover»«mover»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mrow»«mrow/»«/mover»«mi mathvariant=¨bold¨»m«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«msub»«mi mathvariant=¨bold¨»F«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/mrow»«mi mathvariant=¨bold¨»m«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»6«/mn»«/mrow»«mn mathvariant=¨bold¨»20«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨ bevelled=¨true¨»«mi mathvariant=¨bold¨»m«/mi»«msup»«mi mathvariant=¨bold¨»s«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mfrac»«mspace linebreak=¨newline¨/»«/math»

نستخدم مبادئ الكينماتيكا ونحسب سرعة الجسم في نهاية تأثير القوة F2 ، أي في اللحظة t = 12s:


«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mstyle mathvariant=¨bold¨ mathcolor=¨#0000FF¨»«mo stretchy=¨true¨»(«/mo»«mrow»«mo»-«/mo»«mn»0«/mn»«mo».«/mo»«mn»3«/mn»«/mrow»«mo stretchy=¨true¨»)«/mo»«/mstyle»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mstyle mathvariant=¨bold¨ mathcolor=¨#0000FF¨»«mo stretchy=¨true¨»(«/mo»«mrow»«mn»12«/mn»«mo»-«/mo»«mn»4«/mn»«/mrow»«mo stretchy=¨true¨»)«/mo»«/mstyle»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨ bevelled=¨true¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/math»

اتجاه متجه السرعة إلى اليمين

14. ג.3.ב-



نحسب الدفع الذي يعمل على الجسم حتى اللحظة t = 12s ، نتطرّق إلى جزئي الحركة: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mstyle mathvariant=¨bold¨ mathcolor=¨#0000FF¨»«mo stretchy=¨true¨»(«/mo»«mrow»«munderover»«mo»§#8721;«/mo»«mrow/»«mrow/»«/munderover»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«/mrow»«mo stretchy=¨true¨»)«/mo»«/mstyle»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mrow mathcolor=¨#0000FF¨»«mo stretchy=¨true¨ mathvariant=¨bold¨»(«/mo»«munderover»«mo mathvariant=¨bold¨»§#8721;«/mo»«mrow/»«mrow/»«/munderover»«mover»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo stretchy=¨true¨ mathvariant=¨bold¨»)«/mo»«/mrow»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mspace linebreak=¨newline¨/»«msub»«mstyle mathvariant=¨bold¨ mathcolor=¨#0000FF¨»«munderover»«mo»§#8721;«/mo»«mrow/»«mrow/»«/munderover»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«/mstyle»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»F«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»F«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»10«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mspace linebreak=¨newline¨/»«msub»«mstyle mathvariant=¨bold¨ mathcolor=¨#0000FF¨»«munderover»«mo»§#8721;«/mo»«mrow/»«mrow/»«/munderover»«mover»«mi»F«/mi»«mo»§#8594;«/mo»«/mover»«/mstyle»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»F«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»12«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«mspace linebreak=¨newline¨/»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mstyle mathvariant=¨bold¨ mathcolor=¨#0000FF¨»«mo stretchy=¨true¨»(«/mo»«mrow»«mo»-«/mo»«mn»6«/mn»«/mrow»«mo stretchy=¨true¨»)«/mo»«/mstyle»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»32«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/math»

اتجاه الدفع المحصّل إلى اليسار.

نستخدم قانون الدفع وكمية الحركة لحساب سرعة الجسم في اللحظة t = 12s: 


«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mrow mathcolor=¨#0000FF¨»«mo stretchy=¨true¨ mathvariant=¨bold¨»(«/mo»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨»-«/mo»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo stretchy=¨true¨ mathvariant=¨bold¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mover»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mi mathvariant=¨bold¨»m«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mover»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mi mathvariant=¨bold¨»m«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»32«/mn»«/mrow»«mn mathvariant=¨bold¨»20«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨ bevelled=¨true¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«/math»

اتجاه متجه السرعة يمينًا في الاتجاه الموجب.


15. ג.4.א-


1. ايجاد مقدار الدفع J الذي يشغّله الجدار على الجسم أثناء عملية الاصطدام.


حسب قانون الدفع وكمية الحركة: 

   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»P«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«/math» - كمية الحركة بعد الاصطدام.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«/math» - كمية الحركة قبل الاصطدام.

نختار اتجاه المحور الموجب إلى اليمين :- 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mfrac mathcolor=¨#0000FF¨ bevelled=¨true¨»«mrow»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mfrac mathcolor=¨#0000FF¨ bevelled=¨true¨»«mrow»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/math»

نُعوّض في معادلة كمية الحركة والدفع:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»P«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mspace linebreak=¨newline¨/»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»200«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«/math»

اتجاه الدفع الذي يشغله الجدار على الجسم هو نحو اليسار.

16. ג.4.ב-


نجد أولًا مقدار الدفع J الذي يشغّله الجدار على الجسم أثناء عملية الاصطدام. 

حسب قانون الدفع وكمية الحركة: 

   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»P«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathcolor=¨#0000FF¨»2«/mn»«/msub»«/math» - كمية الحركة بعد الاصطدام.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«/math» - كمية الحركة قبل الاصطدام.

نختار الاتجاه الموجب نحو اليمين:- 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mfrac mathcolor=¨#0000FF¨ bevelled=¨true¨»«mrow»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mfrac mathcolor=¨#0000FF¨ bevelled=¨true¨»«mrow»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/math»

نُعوّض في معادلة كمية الحركة والدفع:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»P«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mspace linebreak=¨newline¨/»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»200«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«/math»


اتجاه الدفع الذي يعمله الجدار على الجسم هو نحو اليسار.

حسب القانون الثالث لنيوتن، فإن الدفع الذي يُشغّله الجسم على الحائط يساوي الدفع الذي يُشغّله الجدار على الجسم، وبالتالي فإن مقدار الدفع الذي يُشغّله الجسم على الحائط يساوي 200NS ، واتجاه الدفع نحو اليمين.



17. ג.4.ג-


إيجاد مقدار متوسط القوة التي يشغّلها الجدار على الجسم أثناء الاصطدام.

أولاً نجد تأثير الجدار على الجسم. 

حسب قانون الدفع وكمية الحركة:

   «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»P«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«/math» - كمية الحركة بعد الاصطدام.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«/math» - كمية الحركة قبل الاصطدام.

نختار الاتجاه الموجب نحو اليمين:- 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mfrac mathcolor=¨#0000FF¨ bevelled=¨true¨»«mrow»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mfrac mathcolor=¨#0000FF¨ bevelled=¨true¨»«mrow»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/math»

نُعوّض بمعادلة قانون الدفع وكمية الحركة:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»P«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mspace linebreak=¨newline¨/»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»200«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«/math»

اتجاه الدفع الذي يشغله الجدار على الجسم هو إلى اليسار ومقداره  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mrow/»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»200«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«/math».

نجد متوسط ​​القوة التي يشغلها الجدار على الجسم وفقًا لتعريف الدفع «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«/math».

معطى أنّ زمن الاصطدام «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»100«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»s«/mi»«/math».

الدفع الذي يشغله الجدار على الجسم:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mover»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mrow»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»t«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»20«/mn»«/mrow»«mrow»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»200«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«/math»

اتجاه القوة الذي يشغله الجدار على الجسم هو نحو اليسار.


18. ג.4.ד-

القوة التي يشغلها الجسم على الحائط معطاة في الرسم البياني التالي:


في الرسم البياني الذي يصف القوة كدالة للزمن، فإن المساحة المحصورة أسفل الرسم البياني تساوي مقدار الدفع.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»J«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»F«/mi»«mrow mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»a«/mi»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»t«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»F«/mi»«mrow mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»a«/mi»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»J«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»t«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»200«/mn»«/mrow»«mrow»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨».«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»400«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«/math»


اتجاه القوة التي يشغلها الجسم على الحائط نحو جهة اليمين. 


19. ד.א.1-


1. لحساب مقدار سرعة الجسمين U، بعد الاصطدام، نستخدم معادلة حفظ كمية الحركة (يتم حفظ كمية الحركة لأنه لا توجد قوى خارجية تعمل على هيئة الجسمين - هيئة مغلقة). 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mrow mathcolor=¨#0000FF¨»«mo stretchy=¨true¨ mathvariant=¨bold¨»(«/mo»«msub»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»+«/mo»«msub»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo stretchy=¨true¨ mathvariant=¨bold¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»u«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»k«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»g«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»k«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»g«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»u«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«msub»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»+«/mo»«msub»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/mrow»«mrow»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«msub»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»+«/mo»«msub»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»20«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»0«/mn»«/mrow»«mrow»«mn mathvariant=¨bold¨»20«/mn»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»100«/mn»«mn mathvariant=¨bold¨»24«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»16«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/math»


2.  اتجاه حركة الجسمين بعد الاصطدام إلى اليمين 


3. حساب مقدار الدفع الذي يشغله الجسم 1 على الجسم 2. 

    نستعمل قانون الدفع وكمية الحركة:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mrow mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mover mathcolor=¨#0000FF¨»«msup»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»`«/mo»«/msup»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»u«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mrow mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«mover»«mi mathvariant=¨bold¨»u«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨»-«/mo»«msub»«mover»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»16«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»16«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»66«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/math»

يكون الدفع موجبًأ لأن الجسم 1 يشغل على الجسم 2 قوة في اتجاه المحور. 

4.  حساب الدفع الذي يشغله الجسم 2 على الجسم 1. 

 حسب القانون الثالث لنيوتن، القوة التي يشغلها الجسم 2 على الجسم 1 تساوي القوة التي يشغلها الجسم 1 على الجسم 2 ، ولكن في الاتجاه المعاكس ، وبالتالي فإن القوة متساوية: 

  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mrow mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mrow mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»16«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»66«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/math»

أو يمكننا استخدام قانون الدفع وكمية الحركة: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mrow mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mover mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»P«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mover mathcolor=¨#0000FF¨»«msup»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»`«/mo»«/msup»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»u«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mrow mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«mover»«mi mathvariant=¨bold¨»u«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨»-«/mo»«msub»«mover»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»16«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»16«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»66«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/math»

يكون الدفع سالبًا لأن الجسم 2 يشغل على الجسم 1 قوة في الاتجاه المعاكس لاتجاه المحور.

20. ד.א.2-


1. حساب مقدار سرعة الجسمين U، بعد الاصطدام، نستخدم معادلة حفظ كمية الحركة (يتم حفظ كمية الحركة لأنه لا توجد قوى خارجية تعمل على هيئة الجسمين - هيئة مغلقة).  

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«msub»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»+«/mo»«msub»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»u«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»k«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»g«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»k«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»g«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»5«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»u«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«msub»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»+«/mo»«msub»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/mrow»«mrow»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«msub»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»+«/mo»«msub»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»20«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mstyle mathvariant=¨bold¨»«mo stretchy=¨true¨»(«/mo»«mrow»«mo»-«/mo»«mn»5«/mn»«/mrow»«mo stretchy=¨true¨»)«/mo»«/mstyle»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»8«/mn»«/mrow»«mrow»«mn mathvariant=¨bold¨»20«/mn»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»68«/mn»«/mrow»«mn mathvariant=¨bold¨»24«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»833«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«/math»


2. اتجاه حركة الجسمين بعد الاصطدام إلى اليمين. اتجاه حركة الجسمين عكس اتجاه المحور.


3. حساب مقدار الدفع الذي يشغله الجسم 1 على الجسم 2. 

    نستعمل قانون الدفع وكمية الحركة:


«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mrow mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mover mathcolor=¨#0000FF¨»«msup»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»`«/mo»«/msup»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»P«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»u«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mspace linebreak=¨newline¨/»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mrow mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»(«/mo»«mover»«mi mathvariant=¨bold¨»u«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨»-«/mo»«msub»«mover»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ stretchy=¨true¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»833«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»8«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»43«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»33«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/math»

يكون الدفع سالبًأ لأن الجسم 1 يشغل على الجسم 2 قوة في اتجاه عكس المحور. 

4.  حساب الدفع الذي يشغله الجسم 2 على الجسم 1. 

 حسب القانون الثالث لنيوتن، القوة التي يشغلها الجسم 2 على الجسم 1 تساوي القوة التي يشغلها الجسم 1 على الجسم 2 ، ولكن في الاتجاه المعاكس ، وبالتالي فإن الدفع يساوي: 

 

  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mrow mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msub»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»J«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mrow mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»43«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»33«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/math»

أو يمكننا استخدام قانون الدفع وكمية الحركة: 

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يكون الدفع موجبًا لأن الجسم 2 يشغل على الجسم 1 قوة في اتجاه المحور.