حلول التدريبات العملية 1- قانون الشغل والطاقة

20. 2.4-

نكتب معطيات السؤال:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»20«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»k«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»g«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»30«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»N«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msup»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»60«/mn»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msup»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»V«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8710;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»X«/mi»«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¨»m«/mi»«/math»

نرسم مخطط للقوى المؤثرة على الجسم.

نكتب معادلات الحركة في الاتجاه العمودي.

معادلة الحركة في اتجاه المحور y العمودي:

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نكتب معادلة الحركة في اتجاه المحور x:

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حسب الكينماتيكا، نستخدم دالة مربع السرعة: -

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حسب قانون الشغل والطاقة:-

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mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«msup»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mspace linebreak=¨newline¨/»«msup»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msup»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»0«/mn»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#8710;«/mo»«msub»«mi mathvariant=¨bold¨»E«/mi»«mi mathvariant=¨bold¨»k«/mi»«/msub»«/mrow»«mi mathvariant=¨bold¨»m«/mi»«/mfrac»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»W«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»F«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«mover»«mi mathvariant=¨bold¨»F«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«mover»«mrow»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»X«/mi»«/mrow»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»C«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»O«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»S«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»§#952;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»30«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»40«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»C«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»O«/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»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1200«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»J«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»W«/mi»«mrow mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»g«/mi»«/mrow»«/msub»«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¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mrow mathcolor=¨#0000FF¨»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«mover»«mrow»«mo mathvariant=¨bold¨»§#8710;«/mo»«mi mathvariant=¨bold¨»X«/mi»«/mrow»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ stretchy=¨true¨»|«/mo»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»C«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»O«/mi»«mi mathvariant=¨bold-italic¨ 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mathcolor=¨#0000FF¨».«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»J«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»W«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»N«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»W«/mi»«mstyle mathcolor=¨#0000FF¨ displaystyle=¨false¨»«munder»«mrow»«mo mathvariant=¨bold¨»§#8721;«/mo»«mi mathvariant=¨bold¨»F«/mi»«/mrow»«mrow/»«/munder»«/mstyle»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»W«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»F«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»W«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»mg«/mi»«/msub»«mo mathvariant=¨bold¨ 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