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    تمرين الكيمياء (7 نقط)

    دراسة مقلح تجاري

    ﺗﺘﻌﺮض أﻏﻠﺐ اﻷﺟﮭﺰة اﻟﻜﮭﺮﺑﺎﺋﯿﺔ اﻟﻤﻨﺰلية مثل: اﻟﻤﺴﺨﻦ اﻟﻤﺎﺋﻲ اﻟﻜﮭﺮﺑﺎﺋﻲ وآﻟﺔ ﺗﻘﻄﯿﺮ اﻟﻘﮭﻮة ... إﻟﻰ ﺗﺮﺳﺒﺎت  كلسية ﯾُﻤﻜﻦ إزاﻟﺘﮭﺎ ﺑﺎﺳﺘﻌﻤﺎل مقلحات ( détartrant) تجارية. يفضل اﺳﺘﻌﻤﺎل اﻟﻤﻘﻠﺤﺎت اﻟﺘﻲ ﺗﺤﺘﻮي ﻋﻠﻰ ﺣﻤﺾ اللاكتيك C 3 H 6 O 3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaaIZaaabeaakiaadIeadaWgaaWcbaGaaGOnaaqabaGccaWG pbWaaSbaaSqaaiaaiodaaeqaaaaa@3B32@ ﻧﻈﺮا لفعاليته وﻋﺪم تفاعله ﻣﻊ ﻣﻜﻮﻧﺎت اﻷﺟﮭﺰة، وتحلله ﺑﺴﮭﻮﻟﺔ ﻓﻲ اﻟﻄﺒﯿﻌﺔ إﺿﺎﻓﺔ إﻟﻰ كونه غير ﻣﻠﻮث ﻟﻠﺒﯿﺌﺔ.

    ﯾﮭﺪف ھﺬا اﻟﺘﻤﺮﯾﻦ إﻟﻰ دراﺳﺔ محلول ﻣﺎﺋﻲ لحمض اﻟﻼﻛﺘﯿﻚ، واﻟﺘﺤﻘﻖ ﻣﻦ اﻟﻨﺴﺒﺔ اﻟﻤﺌﻮﯾﺔ اﻟﻜﺘﻠﯿﺔ ﻟﮭﺬا اﻟﺤﻤﺾ ﻓﻲ مقلح تجاري، ﺛﻢ دراﺳﺔ ﺗﺘﺒﻊ ﺗﻄﻮر ﺳﺮﻋﺔ اﻟﺘﻔﺎﻋﻞ أﺛﻨﺎء إزاﻟﺔ راﺳﺐ كلسي.

    المعطيات:

     

    1 - دراﺳﺔ ﻣﺤﻠﻮل ﻣﺎﺋﻲ لحمض اﻟﻼﻛﺘﯿﻚ

    نحضر ﺣﺠﻤﺎ V 0 =500mL MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvamaaBa aaleaacaaIWaaabeaakiabg2da9iaaiwdacaaIWaGaaGimaiaaykW7 caWGTbGaamitaaaa@3E49@  ﻟﻤﺤﻠﻮل ﻣﺎﺋﻲ ﻟﺤﻤﺾ اﻟﻼﻛﺘﯿﻚ C 3 H 6 O 3(aq) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaaIZaaabeaakiaadIeadaWgaaWcbaGaaGOnaaqabaGccaWG pbWaaSbaaSqaaiaaiodacaGGOaGaamyyaiaadghacaGGPaaabeaaaa a@3E67@  تركيزه المولي C 0 =0,1mol. L 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaaIWaaabeaakiabg2da9iaaicdacaGGSaGaaGymaiaaykW7 caWGTbGaam4BaiaadYgacaGGUaGaamitamaaCaaaleqabiqaaOmccq GHsislcaaIXaaaaaaa@4369@ .

    اعطى قياس pH MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCaiaadI eaaaa@37B9@  هذا المحلول  القيمة pH=2,44 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCaiaadI eacqGH9aqpcaaIYaGaaiilaiaaisdacaaI0aaaaa@3BA7@ .

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  1 اُﻛﺘﺐ اﻟﻤﻌﺎدﻟﺔ اﻟﻜﯿﻤﯿﺎﺋﯿﺔ اﻟﻤﻨﻤﺬﺟﺔ ﻟﺘﻔﺎﻋﻞ ﺣﻤﺾ اﻟﻼﻛﺘﯿﻚ ﻣﻊ اﻟﻤﺎء ﻋﻠﻤﺎ أن اﻟﺘﺤﻮل ﻏﯿﺮ كلي.

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  2  أﻧﺸﺊ اﻟﺠﺪول اﻟﻮﺻﻔﻲ ﻟﺘﻘﺪم اﻟﺘﻔﺎﻋل.

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  3 ﺗﺤﻘﻖ أن قيمة x éq MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaWGPdGaamyCaaqabaaaaa@3984@  اﻟﺘﻘﺪم اﻟﻨﮭﺎﺋﻲ ﻟﻠﺘﻔﺎﻋﻞ ﻋﻨﺪ ﺣﺎﻟﺔ ﺗﻮازن اﻟﻤﺠﻤﻮﻋﺔ  هي  x éq = 1,81.10 3 mol MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaWGPdGaamyCaaqabaGccqGH9aqpcaaIXaGaaiilaiaaiIda caaIXaGaaiOlaiaaigdacaaIWaWaaWbaaSqabeaacqGHsislcaaIZa aaaOGaamyBaiaad+gacaWGSbaaaa@445B@

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  4 أوجد قيمة p K A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiCaiaadU eadaWgaaWcbaGaamyqaaqabaaaaa@38AE@  للمزدوجة C 3 H 6 O 3(aq) / C 3 H 5 O 3(aq) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaaIZaaabeaakiaadIeadaWgaaWcbaGaaGOnaaqabaGccaWG pbWaaSbaaSqaaiaaiodacaGGOaGaamyyaiaadghacaGGPaaabeaaki aac+cacaWGdbWaaSbaaSqaaiaaiodaaeqaaOGaamisamaaBaaaleaa caaI1aaabeaakiaad+eadaqhaaWcbaGaaG4maiaacIcacaWGHbGaam yCaiaacMcaaeaacqGHsislaaaaaa@4881@  .

     2 -  ﺗﺤﺪﯾﺪ اﻟﻨﺴﺒﺔ اﻟﻤﺌﻮﯾﺔ اﻟﻜﺘﻠﯿﺔ ﻟﺤﻤﺾ اﻟﻼﻛﺘﯿﻚ ﻓﻲ ﻣُﻘَﻠﱢﺢ ﺗﺠﺎري.

    ﻧﺴﺘﻌﻤﻞ ﻣﻘﻠﺤﺎ ﺗﺠﺎرﯾﺎ ﻣﺮﻛﺰا ﯾﺤﺘﻮي ﻋﻠﻰ ﺣﻤﺾ اﻟﻼﻛﺘﯿﻚ ﺗﺮﻛﯿﺰه اﻟﻤﻮلي C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qaaaa@36BF@ . ﻠﺘﺤﻘﻖ ﻣﻦ ﻗﯿﻤﺔ اﻟﻨﺴﺒﺔ اﻟﻤﺌﻮﯾﺔ اﻟﻜﺘﻠﯿﺔ  ﻟﺤﻤﺾ اﻟﻼﻛﺘﯿﻚ ﻓﻲ ھﺬا اﻟﻤﻘﻠﺢ، ﻧﺨﻔﻒ اﻟﻤﻘﻠﺢ اﻟﺘﺠﺎري المركز 100  ﻣﺮة ﻓﻨﺤﺼﻞ ﻋﻠﻰ محلول مائي ( S A ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaado fadaWgaaWcbaGaamyqaaqabaGccaGGPaaaaa@3924@  لحمض اللاكتيك تركيزه المولي ( C A = C 100 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaado eadaWgaaWcbaGaamyqaaqabaGccqGH9aqpdaWcaaqaaiaadoeaaeaa caaIXaGaaGimaiaaicdaaaGaaiykaaaa@3D21@ . نعاير الحجم V A =10mL MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvamaaBa aaleaacaWGbbaabeaakiabg2da9iaaigdacaaIWaGaamyBaiaadYea aaa@3C0C@  من المحلول ( S A ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaado fadaWgaaWcbaGaamyqaaqabaGccaGGPaaaaa@3924@  بواسطة محلول مائي لهيدروكسيد الصوديوم N a (aq) + +H O (aq) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtaiaadg gadaqhaaWcbaGaaiikaiaadggacaWGXbGaaiykaaqaaiabgUcaRaaa kiabgUcaRiaadIeacaWGpbWaa0baaSqaaiaacIcacaWGHbGaamyCai aacMcaaeaacqGHsislaaaaaa@42D0@  تركيزه المولي C B = 2,10 2 mol. L 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaWGcbaabeaakiabg2da9iaaikdacaGGSaGaaGymaiaaicda daahaaWcbeqaaiabgkHiTiaaikdaaaGccaWGTbGaam4BaiaadYgaca GGUaGaamitamaaCaaaleqabaGaeyOeI0IaaGymaaaaaaa@43B2@  الحجم المضاف عند التكافؤ هو V E,E =28,3mL MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvamaaBa aaleaacaWGfbGaaiilaiaadweaaeqaaOGaeyypa0JaaGOmaiaaiIda caGGSaGaaG4maiaad2gacaWGmbaaaa@3F00@  .

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  1 اُﻛﺘﺐ اﻟﻤﻌﺎدﻟﺔ اﻟﻜﯿﻤﯿﺎﺋﯿﺔ ﻟﻠﺘﻔﺎﻋﻞ اﻟﺤﺎﺻﻞ أﺛﻨﺎء اﻟﻤﻌﺎﯾﺮة واﻟﺬي ﻧﻌﺘﺒﺮه ﻛﻠﯿﺎ.

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  2 اُﺣﺴﺐ C A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaWGbbaabeaaaaa@37B1@  .  . اِﺳﺘﻨﺘﺞ  قيمة C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qaaaa@36BF@  .

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  3 ﯾﻌﺒﺮ ﻋﻦ اﻟﻨﺴﺒﺔ اﻟﻤﺌﻮﯾﺔ اﻟﻜﺘﻠﯿﺔ ﻟﺤﻤﺾ اﻟﻼﻛﺘﯿﻚ ﻓﻲ اﻟﻤﻘﻠﺢ اﻟﺘﺠﺎري ﺑﺎﻟﻌﻼﻗﺔ P= C.M( C 3 H 6 O 3 ) ρ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiabg2 da9maalaaabaGaam4qaiaac6cacaWGnbGaaiikaiaadoeadaWgaaWc baGaaG4maaqabaGccaWGibWaaSbaaSqaaiaaiAdaaeqaaOGaam4tam aaBaaaleaacaaIZaaabeaakiaacMcaaeaacqaHbpGCaaaaaa@428C@  .

    ﺗﺤﻘﻖ ﻣﻦ ﻗﯿﻤﺔ اﻟﻨﺴﺒﺔ اﻟﻤﺌﻮﯾﺔ اﻟﻜﺘﻠﯿﺔ ﻟﺤﻤﺾ اﻟﻼﻛﺘﯿﻚ ﻓﻲ اﻟﻤﻘﻠﺢ اﻟﺘﺠﺎري.

    3 - دراﺳﺔ ﺗﺘﺒﻊ ﺗﻄﻮر ﺳﺮﻋﺔ اﻟﺘﻔﺎﻋﻞ أﺛﻨﺎء إزاﻟﺔ راﺳﺐ كلسي.

    ﯾﺘﻜﻮن الراسب اﻟﻜﻠﺴﻲ اﻟﻤﺘﻜﻮن ﻓﻲ آﻟﺔ ﺗﻘﻄﯿﺮ اﻟﻘﮭﻮة أﺳﺎﺳﺎ ﻣﻦ ﻛﺮﺑﻮﻧﺎت اﻟﻜﺎﻟﺴﯿﻮم CaC O 3(s) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qaiaadg gacaWGdbGaam4tamaaBaaaleaacaaIZaGaaiikaiaadohacaGGPaaa beaaaaa@3C7B@  . ﯾُﺆﺛﺮ ﺣﻤﺾ اﻟﻼﻛﺘﯿﻚ ﻋﻠﻰ ﻛﺮﺑﻮﻧﺎت اﻟﻜﺎﻟﺴﯿﻮم أﺛﻨﺎء ﻋﻤﻠﯿﺔ إزاﻟﺔ ھﺬا اﻟﺮاﺳﺐ. 

    للوقوف  ﻋﻠﻰ ﺑﻌﺾ اﻟﻌﻮاﻣﻞ اﻟﻤﺆﺛﺮة ﻋﻠﻰ ﻣﺪة إزاﻟﺔ اﻟﺮاﺳﺐ، ﻧﺼﺐ ﺣﺠﻤﺎ V=10mL MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvaiabg2 da9iaaigdacaaIWaGaamyBaiaadYeaaaa@3B10@   ﻣﻦ اﻟﻤﺤﻠﻮل المخفف ( S A ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaado fadaWgaaWcbaGaamyqaaqabaGccaGGPaaaaa@3924@   اﻟﺴﺎﺑﻖ ﻟﻠﻤﻘﻠﺢ اﻟﺘﺠﺎري ﻋﻠﻰ ﻛﻤﯿﺔ  من ﻛﺮﺑﻮﻧﺎت اﻟﻜﺎﻟﺴﯿﻮم اﻟﺼﻠﺐ، وﻧﺘﺘﺒﻊ ﺑﺎﺳﺘﻌﻤﺎل ﺗﺮﻛﯿﺐ ﺗﺠﺮﯾﺒﻲ ﻣﻼﺋﻢ ﺗﻄﻮر ﺗﻘﺪم التفاعل. مكنت اﻟﺪراﺳﺔ اﻟﺘﺠﺮﯾﺒﯿﺔ ﺑﺎﺳﺘﻌﻤﺎل وﺳﯿﻂ معلوماتي من ﺧﻂ اﻟﻤﻨﺤﻨﻰ ﺟﺎنبه اﻟﻤﻤﺜﻞ ﻟﺘﻐﯿﺮ اﻟﺘﻘﺪم x MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaaaa@36F4@  للتفاعل بدلالة الزمن.

    3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  1 قيمة زمن نصف التفاعل هي t 1 2 =15 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDamaaBa aaleaadaWccaqaaiaaigdaaeaacaaIYaaaaaqabaGccqGH9aqpcaaI XaGaaGynaaaa@3B2F@  أوجد قيمة x f MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaWGMbaabeaaaaa@380B@  التقدم النهائي للتفاعل.

    3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  2 ﻋﯿﻦ ﻣﺒﯿﺎﻧﯿﺎ قيمة v MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODaaaa@36F2@  السرعة الحجمية للتفاعل عند اللحظة t=22,5s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaiabg2 da9iaaikdacaaIYaGaaiilaiaaiwdacaaMc8Uaam4Caaaa@3D60@  (نذكر أن v= 1 V . dx dt MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODaiabg2 da9maalaaabaGaaGymaaqaaiaadAfaaaGaaiOlamaalaaabaGaamiz aiaadIhaaeaacaWGKbGaamiDaaaaaaa@3E28@  و يمثل المستقيم (Δ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiabfs 5aejaacMcaaaa@38B6@  المماس للمنحنى عند اللحظة t=22,5s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaiabg2 da9iaaikdacaaIYaGaaiilaiaaiwdacaaMc8Uaam4Caaaa@3D60@  ).

    3 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  3  ﺗﺸﯿﺮ اﻟﻠﺼﯿﻘﺔ إﻟﻰ أﻧﮫ ﺧﻼل ﻋﻤﻠﯿﺔ اﻟﺘﻨﻈﯿﻒ ﯾﺠﺐ اﺳﺘﻌﻤﺎل اﻟﻤﻘﻠﺢ اﻟﺘﺠﺎري اﻟﻤﺮﻛﺰ ﻣﻊ اﻟﺘﺴﺨﯿﻦ . ﻣﺎ ھﻮ أﺛﺮ اﺳﺘﻌﻤﺎل اﻟﻤﻘﻠﺢ اﻟﺘﺠﺎري اﻟﻤﺮﻛﺰ ﻣﻊ اﻟﺘﺴﺨﯿﻦ ﻋﻠﻰ اﻟﻤﺪة اﻟﺰﻣﻨﯿﺔ اﻟﻼزﻣﺔ ﻹزاﻟﺔ اﻟﺮاﺳﺐ؟ ﻋﻠﻞ ﺟﻮاﺑﻚ.

    الفيزياء (13 نقطة)

     تمرين النشاط الإشعاعي (3 نقط)

    الإشعاعات النووية في خدمة الطب

    يعتبر اﻟﻄﺐ أﺣﺪ اﻟﻤﺠﺎﻻت اﻟﺮﺋﯿﺴﯿﺔ اﻟﺘﻲ ﻋﺮﻓﺖ ﺗﻄﺒﯿﻘﺎت ﻟﻸﻧﺸﻄﺔ اﻹﺷﻌﺎﻋﯿﺔ؛ ﺣﯿﺚ يوظﻒ ﻋﺪد ﻣﻦ اﻟﻨﻮﯾﺪات اﻟﻤﺸﻌﺔ ﻟﺘﺸﺨﯿﺺ اﻷﻣﺮاض وﻣﻌﺎﻟﺠﺘﮭﺎ، وﻣﻦ بينها الرينيوم R 75 186 e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0raaSqaai aaiEdacaaI1aaabaGaaGymaiaaiIdacaaI2aaaaOGaciOuaiaacwga aaa@3BAD@  الذي تستعمل جرعات منه للتخفيف من ألام الروماتيزم عن طريق الحقن الموضعي.

    المعطيات:

    ثابتة النشاط الإشعاعي للرينيوم R 75 186 e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0raaSqaai aaiEdacaaI1aaabaGaaGymaiaaiIdacaaI2aaaaOGaciOuaiaacwga aaa@3BAD@  : λ= 2,2.10 6 s 1 =0,19jou r 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4UdWMaey ypa0JaaGOmaiaacYcacaaIYaGaaiOlaiaaigdacaaIWaWaaWbaaSqa beaacqGHsislcaaI2aaaaOGaam4CamaaCaaaleqabaGaeyOeI0IaaG ymaaaakiabg2da9iaaicdacaGGSaGaaGymaiaaiMdacaWGQbGaam4B aiaadwhacaWGYbWaaWbaaSqabeaacqGHsislcaaIXaaaaaaa@4B52@  

    1 -  ﺗﻔﺘﺖ ﻧﻮﯾﺪة اﻟﺮﯾﻨﯿﻮم R 75 186 e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0raaSqaai aaiEdacaaI1aaabaGaaGymaiaaiIdacaaI2aaaaOGaciOuaiaacwga aaa@3BAD@

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  1 أﻋﻂ ﺗﺮﻛﯿﺐ ﻧﻮﯾﺪة الرينيوم R 75 186 e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0raaSqaai aaiEdacaaI1aaabaGaaGymaiaaiIdacaaI2aaaaOGaciOuaiaacwga aaa@3BAD@ .

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  2  ينتج عن تفتت نويدة الرينيوم، و حدد طراز هذا الإشعاع.

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbeqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@4150@  الحقن الموضعي بالرينيوم

    يوجد الدواء المستعمل للحقن على شكل جرعات، تحتوي على الرينيوم R 75 186 e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0raaSqaai aaiEdacaaI1aaabaGaaGymaiaaiIdacaaI2aaaaOGaciOuaiaacwga aaa@3BAD@ ، حجم كل واحدة منها V 0 =10mL MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvamaaBa aaleaacaaIWaaabeaakiabg2da9iaaigdacaaIWaGaaGPaVlaad2ga caWGmbaaaa@3D8B@ .

    اﻟﻨﺸﺎط اﻹﺷﻌﺎﻋﻲ ﻟﻠﺮﯾﻨﯿﻮم اﻟﻤﻮﺟﻮد ﻓﻲ ﻛﻞ ﺟﺮﻋﺔ ﻋﻨﺪ اﻟﻠﺤﻈﺔ t 0 =0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDamaaBa aaleaacaaIWaaabeaakiabg2da9iaaicdaaaa@39A0@  هو a 0 = 4.10 9 Bq MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyamaaBa aaleaacaaIWaaabeaakiabg2da9iaaisdacaGGUaGaaGymaiaaicda daahaaWcbeqaaiaaiMdaaaGccaWGcbGaamyCaaaa@3E6F@ .

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  1  ﺣﺪد، ﺑﺎﻟﻮﺣﺪة (jours) ، ﻗﯿﻤﺔ ﻋﻤﺮ اﻟﻨﺼﻒ t 1 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDamaaBa aaleaadaWccaqaaiaaigdaaeaacaaIYaaaaaqabaaaaa@38A5@  للرينيوم R 75 186 e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0raaSqaai aaiEdacaaI1aaabaGaaGymaiaaiIdacaaI2aaaaOGaciOuaiaacwga aaa@3BAD@ .

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  2 أوجد ، عند اللحظة t 1 =4,8jours MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDamaaBa aaleaacaaIXaaabeaakiabg2da9iaaisdacaGGSaGaaGioaiaadQga caWGVbGaamyDaiaadkhacaWGZbaaaa@3FE3@  قيمة N 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtamaaBa aaleaacaaIXaaabeaaaaa@37B1@  ﻋﺪد ﻧﻮﯾﺪات اﻟﺮﯾﻨﯿﻮم اﻟﻤﻮﺟﻮدة ﻓﻲ ﻛﻞ ﺟﺮﻋﺔ.

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  3 عند نفس اللحظة t 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDamaaBa aaleaacaaIXaaabeaaaaa@37D7@  نأخذ من الجرعة ذات الحجم V 0 =10mL MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvamaaBa aaleaacaaIWaaabeaakiabg2da9iaaigdacaaIWaGaaGPaVlaad2ga caWGmbaaaa@3D8B@ ، ﺣﻘﻨﺔ حجمها V MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvaaaa@36D2@  و ﻋﺪد ﻧﻮﯾﺪات اﻟﺮﯾﻨﯿﻮم ﻓﯿﮭﺎ هو N= 3,65.10 13 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtaiabg2 da9iaaiodacaGGSaGaaGOnaiaaiwdacaGGUaGaaGymaiaaicdadaah aaWcbeqaaiaaigdacaaIZaaaaaaa@3E88@  ، ثم نحقن بها مريضا في مفصل الكتف. أوجد قيمة V MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvaaaa@36D2@ .

    تمرين الكهرباء (5 نقط)

    اﻟﻤﻜﺜﻔﺎت اﻟﻌﺎدﯾﺔ واﻟﻤﻜﺜﻔﺎت اﻟﻔﺎﺋﻘﺔ

    اﻟﻤﻜﺜﻔﺎت ﻣﺮﻛﺒﺎت إﻟﻜﺘﺮوﻧﯿﺔ ﺗﺨﺘﻠﻒ ﻣﻦ ﺣﯿﺚ رﺗﺒﺔ ﻗﺪر ﺳﻌﺘﮭﺎ ووظﯿﻔﺘﮭﺎ، إذ ﺗﺴﺘﻌﻤﻞ اﻟﻤﻜﺜﻔﺎت اﻟﻌﺎدﯾﺔ ذات اﻟﺴﻌﺔ ﻣﻦ رﺗﺒﺔ ﻗﺪر اﻟﻤﯿﻜﺮوﻓﺎراد "µF" MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiOiaiaadw lacaWGgbGaaiOiaaaa@3948@  ﻓﻲ اﻷﺟﮭﺰة واﻷﻧﻈﻤﺔ اﻟﻜﮭﺮﺑﺎﺋﯿﺔ واﻹﻟﻜﺘﺮوﻧﯿﺔ اﻟﻤﺘﺪاوﻟﺔ اﻟﺘﻲ ﺗﻌﺘﻤﺪ ﻓﻲ ﻣﺒﺪإ اشتغالها ﻋﻠﻰ اﻟﺘﺬﺑﺬﺑﺎت اﻟﻜﮭﺮﺑﺎﺋﯿﺔ، وﺑﺎﻟﻤﻘﺎﺑﻞ ﺗﻮظﻒ اﻟﻤﻜﺜﻔﺎت اﻟﻔﺎﺋﻘﺔ (supercondensateurs) ذات اﻟﺴﻌﺔ ﻣﻦ رﺗﺒﺔ ﻗﺪر الكيلوفاراد " 10 3 F" MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiOiaiaaig dacaaIWaWaaWbaaSqabeaacaaIZaaaaOGaamOraiaackcaaaa@3A77@  ﻓﻲ ﻣﺤﺮﻛﺎت اﻟﺴﯿﺎرات اﻟﻜﮭﺮﺑﺎﺋﯿﺔ اﻟﮭﺠﯿﻨﺔ (hybrides ) ودارة إﻗﻼع ﻣﺤﺮﻛﺎت اﻟﺘﺮاﻣﻮاي...

    ﯾﮭﺪف ھﺬا اﻟﺘﻤﺮﯾﻦ إﻟﻰ دراﺳﺔ ﺗﺼﺮف ﻣﻜﺜﻒ (ﻋﺎدي/ﻓﺎﺋﻖ) ﻓﻲ دارة ﻛﮭﺮﺑﺎﺋﯿﺔ، وﻣﻘﺎرﻧﺔ ﺗﺨﺰﯾﻦ اﻟﻄﺎﻗﺔ اﻟﻜﮭﺮﺑﺎﺋﯿﺔ ﻓﻲ ھﺬﯾﻦ اﻟﻨﻮﻋﯿﻦ ﻣﻦ اﻟﻤﻜﺜﻔﺎت، وﻛﺬا دراﺳﺔ اﻧﺘﻘﺎل اﻟﻄﺎﻗﺔ ﺑﯿﻦ ﻣﻜﺜﻒ  ووﺷﯿﻌﺔ ﻓﻲ دارة  RLC ﻣﺘﻮاﻟﯿﺔ.

    1 - ﺗﺼﺮف ﻣﻜﺜﻒ ﻓﻲ دارة ﻛﮭﺮﺑﺎﺋﯿﺔ.

    نعتبر  التركيب الممثل في الشكل (1) و المكون من :

    - مولد مؤمثل للتوتر قوته الكهرمحركة E=6V MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyraiabg2 da9iaaiAdacaWGwbaaaa@3962@  

    - مكثف عادي سعته C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qaaaa@36BF@  غير مشحون بدئيا،

    - موصل أومي مقاومته R=65Ω MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOuaiabg2 da9iaaiAdacaaI1aGaeuyQdCfaaa@3AE1@  

    - قاطع التيار K MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4saaaa@36C7@  .

    عند اللحظة t=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaiabg2 da9iaaicdaaaa@38B0@  ، نغلق قاطع التيار فيشحن المكثف.

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  1 أثبت أن المعادلة التفاضلية التي يحققها التوتر u C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaWGdbaabeaaaaa@37E5@  تكتب: d u C dt + 1 R.C . u C = E RC MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGKbGaamyDamaaBaaaleaacaWGdbaabeaaaOqaaiaadsgacaWG0baa aiabgUcaRmaalaaabaGaaGymaaqaaiaadkfacaGGUaGaam4qaaaaca GGUaGaamyDamaaBaaaleaacaWGdbaabeaakiabg2da9maalaaabaGa amyraaqaaiaadkfacaWGdbaaaaaa@44F1@  

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  2 ﺣﻞ اﻟﻤﻌﺎدﻟﺔ اﻟﺘﻔﺎﺿﻠﯿﺔ هو u C =A.(1 e t τ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaWGdbaabeaakiabg2da9iaadgeacaGGUaGaaiikaiaaigda cqGHsislcaWGLbWaaWbaaSqabeaacqGHsisldaWcaaqaaiaadshaae aacqaHepaDaaaaaOGaaiykaaaa@424A@ . أوجد تعبيري الثابتة A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaaaa@36BD@  و ثابتة الزمن τ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdqhaaa@37BC@  بدلالة برامترات الدارة.

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  3 قيمة ثابتة الزمن هي τ= 6,5.10 4 s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdqNaey ypa0JaaGOnaiaacYcacaaI1aGaaiOlaiaaigdacaaIWaWaaWbaaSqa beaacqGHsislcaaI0aaaaOGaam4Caaaa@3FF2@  . استنتج قيمة C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qaaaa@36BF@ .

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  4 احسب قيمة الطاقة الكهربائية ξ e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdG3aaS baaSqaaiaadwgaaeqaaaaa@38D0@  المخزونة في المكثف في النظام الدائم.

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  5 نستبدل في التركيب السابق المكثف العادي بمكثف فائق سعته C 1 = 10 3 F MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qamaaBa aaleaacaaIXaaabeaakiabg2da9iaaigdacaaIWaWaaWbaaSqabeaa caaIZaaaaOGaamOraaaa@3BEA@  و نغلق من جديد قاطع التيار K MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4saaaa@36C7@  .

    أ - ﺣﺪد، ﻣﻌﻠﻼ ﺟﻮاﺑﻚ، ﺗﺄﺛﯿﺮ اﺳﺘﺒﺪال اﻟﻤﻜﺜﻒ اﻟﻌﺎدي ﺑﺎﻟﻤﻜﺜﻒ اﻟﻔﺎﺋﻖ ﻋﻠﻰ ﻣﺪة الشحن.

    ب - ﻧﻌﺘﺒﺮ ξ e1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdG3aaS baaSqaaiaadwgacaaIXaaabeaaaaa@398B@  الطاقة الكهربائية المخزونة في المكثف الفائق عند نهاية الشحن. احسب قيمة النسبة ξ e1 ξ e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaacq aH+oaEdaWgaaWcbaGaamyzaiaaigdaaeqaaaGcbaGaeqOVdG3aaSba aSqaaiaadwgaaeqaaaaaaaa@3C7E@  

    استنتج ﻓﺎﺋﺪة اﻟﻤﻜﺜﻒ اﻟﻔﺎﺋﻖ ﻣُﻘﺎرﻧﺔ ﻣﻊ اﻟﻤﻜﺜﻒ العادي.

    2 - انتقال اﻟﻄﺎﻗﺔ ﺑﯿﻦ ﻣﻜﺜﻒ ووﺷﯿﻌﺔ ﻓﻲ دارة  RLC ﻣﺘﻮاﻟﯿﺔ

    ﻧﻌﻮض ﻓﻲ ﺗﺮﻛﯿﺐ اﻟﺸﻜﻞ (1) اﻟﻤﻮﻟﺪ اﻟﻤﺆﻣﺜﻞ ﻟﻠﺘﻮﺗﺮ ﺑﻮﺷﯿﻌﺔ ﻣﻊاﻣﻞ ﺗﺤﺮﯾﻀﮭﺎ وﻣﻘﺎومتها ﻣﮭﻤﻠﺔ ، وﻧﺴﺘﻌﻤﻞ ﻣﻜﺜﻒ عادي سعته C=10µF MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qaiabg2 da9iaaigdacaaIWaGaaGzaVlaadwlacaWGgbaaaa@3CC9@  مشحون كليا،  ﻛﻠﯿﺎ، ﺛﻢ ﻧﻐﻠﻖ ﻗﺎطﻊ اﻟﺘﯿﺎر ﻋﻨﺪ اللحظة t=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaiabg2 da9iaaicdaaaa@38B0@ . تمَ  اﻟﺤﺼﻮل، ﺑﻮاﺳﻄﺔ وﺳﯿﻂ ﻣﻌﻠﻮﻣﺎتي و لاقط التوتر، على المنحنيين (1) و (2) الممثلين لتغيرات كل من التوتر u C (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaWGdbaabeaakiaacIcacaWG0bGaaiykaaaa@3A41@  بين مربطي المكثف و التوتر u R (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaWGsbaabeaakiaacIcacaWG0bGaaiykaaaa@3A50@  بين مربطي الموصل الأومي (الشكل 2).

     

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  1 ﺑﯿﻦ أن اﻟﻤﻨﺤﻨﻰ (1) ﯾﻤﺜﻞ ﺗﻐﯿﺮات التوتر u C (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaWGdbaabeaakiaacIcacaWG0bGaaiykaaaa@3A41@ .

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  2  ﻋﯿﻦ ﻣﺒﯿﺎﻧﯿﺎ ﻗﯿﻤﺔ ﺷﺒﮫ الدور T MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivaaaa@36D0@  اﺳﺘﻨﺘﺞ ﻗﯿﻤﺔ ﻣﻌﺎﻣﻞ اﻟﺘﺤﺮيض L MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitaaaa@36C8@  للوشيعة باعتبار الدور الخاص T 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivamaaBa aaleaacaaIWaaabeaaaaa@37B6@  للتذبذبات الكهربائية الحرة غير المخمدة يساوي شبه الدور T MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamivaaaa@36D0@  (نأخذ π 2 =10 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiWda3aaW baaSqabeaacaaIYaaaaOGaeyypa0JaaGymaiaaicdaaaa@3B22@  ).

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  3  يعبر عن الطاقة الكلية ξ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdGhaaa@37BA@  للدارة بالعلاقة ξ= ξ e + ξ m MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdGNaey ypa0JaeqOVdG3aaSbaaSqaaiaadwgaaeqaaOGaey4kaSIaeqOVdG3a aSbaaSqaaiaad2gaaeqaaaaa@3F66@ ، حيث ξ e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdG3aaS baaSqaaiaadwgaaeqaaaaa@38D0@  الطاقة الكهربائية المخزونة في المكثف و ξ m MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdG3aaS baaSqaaiaad2gaaeqaaaaa@38D8@  الطاقة المغنطيسية المخزونة في الوشيعة . حدد عند اللحظة t=15ms MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaiabg2 da9iaaigdacaaI1aGaaGPaVlaad2gacaWGZbaaaa@3CE5@  قيمة الطاقة الكلية للدارة.

    تمرين الميكانيك (5 نقط)

     ﻣﻣﯾزات ﺑﻌض اﻟﻣﻘﺎدﯾر اﻟﻣرﺗﺑطﺔ ﺑﺣرﻛﺔ ﺟﺳم ﺻلب

    ﻧﺼﺎدف ﻓﻲ ﺣﯿﺎﺗﻨﺎ اﻟﯿﻮﻣﯿﺔ ﺣﺮﻛﺎت ﻣﺴﺘﻘﯿﻤﯿﺔ ﺗﺨﺘﻠﻒ طﺒﯿﻌﺘﮭﺎ ﺣﺴﺐ ﻧﻮﻋﻲة اﻟﺘﺄﺛﯿﺮات اﻟﻤﯿﻜﺎﻧﯿﻜﯿﺔ ، وﯾﺴﻤﺢ ﺗﻄﺒﯿﻖ ﻗﻮاﻧﯿﻦ ﻧﯿﻮﺗﻦ ﺑﺘﺤﺪﯾﺪ طﺒﯿﻌﺔ ھﺬه اﻟﺤﺮكات وﻣﻤﯿﺰات ﺑﻌﺾ اﻟﻤﻘﺎدﯾﺮ اﻟﻤﺮﺗﺒﻄﺔ ﺑﮭﺎ.

    ﯾﮭﺪف ھﺬا اﻟﺘﻤﺮﯾﻦ إﻟﻰ دراﺳﺔ ﺣﺮﻛﺔ ﺟﺴﻢ ﺻﻠﺐ ﻓﻲ ﺣﺎﻟﺘﯿﻦ، ﺣﯿﺚ ﯾﺨﻀﻊ  في اﻟﺤﺎﻟﺔ اﻷوﻟﻰ إﻟﻰ ﻗﻮة ﺛﺎﺑﺘﺔ و يخضع في الحالة التالية إلى قوة ارتداد.

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbeqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@4150@  الحالة الأولى : دراﺳﺔ ﺣﺮﻛﺔ إزاﺣﺔ ﺟﺴﻢ ﺻﻠﺐ ﻓﻮق ﻣﺴﺘﻮى أﻓﻘﻲ

    ﻧﻀﻊ ﺟﺴﻤﺎ ﺻﻠﺒﺎ (S) ﻣﺮﻛﺰ ﻗﺼﻮره G وﻛﺘﻠﺘﮫ  ﻓﻮق ﻣﺴﺘﻮى أﻓﻘﻲ، وﻧﻄﺒﻖ ﻋﻠﯿﮫ ﺑﻮاﺳﻄﺔ ﺧﯿﻂ ﻗﻮة  F MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmOrayaala aaaa@36D4@  ﺛﺎﺑﺘﺔ أﻓﻘﯿﺔ ﻣﻨﺤﺎھﺎ ھﻮ ﻣﻨﺤﻰ اﻟﺤﺮﻛﺔ . ﻟﺪراﺳﺔ ﺣﺮﻛﺔ G ﻧﺨﺘﺎر ﻣﻌﻠﻤﺎ (A, i ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadg eacaGGSaGabmyAayaalaGaaiykaaaa@39C6@   ﻣﺮﺗﺒﻂا ﺑﺎﻷرض، وﻧﻌﺘﺒﺮ ﻟﺤﻈﺔ اﻧﻄﻼق G ﻣﻦ A  ﺑﺪون ﺳﺮﻋﺔ ﺑﺪﺋﯿﺔ أﺻﻼ ﻟﻠﺘﻮارﯾﺦ (t=0) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaads hacqGH9aqpcaaIWaGaaiykaaaa@3A09@  . ﯾﻤﺮ G ﻣﻦ اﻟﻤﻮﺿﻊ B ﻓﻲ اﻟﻠﺤﻈﺔ t B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDamaaBa aaleaacaWGcbaabeaaaaa@37E3@   ﺑﺎﻟﺴﺮﻋﺔ v B MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmODayaala WaaSbaaSqaaiaadkeaaeqaaaaa@37F7@  (اﻟﺸﻜﻞ 1).

    المعطيات:

    ·         ﻧﮭﻤﻞ ﺟﻤﯿﻊ اﻻﺣﺘﻜﺎﻛﺎت؛

    ·        v B =2m. s 1 ; t b =2s;m=0,25kg MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODamaaBa aaleaacaWGcbaabeaakiabg2da9iaaikdacaWGTbGaaiOlaiaadoha daahaaWcbeqaaiabgkHiTiaaigdaaaGccaaMc8UaaGPaVlaaykW7ca GG7aGaaGPaVlaaykW7caaMc8UaaGPaVlaadshadaWgaaWcbaGaamOy aaqabaGccqGH9aqpcaaIYaGaam4CaiaaygW7caaMb8UaaGzaVlaayg W7caaMb8UaaGzaVlaaygW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPa VlaaykW7caGG7aGaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8 UaamyBaiabg2da9iaaicdacaGGSaGaaGOmaiaaiwdacaWGRbGaam4z aaaa@734A@  

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  1 ﺑﺘﻄﺒﯿﻖ اﻟﻘﺎﻧﻮن اﻟﺜﺎﻧﻲ ﻟﻨﯿﻮﺗﻦ، أﺛﺒﺖ أن اﻟﻤﻌﺎدﻟﺔ اﻟﺘﻔﺎﺿﻠﯿﺔ التي يحققها x G MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaWGhbaabeaaaaa@37EC@  أفصول G MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4raaaa@36C3@  في المعلم (A, i ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadg eacaGGSaGabmyAayaalaGaaiykaaaa@39C6@  هي: d 2 x G d t 2 = F m MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGKbWaaWbaaSqabeaacaaIYaaaaOGaamiEamaaBaaaleaacaWGhbaa beaaaOqaaiaadsgacaWG0bWaaWbaaSqabeaacaaIYaaaaaaakiabg2 da9maalaaabaGaamOraaqaaiaad2gaaaaaaa@3F8A@ .

    استنتج طبيعة حركة G MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4raaaa@36C3@ .

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  2 أوجد التعبير العددي لمتجهة التسارع a 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyyayaala WaaSbaaSqaaiaaigdaaeqaaaaa@37D6@  لحركة G MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4raaaa@36C3@  .

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  3  اُﺣﺴﺐ ﺷﺪة اﻟﻘﻮة F MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmOrayaala aaaa@36D4@ .

    2 -  اﻟﺤﺎﻟﺔ اﻟﺜﺎﻧﯿﺔ: دراﺳﺔ ﺣﺮﻛﺔ ﻣﺠﻤﻮﻋﺔ ﻣﺘﺬﺑﺬﺑﺔ {ﺟﺴﻢ ﺻﻠﺐ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbeqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@4150@  ﻧﺎﺑﺾ}

    نثبت الجسم الصلب (S) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaado facaGGPaaaaa@3828@  السابق بطرف نابض أفقي لفاته غير متصلة و كتلته مهملة و صلابته K MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4saaaa@36C7@ . الجسم (S) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaado facaGGPaaaaa@3828@  قابل للانزلاق بدون احتكاك فوق مستوى أفقي . لدراسة حركة G MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4raaaa@36C3@  نختار معلما (O, i ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaad+ eacaGGSaGabmyAayaalaGaaiykaaaa@39D4@  مرتبطا بالأرض، حيث يكون أفصول G MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4raaaa@36C3@  منعدما عند التوازن ( x G =0) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadI hadaWgaaWcbaGaam4raaqabaGccqGH9aqpcaaIWaGaaiykaaaa@3B0F@  (الشكل 2).

    نزيح الجسم (S) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaado facaGGPaaaaa@3828@  أفقيا عن موضع توازنه في المنحى الموجب بالمسافة X 0 =4cm MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBa aaleaacaaIWaaabeaakiabg2da9iaaisdacaWGJbGaamyBaaaa@3B62@  ثم نحرره بدون سرعة بدئية عند اللحظة t=0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDaiabg2 da9iaaicdaaaa@38B0@  .

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  1 ﺑﺘﻄﺒﯿﻖ اﻟﻘﺎﻧﻮن اﻟﺜﺎﻧﻲ ﻟﻨﯿﻮﺗﻦ، أﺛﺒﺖ اﻟﻤﻌﺎدﻟﺔ اﻟﺘﻔﺎﺿﻠﯿﺔ اﻟﺘﻲ ﯾﺤﻘﻘﮭﺎ اﻷﻓﺼﻮل x G MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaWGhbaabeaaaaa@37EC@  .

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  2 ينجز المتذبذب 10 تذبذبات في المدة الزمنية Δt=10s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaam iDaiabg2da9iaaigdacaaIWaGaaGPaVlaadohaaaa@3D54@  أوجد قيمة K MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4saaaa@36C7@  (نأخذ π 2 =10 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiWda3aaW baaSqabeaacaaIYaaaaOGaeyypa0JaaGymaiaaicdaaaa@3B22@  ).

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  3  حل المعادلة التفاضلية يكتب x(t)= X m .cos( 2π T 0 .t+φ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiaacI cacaWG0bGaaiykaiabg2da9iaadIfadaWgaaWcbaGaamyBaaqabaGc caGGUaGaci4yaiaac+gacaGGZbWaaeWaaeaadaWcaaqaaiaaikdacq aHapaCaeaacaWGubWaaSbaaSqaaiaaicdaaeqaaaaakiaac6cacaGG 0bGaey4kaSIaeqOXdOgacaGLOaGaayzkaaaaaa@49FA@  اوجد التعبير العددي ل x(t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiaacI cacaWG0bGaaiykaaaa@3946@  .

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  4  أوﺟﺪ اﻟﺘﻌﺒﯿﺮ اﻟﻌﺪدي ﻟـ x ˙ (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmiEayaaca GaaiikaiaadshacaGGPaaaaa@394F@   ﺳﺮﻋﺔ ﻣﺮﻛﺰ اﻟﻘﺼﻮرG. ﺣﺪد ﻗﯿﻤﺘﮭﺎ ﻋﻨﺪ ﻣﺮور G ﻣﻦ ﻣﻮﺿﻊ اﻟﺘﻮازن ﻓﻲ المنحى الموجب للمرة الأولى.

    3 - . ترﻣﺰ a 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyyayaala WaaSbaaSqaaiaaikdaaeqaaaaa@37D7@   ﻟﻤﺘﺠﮭﺔ اﻟﺘﺴﺎرع ﻟﺤﺮﻛﺔ G في الحالة الثانية، قارن  a 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyyayaala WaaSbaaSqaaiaaigdaaeqaaaaa@37D6@  و a 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyyayaala WaaSbaaSqaaiaaikdaaeqaaaaa@37D7@ .