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    تمرين الكيمياء (7 نقط)

    ﺗﺼﻨﯿﻊ إﺳﺘﺮ ذي ﻧﻜﮭﺔ اﻟﺘﻔﺎح ـ اﻟﻌﻤﻮد ﻧﺤﺎس/أﻟﻮمينيوم

    ·        اﻟﺠﺰءان 1 و 2 ﻣﺴﺘﻘﻼن

    اﻟﺠﺰء1: ﺗﺼﻨﯿﻊ إﺳﺘﺮ ذي ﻧﻜﮭﺔ اﻟﺘﻔﺎح

    اﻟﻨﻜﮭﺎت اﻟﻐﺬاﺋﯿﺔ ﻣﺮﻛﺒﺎت ﻛﯿﻤﯿﺎﺋﯿﺔ طﺒﯿﻌﯿﺔ ﯾُﺴﺘﺨﺮج أﻏﻠﺒﮭﺎ ﻣﻦ اﻟﻔﻮاﻛﮫ، ﻛﻤﺎ ﯾُﻠﺠﺄ إﻟﻰ ﺗﺼﻨﯿﻌﮭﺎ ﻓﻲ اﻟﻤﺨﺘﺒﺮات، ومن ﺑﯿﻦ ھﺬه اﻟﻨﻜﮭﺎت ﻧﻜﮭﺔ ﻓﺎﻛﮭﺔ التفاح اﻟﺘﻲ ﺗﻌﺰى إﻟﻰ وﺟﻮد ﻣُﺴﺘﺨﺮج طﺒﯿﻌﻲ ﻣﻦ اﻟﺘﻔﺎح أو إﻟﻰ وﺟﻮد إستر (E) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaadw eacaGGPaaaaa@381A@  ﻣُﺼﻨﻊ ھﻮ ﺑﻮﺗﺎﻧﻮات 3- ﻣﺜﯿﻞ اﻟﺒﻮﺗﯿﻞ اﻟﺬي ﯾﺴﺘﻌﻤﻞ ﻛﺜﯿﺮا ﻓﻲ اﻟﺼﻨﺎﻋﺔ اﻟﻐﺬاﺋﯿﺔ واﻟﻌﻄﻮر.

    يهدف ھﺬا اﻟﺠﺰء إﻟﻰ دراﺳﺔ ﺗﺼﻨﯿﻊ اﻹﺳﺘﺮ (E) وﺗﺘﺒﻊ اﻟﺘﻄﻮر اﻟﺰﻣﻨﻲ ﻟﮭﺬه اﻷﺳﺘﺮة.

     

    1.  ﯾُﻤﻜﻦ ﺗﺼﻨﯿﻊ اﻹﺳﺘﺮ(E) اﻧﻄﻼﻗﺎ ﻣﻦ ﺣﻤﺾ ﻛﺮﺑﻮﻛﺴﯿﻠﻲ (A ) وﻛﺤﻮل (B ). ﺣﺪد اﻟﺼﯿﻐﺔ ﻧﺼﻒ اﻟﻤﻨﺸﻮرة ﻟﻜﻞ ﻣﻦ اﻟﺤﻤﺾ (A ) واﻟﻜﺤﻮل (B).

     

    2. ﻧﻨﺠﺰ ھﺬا اﻟﺘﺼﻨﯿﻊ ﺑﺎﺳﺘﻌﻤﺎل ﺗﺮﻛﯿﺐ اﻟﺘﺴﺨﯿﻦ ﺑﺎﻻرﺗﺪاد، ﺣﯿﺚ ﻧﺪﺧﻞ ﻓﻲ ﺣﻮﺟﻠﺔ اﻟﺘﺮﻛﯿﺐ  n A =0,12mol MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBamaaBa aaleaacaWGbbaabeaakiabg2da9iaaicdacaGGSaGaaGymaiaaikda caaMc8UaamyBaiaad+gacaWGSbaaaa@402F@  ﻣن اﻟﺤﻤﺾ (A ) و  n B =0,12mol MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBamaaBa aaleaacaWGcbaabeaakiabg2da9iaaicdacaGGSaGaaGymaiaaikda caaMc8UaamyBaiaad+gacaWGSbaaaa@4030@  ﻣﻦ اﻟﻜﺤﻮل (B ) وﻗﻄﺮات ﻣﻦ ﻣﺤﻠﻮل ﺣﻤﺾ اﻟﻜﺒﺮﯾﺘﯿﻚ وﺑﻌﺾ ﺣﺼﻰ اﻟﺨﻔﺎن 

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  1 اذكر الفائدة من استعمال التسخين بالارتداد.

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  2 أعط اﻟﺪور اﻟﺬي ﯾﻘﻮم به ﺣﻤﺾ اﻟﻜﺒﺮﯾﺘﯿﻚ أﺛﻨﺎء ﻋﻤﻠﯿﺔ اﻟﺘﺼﻨﯿﻊ.

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  3  أﻧﺸﻰء اﻟﺠﺪول اﻟﻮﺻﻔﻲ ﻟﺘﻘﺪم اﻟﺘﻔﺎﻋﻞ اﻟﺤﺎﺻﻞ.

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  4 أثبت أن ﺗﻌﺒﯿﺮ ﺛﺎﺑﺘﺔ اﻟﺘﻮازن اﻟﻤﻘﺮوﻧﺔ ﺑﮭﺬا اﻟﺘﻔﺎﻋﻞ هو K= x éq 2 ( n A x éq ) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4saiabg2 da9maalaaabaGaamiEamaaDaaaleaacaWGPdGaamyCaaqaaiaaikda aaaakeaadaqadaqaaiaad6gadaWgaaWcbaGaamyqaaqabaGccqGHsi slcaWG4bWaaSbaaSqaaiaadMoacaWGXbaabeaaaOGaayjkaiaawMca amaaCaaaleqabaGaaGOmaaaaaaaaaa@4516@  حيث x éq MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaWGPdGaamyCaaqabaaaaa@3984@   ﺗﻘﺪم اﻟﺘﻔﺎﻋﻞ ﻋﻨﺪ ﺣﺎﻟﺔ ﺗﻮازن اﻟﻤﺠﻤﻮﻋﺔ اﻟﻜﯿﻤﯿﺎﺋﯿﺔ. اﺳﺘﻨﺘﺞ قيمة x éq MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaWGPdGaamyCaaqabaaaaa@3984@ .

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  5 احسب  ﻗﯿﻤﺔ  r MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOCaaaa@36EE@  ﻣﺮدود ھﺬا اﻟﺘﺼﻨﯿﻊ.

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  6  ﺑﺎﺳﺘﻌﻤﺎل ﻧﻔﺲ اﻟﺘﺮﻛﯿﺐ اﻟﺘﺠﺮﯾﺒﻲ وﻧﻔﺲ اﻟﺤﺎﻟﺔ اﻟﺒﺪﺋﯿﺔ ﻟﻠﻤﺘﻔﺎﻋﻠﯿﻦ وﻧﻔﺲ اﻟﺤﻔﺎز:

    أ - كيف ﯾﻤﻜﻦ ﺗﺴﺮﯾﻊ ﺗﺼﻨﯿﻊ اﻹﺳﺘﺮ (E) ؟

    ب - ﻛﯿﻒ ﯾﻤﻜﻦ رﻓﻊ ﻗﯿﻤﺔ x éq MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaWGPdGaamyCaaqabaaaaa@3984@ ؟

     

    الجزء 2: اﻟﻌﻤﻮد ﻧﺤﺎس/أﻟﻮمينيوم

    ننجز عمودا ﺑﺎﺳﺘﻌﻤﺎل ﻣﺰدوﺟﺘﯿﻦ (ﻣﺨﺘﺰل/ﻣﺆﻛﺴﺪ) ﻣﻦ ﻧﻮع M (aq) n+ / M (s) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamytamaaDa aaleaacaGGOaGaamyyaiaadghacaGGPaaabaGaamOBaiabgUcaRaaa kiaac+cacaWGnbWaaSbaaSqaaiaacIcacaGGZbGaaiykaaqabaaaaa@400B@   ﺣﯿﺚ M ﻓﻠﺰ و M n+ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamytamaaCa aaleqabaGaamOBaiabgUcaRaaaaaa@38CB@   اﻷﯾﻮن اﻟﻔﻠﺰي المواﻓﻖ ﻟﮫ. ﻣﻜﻮﻧﺎت ھﺬا اﻟﻌﻤﻮد هي:

    - محلول مائي لكلورور الألومينيوم A l (aq) 3+ +3C l (aq) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaiaadY gadaqhaaWcbaGaaiikaiaadggacaWGXbGaaiykaaqaaiaaiodacqGH RaWkaaGccqGHRaWkcaaIZaGaam4qaiaadYgadaqhaaWcbaGaaiikai aadggacaWGXbGaaiykaaqaaiabgkHiTaaaaaa@4460@  تركيزه المولي C=0,1mol. L 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qaiabg2 da9iaaicdacaGGSaGaaGymaiaaykW7caWGTbGaam4BaiaadYgacaGG UaGaamitamaaCaaaleqabaGaeyOeI0IaaGymamaaCaaameqabaaaaa aaaaa@41D2@  

    - محلول مائي لكبريتات النحاس II C u (aq) 2+ +S O 4(aq) 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qaiaadw hadaqhaaWcbaGaaiikaiaadggacaWGXbGaaiykaaqaaiaaikdacqGH RaWkaaGccqGHRaWkcaWGtbGaam4tamaaDaaaleaacaaI0aGaaiikai aadggacaWGXbGaaiykaaqaaiaaikdacqGHsislaaaaaa@451A@  تركيزه المولي C=0,1mol. L 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qaiabg2 da9iaaicdacaGGSaGaaGymaiaaykW7caWGTbGaam4BaiaadYgacaGG UaGaamitamaaCaaaleqabaGaeyOeI0IaaGymamaaCaaameqabaaaaa aaaaa@41D2@  

    - ﺻﻔﯿﺤﺔ ﻣﻦ اﻷﻟﻮمينيوم A l (s) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaiaadY gadaWgaaWcbaGaaiikaiaadohacaGGPaaabeaaaaa@3A2B@  

    - ﺻﻔﯿﺤﺔ ﻣﻦ النحاس C u (s) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qaiaadw hadaWgaaWcbaGaaiikaiaadohacaGGPaaabeaaaaa@3A36@

    - قنطرة ايونية من نترات البوتاسيوم.

    المعطيات:

     للمحلولين نفس الحجم M(Al)=27g.mo l 1 ;lF= 9,65.10 4 C.mo l 1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamytaiaacI cacaWGbbGaamiBaiaacMcacqGH9aqpcaaIYaGaaG4naiaaykW7caWG NbGaaiOlaiaad2gacaWGVbGaamiBamaaCaaaleqabaGaeyOeI0IaaG ymaaaakiaaykW7caaMc8Uaai4oaiaaykW7caaMc8UaaGPaVlaaykW7 caWGSbGaamOraiabg2da9iaaiMdacaGGSaGaaGOnaiaaiwdacaGGUa GaaGymaiaaicdadaahaaWcbeqaaiaaisdaaaGccaWGdbGaaiOlaiaa d2gacaWGVbGaamiBamaaCaaaleqabaGaeyOeI0IaaGymaaaaaaa@5D32@  

     ﺛﺎﺑﺘﺔ اﻟﺘﻮازن اﻟﻤﻘﺮوﻧﺔ بالمعادلة 3C u (aq) 2+ +2A l (s) 3C u (s) +2A l (aq) 3+ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG4maiaado eacaWG1bWaa0baaSqaaiaacIcacaWGHbGaamyCaiaacMcaaeaacaaI YaGaey4kaScaaOGaey4kaSIaaGOmaiaadgeacaWGSbWaaSbaaSqaai aacIcacaWGZbGaaiykaaqabaGccqWImhYGcaaIZaGaam4qaiaadwha daWgaaWcbaGaaiikaiaadohacaGGPaaabeaakiabgUcaRiaaikdaca WGbbGaamiBamaaDaaaleaacaGGOaGaamyyaiaadghacaGGPaaabaGa aG4maiabgUcaRaaaaaa@52B9@   هي K= 10 20 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4saiabg2 da9iaaigdacaaIWaWaaWbaaSqabeaacaaIYaGaaGimaaaaaaa@3AE5@ .

    1 - اُﺣﺴﺐ ﻗﯿﻤﺔ Q r,i MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyuamaaBa aaleaacaWGYbGaaiilaiaadMgaaeqaaaaa@398E@  خارج التفاعل عند الحالة البدئية للمجموعة الكيميائية.

    2 - اﺳﺘﻨﺘﺞ ﻣﻨﺤﻰ اﻟﺘﻄﻮر اﻟﺘﻠﻘﺎﺋﻲ ﻟﻠﻤﺠﻤﻮﻋﺔ اﻟﻜﯿﻤﯿﺎﺋﯿﺔ عند اشتغال العمود.

    3 - حدد، ﻣﻌﻠﻼ ﺟﻮاﺑﻚ، ﻗﻄﺒﯿﺔ ﻛﻞ إﻟﻜﺘﺮود.

    4 - ﻧﺮﻛﺐ ﺑﯿﻦ ﻣﺮﺑﻄﻲ ھﺬا اﻟﻌﻤﻮد ﻣﻮﺻﻼ أوﻣﯿﺎ ﻓﯿﻤﺮ ﻓﻲ اﻟﺪارة ﺗﯿﺎر ﻛﮭﺮﺑﺎﺋﻲ ﺷﺪته I=40mA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysaiabg2 da9iaaisdacaaIWaGaaGPaVlaad2gacaWGbbaaaa@3C86@  ﻟﻤﺪة زﻣﻨﯿﺔ Δt=1h30min MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaam iDaiabg2da9iaaigdacaaMc8UaaGPaVlaadIgacaaMc8UaaGPaVlaa iodacaaIWaGaaGPaVlaaykW7ciGGTbGaaiyAaiaac6gaaaa@488F@  .

    4 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  1 بين أن ﺗﻌﺒﯿﺮ ﻛﻤﯿﺔ ﻣﺎدة اﻷﻟﻮﻣﯿﻨﯿﻮم اﻟﻤﺘﻔﺎﻋﻞ هو n(Al)= I.Δt 3.F MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBaiaacI cacaWGbbGaamiBaiaacMcacqGH9aqpdaWcaaqaaiaadMeacaGGUaGa euiLdqKaamiDaaqaaiaaiodacaGGUaGaamOraaaaaaa@4129@  

    4 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  2  اﺳﺘﻨﺘﺞ ﻗﯿﻤﺔ m(Al) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBaiaacI cacaWGbbGaamiBaiaacMcaaaa@39F9@   ﻛﺘﻠﺔ اﻷﻟﻮﻣﯿﻨﯿﻮم اﻟﻤﺘﻔﺎﻋﻞ ﺧﻼل اﻟﻤﺪة Δt MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaam iDaaaa@3856@  .

    الفيزياء (13 نقطة)

     تمرين الموجات (3 نقط)

    انتشار موجة ميكانيكية متوالية

    ﺧﻼل ﺣﺼﺔ ﻟﻸﺷﻐﺎل التطبيقية، ﻗﺎم أﺳﺘﺎذ ﻣﻊ ﺗﻼﻣﯿﺬه ﺑﺪراﺳﺔ اﻧﺘﺸﺎر ﻣﻮﺟﺔ ﻣﯿﻜﺎﻧﯿﻜﯿﺔ ﻣﺘﻮاﻟﯿﺔ ﻋﻠﻰ ﺳﻄﺢ اﻟﻤﺎء باستعمال حوض الموجات، قصد التعرف على بعض خاصياتها.

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbeqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@4150@  يحدث مسمار رأسي (S) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaado facaGGPaaaaa@3828@   ﻣﺘﺼﻞ ﺑﮭﺰاز ﺗﺮدده N=20Hz MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtaiabg2 da9iaaikdacaaIWaGaaGPaVlaadIeacaWG6baaaa@3C9D@  ، ﻋﻨﺪ اﻟﻠﺤﻈﺔ t 0 =0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDamaaBa aaleaacaaIWaaabeaakiabg2da9iaaicdaaaa@39A0@   ﻣﻮﺟﺔ ﻣﺘﻮاﻟﯿﺔ ﺟﯿﺒﯿﺔ ﻋﻠﻰ اﻟﺴﻄﺢ اﻟﺤﺮ ﻟﻤﺎء ﺣﻮض اﻟﻤﻮﺟﺎت، ﻓﺘﻨﺘﺸﺮ دون ﺧﻤﻮد وﻻ اﻧﻌﻜﺎس. ﯾﻤﺜﻞ الشكل (1)  ﻣﻈﮭﺮ ﺳﻄﺢ اﻟﻤﺎء ﻋﻨﺪ اﻟﻠﺤﻈﺔ ﺣﯿﺚ ﺗﻤﺜﻞ اﻟﺪواﺋﺮ ﺧﻄﻮط اﻟﺬرى.

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  1  ھﻞ اﻟﻤﻮﺟﺔ اﻟﻤﻦتﺷﺮة ﻋﻠﻰ ﺳﻄﺢ اﻟﻤﺎء طﻮﻟﯿﺔ أم ﻣﺴﺘﻌﺮﺿﺔ؟ ﻋﻠﻞ ﺟﻮاﺑﻚ.

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  2  ﻋﯿﻦ قيمة طﻮل اﻟﻤﻮﺟﺔ λ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4UdWgaaa@37AB@   .

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  3 اﺳﺘﻨﺘﺞ ﻗﯿﻤﺔ  ﺳﺮﻋﺔ اﻧﺘﺸﺎر اﻟﻤﻮﺟﺔ ﻋﻠﻰ ﺳﻄﺢ اﻟﻤﺎء.

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  4  ﻧﻌﺘﺒﺮ ﻧﻘﻄﺔ M ﻣﻦ وﺳﻂ اﻻﻧﺘﺸﺎر ﺗﺒﻌﺪ ﻋﻦ اﻟﻤﻨﺒﻊ S ﺑﺎﻟﻤﺴﺎﻓﺔ SM=5cm MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4uaiaad2 eacqGH9aqpcaaI1aGaaGPaVlaadogacaWGTbaaaa@3CCB@  . اُﺣﺴﺐ ﻗﯿﻤﺔ اﻟﺘﺄﺧﺮ اﻟﺰﻣﻨﻲ τ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdqhaaa@37BC@   ﻟﺤﺮﻛﺔ M ﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﻤﻨﺒﻊ S .

    2 - ﻧﻀﻊ ﻓﻲ ﺣﻮض اﻟﻤﻮﺟﺎت ﺻﻔﯿﺤﺘﯿﻦ رأﺳﯿﺘﯿﻦ تﺷﻜﻼن ﺣﺎﺟﺰا ﺑﮫ ﻓﺘﺤﺔ ﻋﺮﺿﮭﺎ a MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyyaaaa@36DD@  وﻧﺸﻐﻞ ﻣﻦ ﺟﺪﯾﺪ اﻟﮭﺰاز ﺑﺎﻟﺘﺮدد N=20Hz MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtaiabg2 da9iaaikdacaaIWaGaaGPaVlaadIeacaWG6baaaa@3C9D@   . ﯾﻤﺜﻞ اﻟﺸﻜﻞ (2) ﻣﻈﮭﺮ ﺳﻄﺢ اﻟﻤﺎء ﻋﻨﺪ ﻟﺤﻈﺔ t .

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  1 سم اﻟﻈﺎھﺮة اﻟﺘﻲ ﯾﺒﺮزھﺎ الشكل (2). ﻋﻠﻞ ﺟﻮاﺑﻚ.

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  2 ﺣﺪد، ﻣﻌﻠﻼ ﺟﻮاﺑﻚ، ﻗﯿﻤﺔ ﺳﺮﻋﺔ اﻧﺘﺸﺎر اﻟﻤﻮﺟﺔ ﺑﻌﺪ اﺟﺘﯿﺎزھﺎ ﻟﻠﺤﺎﺟﺰ.

    تمرين الكهرباء (5 نقط)

    دراسة ثنائيات القطب RC MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOuaiaado eaaaa@3796@  و RL MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOuaiaadY eaaaa@379F@  و RLC MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOuaiaadY eacaWGdbaaaa@3867@  

    ﺗُﻤﻜﻦ ﻣﻌﺎﯾﻨﺔ اﻟﺘﻮﺗﺮ u R (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaWGsbaabeaakiaacIcacaWG0bGaaiykaaaa@3A50@    ﺑﯿﻦ ﻣﺮﺑﻄﻲ ﻣﻮﺻﻞ أوﻣﻲ ﻣﻦ دراﺳﺔ اﺳﺘﺠﺎﺑﺔ ﺛﻨﺎئي اﻟﻘﻄﺐ RL أو RC  ﻟﺮﺗﺒﺔ ﺗﻮﺗﺮ، و ﺗﺼﺮفه ﻓﻲ دارة ﻛﮭﺮﺑﺎﺋﯿﺔ، وﻛﺬا دراﺳﺔ اﻟﺘﺬﺑﺬﺑﺎت اﻟﻜﮭﺮﺑﺎﺋﯿﺔ ﻓﻲ دارة RLC ﻣﺘﻮاﻟﯿﺔ. 

    يهدف ھﺬا اﻟﺘﻤﺮﯾﻦ إﻟﻰ ﺗﻌﺮف  ﻧﻮع ﺛﻨﺎﺋﻲ اﻟﻘﻄﺐ وﺗﺤﺪﯾﺪ ﺑﻌﺾ اﻟﻤﻘﺎدﯾﺮ اﻟﻤﻤﯿﺰة ﻟﻤﺮﻛﺒﺎته ، وﻛﺬا دراﺳﺔ اﻟﺘﺒﺎدل اﻟﻄﺎﻗﻲ ﻓﻲ دارة RLC ﻣﺘﻮاﻟﯿﺔ.

    1 - دراﺳﺔ ﺛﻨﺎﺋﯿﻲ اﻟﻘﻄﺐ RL  و RC

    يتكون اﻟﺘﺮﻛﯿﺐ (1) ﻣﻦ ﻣﻮﻟﺪ G ﻣﺆﻣﺜﻞ ﻟﻠﺘﻮﺗﺮ ﻗﻮﺗﮫ اﻟﻜﮭﺮﻣﺤﺮﻛﺔ E ووﺷﯿﻌﺔ ﻣﻌﺎﻣﻞ ﺗﺤﺮﯾﻀﮭﺎ L وﻣﻘﺎوﻣﺘﮭﺎ ﻣﮭﻤﻠﺔ و موصل أومي مقاومته R=10Ω MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOuaiabg2 da9iaaigdacaaIWaGaeuyQdCfaaa@3AD7@  و قاطع التيار K.

    - يتكون  اﻟﺘﺮﻛﯿﺐ (2) ﻣﻦ ﻣﻮلد G ﻣﺆﻣﺜﻞ ﻟﻠﺘﻮﺗﺮ ﻗﻮته اﻟﻜﮭﺮﻣﺤﺮﻛﺔ E وﻣﻜﺜﻒ ﺳﻌته C  وﻣﻮﺻﻞ أوﻣﻲ مقاومته R=10Ω MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOuaiabg2 da9iaaigdacaaIWaGaaGPaVlabfM6axbaa@3C62@  و قاطع التيار K.

     

    عند اللحظة (t=0) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaads hacqGH9aqpcaaIWaGaaiykaaaa@3A09@  ، ﻧﻐﻠﻖ ﻗﺎطﻊ اﻟﺘﯿﺎر ﻓﻲ ﻛﻞ ﺗﺮﻛﯿﺐ وﻧﻌﺎﯾﻦ ﺑﻮاﺳﻄﺔ ﺟﮭﺎز ﻣﻼﺋﻢ اﻟﺘﻮﺗﺮ u R (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaWGsbaabeaakiaacIcacaWG0bGaaiykaaaa@3A50@    ﺑﯿﻦ ﻣﺮﺑﻄﻲ اﻟﻤﻮﺻﻞ اﻷوﻣﻲ ﻓﻲ ﻛﻞ ﺗﺮﻛﯿﺐ فنحصل ﻋﻠﻰ اﻟﻤﻨﺤﻨﯿﯿﻦ (أ) و (ب) اﻟﻤﻤﺜﻠﯿﻦ ﻓﻲ اﻟﺸﻜﻞ (2).

     

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  1 بين أن اﻟﻤﻨﺤﻨﻰ (أ) ﯾﻮاﻓﻖ اﻟﺘﺮﻛﯿﺐ اﻟﻜﮭﺮﺑﺎﺋﻲ (1).

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  2  أﺛﺒﺖ أن اﻟﻤﻌﺎدﻟﺔ اﻟﺘﻔﺎﺿﻠﯿﺔ اﻟﺘﻲ ﯾﺤﻘﻘﮭﺎ اﻟﺘﻮﺗﺮ u R (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaWGsbaabeaakiaacIcacaWG0bGaaiykaaaa@3A50@   ﺑﯿﻦ ﻣﺮﺑﻄﻲ اﻟﻤﻮﺻﻞ اﻷوﻣﻲ ﻓﻲ اﻟﺘﺮﻛﯿﺐ (1) ﺗﻜﺘﺐ: d u R dt + R L . u R = R.E L MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaca WGKbGaamyDamaaBaaaleaacaWGsbaabeaaaOqaaiaadsgacaWG0baa aiabgUcaRmaalaaabaGaamOuaaqaaiaadYeaaaGaaiOlaiaadwhada WgaaWcbaGaamOuaaqabaGccqGH9aqpdaWcaaqaaiaadkfacaGGUaGa amyraaqaaiaadYeaaaaaaa@4466@  

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  3 ﺣﻞ اﻟﻤﻌﺎدﻟﺔ اﻟﺘﻔﺎﺿﻠﯿﺔ هو u R =A(1 e t τ ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyDamaaBa aaleaacaWGsbaabeaakiabg2da9iaadgeacaGGOaGaaGymaiabgkHi TiaadwgadaahaaWcbeqaaiabgkHiTmaalaaabaGaamiDaaqaaiabes 8a0baaaaGccaGGPaaaaa@41A7@  . أوجد تعبير كل من الثابتتين A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaaaa@36BD@  و 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@  4 باستغلال اﻟﻤﻨﺤﻨﻰ (أ):

    أ - عين ﻣﺒﯿﺎﻧﯿﺎ ﻗﯿﻤﺔ ﻛﻞ ﻣﻦ اﻟﻘﻮة اﻟﻜﮭﺮﻣﺤﺮﻛﺔ E وﺛﺎﺑﺘﺔ اﻟﺰﻣﻦ τ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqiXdqhaaa@37BC@  .

    ب - اﺳﺘﻨﺘﺞ ﻗﯿﻤﺔ ﻣﻌﺎﻣﻞ اﻟﺘﺤﺮﯾﺾ L MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitaaaa@36C8@  للوشيعة.

    1 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  5 باﺳﺘﻐﻼل اﻟﻤﻨﺤﻨﻰ (ب) اﻟﺬي ﯾﻮاﻓﻖ اﻟﺘﺮﻛﯿﺐ (2):

    أ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  أوجد قيمة C MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4qaaaa@36BF@  ﺳﻌﺔ اﻟﻤﻜﺜﻒ.

    ب - ﻋﯿﻦ اﻟﻠﺤﻈﺔ اﻟﺘﻲ ﯾﺸﺤﻦ ﻓيه اﻟﻤﻜﺜﻒ ﻛﻠﯿﺎ.

     

    2 - ﻧﻌﻮض ﻓﻲ اﻟﺘﺮﻛﯿﺐ (1) اﻟﻤﻮلد G MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4raaaa@36C3@  بمكثف مشحون بدئيا. ﺗﻤﺜﻞ وﺛﯿﻘﺔ اﻟﺸﻜﻞ (3) اﻟﺘﻄﻮر اﻟﺰﻣﻨﻲ ﻟﻠﻄﺎﻗﺔ اﻟﻜﮭﺮﺑﺎﺋﯿﺔ ξ e MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdG3aaS baaSqaaiaadwgaaeqaaaaa@38D0@  اﻟﻤﺨﺰوﻧﺔ ﻓﻲ اﻟﻤﻜﺜﻒ، واﻟﻄﺎﻗﺔ اﻟﻤﻐﻨﻄﯿﺴﯿﺔ ξ m MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdG3aaS baaSqaaiaad2gaaeqaaaaa@38D8@  اﻟﻤﺨﺰوﻧﺔ ﻓﻲ اﻟﻮﺷﯿﻌﺔ، واﻟﻄﺎﻗﺔ اﻟﻜﻠﯿﺔ ξ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdGhaaa@37BA@  للدارة حيث ξ= ξ e + ξ m MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqOVdGNaey ypa0JaeqOVdG3aaSbaaSqaaiaadwgaaeqaaOGaey4kaSIaeqOVdG3a aSbaaSqaaiaad2gaaeqaaaaa@3F66@  .

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  1 أقرن ﻛﻞ ﻣﻨﺤﻨﻰ ﺑﺎﻟﻄﺎﻗﺔ اﻟﻤﻮاﻓﻘﺔ له.

    2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  2 حدد، بين اللحظتين t 0 =0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDamaaBa aaleaacaaIWaaabeaakiabg2da9iaaicdaaaa@39A0@  و t 1 =30ms MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiDamaaBa aaleaacaaIXaaabeaakiabg2da9iaaiodacaaIWaGaaGPaVlaad2ga caWGZbaaaa@3DD3@  قيمة Δξ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq OVdGhaaa@3920@  ﺗﻐﯿﺮ اﻟﻄﺎﻗﺔ اﻟﻜﻠﯿﺔ ﻟﻠﺪارة.

    تمرين الميكانيك (5 نقط)

    الكرة المستطيلة

    يستأثر ﻋﺪد ﻣﻦ اﻟﺮﯾﺎﺿﺎت اﻟﺠﻤﺎﻋﯿﺔ ﻛﻜﺮة اﻟﻘﺪم واﻟﻜﺮة اﻟﻤﺴﺘﻄﯿﻠﺔ وﻛﺮة اﻟﺴﻠﺔ ... ﺑﺘﺘﺒﻊ اﻟﻤﻼﯾﯿﻦ ﻣﻦ اﻟﻤﺘﻔﺮﺟﯿﻦ ﻋﺒﺮ اﻟﻌﺎﻟﻢ، وتشكل ﺿﺮﺑﺎت الجزاء ﻓﺮﺻﺎ ﺣﻘﯿﻘﯿﺔ ﻟﺘﺴﺠﯿﻞ اﻷھﺪاف ﺣﯿﺚ ﺗﻠlﻌﺐ اﻟﺸﺮوط اﻟﺒﺪﺋﯿﺔ دورا أﺳﺎﺳﯿﺎ ﻓﻲ ذﻟﻚ.  

     ﺘﻜﻮن ﻣﺮﻣﻰ ﻣﻠﻌﺐ اﻟﻜﺮة اﻟﻤﺴﺘﻄﯿﻠﺔ ﻣﻦ ﻋﺎرﺿﺘﯿﻦ رأﺳﯿﺘﯿﻦ ﻣﺘﻮازﯾﺘﯿﻦ وﻋﺎرﺿﺔ أﻓﻘﯿﺔ ﺗﻮﺟﺪ ﻋﻠﻰ ﻋﻠﻮ h MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiAaaaa@36E4@  ﻣﻦ ﺳﻄﺢ اﻷرض (اﻟﺸﻜﻞ1)

    يهدف ھﺬا اﻟﺘﻤﺮﯾﻦ إﻟﻰ دراﺳﺔ حرﻛﺔ G ﻣﺮﻛﺰ ﻗﺼﻮر ﻛﺮة ﻣﺴﺘﻄﯿﻠﺔ ﻓﻲ ﻣﺠﺎل اﻟﺜﻘﺎﻟﺔ اﻟﻤﻨﺘﻈﻢ، وﺗﻌﺮف ﺗﺄﺛﯿﺮ اﻟﺸﺮوط ﻋﻠﻰ ﺗﺴﺠﯿﻞ ﺿﺮﺑﺔ اﻟﺠﺰاء.

     

    ﺧﻼل ﺣﺼﺔ ﺗﺪرﯾﺒﯿﺔ ﻟﻔﺮﯾﻖ ﻋﻠﻰ ﺗﺴﺪﯾﺪ ﺿﺮﺑﺎت اﻟﺠﺰاء، ﻧﻔﺬ ﻻﻋﺐ ﺿﺮﺑﺔ ﺟﺰاء ﻣﻦ ﻣﻮﺿﻊ O ﯾﻮﺟﺪ ﻋﻠﻰ اﻟﻤﺴﺎﻓﺔ OM MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4taiaad2 eaaaa@379D@  من خط المرمى في لحظة نعتبرها أصلا للتواريخ (t=0) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikaiaads hacqGH9aqpcaaIWaGaaiykaaaa@3A09@  بسرعة بدئية v 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmODayaala WaaSbaaSqaaiaaicdaaeqaaaaa@37EA@  تكون زاوية α MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegaaa@3796@  مع المستوى الأفقي.

    M MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamytaaaa@36C9@   وﺳﻂ ﺧﻂ اﻟﻤﺮﻣﻰ اﻟﻤﺤﺼﻮر ﺑﯿﻦ اﻟﻌﺎرﺿﺘﯿﻦ اﻟﺮأسيتين.

    ﻟﺪراﺳﺔ ﺣﺮﻛﺔ ﻣﺮﻛﺰ اﻟﻘﺼﻮر G ﻟﻜﺮة ﻣﺴﺘﻄﯿﻠﺔ ﻛﺘﻠﺘﮭﺎ m MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBaaaa@36E9@   ، ﻧﺨﺘﺎر ﻣﻌﻠﻤﺎ ﻣﺘﻌﺎمدا ﻣﻤﻨﻈﻤﺎ ( O, i , j ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca WGpbGaaiilaiqadMgagaWcaiaacYcaceWGQbGbaSaaaiaawIcacaGL Paaaaaa@3BB5@  ﻣﺮﺗﺒﻄﺎ ﺑﺎﻷرض الشكل (1).

    المعطيات:

    - نهمل تأثير الهواء و جميع الاحتكاكات،

    - h=3m;OM=22m;g=10m. s 2 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiAaiabg2 da9iaaiodacaWGTbGaaGPaVlaaykW7caaMc8UaaGPaVlaacUdacaaM c8UaaGPaVlaaykW7caaMc8Uaam4taiaad2eacqGH9aqpcaaIYaGaaG Omaiaad2gacaaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caGG 7aGaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8Uaam4zaiabg2 da9iaaigdacaaIWaGaaGPaVlaad2gacaGGUaGaam4CamaaCaaaleqa baGaeyOeI0IaaGOmaaaaaaa@686D@  

     

    1 - ﺑﺘﻄﺒﯿﻖ اﻟﻘﺎﻧﻮن اﻟﺜﺎﻧﻲ ﻟﻨﯿﻮﺗﻦ، أﺛﺒﺖ اﻟﻤﻌﺎدﻟﺘﯿﻦ اﻟﺘﻔﺎﺿﻠﯿﺘﯿﻦ اﻟﻠﺘﯿﻦ ﺗﺤﻘﻘﮭﻤﺎ  v x MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODamaaBa aaleaacaWG4baabeaaaaa@381B@  و v y MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODamaaBa aaleaacaWG5bWaaSbaaWqaaaqabaaaleqaaaaa@3854@  إﺣﺪاﺛﯿﺘﻲ ﻣﺘﺠﮭﺔ اﻟﺴﺮﻋﺔ v G MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmODayaala WaaSbaaSqaaiaadEeaaeqaaaaa@37FC@  في المعلم ( O, i , j ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaaca WGpbGaaiilaiqadMgagaWcaiaacYcaceWGQbGbaSaaaiaawIcacaGL Paaaaaa@3BB5@  .

    2 - أوﺟﺪ اﻟﺘﻌﺒﯿﺮ اﻟﺤﺮﻓﻲ ﻟﻠﻤﻌﺎدﻟﺘﯿﻦ اﻟﺰﻣﻨﯿﺘﯿﻦ x(t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaiaacI cacaWG0bGaaiykaaaa@3946@  و y(t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiyEaiaacI cacaWG0bGaaiykaaaa@3946@   ﻟﺤﺮﻛﺔ G MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4raaaa@36C3@  .

    3 -  اﺳﺘﻨﺘﺞ اﻟﺘﻌﺒﯿﺮ اﻟﺤﺮﻓﻲ ﻟﻤﻌﺎدﻟﺔ ﻣﺴﺎر ﺣﺮﻛﺔ G MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4raaaa@36C3@  .

    4 -  ﺑﯿﻦ أن ﺗﻌﺒﯿﺮ اﻟﻤدى هو x P = v 0 2 sin2α g MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEamaaBa aaleaacaWGqbaabeaakiabg2da9maalaaabaGaamODamaaDaaaleaa caaIWaaabaGaaGOmaaaakiGacohacaGGPbGaaiOBaiaaikdacqaHXo qyaeaacaWGNbaaaaaa@41DC@  .

    5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbeqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@4150@  يعتبر  اﻟﮭﺪف ﻣﺴﺠﻼ ﻋﻨﺪ ﻣﺮور اﻟﻜﺮة ﻓﻮق اﻟﻌﺎرﺿﺔ اﻷﻓﻘﯿﺔ وﺑﯿﻦ اﻟﻌﺎرضتين اﻟﺮأسيتين.

    ﺧﻼل ﻣﺤﺎوﻻت ﻗﺬف ﺿﺮﺑﺔ اﻟﺠﺰاء ﺑﻨﻔﺲ اﻟﺰاوﯾﺔ α 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS baaSqaaiaaicdaaeqaaaaa@387C@   وﺑﺴﺮﻋﺎت ﺑﺪﺋﯿﺔ ﻣﺨﺘﻠﻔﺔ ﻟﺜﻼﺛﺔ ﻻﻋﺒﯿﻦ (1) و (2) و (3) ﺗﻢ ﺗﺼﻮير ﺣﺮﻛﺔ اﻟﻜﺮة. وﺑﺎﺳﺘﻌﻤﺎل وﺳﺎﺋﻞ ﻣﻌﻠﻮﻣﺎﺗﯿﺔ ﺗﻢ اﻟﺤﺼﻮل ﻋﻠﻰ وﺛﯿﻘﺔ اﻟﺸﻜﻞ (2) اﻟﻤﻤﺜﻠﺔ ﻟﻤﺴﺎرات ﺣﺮﻛﺔ G.

    باﺳﺘﻐﻼل ﻣﻌﻄﯿﺎت وﺛﯿﻘﺔ اﻟﺸﻜﻞ (2):

    5 - 1 ﺣﺪد ﻣﻦ ﺑﯿﻦ اﻟﻼﻋﺒﯿﻦ ﻣﻦ ﺳﯿﺘﻤﻜﻦ من ﺗﺴﺠﯿﻞ اﻟﮭﺪف. ﻋﻠﻞ ﺟﻮاﺑﻚ.

    5 - 2 ﻣﺎ ھﻮ ﺗﺄﺛﯿﺮ ﻗﯿﻤﺔ اﻟﺴﺮﻋﺔ اﻟﺒﺪﺋﯿﺔ ﻋﻠﻰ ﻣﺪى وﻗﻤﺔ اﻟﻤﺴﺎر؟

    5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbgjxD0L 2zLjhimrfibjxyIL2yGutnGi1BTfMBaeXatLxBI9gBaerbd9wDYLwz YbItLDharuavP1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGGipv 0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9 pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaae GaciGaaiaabeqaamaaeaqbaaGcbaacbaqcLbCaqaaaaaaaaaWdbiaa =nbiaaa@414F@  3  أوﺟﺪ ﻗﯿﻤﺔ اﻟﺰاوﯾﺔ α 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS baaSqaaiaaicdaaeqaaaaa@387C@ .