10. جسمان على سطحين مائلين

10.2. ايجاد النسبة بين الكتل

عندما يتحرك الجسمان بسرعة ثابتة، فهذا يعني أن تسارعهما يساوي صفرًا.

نستخدم تعبير التسارع الذي قمنا بتطويره في البند السابق:


«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«msub»«mi mathvariant=¨bold¨»M«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mi mathvariant=¨bold¨»gsin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#946;«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨»M«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mi mathvariant=¨bold¨»gsin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«msub»«mi mathvariant=¨bold¨»M«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨»M«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/mrow»«/mfrac»«/math»


نعوّض a = 0:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«msub»«mi mathvariant=¨bold¨»M«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mi mathvariant=¨bold¨»gsin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#946;«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨»M«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mi mathvariant=¨bold¨»gsin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«msub»«mi mathvariant=¨bold¨»M«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨»M«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»M«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»gsin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#946;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»M«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»gsin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»M«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»gsin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#946;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»M«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»gsin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»/«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»M«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/msub»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»gsin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#946;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mfrac mathcolor=¨#0000FF¨»«mrow»«msub»«mi mathvariant=¨bold¨»M«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«menclose notation=¨updiagonalstrike¨»«mi mathvariant=¨bold¨»gsin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#946;«/mi»«mo mathvariant=¨bold¨»)«/mo»«/menclose»«/mrow»«mrow»«msub»«mi mathvariant=¨bold¨»M«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«menclose notation=¨updiagonalstrike¨»«mi mathvariant=¨bold¨»gsin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#946;«/mi»«mo mathvariant=¨bold¨»)«/mo»«/menclose»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«menclose notation=¨updiagonalstrike¨»«msub»«mi mathvariant=¨bold¨»M«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mi mathvariant=¨bold¨»g«/mi»«/menclose»«mi mathvariant=¨bold¨»sin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«menclose notation=¨updiagonalstrike¨»«msub»«mi mathvariant=¨bold¨»M«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mi mathvariant=¨bold¨»g«/mi»«/menclose»«mi mathvariant=¨bold¨»sin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#946;«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«menclose mathcolor=¨#0000FF¨ notation=¨circle¨»«mfrac»«msub»«mi mathvariant=¨bold¨»M«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«msub»«mi mathvariant=¨bold¨»M«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/mfrac»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mfrac»«mrow»«mi mathvariant=¨bold¨»sin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mi mathvariant=¨bold¨»sin«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»§#946;«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfrac»«/menclose»«/math»