حلول التدريبات العملية 3- مسارات رأسية

13. 4.2-

في البند السابق وجدنا تعبيرًا للقوة العمودية في النقطة C كدالة لسرعة الجسم في النقطة C. 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»N«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfrac mathcolor=¨#0000FF¨»«msup»«msub»«mi mathvariant=¨bold¨»v«/mi»«mi mathvariant=¨bold¨»C«/mi»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»R«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«/mstyle»«/math»

أثناء حركة الجسم على المسار الأملس، لم تبذل شغلل على الجسم سوى قوة الجاذبية. لذلك يتم حفظ الطاقة الميكانيكية. 

 نعبّر عن السرعة V_C كدالة للسرعة V_A, بواسطة معادلة حفظ الطاقة.

                                                                                         «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»A«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«/msub»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»k«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»A«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»k«/mi»«mi mathvariant=¨bold¨»C«/mi»«/msub»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»U«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«/msub»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»h«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»A«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msup»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mi mathvariant=¨bold¨»C«/mi»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»h«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«/msub»«/mstyle»«/math»

نختار مستوى الانتساب في ارتفاع النقطة A ، بحيث تكون الطاقة الوضعية في النقطة A مساوية لصفر.

ارتفاع النقطة C يساوي ضعف نصف قطر الدوران. 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mspace linebreak=¨newline¨/»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨ mathsize=¨20px¨»1«/mn»«mn mathvariant=¨bold¨ mathsize=¨20px¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«msup»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathsize=¨20px¨»v«/mi»«mi mathvariant=¨bold¨ mathsize=¨20px¨»A«/mi»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»+«/mo»«menclose mathcolor=¨#0000FF¨ notation=¨updiagonalstrike¨»«mi mathvariant=¨bold¨ mathsize=¨20px¨»m«/mi»«mo mathvariant=¨bold¨ mathsize=¨20px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathsize=¨20px¨»g«/mi»«mo mathvariant=¨bold¨ mathsize=¨20px¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathsize=¨20px¨»h«/mi»«mi mathvariant=¨bold¨ mathsize=¨20px¨»A«/mi»«/msub»«/menclose»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨ mathsize=¨20px¨»1«/mn»«mn mathvariant=¨bold¨ mathsize=¨20px¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«msup»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathsize=¨20px¨»v«/mi»«mi mathvariant=¨bold¨ mathsize=¨20px¨»C«/mi»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨ mathsize=¨20px¨»h«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨ mathsize=¨20px¨»C«/mi»«/msub»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨ mathsize=¨20px¨»1«/mn»«mn mathvariant=¨bold¨ mathsize=¨20px¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«msup»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathsize=¨20px¨»v«/mi»«mi mathvariant=¨bold¨ mathsize=¨20px¨»A«/mi»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨ mathsize=¨20px¨»1«/mn»«mn mathvariant=¨bold¨ mathsize=¨20px¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«msup»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathsize=¨20px¨»v«/mi»«mi mathvariant=¨bold¨ mathsize=¨20px¨»C«/mi»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨ mathsize=¨20px¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨ mathsize=¨20px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨ mathsize=¨20px¨»R«/mi»«/math»

نختزل الكتلة ونعبر عن سرعة V_C:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mspace linebreak=¨newline¨/»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨ mathsize=¨20px¨»1«/mn»«mn mathvariant=¨bold¨ mathsize=¨20px¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«menclose mathcolor=¨#0000FF¨ notation=¨downdiagonalstrike¨»«mi mathvariant=¨bold¨ mathsize=¨20px¨»m«/mi»«/menclose»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«msup»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathsize=¨20px¨»V«/mi»«mi mathvariant=¨bold¨ mathsize=¨20px¨»A«/mi»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨ mathsize=¨20px¨»1«/mn»«mn mathvariant=¨bold¨ mathsize=¨20px¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«menclose mathcolor=¨#0000FF¨ notation=¨downdiagonalstrike¨»«mi mathvariant=¨bold¨ mathsize=¨20px¨»m«/mi»«/menclose»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«msup»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathsize=¨20px¨»V«/mi»«mi mathvariant=¨bold¨ mathsize=¨20px¨»C«/mi»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»+«/mo»«menclose mathcolor=¨#0000FF¨ notation=¨downdiagonalstrike¨»«mi mathvariant=¨bold¨ mathsize=¨20px¨»m«/mi»«/menclose»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»R«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msup»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathsize=¨20px¨»V«/mi»«mi mathvariant=¨bold¨ mathsize=¨20px¨»A«/mi»«/msub»«mn mathcolor=¨#0000FF¨ mathvariant=¨bold¨ mathsize=¨20px¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»=«/mo»«msup»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathsize=¨20px¨»v«/mi»«mi mathvariant=¨bold¨ mathsize=¨20px¨»C«/mi»«/msub»«mn mathcolor=¨#0000FF¨ mathvariant=¨bold¨ mathsize=¨20px¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»R«/mi»«mspace linebreak=¨newline¨/»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mo mathsize=¨20px¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«msup»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathsize=¨20px¨»V«/mi»«mi mathvariant=¨bold¨ mathsize=¨20px¨»C«/mi»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»=«/mo»«msup»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»v«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»A«/mi»«/msub»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»R«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»V«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»C«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨ mathsize=¨20px¨»=«/mo»«msqrt mathcolor=¨#0000FF¨»«msup»«msub»«mi mathvariant=¨bold¨ mathsize=¨20px¨»v«/mi»«mi mathvariant=¨bold¨ mathsize=¨20px¨»A«/mi»«/msub»«mn mathvariant=¨bold¨ mathsize=¨20px¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathsize=¨20px¨»-«/mo»«mn mathvariant=¨bold¨ mathsize=¨20px¨»4«/mn»«mo mathvariant=¨bold¨ mathsize=¨20px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathsize=¨20px¨»g«/mi»«mo mathvariant=¨bold¨ mathsize=¨20px¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathsize=¨20px¨»R«/mi»«/msqrt»«mspace linebreak=¨newline¨/»«/math»

نعوّض السرعة Vc في تعبير القوة العمودية في النقطة C: 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨20px¨»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»N«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfrac mathcolor=¨#0000FF¨»«msup»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»v«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»C«/mi»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»R«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»N«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfrac mathcolor=¨#0000FF¨»«msup»«mstyle mathvariant=¨bold¨»«mo stretchy=¨true¨»(«/mo»«msqrt mathcolor=¨#FF0000¨»«msup»«msub»«mi»v«/mi»«mi»A«/mi»«/msub»«mn»2«/mn»«/msup»«mo»-«/mo»«mn»4«/mn»«mo»§#183;«/mo»«mi»g«/mi»«mo»§#183;«/mo»«mi»R«/mi»«/msqrt»«mo stretchy=¨true¨»)«/mo»«/mstyle»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»R«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»N«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«msup»«msub»«mi mathvariant=¨bold¨»v«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»R«/mi»«/mrow»«mi mathvariant=¨bold¨»R«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»N«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«msub»«mi mathvariant=¨bold¨»v«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mi mathvariant=¨bold¨»R«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»R«/mi»«/mrow»«mi mathvariant=¨bold¨»R«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»N«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«msub»«mi mathvariant=¨bold¨»v«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mi mathvariant=¨bold¨»R«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»g«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«menclose notation=¨updiagonalstrike¨»«mi mathvariant=¨bold¨»R«/mi»«/menclose»«/mrow»«menclose notation=¨updiagonalstrike¨»«mi mathvariant=¨bold¨»R«/mi»«/menclose»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»N«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«msub»«mi mathvariant=¨bold¨»v«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«mi mathvariant=¨bold¨»R«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»g«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«msub»«mi mathvariant=¨bold¨»N«/mi»«mi mathvariant=¨bold¨»C«/mi»«/msub»«mo mathvariant=¨bold¨»=«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mfrac»«msup»«msub»«mi mathvariant=¨bold¨»v«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»R«/mi»«/mfrac»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»g«/mi»«/menclose»«/mstyle»«/math»