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‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫اﻟﻮﺣﺪة‬ ‫ﻣﻘﺪﻣﺔ‬
‫اﻟﻄﻠﻘ...
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٢
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫ع‬‫ن‬
‫ف‬
) ‫ﻣﺜﺎل‬٢(:‫...
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٣
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫ث‬ / ‫م‬ =
‫اﻟﻤﺘﻮﺳﻄ‬ ‫...
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٤
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫؟‬ ‫ﺳﺎﻛﻨﺔ‬ ‫ﻛﺎﻧﮭﺎ‬ ‫و‬...
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٤-‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﺑﯿﻦ‬ ‫ﺑﯿﺎﻧ...
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٦
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‫اﻟﻌﺠﻠﺔ‬ ‫اﻧﻮاع‬
١-‫ﻣﻨﺘ...
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٣‫واﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﻘﯿﺎﺳﯿﺔ‬ ...
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‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫ﺟﺴﻢ‬ ‫ازاﺣﺔ‬ : ‫ان‬ ‫ﯾ...
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٩
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫اﻟﺴ‬‫اﻟﻤﺘﺠﮭـــــــــــ...
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Page |١٠ : ‫اﻟﻀﻮء‬‫اﻹ‬ ‫ﺣﺎﺳﺔ‬ ...
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١١
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: ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻘﺎﻧﻮن‬‫...
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:‫اﻟﻤﺴﺘﻮﯾﺔ‬ ‫ﺑﺎﻟﻤﺮآة‬...
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: ‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮاة‬ ...
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: ‫اﻟﻌﺪﺳﺎت‬-‫ﻟ‬ ‫ﻛﺎﺳﺮ...
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‫أﻛﺒﺮ‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫ا...
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: ‫اﻟﻌﻼج‬
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سلسلة المظالى 3 اعدادى 2015
سلسلة المظالى 3 اعدادى 2015
سلسلة المظالى 3 اعدادى 2015
سلسلة المظالى 3 اعدادى 2015
سلسلة المظالى 3 اعدادى 2015
سلسلة المظالى 3 اعدادى 2015
سلسلة المظالى 3 اعدادى 2015
سلسلة المظالى 3 اعدادى 2015
سلسلة المظالى 3 اعدادى 2015
سلسلة المظالى 3 اعدادى 2015
سلسلة المظالى 3 اعدادى 2015
سلسلة المظالى 3 اعدادى 2015
سلسلة المظالى 3 اعدادى 2015
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سلسلة المظالى 3 اعدادى 2015

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سلسلة المظالى 3 اعدادى 2015

  1. 1. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |١ ‫اﻟﻮﺣﺪة‬ ‫ﻣﻘﺪﻣﺔ‬ ‫اﻟﻄﻠﻘﺔ‬ ‫اﻟﻘﻄﺎر‬ ) ‫اﻟﻰ‬ ‫ﺳﺮﻋﺘﺔ‬ ‫ﺗﺼﻞ‬ ‫ﺳﺮﯾﻊ‬ ‫ﻛﮭﺮﺑﺎﺋﻲ‬ ‫ﻗﻄﺎر‬ ‫اول‬ ‫ھﻮ‬٢٠٠) ‫ﺳﺮﻋﺘﮫ‬ ‫ﺑﻠﻐﺖ‬ ‫ﺣﺘﻲ‬ ‫اﻟﻘﻄﺎر‬ ‫ھﺬا‬ ‫ﱢر‬‫ﻮ‬‫ﻃ‬ ‫ﺛﻢ‬ ، ( ‫ﻛﻢ/ﺳﺎﻋﺔ‬٢٧٠( ‫ﻛﻢ/ﺳﺎﻋﺔ‬ ‫اﻟﯿﺎﺑﺎن‬ ‫واﻧﺘﺠﺘﮫ‬ ‫؟‬ ‫اﻟﻤﻌﺘﺎد‬ ‫اﻟﻘﻄﺎر‬ ‫ﻋﻦ‬ ‫اﻟﻄﻠﻘﺔ‬ ‫اﻟﻘﻄﺎر‬ ‫ﯾﺨﺘﻠﻒ‬ ‫ﻋﻠﻞ‬ ‫اﻟﻄﺮﯾ‬ ‫ﺑﮭﺬة‬ ‫و‬ ‫ﺑﮭﺎ‬ ‫ﺧﺎص‬ ‫ﻣﻮﺗﻮر‬ ‫ﯾﺤﺮﻛﮭﺎ‬ ‫ﻋﺮﺑﺎﺗﺔ‬ ‫ﻣﻦ‬ ‫ﻋﺮﺑﺔ‬ ‫ﻛﻞ‬ ‫ﻻن‬‫ﺟﺪا‬ ‫ﻋﺎﻟﯿﺔ‬ ‫ﺑﺴﺮﻋﺎت‬ ‫ﯾﺘﺤﺮك‬ ‫ان‬ ‫ﻟﻠﻘﻄﺎر‬ ‫ﯾﻤﻜﻦ‬ ‫ﻘﺔ‬ . ‫اﻟﺰﻣﻦ‬ ‫ﺑﻤﺮور‬ ‫آﺧﺮ‬ ‫ﻟﺠﺴﻢ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫اﺗﺠﺎھﮫ‬ ‫أو‬ ‫اﻟﺠﺴﻢ‬ ‫ﻣﻮﺿﻊ‬ ‫ﺗﻐﯿﺮ‬ ‫ھﻲ‬ ‫اﻟﺴﺎﻛﻦ‬ ‫اﻟﺠﺴﻢ‬‫ﺑﻤﺮو‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ﻟﻨﻘﻄﺔ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﻣﻮﺿﻌﺔ‬ ‫ﯾﺘﻐﯿﺮ‬ ‫ﻻ‬ ‫اﻟﺬى‬ ‫اﻟﺠﺴﻢ‬ ‫ھﻮ‬‫اﻟﺰﻣﻦ‬ ‫ر‬ ‫اﻟﻤﺘﺤﺮك‬ ‫اﻟﺠﺴﻢ‬‫اﻟﺰﻣﻦ‬ ‫ﺑﻤﺮور‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ﻟﻨﻘﻄﺔ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﻣﻮﺿﻌﺔ‬ ‫ﯾﺘﻐﯿﺮ‬ ‫اﻟﺬى‬ ‫اﻟﺠﺴﻢ‬ ‫ھﻮ‬ ‫اﻟﺤﺮﻛﺔ‬‫ﻓﻰ‬‫اﺗﺠﺎه‬‫واﺣﺪ‬: ‫اﻟﺠﺴﻢ‬ ‫ﺣﺮﻛﺔ‬ ‫ھﻰ‬‫ﻟ‬‫أو‬ ‫ﻸﻣﺎم‬‫ﻷﺳﻔﻞ‬ ‫أو‬ ‫ﻷﻋﻠﻲ‬ ‫ﯾﺘﺤﺮك‬ ‫وﻻ‬ ‫ﻓﻘﻂ‬ ‫ﻟﻠﺨﻠﻒ‬‫و‬ً‫ﺎ‬‫ﺗﺮﻛﯿﺒ‬ ‫أو‬ ً‫ﺎ‬‫ﻣﻨﺤﻨﯿ‬ ‫أو‬ ً‫ﺎ‬‫ﻣﺴﺘﻘﯿﻤ‬ ‫ﺧﻂ‬ ‫ﻓﻲ‬ ‫ﻣﺴﺎره‬ ‫ﯾﻜﻮن‬ ‫ﻗﺪ‬ ‫ﻣﻨﮭﻤﺎ‬ ‫واﺣﺪ‬ ‫اﺗﺠﺎه‬ ‫ﻓﻲ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫أﻣﺜﻠﺔ‬‫اﻟﻘﻀﺒﺎن‬ ‫ﻋﻠﻰ‬ ‫ﻟﻠﺨﻠﻒ‬ ‫او‬ ‫ﻟﻼﻣﺎم‬ ‫اﻟﻤﺘﺮو‬ ‫اﻟﻘﻄﺎراو‬ ‫ﺣﺮﻛﺔ‬ : ‫اﻟﺤﺮﻛﺔ‬ ‫أﻧﻮاع‬ ‫أﺑﺴﻂ‬‫واﺣﺪ‬ ‫اﺗﺠﺎه‬ ‫وﻓﻲ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ﻓﻲ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ھﻰ‬ : ‫ﻓﻤﺜﻼ‬‫اﻟﺤﺮﻛﺔ‬ ‫ﺳﻤﯿﺖ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ﻓﻲ‬ ‫اﻟﻘﻄﺎر‬ ‫ﺗﺤﺮك‬ ‫إذا‬‫ﺣﺮﻛﺔ‬ )‫واﺣﺪ‬ ‫اﺗﺠﺎه‬ ‫وﻓﻲ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ﻓﻲ‬( ‫وھﺬه‬‫اﻟﺤﺮﻛﺔ‬‫ھﻰ‬‫اﻟﺤﺮﻛﺔ‬ ‫أﻧﻮاع‬ ‫أﺑﺴﻂ‬. ‫ھﻰ‬‫اﻟﻤﺴﺎﻓﺔ‬‫ا‬‫اﻟﺠﺴﻢ‬ ‫ﯾﻘﻄﻌﮭﺎ‬ ‫ﻟﺘﻰ‬‫اﻟﻮاﺣﺪة‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫ﻓﻲ‬ ‫اﻟﺠﺴﻢ‬ ‫ﯾﻘﻄﻌﮭﺎ‬ ‫اﻟﺘﻲ‬ ‫أواﻟﻤﺴﺎﻓﺔ‬ . ‫اﻟﺰﻣﻦ‬ ‫وﺣﺪة‬ ‫ﺧﻼل‬ ‫اﻟﻤﺴﺎﻓﺔ‬‫ف‬ = ‫اﻟﺴﺮﻋﺔ‬= ‫ع‬ ‫اﻟﺰﻣﻦ‬‫ز‬ ‫وﺻﻒ‬ ‫ﻓﻰ‬ ‫ﺗﺴﺘﺨﺪم‬ ‫اﻟﺘﻰ‬ ‫اﻻﺳﺎﺳﯿﺔ‬ ‫اﻟﻌﻮاﻣﻞ‬‫اﻟﺤﺮﻛﺔ‬ ‫ﺗﻮﺻﻒ‬‫ﺣﺮﻛﺔ‬‫ﺑﻌﺾ‬‫اﻻﺟﺴﺎم‬‫ﺳﺮﯾﻌﺔ‬ ‫ﺑﺎﻧﮭﺎ‬‫اﻻﺧﺮ‬ ‫واﻟﺒﻌﺾ‬‫ﺗﻮﺻﻒ‬‫ﺑﻄﯿﺌﺔ‬ ‫ﺑﺎﻧﮭﺎ‬. ‫ﻣﺜﺎل‬)١:( ‫ﺑﯿﻀﺎء‬ ‫و‬ ‫ﺳﻮداء‬ ‫ﺳﯿﺎرﺗﺎن‬ ‫ﺗﺤﺮﻛﺖ‬ ‫ذ‬‫ﻣﺴﺎﻓﺔ‬١٠٠‫ﻣﺘﺮ‬‫أن‬ ‫وﻟﻮﺣﻆ‬ ‫زﻣﻨﯿﺔ‬ ‫ﻓﺘﺮة‬ ‫اﺳﺘﻐﺮﻗﺖ‬ ‫اﻟﺴﻮداء‬ ‫اﻟﺴﯿﺎرة‬)١٠‫ھﺬ‬ ‫ﻟﻘﻄﻊ‬ (‫ﺛﻮاﻧﻰ‬‫اﻟﻤﺴﺎﻓﺔ‬ ‫ة‬. ) ‫زﻣﻨﯿﺔ‬ ‫ﻓﺘﺮة‬ ‫اﺳﺘﻐﺮﻗﺖ‬ ‫اﻟﺒﯿﻀﺎء‬ ‫اﻟﺴﯿﺎرة‬١٥‫ﻟﻘﻄ‬ (‫ﺛﺎﻧﯿﺔ‬‫ﻧﻔﺲ‬ ‫ﻊ‬‫اﻟﻤﺴﺎﻓﺔ‬ ‫اى‬‫ﻟﻤﺎذا؟‬ ‫و‬ ‫اﺳﺮع‬ ‫اﻟﺴﯿﺎرﺗﯿﻦ‬ ‫اﻻﺟﺎﺑﺔ‬‫اﻟﺴﻮداء‬ ‫اﻟﺴﯿﺎرة‬‫ﻗﻄﻌﺖ‬ ‫ﻻﻧﮭﺎ‬ ‫اﺳﺮع‬‫ﻓﻰ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻧﻔﺲ‬‫اﻟﺴﯿﺎرة‬ ‫ﻣﻦ‬ ‫أﻗﻞ‬ ‫زﻣﻦ‬‫ا‬‫ﻟﺒﯿﻀﺎء‬ ‫اﻟﺴﺮﻋﺔ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﻣﻔﮭﻮم‬ ‫واﺣﺪ‬ ‫اﺗﺠﺎة‬ ‫ﻓﻰ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ع‬‫ز‬ ‫ف‬
  2. 2. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٢ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |٢ ‫ع‬‫ن‬ ‫ف‬ ) ‫ﻣﺜﺎل‬٢(:‫ﺗﺤﺮﻛﺖ‬ ‫اذا‬‫اﻟﺴﯿﺎرﺗﺎن‬‫ﻟﻤﺪة‬١٥‫ﺛﺎﻧﯿﺔ‬ ‫اﻟﺴﯿﺎرةاﻟﺴﻮداء‬‫ﻣﺴﺎﻓﺔ‬ ‫ﻗﻄﻌﺖ‬)١٠٠‫ﻣﺘﺮ‬ ( ‫اﻟﺒﯿﻀﺎء‬ ‫اﻟﺴﯿﺎرة‬ ‫و‬‫ﻣﺴﺎﻓﺔ‬ ‫ﻗﻄﻌﺖ‬)٥٠(‫ﻣﺘﺮ‬‫؟‬ ‫وﻟﻤﺎذا‬ ‫؟‬ ‫أﺳﺮع‬ ‫ﺗﻜﻮن‬ ‫اﻟﺴﯿﺎرﺗﯿﻦ‬ ‫أي‬ ‫اﻻﺟﺎﺑﺔ‬:‫اﻟﺴﯿﺎرة‬‫ھﻰ‬ ‫اﻟﺴﻮداء‬‫ا‬‫ﻣﺴﺎﻓﺔ‬ ‫ﻗﻄﻌﺖ‬ ‫ﻷﻧﮭﺎ‬ ‫ﻷﺳﺮع‬‫اﻛﺒﺮ‬‫ﻧﻔﺲ‬ ‫ﻓﻲ‬‫اﻟﺰﻣﻦ‬. ‫ﺳﺒﻖ‬ ‫ﻣﺎ‬ ‫ﺟﻤﯿﻊ‬ ‫ﻣﻦ‬ ‫ﻧﺴﺘﻨﺘﺞ‬: ‫ان‬‫ﻋﺎﻣﻼن‬ ‫ھﻨﺎك‬‫اﺳﺎﺳﯿﺎن‬‫ﻓﻰ‬ ‫ﺗﺴﺘﺨﺪم‬‫اﻟﺤﺮﻛﺔ‬ ‫وﺻﻒ‬‫ھﻤﺎ‬: ١-. ‫اﻟﺠﺴﻢ‬ ‫ﯾﻘﻄﻌﮭﺎ‬ ‫اﻟﺘﻲ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ٢-‫و‬‫ﯾﺴﺘﻐﺮﻗﮫ‬ ‫اﻟﺬي‬ ‫اﻟﺰﻣﻦ‬‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﺬه‬ ‫ﻗﻄﻊ‬ ‫ﻓﻲ‬ ‫اﻟﻌﻮاﻣﻞ‬ ‫ھﺬه‬ ‫ﻣﻦ‬ *‫ﺗﻌﺮﯾﻒ‬ ‫ﯾﻤﻜﻦ‬‫ﻓﯿﺰﯾﺎﺋ‬ ‫ﻛﻤﯿﺔ‬‫ﯿﺔ‬‫ﺗﺴﻤﻰ‬" ‫اﻟﺴﺮﻋﺔ‬ " ‫ھﻰ‬‫اﻟﻤﺴﺎﻓﺔ‬‫اﻟﺠﺴﻢ‬ ‫ﯾﻘﻄﻌﮭﺎ‬ ‫اﻟﺘﻰ‬‫ﺧﻼل‬‫وﺣﺪة‬‫اﻟﺰﻣﻦ‬ .:‫اﻟﺴﺮﻋﺔ‬ ‫ﻗﯿﺎس‬ ‫وﺣﺪة‬ ١-: ‫ﺛﺎﻧﯿﺔ‬ / ‫ﻣﺘﺮ‬‫ﻋﻨﺪﻣﺎ‬‫ﺗﻘﺎس‬‫اﻟﻤﺴﺎﻓﺔ‬‫ﺑﺎﻟﻤﺘﺮ‬‫واﻟﺰﻣﻦ‬‫ﺑﺎﻟﺜﺎﻧﯿﺔ‬. ٢-: ‫اﻟﺴﺎﻋﺔ‬ / ‫ﻣﺘﺮ‬ ‫ﻛﯿﻠﻮ‬‫ﻋﻨﺪﻣﺎ‬‫ﺗﻘﺎس‬‫اﻟﻤﺴﺎﻓﺔ‬‫ﺑﺎﻟﻜﯿﻠﻮﻣﺘﺮ‬‫واﻟﺰﻣﻦ‬‫ﺑﺎﻟﺴﺎﻋﺔ‬‫ﻛﻤﺎ‬‫ﻓﻰ‬‫ﺣﺎﻟﺔ‬‫اﻟﻄﺎﺋﺮات‬ ‫و‬ ‫اﻟﻘﻄﺎرات‬ ‫و‬ ‫اﻟﺴﯿﺎرات‬ ‫ﻟﻠﺘﺤﻮﯾﻞ‬‫ﻓﻰ‬ ‫ﻧﻀﺮب‬ ‫م/ث‬ ‫اﻟﻰ‬ ‫ﻛﻢ/س‬ ‫ﻣﻦ‬٥/١٨‫ﻟﻠﺘﺤﻮﯾﻞ‬/‫ﻛﻢ‬ ‫اﻟﻰ‬ ‫م/ث‬ ‫ﻣﻦ‬‫ﻓﻰ‬ ‫ﻧﻀﺮب‬ ‫س‬١٨/٥ ١-‫ﻣﺴﺎﻓﺔ‬ ‫ﻋﺪاء‬ ‫ﻗﻄﻊ‬١٠٠‫ﺧﻼل‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺳﺒﺎق‬ ‫ﻣﻀﻤﺎر‬ ‫ﻣﻦ‬ ‫ﻣﺘﺮ‬١٠. ‫اﻟﻌﺪاء‬ ‫ھﺬا‬ ‫ﺳﺮﻋﺔ‬ ‫اﺣﺴﺐ‬ .. ‫ﺛﻮاﻧﻲ‬ ٢-‫ﻣﺴﺎﻓﺔ‬ ‫ﻋﺪاءان‬ ‫ﯾﺘﺴﺎﺑﻖ‬١٠٠‫ﻓﻲ‬ ‫اﻷول‬ ‫ﻗﻄﻌﮭﺎ‬ ‫ﻣﺘﺮ‬١٠‫ﻓﻲ‬ ‫اﻟﺜﺎﻧﻲ‬ ‫و‬ ‫ﺛﻮاﻧﻲ‬٢٠‫ﺛﺎﻧﯿﺔ‬‫ﻣﻨﮭﻤﺎ‬ ً‫ﻼ‬‫ﻛ‬ ‫ﺳﺮﻋﺔ‬ ‫اﺣﺴﺐ‬ ٣-‫ﺑﺴﺮﻋﺔ‬ ‫ﺳﯿﺎرة‬ ‫ﺗﺴﯿﺮ‬٧٠‫ﻣﺴﺎﻓﺔ‬ ‫ﻓﻘﻄﻌﺖ‬ ‫ﺳﺎﻋﺔ‬ /‫ﻛﻢ‬١٤٠. ‫اﻟﺮﺣﻠﺔ‬ ‫ﻹﺳﺘﻐﺮاق‬ ‫اﻟﻼزم‬ ‫اﻟﺰﻣﻦ‬ ‫ھﻮ‬ ‫ﻓﻤﺎ‬ ‫ﻛﯿﻠﻮﻣﺘﺮ‬ ١-‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﺴﺮﻋﺔ‬٢-‫ﻣﻨﺘﻈﻤﺔ‬ ‫اﻟﻐﯿﺮ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ﻓﻰ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺑﮭﺎ‬ ‫ﯾﺘﺤﺮك‬ ‫اﻟﺘﻲ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ھﻲ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ازﻣﻨﺔ‬ ‫ﻓﻲ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ﻣﺴﺎﻓﺎت‬ ‫ﯾﻘﻄﻊ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ھﻰ‬‫ﯾﻘﻄﻊ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺑﮭﺎ‬ ‫ﯾﺘﺤﺮك‬ ‫اﻟﺘﻰ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ازﻣﻨﺔ‬ ‫ﻓﻰ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ﻏﯿﺮ‬ ‫ﻣﺴﺎﻓﺎت‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ﻏﯿﺮ‬ ‫ازﻣﻨﺔ‬ ‫ﻓﻰ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ﻣﺴﺎﻓﺎت‬ ‫او‬ ‫و‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻋﺪاد‬ ‫ﻣﺜﻞ‬ ‫اﻟﻌﺪادات‬ ‫ﻣﻦ‬ ‫ﺑﻤﺠﻤﻮﻋﺔ‬ ‫ﻋﺎدة‬ ‫اﻟﺴﯿﺎرات‬ ‫و‬ ‫اﻟﻄﺎﺋﺮات‬ ‫ﺗﺰود‬‫ﻋﺪاد‬‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻋﺪاد‬‫ﯾﺴﺎﻋﺪ‬ ‫ﺟﮭﺎز‬‫ﻋﻠﻰ‬‫ﻣﻌﺮﻓﺔ‬‫ﺳﺮﻋﺔ‬‫اﻟﺴﯿﺎرة‬‫ﻣﺒ‬‫ﺎﺷﺮة‬ ‫ﯾﻌ‬ ‫ﻣﺎذا‬‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﺗﺴﯿﺮ‬ ‫ﺳﯿﺎرة‬ ‫ان‬ ‫ﻨﻰ‬٧٠‫ﻛﻢ‬/‫س‬‫؟؟‬‫ﻣﺴﺎﻓﺔ‬ ‫ﺗﻘﻄﻊ‬ ‫اﻟﺴﯿﺎرة‬ ‫ان‬ ‫اى‬٧٠‫ﻛ‬‫ﻛﻞ‬ ‫ﻢ‬‫ﺳﺎﻋﺔ‬‫ﺑﺎﻧﺘﻈﺎم‬ ‫ﻋﻤﻠﯿﺎ‬ ‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﺤﻘﯿﻖ‬ ‫ﯾﺼﻌﺐ‬ ‫ﻋﻠﻞ‬‫؟‬ ‫ﺗ‬ ‫ﻓﮭﻰ‬ ‫اﻟﻄﺮﯾﻖ‬ ‫اﺣﻮال‬ ‫ﺣﺴﺐ‬ ‫ﺗﺘﻐﯿﺮ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﻻن‬‫اﺧﺮى‬ ‫ﺣﯿﺎﻧﺎ‬ ‫وﺗﻘﻞ‬ ‫اﺣﯿﺎﻧﺎ‬ ‫ﺰداد‬ ‫اﻟﺴﺮﻋﺔ‬ ‫اﻧﻮاع‬ ‫اﻟﺴﺮﻋﺔ‬
  3. 3. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٣ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |٣ ‫ث‬ / ‫م‬ = ‫اﻟﻤﺘﻮﺳﻄ‬ ‫اﻟﺴﺮﻋﺔ‬: (/‫ع‬ ) ‫ﺔ‬‫ﺗﺴﺎوى‬‫اﻟﻤﺴﺎﻓﺔ‬‫اﻟﻜﻠﯿﺔ‬‫اﻟﺘﻲ‬‫ﯾﻘﻄﻌﮭﺎ‬‫اﻟﺠﺴﻢ‬‫اﻟﻤﺘﺤﺮك‬‫ﻣﻘﺴﻮﻣﺔ‬‫ﻋﻠﻰ‬‫اﻟﺰﻣﻦ‬‫اﻟﻤﺴﺘﻐﺮ‬ ‫اﻟﻜﻠﻰ‬‫ق‬ ‫ﻟﻘﻄﻊ‬‫ھﺬه‬‫اﻟﻤﺴﺎﻓﺔ‬. : ( /‫)ع‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﺴﺮﻋﺔ‬‫اﻟﻼزم‬ ‫اﻟﺰﻣﻦ‬ ‫ﻧﻔﺲ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻧﻔﺲ‬ ‫ﻟﻘﻄﻊ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺑﮭﺎ‬ ‫ﺳﺎر‬ ‫ﻟﻮ‬ ‫اﻟﺘﻲ‬ ‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ھﻲ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﺬه‬ ‫ﻟﻘﻄﻊ‬ ‫ﺑﯿﻦ‬ ‫ﻗﺎرن‬‫اﻟﻤﻨ‬ ‫اﻟﺤﺮﻛﺔ‬‫و‬ ‫ﺘﻈﻤﺔ‬‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﻐﯿﺮ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﺤﺮﻛﺔ‬‫ﻣﻨﺘﻈﻤﺔ‬ ‫اﻟﻐﯿﺮ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﻟﻠﺠﺴﻢ‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﺴﺎوي‬ ‫ع‬ = /‫ع‬ )‫اﻟﻤﻨﺘﻈﻤﺔ‬( ‫ﻣﻨﺘﻈﻤﺔ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺣﺮﻛﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻟﻠﺠﺴﻢ‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﺴﺎوي‬ ‫ﻻ‬ /‫)ع‬≠‫ع‬‫اﻟﻤﻨﺘﻈﻤﺔ‬( ‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﻏﯿﺮ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺣﺮﻛﺔ‬ ‫ﺗﻜﻮن‬ ‫)ع(؟؟‬ ‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻣﻊ‬ (/‫)ع‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﺘﺴﺎوى‬ ‫ﻣﺘﻰ‬‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﺣﺮﻛﺔ‬ ‫اﻟﺠﺴﻢ‬ ‫ﯾﺘﺤﺮك‬ ‫ﻋﻨﺪﻣﺎ‬ : ‫ﻣﺜﺎل‬‫ﻣﺴﺎﻓﺔ‬ ‫ﻋﺪاء‬ ‫ﻗﻄﻊ‬١٠٠‫ﻣﺘﺮ‬‫ﺧﻼل‬١٠‫ﺛﻮاﻧﻲ‬‫ﺟﺮﯾﺎ‬‫ﺛﻢ‬ ،‫اﻟﺒﺪاﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫اﻟﻰ‬ ‫ﻋﺎد‬ً‫ﺎ‬‫ﻣﺸﯿ‬‫ﻓﺎﺳﺘﻐﺮق‬ ‫اﻷﻗﺪام‬ ‫ﻋﻠﻲ‬٨٠‫ﺛﺎﻧﯿﺔ‬ : ‫اﺣﺴﺐ‬١-‫اﻟﻤﺘ‬ ‫اﻟﺴﺮﻋﺔ‬‫ذاھﺐ‬ ‫وھﻮ‬ ‫ﻟﻠﻌﺪاء‬ ‫ﻮﺳﻄﺔ‬‫؟‬ ٢-‫؟‬ ‫ﻋﺎﺋﺪ‬ ‫وھﻮ‬ ‫ﻟﻠﻌﺪاء‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ٣-‫؟‬ ‫اﻟﺮﺣﻠﺔ‬ ‫ﺧﻼل‬ ‫ﻟﻠﻌﺪاء‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ : ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺳﺮﻋﺔ‬ ‫ھﻰ‬‫ﺟﺴﻢ‬‫ﻣﺘﺤﺮك‬‫ﺑﺎﻟﻨﺴﺒﺔ‬‫ﻟﻤﺮاﻗﺐ‬ :‫اﻟﻤﺮاﻗﺐ‬‫ﯾﻘﻮ‬ ‫ﻣﺘﺤﺮك‬ ‫او‬ ‫ﺳﺎﻛﻦ‬ ‫ﺷﺨﺺ‬ ‫ھﻮ‬‫اﻟﻤﺘﺤﺮﻛﺔ‬ ‫ﻟﻼﺟﺴﺎم‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﻘﺪﯾﺮ‬ ‫و‬ ‫ﺑﻤﺮاﻗﺒﺔ‬ ‫م‬ ‫ﺳﯿﺎرة‬ ‫ﻟﯿﻜﻦ‬ ‫و‬ ‫ﻣﺘﺤﺮك‬ ‫ﻟﺠﺴﻢ‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺣﺴﺎب‬ ١-‫ﻓﺎن‬ ‫ﺳﺎﻛﻦ‬ ‫اﻟﻤﺮاﻗﺐ‬ ‫ﻛﺎن‬ ‫اذا‬( ‫اﻟﻔﻌﻠﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ = ‫ﻟﻠﺴﯿﺎرة‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫)اﻟﺴﺮﻋﺔ‬ ٢-‫ﻓﺎن‬ ‫اﻻﺗﺠﺎة‬ ‫ﻧﻔﺲ‬ ‫ﻓﻰ‬ ‫ﻣﺘﺤﺮك‬ ‫اﻟﻤﺮاﻗﺐ‬ ‫ﻛﺎن‬ ‫اذا‬‫اﻟﺴﺮﻋﺔ‬ = ‫ﻟﻠﺴﯿﺎرة‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬‫اﻟﻔﻌﻠﯿﺔ‬-‫اﻟﻤﺮاﻗﺐ‬ ‫ﺳﺮﻋﺔ‬ ‫)اى‬‫ﺗﺴﺎوى‬( ‫اﻟﺴﺮﻋﺘﯿﻦ‬ ‫ﻓﺮق‬ ٣-‫اﻟﻤﺮاﻗﺐ‬ ‫ﺳﺮﻋﺔ‬ + ‫اﻟﻔﻌﻠﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ = ‫ﻟﻠﺴﯿﺎرة‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻓﺎن‬ ‫اﻻﺗﺠﺎة‬ ‫ﻋﻜﺲ‬ ‫ﻓﻰ‬ ‫ﻣﺘﺤﺮك‬ ‫اﻟﻤﺮاﻗﺐ‬ ‫ﻛﺎن‬ ‫اذا‬ ( ‫اﻟﺴﺮﻋﺘﯿﻦ‬ ‫ﻣﺠﻤﻮع‬ ‫ﺗﺴﺎوى‬ ‫اى‬ ) : ‫اﻻﺳﺘﻨﺘﺎج‬ ‫ان‬‫ﺳﺮﻋﺔ‬‫اﻟﺴﯿﺎرة‬‫ﺑﺎﻟﻨﺴﺒﺔ‬‫ﻟﻠﻤﺮاﻗﺐ‬‫اﻟﺬي‬‫ﯾﻘﻒ‬‫ﻋﻠﻰ‬‫اﻷرض‬‫ﺗ‬‫ﻋﻦ‬ ‫ﺨﺘﻠﻒ‬‫ﺳﺮﻋﺔ‬‫اﻟﺴﯿﺎرة‬‫ﺑﺎﻟﻨﺴﺒﺔ‬‫ﻟﻤﺮاﻗﺐ‬‫ﻣﻮﺟﻮد‬‫ﺳﯿﺎرة‬ ‫ﻓﻲ‬ ‫أﺧﺮى‬‫ﻣﺘﺤﺮﻛﺔ‬.‫اى‬‫أن‬‫اﻟ‬‫ﺴﺮﻋﺔ‬‫اﻟﻨﺴﺒﯿ‬‫ﺔ‬‫ﻟ‬‫اﻟﻤﺮاﻗﺐ‬ ‫ﻣﻮﺿﻊ‬ ‫ﺑﺎﺧﺘﻼف‬ ‫ﺗﺨﺘﻠﻒ‬ ‫ﻠﺴﯿﺎرة‬ ‫ع‬/ =‫ف‬ ‫ز‬ ‫اﻟﻤﻘﻄﻮﻋﺔ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﺴﺮﻋﺔ‬= ‫اﻟﻜﻠﻰ‬ ‫اﻟﺰﻣﻦ‬ ٣-‫اﻟﺴﺮﻋﺔاﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬
  4. 4. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٤ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |٤ ‫؟‬ ‫ﺳﺎﻛﻨﺔ‬ ‫ﻛﺎﻧﮭﺎ‬ ‫و‬ ‫اﺗﺠﺎھﮭﺎ‬ ‫ﻧﻔﺲ‬ ‫ﻓﻰ‬ ‫و‬ ‫ﺳﺮﻋﺘﮭﺎ‬ ‫ﺑﻨﻔﺲ‬ ‫ﯾﺘﺤﺮك‬ ‫ﻟﻤﺮاﻗﺐ‬ ‫ﻣﺎ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫اﻟﻤﺘﺤﺮﻛﺔ‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺗﺒﺪو‬ ‫ﻋﻠﻞ‬ ‫ﺻﻔﺮ‬ ‫ﯾﺴﺎوى‬ ‫ﺑﯿﻨﮭﻤﺎ‬ ‫اﻟﻔﺮق‬ ‫اذن‬ ‫ﻣﺘﺴﺎوﯾﺘﯿﻦ‬ ‫اﻟﺴﺮﻋﺘﯿﻦ‬ ‫ﺑﻤﺎن‬ ‫و‬ ‫اﻟﺴﺮﻋﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻔﺮق‬ ‫ﺗﺴﺎوى‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻻن‬ ‫ﺑﺎﻟﺘﺎﻟﻰ‬ ‫و‬‫ﺳﺎﻛﻨﺔ‬ ‫ﻛﺎﻧﮭﺎ‬ ‫و‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺗﺒﺪو‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺴﺎﺋﻞ‬ ‫ﻣﺜﺎل‬١-‫اﻻوﻟﻰ‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺳﺮﻋﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫ﻓﺎذا‬ ‫اﻻﺗﺠﺎة‬ ‫ﻧﻔﺲ‬ ‫ﻓﻰ‬ ‫اﻟﻄﺮﯾﻖ‬ ‫ﻋﻠﻰ‬ ‫ﺗﺘﺤﺮﻛﺎن‬ ‫ﺳﯿﺎرﺗﺎن‬٤٠‫ﻛﻢ/س‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺳﺮﻋﺔ‬ ‫و‬٧٠‫اﻟﺜﺎﻧﯿﺔ‬ ‫ﻟﻠﺴﯿﺎرة‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻓﻜﻢ‬ ‫ﻛﻢ/س‬ ١-‫اﻻرض‬ ‫ﻋﻠﻰ‬ ‫ﯾﻘﻒ‬ ‫ﻟﻤﺮاﻗﺐ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ٢-‫ﺑ‬‫ﺎﻟﻨﺴﺒﺔ‬‫ﻓﻰ‬ ‫ﻟﻤﺮاﻗﺐ‬‫اﻻوﻟﻰ‬ ‫اﻟﺴﯿﺎرة‬ ٣-‫اﻟﺴﯿﺎرة‬ ‫ﻧﻔﺲ‬ ‫ﻓﻰ‬ ‫ﻟﻤﺮاﻗﺐ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﻣﺜﺎل‬٢‫اﻟﻨﺴﺒﯿﺔ‬ ‫ﺳﺮﻋﺘﮭﺎ‬ ‫ﻟﺴﯿﺎرة‬ ‫اﻟﻔﻌﻠﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫اﺣﺴﺒﻰ‬٨٠‫ﺑﺴﺮﻋﺔ‬ ‫اﺗﺠﺎھﮭﺎ‬ ‫ﻧﻔﺲ‬ ‫ﻓﻰ‬ ‫ﯾﺘﺤﺮك‬ ‫ﻟﻤﺮاﻗﺐ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﻛﻢ/س‬٤٠‫ﻛﻢ/س‬ ‫ﻣﺜﺎل‬٣–‫ﻣﺴﺎﻓﺔ‬ ‫ﻋﻠﻰ‬ ‫اﺻﺒﺤﺖ‬ ‫ﻟﻤﺎ‬ ‫و‬ ‫اﻟﻘﺎھﺮة‬ ‫ﺑﺮج‬ ‫اﺗﺠﺎة‬ ‫ﻓﻰ‬ ‫ﺗﺘﺤﺮك‬ ‫ﺳﯿﺎرة‬٥٠‫ﺣﺮاﺳﺔ‬ ‫ﻃﺎﺋﺮة‬ ‫رﺻﺪﺗﮭﺎ‬ ‫ﻛﻢ‬‫ﺑﺴﺮﻋﺔ‬ ‫ﺗﺴﯿﺮ‬ ‫ﺧﺎﺻﺔ‬ ٢٥٥‫ﺑﺴﺮﻋﺔ‬ ‫ﺗﺴﯿﺮ‬ ‫ﻛﺎﻧﮭﺎ‬ ‫اﻟﺴﯿﺎرة‬ ‫ﻓﺒﺪت‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺣﺮﻛﺔ‬ ‫ﻋﻜﺲ‬ ‫اﺗﺠﺎة‬ ‫ﻓﻰ‬ ‫ﻛﻢ/س‬٢٧٠‫اﻟﻘﺎھﺮة‬ ‫ﺑﺮج‬ ‫اﻟﻰ‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺗﺼﻞ‬ ‫ﻓﻤﺘﻰ‬ ‫ﻛﻢ/س‬ ‫ﻋﻠﻤﺎء‬ ‫ﯾﺴﺘﺨﺪم‬‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﻋﻠﻤﺎء‬ ‫و‬ ‫اﻟﻔﯿﺰﯾﺎء‬‫اﻟﻤﺨﺘﻠﻔﺔ‬ ‫اﻟﻤﺘﻐﯿﺮات‬ ‫ﺑﯿﻦ‬ ‫اﻟﺮﯾﺎﺿﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬‫و‬‫اﻟﺮﯾﺎﺿﯿﺔ‬ ‫اﻟﻮﺳﺎﺋﻞ‬ ‫اﻟﺒﯿﺎﻧﯿﺔ‬ ‫اﻟﺮﺳﻮم‬ ‫و‬ ‫ﻛﺎﻟﺠﺪاول‬‫ﻋﻠﻞ‬‫؟‬ ‫ﺣـ‬-‫و‬ ‫أﺳﮭﻞ‬ ‫ﺑﻄﺮﯾﻘﺔ‬ ‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻈﻮاھﺮ‬ ‫ﻟﻮﺻﻒ‬‫ﺑﺎﻟﻌﻼﻗ‬ ‫اﻟﺘﻨﺒﺆ‬‫ﺗﺠﻤﻊ‬ ‫اﻟﺘﻰ‬ ‫ﺎت‬‫ﺑﯿﻦ‬‫اﻟ‬‫ﻜﻤﯿﺎت‬‫اﻟ‬‫ﻔﯿﺰﯾﺎﺋﯿﺔ‬‫اﻟﻤﺨﺘﻠﻔﺔ‬ ‫ﺗﺠﺮﺑﺔ‬‫ﺗﻤﺜﯿﻞ‬ .. :‫ا‬‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫ﻟﺴﺮﻋﺔ‬: ‫ﺑﯿﺎﻧﯿﺎ‬- ‫اﻷدوات‬:‫ﺑ‬ ‫ﺗﻌﻤﻞ‬ ‫أﻃﻔﺎل‬ ‫ﻟﻌﺐ‬ ‫ﺳﯿﺎرة‬‫ﻛﻨﺘﺮول‬ ‫ﺎﻟﺮﯾﻤﻮت‬–‫ﺧﺸﺒﻲ‬ ‫ﻟﻮح‬‫اﻣﻠﺲ‬ ‫ﻃﻮﻟﺔ‬٢‫ﻣﺘﺮ‬–‫ﻣﺘﺮﯾﺔ‬ ‫ﻣﺴﻄﺮة‬–‫ﺳ‬‫إﯾﻘﺎف‬ ‫ﺎﻋﺔ‬–‫ﻣﻠﻮن‬ ‫ﻗﻠﻢ‬ ‫اﻟﻌﻤﻞ‬ ‫ﺧﻄﻮات‬: ١-‫ﻧ‬‫ﺛﻢ‬ ‫أﻓﻘﻲ‬ ‫ﺿﻊ‬ ‫و‬ ‫ﻓﻲ‬ ‫اﻟﺨﺸﺒﻲ‬ ‫اﻟﻠﻮح‬ ‫ﻀﻊ‬‫ﻧ‬‫ﻋﻼﻣﺘﯿﻦ‬ ‫ﻀﻊ‬‫اﻟﻠﻮح‬ ‫ﻋﻠﻰ‬‫اﻟﺨﺸﺒﻰ‬‫و‬ ‫ﻧ‬‫ﻘ‬‫ﯿ‬‫ﺑﯿﻨ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﺲ‬‫ﮭﻤﺎ‬(‫)ف‬ ٢-‫ﻧ‬‫اﻟﺴﯿﺎرة‬ ‫ﺸﻐﻞ‬‫و‬‫ﻧ‬‫اﻟﺰﻣﻦ‬ ‫ﻌﯿﻦ‬(‫)ز‬‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻟﻘﻄﻊ‬ ‫اﻟﻼزم‬(‫)ف‬ ٣-‫ﻧ‬‫ﻣﺮات‬ ‫ﻋﺪة‬ ‫اﻟﺴﺎﺑﻘﺔ‬ ‫اﻟﺨﻄﻮة‬ ‫ﻜﺮر‬‫ﻣﺮة‬ ‫ﻛﻞ‬ ‫ﻓﻰ‬ ‫و‬‫ﻧ‬‫ﻐﯿﺮ‬ ‫و‬ ‫اﻟﻌﻼﻣﺘﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬‫ﻧ‬‫اﻟﻘﺮا‬ ‫ﺴﺠﻞ‬‫ء‬‫ا‬‫ﺛﻢ‬ ‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫ت‬ ‫ﻧ‬‫ﺤﺴﺐ‬‫ﺳﺮﻋﺔ‬‫اﻟﺴﯿﺎرة‬‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬= (‫)ع‬/‫ف‬‫ز‬ ‫م‬(‫)ف‬ ‫اﻟﻤﺴﺎﻓﺔ‬) ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻗﻄﻊ‬ ‫زﻣﻦ‬‫ز‬(‫ف‬ =(‫)ع‬ ‫اﻟﺴﺮﻋﺔ‬÷‫ز‬ ١٠.٤٥٠.٠٨ ٢٠.٦٧.٥.٠٨ ٣٠.٨١٠٠.٠٨ ٤١١٢.٥٠.٠٨ ‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫ﻟﻠﺴﺮﻋﺔ‬ ‫اﻟﺒﯿﺎﻧﻰ‬ ‫اﻟﺘﻤﯿﻞ‬ ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﺪرس‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ﻓﻰ‬ ‫ﻟﻠﺤﺮﻛﺔ‬ ‫اﻟﺒﯿﺎﻧﻰ‬ ‫اﻟﺘﻤﺜﯿﻞ‬
  5. 5. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٥ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |٥ ٤-‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﺑﯿﻦ‬ ‫ﺑﯿﺎﻧﯿﺔ‬ ‫ﻋﻼﻗﺔ‬ ‫ارﺳﻢ‬‫اﻟﺮاﺳﻲ‬ ‫اﻟﻤﺤﻮر‬ ‫ﻋﻠﻲ‬ (‫)ف‬ ‫اﻟﺰﻣﻦ‬ ‫و‬)‫ز‬‫اﻷﻓﻘﻲ‬ ‫اﻟﻤﺤﻮر‬ ‫ﻋﻠﻲ‬ (‫اﻻﺻﻞ‬ ‫ﺑﻨﻘﻄﺔ‬ ‫ﯾﻤﺮ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ﻋﻠﻰ‬ ‫ﻧﺤﺼﻞ‬ : ‫ﺣﻘﺎﺋﻖ‬ ‫ﻋﺪة‬ ‫اﻟﺴﺎﺑﻖ‬ ‫اﻟﻨﺸﺎط‬ ‫ﻣﻦ‬ ‫ﯾﺘﻀﺢ‬ ١-( ‫اﻟﺰﻣﻦ‬ ‫و‬ ‫)اﻟﻤﺴﺎﻓﺔ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﯿﺎﻧﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﻟﻠﺤﺮﻛﺔ‬) ‫ﻣﻨﺘﻈﻤﺔ‬‫ﺛﺎﺑﺘﺔ‬( -( ‫ﻟﺰﻣﻦ‬ ‫و‬ ‫)اﻟﺴﺮﻋﺔ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﯿﺎﻧﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﻟﻠﺤﺮﻛﺔ‬) ‫ﻣﻨﺘﻈﻤﺔ‬‫ﺛﺎﺑﺘﺔ‬( ٣-‫و‬ ‫ﺑﯿﻦ)اﻟﻤﺴﺎﻓﺔ‬ ‫اﻟﺒﯿﺎﻧﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻟﻠﺠﺴﻢ‬ (‫اﻟﺰﻣﻦ‬‫ا‬‫ﻟﺴﺎﻛﻦ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺑﺨﻂ‬ ‫ﺗﻤﺜﻞ‬‫ﻣﺎﺋﻞ‬‫اﻷﺻﻞ‬ ‫ﺑﻨﻘﻄﺔ‬ ‫ﯾﻤﺮ‬‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺑﺨﻂ‬ ‫ﺗﻤﺜﻞ‬‫اﻓﻘﻰ‬‫ﻣﺤﻮر‬ ‫ﯾﻮازي‬ ‫اﻟﺰﻣﻦ‬ ‫اﻟﺰﻣﻦ‬ ‫ﻣﺤﻮر‬ ‫ﯾﻮازي‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺑﺨﻂ‬ ‫ﺗﻤﺜﻞ‬ :‫ﻋﻠﻞ‬) ‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﺗﺘﺤﺮك‬ ‫اﻟﺴﯿﺎرة‬ ‫(.؟‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ازﻣﻨﺔ‬ ‫ﻓﻰ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ﻣﺴﺎﻓﺎت‬ ‫ﺗﻘﻄﻊ‬ ‫ﻻﻧﮭﺎ‬ ‫ﻣﺘﺴﺎ‬‫وﯾﺔ‬ :‫ﻋﻠﻞ‬) ‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﺗﺘﺤﺮك‬ ‫اﻟﺴﯿﺎرة‬ ( ‫ﺛﺎﺑﺘﺔ‬‫؟‬ ‫اﻟﺰﻣﻦ‬ ‫ﺑﻤﺮور‬ ‫ﺛﺎﺑﺘﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻻن‬ ‫؟‬ ‫ﺳﺎﻛﻦ‬ ‫اﻟﺠﺴﻢ‬ ‫ﻋﻠﻞ‬ ‫ﻻ‬ ‫ﻻﻧﺔ‬‫ﯾﺘ‬‫اﻟﺰﻣﻦ‬ ‫ﺑﻤﺮور‬ ‫ﻣﻮﺿﻌﺔ‬ ‫ﻐﯿﺮ‬ ‫ﺳﺮﻋﺔ‬ ‫ﻓﻲ‬ ‫اﻟﺘﻐﯿﺮ‬ ‫ﻣﻘﺪار‬ ‫ھﻲ‬‫اﻟ‬‫اﻟﻮاﺣﺪة‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫ﻓﻲ‬ ‫ﺠﺴﻢ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻓﻰ‬ ‫ﻟﻠﺘﻐﯿﺮ‬ ‫اﻟﺰﻣﻨﻰ‬ ‫اﻟﻤﻌﺪل‬ ‫ھﻰ‬ ‫او‬ : ‫اﻟﻤﻌﺠﻠﺔ‬ ‫اﻟﺤﺮﻛﺔ‬‫اﻟﺘﻰ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ھﻰ‬‫اﻟﺰﻣﻦ‬ ‫ﺑﻤﺮور‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﻓﯿﮭﺎ‬ ‫ﺗﺘﻐﯿﺮ‬ ١٢.٥٢.٥ ٥ ٧.٥١٠ ٠.٢ ٠.٤ ٠.٨ ١ ١٥ (‫)ﻣﺘﺮ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﻟﺰﻣﻦ‬ ‫ﺑﺎﻟﺜﺎﻧﯿﺔ‬ ‫اﻟﻌﺠﻠﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﻟﺰﻣﻦ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫اﻟﺰﻣﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﻟﺰﻣﻦ‬
  6. 6. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٦ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |٦ ‫اﻟﻌﺠﻠﺔ‬ ‫اﻧﻮاع‬ ١-‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﻋﺠﻠﺔ‬٢-‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﻏﯿﺮ‬ ‫ﻋﺠﻠﺔ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ﺑﻤﻘﺎدﯾﺮ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﻓﯿﮭﺎ‬ ‫ﺗﺘﻐﯿﺮ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ازﻣﻨﺔ‬ ‫ﻓﻰ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ﺑﻤﻘﺎدﯾﺮﻏﯿﺮ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﻓﯿﮭﺎ‬ ‫ﺗﺘﻐﯿﺮ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ازﻣﻨﺔ‬ ‫ﻓﻰ‬ :‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﻌﺠﻠﺔ‬ ‫أﻧﻮاع‬- ١-(+ ) ‫ﺗﺰﯾﺎدﯾﺔ‬ ‫ﻋﺠﻠﺔ‬-) ‫ﺗﻨﺎﻗﺼﯿﺔ‬ ‫ﻋﺠﻠﺔ‬-: ( ‫ﺛﺎﺑﺖ‬ ‫ﺑﻤﻘﺪار‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﻓﯿﮭﺎ‬ ‫ﺗﺰداد‬ ‫اﻟﺰﻣﻦ‬ ‫ﺑﻤﺮور‬ ‫ﺛﺎﺑﺖ‬ ‫ﺑﻤﻘﺪار‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﻓﯿﮭﺎ‬ ‫ﺗﺘﻨﺎﻗﺺ‬ ‫اﻟﺰﻣﻦ‬ ‫ﺑﻤﺮور‬ ‫ع‬ ‫ﻓﯿﮭﺎ‬ ‫ﺗﻜﻮن‬٢‫ع‬ <١‫ع‬ ‫ﻓﯿﮭﺎ‬ ‫ﺗﻜﻮن‬ ‫و‬١‫ع‬ <٢ ‫ﻣﻮﺟﺒﺔ‬ ‫ﻗﯿﻤﺘﮭﺎ‬ ‫و‬‫ﺳﺎﻟﺒﺔ‬ ‫ﻗﯿﻤﺘﮭﺎ‬ ‫و‬ ‫اﻵﺗﯿﺔ‬ ‫اﻟﺤﺎﻻت‬ ‫ﻓﻰ‬ ‫ﯾﺤﺪث‬ ‫ﻣﺎذا‬ ‫س‬ ١-‫ﺛﺎ‬ ‫ﺑﻤﻌﺪل‬ ‫ﺳﯿﺎرة‬ ‫ﺳﺮﻋﺔ‬ ‫زادت‬ ‫اذا‬‫ﺣـ‬ ‫ﻣﻌﯿﻦ‬ ‫اﺗﺠﺎه‬ ‫ﻓﻰ‬ ‫ﺑﺖ‬-‫ﻗﯿﻤ‬ ‫وﺗﻜﻮن‬ ‫ﺗﺰﯾﺎدﯾﺔ‬ ‫ﺑﻌﺠﻠﺔ‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺗﺘﺤﺮك‬‫ﺘﮭﺎ‬‫ﻣﻮﺟﺒﺔ‬ ٢-‫ﺣـ‬ ‫ﻣﻌﯿﻦ‬ ‫اﺗﺠﺎه‬ ‫ﻓﻰ‬ ‫ﺛﺎﺑﺖ‬ ‫ﺑﻤﻌﺪل‬ ‫ﺳﺮﻋﺔاﻟﺴﯿﺎرة‬ ‫ﺗﻨﺎﻗﺼﺖ‬ ‫ﻟﻮ‬-‫وﺗﻜﻮن‬ ‫ﺗﻨﺎﻗﺼﯿﺔ‬ ‫ﺑﻌﺠﻠﺔ‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺗﺘﺤﺮك‬‫ﻗﯿﻤﺘﮭﺎ‬‫ﺳﺎﻟﺒﺔ‬ ‫ﻋﺠﻠﺔ‬ ‫ﻟﺔ‬ ‫ﻟﯿﺲ‬ ‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫اﻟﺬى‬ ‫اﻟﺠﺴﻢ‬ ‫ﻋﻠﻞ‬ ‫ﺳ‬ ‫ﻓﻰ‬ ‫اﻟﺘﻐﯿﺮ‬ ‫ﻣﻘﺪار‬ ‫ھﻰ‬ ‫اﻟﻌﺠﻠﺔ‬ ‫ﻻن‬‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫اﻟﺠﺴﻢ‬ ‫ان‬ ‫ﺑﻤﺎ‬ ‫و‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫ﻓﻰ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺮﻋﺔ‬ ‫ﻋﺠﻠﺔ‬ ‫ﻟﺔ‬ ‫ﻟﯿﺲ‬ ‫اى‬ ‫ﺻﻔﺮ‬ = ‫اﻟﻌﺠﻠﺔ‬ ‫ﺑﺎﻟﺘﺎﻟﻰ‬ ‫و‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻓﻰ‬ ‫ﺗﻐﯿﺮ‬ ‫ﯾﻮﺟﺪ‬ ‫ﻻ‬ ‫اى‬ ‫س‬٢‫أن‬ ‫ﻣﻌﻨﻰ‬ ‫ﻣﺎ‬ ١-= ‫ﺑﻌﺠﻠﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫ﺟﺴﻢ‬٥‫م/ث‬٢‫ﻣﻌﻨﻰ‬‫ﺑﻤﻌﺪل‬ ‫ﺗﺰداد‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫أن‬ ‫ذﻟﻚ‬٥.‫ﺛﺎﻧﯿﺔ‬ ‫ﻛﻞ‬ ‫ﻓﻰ‬ ‫م/ث‬ ٢-= ‫ﺑﻌﺠﻠﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫ﺟﺴﻢ‬-٢‫م/ث‬٢‫ﻣﻌﻨ‬‫ﺑﻤﻌﺪل‬ ‫ﺗﻘﻞ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫أن‬ ‫ذﻟﻚ‬ ‫ﻰ‬٢.‫ﺛﺎﻧﯿﺔ‬ ‫ﻛﻞ‬ ‫ﻓﻰ‬ ‫م/ث‬ ٣-= ‫ﺑﺘﻘﺼﯿﺮ‬ ‫ﯾﺘﺤﺮك‬ ‫ﺟﺴﻢ‬٣‫م/ث‬٢ ‫ذﻟﻚ‬ ‫ﻣﻌﻨﻰ‬‫ﺑﻤﻌﺪل‬ ‫ﺗﻘﻞ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫أن‬٣.‫ﺛﺎﻧﯿﺔ‬ ‫ﻛﻞ‬ ‫ﻓﻰ‬ ‫م/ث‬ ‫اﻟﻌﺠﻠﺔ‬ ‫ﻣﺴﺎﺋﻞ‬ ‫ﺣﻞ‬ ‫اﺳﺎﺳﯿﺎت‬ ١-‫ع‬ ‫اﻟﺴﻜﻮن‬ ‫ﻣﻦ‬ ‫ﺣﺮﻛﺘﺔ‬ ‫ﺑﺪا‬ ‫ﺟﺴﻢ‬١‫ﺻﻔﺮ‬ = ٢-‫ع‬ ‫اﻟﺴﯿﺎرة‬ ‫ﻓﺘﻮﻗﻔﺖ‬ ‫اﻟﻔﺮاﻣﻞ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺴﺎﺋﻖ‬ ‫ﺿﻐﻂ‬٢‫ﺻﻔﺮ‬ = ٣-‫ﻣﻨﺘﻈﻤ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫ﺟﺴﻢ‬‫اﻟﻌﺠﻠﺔ‬ ‫ﺔ‬‫ﺻﻔﺮ‬ = )‫ﻣﺴـــــــــــــــــﺎﺋﻞ‬( ١-‫إﻟﻰ‬ ‫ﺳﺮﻋﺘﮫ‬ ‫وﺻﻠﺖ‬ ‫ﺳﺎﻛﻦ‬ ‫ﻗﺎرب‬ ‫ﺗﺸﻐﯿﻞ‬ ‫ﻋﻨﺪ‬٢.٥‫ﻣﻘﺪارھﺎ‬ ‫زﻣﻨﯿﺔ‬ ‫ﻓﺘﺮة‬ ‫ﺧﻼل‬ ‫م/ث‬٣٠: ‫أوﺟﺪ‬ ‫ث‬ ١-‫؟‬ ‫اﻟﻘﺎرب‬ ‫ﺑﮭﺎ‬ ‫ﯾﺘﺤﺮك‬ ‫اﻟﺘﻰ‬ ‫اﻟﻌﺠﻠﺔ‬ ‫ﻣﻘﺪار‬٢-‫؟‬ ‫اﻟﺴﺒﺐ‬ ‫ذﻛﺮ‬ ‫ﻣﻊ‬ ‫اﻟﻌﺠﻠﺔ‬ ‫ﻧﻮع‬ ٢-‫ﺑﺴﺮﻋﺔ‬ ‫ﺳﯿﺎرة‬ ‫ﺗﺘﺤﺮك‬٣٠‫وﻋﻨﺪﻣ‬ ‫م/ث‬‫ﻗﺪرة‬ ‫زﻣﻦ‬ ‫ﺧﻼل‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺗﻮﻗﻔﺖ‬ ‫اﻟﻔﺮاﻣﻞ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺴﺎﺋﻖ‬ ‫ﺿﻐﻂ‬ ‫ﺎ‬١٥‫ث‬ : ‫أوﺟﺪ‬١-‫؟‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺑﮭﺎ‬ ‫اﻟﺘىﺘﺘﺤﺮك‬ ‫اﻟﻌﺠﻠﺔ‬ ‫ﻣﻘﺪار‬٢-‫؟‬ ‫اﻟﺴﺒﺐ‬ ‫ذﻛﺮ‬ ‫ﻣﻊ‬ ‫اﻟﻌﺠﻠﺔ‬ ‫ﻧﻮع‬ ٣-‫ﺑﺪأ‬ ‫ﺳﯿﺎرة‬‫ت‬‫ز‬ ‫ﺛﻢ‬ ‫اﻟﺴﻜﻮن‬ ‫ﻣﻦ‬ ‫ﺣﺮﻛﺘﮭﺎ‬‫ا‬‫د‬‫ت‬‫اﻟﻰ‬ ‫ﺳﺮﻋﺘﮭﺎ‬٦٠‫ﺧﻼل‬ ‫ﻛﻢ/ﺳﺎﻋﺔ‬٥‫ﺛﻮاﻧﻲ‬ ‫أﺧﺮى‬ ‫وﺳﯿﺎرة‬‫اﻟﺴ‬ ‫ﻣﻦ‬ ‫ﺣﺮﻛﺘﮭﺎ‬ ‫ت‬ ‫ﺑﺪأ‬‫اﻟﻰ‬ ‫ﺳﺮﻋﺘﮭﺎ‬ ‫زادت‬ ‫ﺛﻢ‬ ‫ﻜﻮن‬٨٠‫ﺧﻼل‬ ‫ﻛﻢ/ﺳﺎﻋﺔ‬١٠‫أﻛﺒﺮ‬ ‫ﺑﻌﺠﻠﺔ‬ ‫ﺗﺴﯿﺮ‬ ‫اﻟﺴﯿﺎرﺗﯿﻦ‬ ‫أي‬ ‫ﺛﻮاﻧﻲ‬ ٤-‫ﻣﻘﺪارھﺎ‬ ‫اﺑﺘﺪاﺋﯿﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫ﻗﻄﺎر‬٧.٥‫ﻣﻘﺪارھﺎ‬ ‫ﺑﻌﺠﻠﺔ‬ ‫و‬ ‫م/ث‬١٠‫م/ث‬٢‫ﺑﻌﺪھﺎ‬ ‫ﺗﺼﺒﺢ‬ ‫اﻟﺘﻰ‬ ‫اﻟﺰﻣﻨﯿﺔ‬ ‫اﻟﻔﺘﺮة‬ ‫ﻣﻘﺪار‬ ‫اﺣﺴﺐ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﻘﻄﺎر‬ ‫ﺳﺮﻋﺔ‬٤‫اﻻﺑﺘﺪاﺋﯿﺔ‬ ‫ﺳﺮﻋﺘﺔ‬ ‫اﻣﺜﺎل‬ ٥-( ‫ب‬ ) ‫و‬ ( ‫أ‬ ) ‫ﺳﯿﺎرﺗﺎن‬‫ﻓﺎﺻﺒﺤﺖ‬ ‫اﻟﺴﻜﻮن‬ ‫ﻣﻦ‬ ‫ﺣﺮﻛﺘﮭﻤﺎ‬ ‫ﺑﺪات‬ ‫اﻻوﻟﻰ‬ ‫ﺳﺮﻋﺔ‬٦٠‫ﻣﺮور‬ ‫ﺑﻌﺪ‬ ‫ث‬ / ‫م‬٥‫اﻟﺜﺎﻧﯿﺔ‬ ‫ﺳﺮﻋﺔ‬ ‫و‬ ‫ﺛﻮاﻧﻰ‬٨٠‫ﻣﺮور‬ ‫ﺑﻌﺪ‬ ‫م/ث‬١٠‫ﺛﻮاﻧﻰ‬ ‫اﻛﺒﺮ‬ ‫ﺑﻌﺠﻠﺔ‬ ‫ﺗﺘﺤﺮك‬ ‫اﻟﺴﯿﺎرﺗﯿﻦ‬ ‫ﻓﺎى‬ ٦-‫ﻣﻘﺪارھﺎ‬ ‫اﺑﺘﺪاﺋﯿﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫ﻗﻄﺎر‬٦٠‫ﻣﺮور‬ ‫ﺑﻌﺪ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻣﻘﺪار‬ ‫اﺣﺴﺐ‬ ‫ﻛﻢ/س‬٤٢‫ﯾﺘﺤﺮك‬ ‫ﺑﺎﻧﺔ‬ ‫ﻋﻠﻤﺎ‬ ‫دﻗﯿﻘﺔ‬ ‫ﺑﻌﺠﻠﺔ‬٥٠/‫ﻛﻢ‬‫س‬٢
  7. 7. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٧ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |٧ ٣‫واﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﻘﯿﺎﺳﯿﺔ‬ ‫اﻟﻔﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻜﻤﯿﺎت‬ : ‫اﻟﻔﯿﺰﯾﺎء‬ ‫ﻋﻠﻢ‬‫اﻟﺬى‬ ‫اﻟﻌﻠﻢ‬ ‫ھﻮ‬‫ﺑﻮﺻﻒ‬ ‫ﯾﮭﺘﻢ‬‫اﻟﻜﻮﻧﯿﺔ‬ ‫و‬ ‫اﻟﻄﺒﯿﻌﯿﺔ‬ ‫اﻟﻈﻮاھﺮ‬‫ﻣ‬ ‫اﻻﺳﺘﻔﺎدة‬ ‫ﺑﮭﺪف‬ ‫ﺗﻔﺴﯿﺮھﺎ‬ ‫ﻣﺤﺎوﻟﺔ‬ ‫و‬‫ﻨﮭﺎ‬ ‫اﻟﺮﯾﺎﺿﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﻋﻠﻰ‬ ‫ﺗﻔﺴﯿﺮة‬ ‫ﻓﻰ‬ ‫ﯾﻌﺘﻤﺪ‬ ‫و‬‫ﺑﯿﻦ‬‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻜﻤﯿﺎت‬ ‫اﻟﻄﺒﯿﻌﯿﺔ‬ ‫اﻟﻈﻮاھﺮ‬:‫ﻣﺜﻞ‬‫اﻟﺠﺎذﺑﯿﺔ‬‫و‬‫اﻟﻔﻌﻞ‬ ‫ورد‬ ‫اﻟﻔﻌﻞ‬ ‫ﻗﻮة‬‫و‬‫اﻟﺴﻮاﺋﻞ‬ ‫ﺣﺮﻛﺔ‬ : ‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻜﻤﯿﺎت‬‫ﻣﺜﻞ‬‫اﻟﻤﺴﺎﻓﺔ‬‫و‬‫اﻟﺰﻣﻦ‬‫و‬‫و‬ ‫اﻟﺴﺮﻋﺔ‬‫اﻟﻜﺘﻠﺔ‬‫و‬‫و‬ ‫اﻟﺤﺠﻢ‬‫اﻟﺤﺮارة‬ ‫درﺟﺔ‬ ‫ﻗﺴﻤﯿﻦ‬ ‫إﻟﻰ‬ ‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻜﻤﯿﺎت‬ ‫ﺗﻨﻘﺴﻢ‬ ‫ﻋﻠﻞ‬ ‫س‬: ‫ﯾﺎﺗﻰ‬ ‫ﻟﻤﺎ‬ ١-‫ﻣﺘﺠﮭﺔ؟‬ ‫ﻛﻤﯿﺔ‬ ‫اﻻزاﺣﺔ‬ ‫ﺑﯿﻨﻤﺎ‬ ‫ﻗﯿﺎﺳﯿﺔ‬ ‫ﻛﻤﯿﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﻟﻤﺴﺎﻓ‬‫ﻣﻘﺪارھﺎ‬ ‫ﻣﻌﺮﻓﺔ‬ ً‫ﺎ‬‫ﺗﺎﻣ‬ ً‫ﺎ‬‫ﺗﻌﺮﯾﻔ‬ ‫ﻟﺘﻌﺮﯾﻔﮭﺎ‬ ‫ﯾﻠﺰم‬ ‫ﻷﻧﮫ‬ ‫ﻗﯿﺎﺳﯿﺔ‬ ‫ﻛﻤﯿﺔ‬ ‫ﺔ‬‫ﻗﯿﺎﺳﮭﺎ‬ ‫ووﺣﺪة‬‫ﯾﻠﺰم‬ ‫ﻷﻧﮫ‬ ‫ﻣﺘﺠﮭﺔ‬ ‫ﻛﻤﯿﺔ‬ ‫اﻻزاﺣﺔ‬ ‫اﻣﺎ‬ ‫ﻓﻘﻂ‬ ‫ﻣﻘﺪارھﺎ‬ ‫ﻣﻌﺮﻓﺔ‬ ً‫ﺎ‬‫ﺗﺎﻣ‬ ً‫ﺎ‬‫ﺗﻌﺮﯾﻔ‬ ‫ﻟﺘﻌﺮﯾﻔﮭﺎ‬‫ﻗﯿﺎﺳﮭﺎ‬ ‫ووﺣﺪة‬‫واﺗﺠﺎھﮭﺎ‬ ٢-‫ﻗﯿﺎﺳﯿﺔ‬ ‫ﻛﻤﯿﺔ‬ ‫اﻟﻜﺘﻠﺔ‬‫؟‬‫ﺣـ‬-ً‫ﺎ‬‫ﺗﺎﻣ‬ ً‫ﺎ‬‫ﺗﻌﺮﯾﻔ‬ ‫ﻟﺘﻌﺮﯾﻔﮭﺎ‬ ‫ﯾﻠﺰم‬ ‫ﻷﻧﮫ‬‫ﻣﻘﺪارھﺎ‬ ‫ﻣﻌﺮﻓﺔ‬‫ﻗﯿﺎﺳﮭﺎ‬ ‫ووﺣﺪة‬‫ﻓﻘﻂ‬ ٣-‫زﻣﻦ؟‬ ‫إﻟﻰ‬ ‫ﻛﺘﻠﺔ‬ ‫إﺿﺎﻓﺔ‬ ‫ﯾﻤﻜﻦ‬ ‫ﻻ‬‫ﺣـ‬-‫ﻷن‬‫ﻟﯿﺲ‬ ‫اﻟﺰﻣﻦ‬ ‫و‬ ‫اﻟﻜﺘﻠﺔ‬‫اﻟﻮﺣﺪة‬ ‫ﻧﻔﺲ‬ ‫ﻟﮭﻤﺎ‬ ٤-‫ﯾﻤﻜﻦ‬‫ﻛﺘﻠﺔ؟‬ ‫إﻟﻰ‬ ‫ﻛﺘﻠﺔ‬ ‫إﺿﺎﻓﺔ‬‫ﺣـ‬-‫اﻟﻮﺣﺪة‬ ‫ﻧﻔﺲ‬ ‫ﻟﮭﻤﺎ‬ ‫ﻷن‬ ‫س‬٢‫ﯾﺄﺗﻲ‬ ‫ﻣﺎ‬ ‫أﻛﻤﻞ‬ ١-‫ﻛﻤﯿ‬ ‫اﻟﻜﺘﻠﺔ‬ ‫ﺑﯿﻨﻤﺎ‬ ،........ ‫ﻗﯿﺎﺳﮭﺎ‬ ‫ووﺣﺪة‬ ............. ‫ﻛﻤﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬................ ‫ﻗﯿﺎﺳﮭﺎ‬ ‫ووﺣﺪة‬ .............. ‫ﺔ‬ ٢-..........................،.............،................ ،................. ‫اﻟﻄﺒﯿﻌﯿﺔ‬ ‫اﻟﻈﻮاھﺮ‬ ‫أﻣﺜﻠﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻘﯿﺎﺳﯿﺔ‬ ‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻜﻤﯿﺎت‬‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻜﻤﯿﺎت‬ ١-‫اﻟﻜﻤﯿ‬ ‫ھﻰ‬‫ﺔ‬‫ﻣﻌﺮﻓﺔ‬ ً‫ﺗﺎﻣﺎ‬ ً‫ﺎ‬‫ﺗﻌﺮﯾﻔ‬ ‫ﻟﺘﻌﺮﯾﻔﮭﺎ‬ ‫ﯾﻠﺰم‬ ‫اﻟﺘﻰ‬ ‫ﻣﻘﺪارھﺎ‬‫ﻗﯿﺎﺳﮭﺎ‬ ‫ووﺣﺪة‬‫ﻓﻘﻂ‬:‫ﻣﺜﻞ‬ )‫اﻟﻤﺴﺎﻓﺔ‬–‫اﻟﺰﻣﻦ‬–‫اﻟﻘﯿﺎﺳﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬-‫ا‬‫ﻟﻜﺘﻠﺔ‬–‫اﻟﺤﺠﻢ‬( ١-‫اﻟﻜﻤﯿ‬ ‫ھﻰ‬‫ﺔ‬ً‫ﺎ‬‫ﺗﺎﻣ‬ ً‫ﺎ‬‫ﺗﻌﺮﯾﻔ‬ ‫ﻟﺘﻌﺮﯾﻔﮭﺎ‬ ‫ﯾﻠﺰم‬ ‫اﻟﺘﻰ‬ ‫و‬ ‫ﻣﻘﺪارھﺎ‬ ‫ﻣﻌﺮﻓﺔ‬‫و‬ ‫ﻗﯿﺎﺳﮭﺎ‬ ‫وﺣﺪة‬‫اﺗﺠﺎھﮭﺎ‬‫ﻣﺜﻞ‬: ‫)اﻹزاﺣﺔ‬–‫اﻟﺴﺮﻋﺔ‬‫اﻟﻤﺘﺠﮭﺔ‬–‫اﻟﻌﺠﻠﺔ‬–‫اﻟﻘﻮة‬( ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﻜﻤﯿﺔ‬‫اﻟﻘﯿﺎس‬ ‫وﺣﺪة‬ ‫اﻹزاﺣﺔ‬ (‫)م‬ ‫اﻟﻤﺘﺮ‬ ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺷﺮﻗﺎ‬ ‫م/ث‬ ‫اﻟﻌﺠﻠﺔ‬‫م/ث‬٢ ‫اﻟﻘﻮة‬ ‫اﻟﻨﯿﻮﺗﻦ‬ ‫اﻟﻘﯿﺎﺳﯿﺔ‬ ‫اﻟﻜﻤﯿﺔ‬‫اﻟﻘﯿﺎس‬ ‫وﺣﺪة‬ )١(‫)اﻟﻄﻮل‬ ‫اﻟﻤﺴﺎﻓﺔ‬ (( ‫)م‬ ‫اﻟﻤﺘﺮ‬ )٢‫اﻟﺰﻣﻦ‬ (( ‫)ث‬ ‫اﻟﺜﺎﻧﯿﺔ‬ )٣(‫اﻟﻘﯿﺎﺳﯿﺔ‬ ‫ﻟﺴﺮﻋﺔ‬‫م/ث‬ )٤(‫اﻟﻜﺘﻠﺔ‬( ‫)ﻛﺠﻢ‬ ‫ﺟﺮام‬ ‫اﻟﻜﯿﻠﻮ‬
  8. 8. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٨ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |٨ ‫ﺟﺴﻢ‬ ‫ازاﺣﺔ‬ : ‫ان‬ ‫ﯾﻌﻨﻰ‬ ‫ﻣﺎذا‬=١٠‫؟‬ ‫ﻣﺘﺮ‬ = ‫ﺣﺮﻛﺘﺔ‬ ‫ﻧﮭﺎﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫و‬ ‫اﻟﺠﺴﻢ‬ ‫ﺣﺮﻛﺔ‬ ‫ﺑﺪاﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﺑﯿﻦ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫اﻗﺼﺮ‬ ‫ان‬ ‫اى‬١٠‫ﻣﺘﺮ‬ ‫س‬١‫ﯾﺄﺗﻲ‬ ‫ﻣﺎ‬ ‫أﻛﻤﻞ‬ .......... ‫......................ووﺣﺪةﻗﯿﺎﺳﮭﺎ‬ ‫ﻛﻤﯿﺔ‬ ‫اﻻزاﺣﺔ‬‫ا‬............. ‫ﻗﯿﺎﺳﮭﺎ‬ ‫ووﺣﺪة‬ ............ ‫ﻛﻤﯿﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻣﺎ‬ ‫س‬٢‫ا‬ ) ‫ﺣﯿﺚ‬ ‫ﻣﻦ‬ ‫واﻟﻤﺴﺎﻓﺔ‬ ‫اﻻزاﺣﺔ‬ ‫ﺑﯿﻦ‬ ‫ﻗﺎرن‬‫ﻟﻤﻔﮭﻮم‬–( ‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻜﻤﯿﺔ‬ ‫ﻧﻮع‬ ‫اﻟﻘﺎھﺮة‬ ‫ﻣﻦ‬ ‫ﺷﺨﺺ‬ ‫ﺑﮭﺎ‬ ‫ﯾﻘﻮم‬ ‫ﻟﺮﺣﻠﺔ‬ ‫دراﺳﺘﻚ‬ ‫ﻣﻦ‬ ‫س‬ ‫اﻟﻔﺮق‬ ‫ﺗﺒﯿﻦ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻤﻤﻜﻨﺔ‬ ‫اﻻﺣﺘﻤﺎﻻت‬ ‫ادرس‬ ‫ﻃﻨﻄﺎ‬ ‫اﻟﻰ‬ ‫ﺑﯿﻦ‬‫واﻹزاﺣﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻣﺘﻰ‬ ‫س‬‫؟‬ ‫اﻹزاﺣﺔ‬ ‫ﻣﻘﺪار‬ ‫ﻣﻊ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﺗﺘﺴﺎوى‬‫ﻣﻮﺿﻌﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫واﺣﺪ‬ ‫اﺗﺠﺎة‬ ‫ﻓﻰ‬ ‫و‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ﻓﻰ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬ :‫ج‬ ‫ھﺎﻣﺔ‬ ‫ﻣﻠﺤﻮﻇﺔ‬:- ١-‫ا‬ (‫أ‬ )‫ﻣﻦ‬ ‫ﺛﺎﺑﺖ‬ ‫واﺣﺪ‬ ‫اﺗﺠﺎه‬ ‫ﻓﻰ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺗﺤﺮك‬ ‫إذا‬‫ﻟﻰ‬‫أ‬ ) ‫اﻟﺤﺎدﺛﺔ‬ ‫اﻻزاﺣﺔ‬ ‫ﻓﺈن‬ (‫ب‬ )(‫ب‬=‫اﻟﻤﻘﻄﻮﻋﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ً‫ﺎ‬‫ﻋﺪدﯾ‬ ٢-، ‫ﺻﻔﺮ‬ = ‫اﻟﺤﺎدﺛﺔ‬ ‫اﻻزاﺣﺔ‬ ‫ﻓﺈن‬ (‫)أ‬ ‫اﻟﻰ‬ ‫أﺧﺮى‬ ‫ﻣﺮة‬ ‫ﻋﺎد‬ ‫ﺛﻢ‬ (‫)ب‬ ‫اﻟﻰ‬ (‫)أ‬ ‫ﻣﻦ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺗﺤﺮك‬ ‫إذا‬ = ‫اﻟﻤﻘﻄﻮﻋﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﺑﯿﻨﻤﺎ‬٢‫أي‬ ‫أب‬٢x‫أب‬ ‫ﻃﻮل‬ ‫ﻣﺴﺎﺋﻞ‬ ١-‫ﻣﺤﯿﻄﮭﺎ‬ ‫داﺋﺮة‬ ‫ﻋﻠﻰ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫ﺣﺮﻛﺘﺔ‬ ‫ﺟﺴﻢ‬ ‫ﺑﺪا‬٥‫ﺛﻢ‬ ‫دورﺗﯿﻦ‬ ‫ﺑﻌﻤﻞ‬ ‫ﻓﻘﺎم‬ ‫ﻣﺘﺮ‬‫ﻣﻨﮭﺎ‬ ‫ﺑﺪا‬ ‫اﻟﺘﻰ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻟﻨﻔﺲ‬ ‫ﻋﺎد‬‫اﻟﺤﺮﻛﺔ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺑﮭﺎ‬ ‫ﺗﺤﺮك‬ ‫اﻟﺘﻰ‬ ‫اﻻزاﺣﺔ‬ ‫و‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﺣﺴﺒﻰ‬ ٢-‫ارﺗﻔﺎع‬ ‫ﻣﻦ‬ ‫ﺣﺠﺮ‬ ‫ﺷﺨﺺ‬ ‫ﻗﺬف‬٢‫اﻻرض‬ ‫ﺳﻄﺢ‬ ‫ﻣﻦ‬ ‫ﻣﺘﺮ‬‫ﻣﻘﺪارھﺎ‬ ‫راﺳﯿﺔ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻻﻋﻠﻰ‬١٠‫ﻓﺘﺮة‬ ‫ﺑﻌﺪ‬ ‫اﻻرض‬ ‫ﻋﻠﻰ‬ ‫ﻓﺴﻘﻂ‬ ‫ﻣﺘﺮ‬ ‫اﻟﺤﺠﺮ‬ ‫ﺗﺤﺮﻛﮭﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻻزاﺣﺔ‬ ‫و‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﺣﺴﺒﻰ‬ ٣-‫ﻃﻮﻟﺔ‬ ‫ﺛﻮاﻧﻰ‬ ‫ﻋﻘﺮب‬٧‫دﻗﯿ‬ ‫ﻧﺼﻒ‬ ‫ﺗﺤﺮك‬ ‫ﺳﻢ‬‫اﻟﺜﻮاﻧﻰ‬ ‫ﻋﻘﺮب‬ ‫ﻗﻄﻌﮭﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻻزاﺣﺔ‬ ‫و‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﺣﺴﺒﻰ‬ ‫ﻘﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬‫اﻻزاﺣﺔ‬ ‫ﺑﺪاﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫اﻟﺠﺴﻢ‬ ‫ﯾﻘﻄﻌﮭﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻔﻌﻠﯿﺔ‬ ‫اﻟﻤﺴﺎﻓﺎت‬ ‫ﻣﺠﻤﻮع‬ ‫ھﻰ‬ ‫ا‬ ‫ﻟﺤﺮﻛﺔ‬ ‫ا‬‫ﻧﮭﺎﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻟﻰ‬ ‫اﻟﻤﺘﺤﺮك‬ ‫اﻟﺠﺴﻢ‬ ‫ﯾﺴﻠﻜﮫ‬ ‫اﻟﺬي‬ ‫اﻟﻔﻌﻠﻰ‬ ‫اﻟﻤﺴﺎر‬ ‫ﻃﻮل‬ ‫اوھﻰ‬‫ﻧﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫ﺑﺪاﯾﺔ‬‫ا‬‫اﻟﺤﺮﻛﺔ‬ ‫ﻧﮭﺎﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫اﻟﻰ‬ ‫ﻟﺤﺮﻛﺔ‬ ‫ھﻰ‬‫ﺛﺎﺑﺖ‬ ‫اﺗﺠﺎه‬ ‫ﻓﻲ‬ ‫اﻟﻤﻘﻄﻮﻋﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬‫اﺑﺘﺪاﺋﻰ‬ ‫ﻣﻮﺿﻊ‬ ‫ﻣﻦ‬ ‫ﻧﮭﺎﺋﻰ‬ ‫ﻣﻮﺿﻊ‬ ‫اﻟﻰ‬ ‫اﻻزاﺣﺔ‬ ‫ﻣﻘﺪار‬‫ﻃﻮ‬ ‫ھﻰ‬‫ﻣﻮﺿﻌﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫أﻗﺼﺮ‬ ‫ل‬ ‫اﻟﻨﮭﺎﯾﺔ‬ ‫وﻧﻘﻄﺔ‬ ‫اﻟﺒﺪاﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﺑﯿﻦ‬ ‫او‬ ‫اﻟﺒﺪاﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺘﻘﯿﻤﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﻰ‬ ‫أو‬‫اﻟﻨﮭﺎﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫و‬ ‫اﻟﻤﺘﺮ‬ ‫ﻗﯿﺎﺳﮭﺎ‬ ‫وﺣﺪة‬ ‫ﻗﯿﺎﺳﯿﺔ‬ ‫ﻓﯿﺰﯾﺎﺋﯿﺔ‬ ‫ﻛﻤﯿﺔ‬‫اﻟﻤﺘﺮ‬ ‫ﻗﯿﺎﺳﮭﺎ‬ ‫وﺣﺪة‬ ‫ﻣﺘﺠﮭﺔ‬ ‫ﻓﯿﺰﯾﺎﺋﯿﺔ‬ ‫ﻛﻤﯿﺔ‬ ‫ﺑﺎﻟﺴﯿﺎرة‬ ‫اﻟﺮﺣﻠﺔ‬ ‫ﻣﺴﺎر‬‫اﻟﻤﺴﺎﻓﺔ‬‫اﻻزاﺣﺔ‬ ‫اﻟﻘﺎھﺮة‬–‫ﺑﻨﮭﺎ‬-‫ﻃﻨﻄﺎ‬١٠٥‫ﻛﻢ‬٩٣(‫)ﻃﻨﻄﺎ‬ ‫اﻟﺸﻤﺎل‬ ‫اﺗﺠﺎه‬ ‫ﻓﻰ‬ ‫ﻛﻢ‬ ‫اﻟﻘﺎھﺮة‬–‫اﻟﺰﻗﺎزﯾﻖ‬-‫ﻃﻨﻄﺎ‬١٦٥‫ﻛﻢ‬٩٣‫اﻟﺸﻤﺎل‬ ‫اﺗﺠﺎه‬ ‫ﻓﻰ‬ ‫ﻛﻢ‬ ‫اﻟﻘﺎھﺮة‬–‫ﻃﻨﻄﺎ‬٩٣‫ﻛﻢ‬٩٣‫اﻟﺸﻤﺎل‬ ‫اﺗﺠﺎه‬ ‫ﻓﻰ‬ ‫ﻛﻢ‬ ٩٣‫ﻛﻢ‬ ‫اﻻزاﺣﺔ‬ ‫و‬ ‫اﻟﻤﺴﺎﻓﺔ‬
  9. 9. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٩ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |٩ ‫اﻟﺴ‬‫اﻟﻤﺘﺠﮭــــــــــــــــﺔ‬ ‫ـــــــــﺮﻋﺔ‬:‫اﻻزاﺣﺔ‬ ‫ﻣﻘﺪار‬ ‫ھﻰ‬‫اﻟﻤﻘﻄﻮﻋﺔ‬‫اﻟﺰﻣﻦ‬ ‫وﺣﺪة‬ ‫ﺧﻼل‬ ‫ﺑﯿﻦ‬ ‫اﻟﻔﺮق‬ ‫ﻣﺎ‬‫اﻟﺴﺮﻋﺔ‬‫اﻟﻘﯿﺎﺳﯿﺔ‬‫؟‬ ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫و‬‫ﻣﺤﺪد‬ ‫اﺗﺠﺎة‬ ‫ﻓﻰ‬ ‫ﻟﻜﻦ‬ ‫ﻗﯿﺎﺳﯿﺔ‬ ‫ﺳﺮﻋﺔ‬ ‫ھﻰ‬ ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ان‬ ‫ﯾﻌﻨﻰ‬ ‫ﻣﺎذا‬‫ﺑﺴﺮﻋﺔ‬ ‫ﺗﺘﺤﺮك‬ ‫ﺳﯿﺎرة‬٥٠‫؟‬ ‫ﺷﻤﺎﻻ‬ ‫ث‬ / ‫م‬= ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ان‬ ‫اى‬٥٠‫ث‬ / ‫م‬ ‫ﻋﻠﻞ‬ ‫س‬‫؟‬ ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﻜﻤﯿﺎت‬ ‫ﻣﻦ‬ ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬‫ﺣـ‬-‫ﻣﻘﺪارھﺎ‬ ‫ﻣﻌﺮﻓﺔ‬ ً‫ﺎ‬‫ﺗﺎﻣ‬ ً‫ﺎ‬‫ﺗﻌﺮﯾﻔ‬ ‫ﻟﺘﻌﺮﯾﻔﮭﺎ‬ ‫ﯾﻠﺰم‬ ‫ﻷﻧﮫ‬‫و‬‫اﺗﺠﺎھﮭﺎ‬ ‫ﻣﺜﺎل‬‫اﻟﻤﻔﺘﺮس‬ ‫اﻟﺤﯿﻮان‬‫اﻟﻔﮭﺪ‬( ‫اﻟﺸﯿﺘﺎ‬ )‫اﻟﺤﯿﻮاﻧﺎت‬ ‫اﺳﺮع‬ ‫ﻣﻦ‬‫ﺳﺮﻋﺘﮫ‬ ‫ﺗﺒﻠﻎ‬٢٧‫أرد‬ ‫ﻓﺈذا‬ ‫م/ث‬‫اﻟﺘﻌﺒﯿﺮ‬ ‫ﻧﺎ‬‫اﻟﻤﺘﺠﮭﺔ‬ ‫ﺳﺮﻋﺘﮫ‬ ‫ﻋﻦ‬ ‫ﻧﻘﻮل‬‫ان‬‫ﻟﻠﺸﯿﺘﺎ‬ ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬٢٧‫اﻟﺸﺮق‬ ‫اﺗﺠﺎه‬ ‫ﻓﻰ‬ ‫م/ث‬ ‫وﺣﺪ‬ ‫ﻧﻔﺲ‬ ‫ھﻰ‬ ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻗﯿﺎس‬ ‫وﺣﺪة‬‫ة‬‫اﻟﺴﺮﻋﺔ‬ ‫ﻗﯿﺎس‬‫اﻟﻘﯿﺎﺳﯿﺔ‬‫م/ث‬ ) ‫وھـــــــﻰ‬‫او‬‫ﻛﻢ/ﺳﺎﻋﺔ‬( : ‫ﻣﺜﺎل‬‫ﻣﺴﺎﻓﺔ‬ ‫ﻓﻘﻄﻊ‬ (‫)أ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫ﺣﺮﻛﺘﺔ‬ ‫ﺟﺴﻢ‬ ‫ﺑﺪأ‬ ‫إذا‬٣٠‫ﺧﻼل‬ ً‫ﻻ‬‫ﺷﻤﺎ‬ ً‫ا‬‫ﻣﺘﺮ‬٣٠‫ﺛﻢ‬ ، ‫ﺛﺎﻧﯿﺔ‬٦٠‫ﺧﻼل‬ ً‫ﺎ‬‫ﺷﺮﻗ‬ ‫ﻣﺘﺮ‬٢٠ ‫ﺛﻢ‬ ، ‫ﺛﺎﻧﯿﺔ‬٣٠‫ﺧﻼل‬ ً‫ﺎ‬‫ﺟﻨﻮﺑ‬ ‫ﻣﺘﺮ‬١٠‫ﺛﻮاﻧﻲ‬ ‫ﯾﺄﺗﻲ‬ ‫ﻋﻤﺎ‬ ‫أﺟﺐ‬١ -‫؟‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﻧﮭﺎﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻣﺎ‬‫؟‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﺑﺪاﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻣﺎ‬ ‫؟‬ ‫اﻟﺸﺨﺺ‬ ‫ﻗﻄﻌﮭﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻣﻘﺪار‬ ‫ﻣﺎ‬ ‫اﻟﺸﺨﺺ‬ ‫اﺳﺘﻐﺮﻗﺔ‬ ‫اﻟﺬي‬ ‫اﻟﻜﻠﻰ‬ ‫اﻟﺰﻣﻦ‬ ‫ﻣﻘﺪار‬ ‫ﻣﺎ‬ ‫؟‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﺬه‬ ‫ﻗﻄﻊ‬ ‫ﻓﻰ‬ = ‫اﻻزاﺣﺔ‬... ‫اﺗﺠﺎه‬ ‫ﻓﻰ‬ ً‫ا‬‫ﻣﺘﺮ‬ ............................... ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫أﺣﺴﺐ‬‫و‬‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻋﻠﻞ‬ ‫ﻟﻠﺮﯾﺎح‬ ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻣﻌﺮﻓﺔ‬ ‫اﻟﻄﯿﺎرون‬ ‫ﯾﺮاﻋﻲ‬‫اﻟﺮﯾﺎح‬ ‫اﺗﺠﺎة‬ ‫ﻋﻠﻰ‬ ‫ﯾﺘﻮﻗﻔﺎن‬ ‫اﻟﻮﻗﻮد‬ ‫اﺳﺘﮭﻼك‬ ‫و‬ ‫اﻟﺮﺣﻠﺔ‬ ‫زﻣﻦ‬ ‫ﻻن‬ ١-‫ﺗﺤﺮك‬ ‫اذا‬‫اﻟﻄﺎﺋﺮة‬‫ﻓﻰ‬‫ﻧﻔﺲ‬‫اﻟﺮﯾﺎح‬ ‫اﺗﺠﺎة‬‫ﺗﺰداد‬‫اﻟﻤﺴﺘﮭﻠﻜﺔ‬ ‫اﻟﻮﻗﻮد‬ ‫ﻛﻤﯿﺔ‬ ‫ﻛﺬﻟﻚ‬ ‫و‬ ‫اﻟﺮﺣﻠﺔ‬ ‫زﻣﻦ‬ ‫ﯾﻘﻞ‬ ‫ﺑﺎﻟﺘﺎﻟﻰ‬ ‫و‬ ‫اﻟﻤﺘﺠﮭﺔ‬ ‫ﺳﺮﻋﺘﮭﺎ‬ ٢-‫ﺗﺤﺮﻛ‬ ‫اذا‬‫ﺎﻟﻄﺎﺋﺮة‬‫اﻟﺮﯾﺎح‬ ‫اﺗﺠﺎة‬ ‫ﻋﻜﺲ‬ ‫ﻓﻰ‬‫اﻟﻤﺴﺘﮭﻠﻜﺔ‬ ‫اﻟﻮﻗﻮد‬ ‫ﻛﻤﯿﺔ‬ ‫ﻛﺬﻟﻚ‬ ‫و‬ ‫اﻟﺮﺣﻠﺔ‬ ‫زﻣﻦ‬ ‫ﯾﺰداد‬ ‫ﺑﺎﻟﺘﺎﻟﻰ‬ ‫و‬ ‫اﻟﻤﺘﺠﮭﺔ‬ ‫ﺳﺮﻋﺘﮭﺎ‬ ‫ﺗﻘﻞ‬ ‫س‬:‫واﻻﺧﺮى‬ ‫اﻟﺮﯾﺎح‬ ‫اﺗﺠﺎه‬ ‫ﻓﻲ‬ ‫اﻻوﻟﻰ‬ ‫وﻟﻜﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻧﻔﺲ‬ ‫ﺗﻘﻄﻌﺎن‬ ‫ﻃﺎﺋﺮﺗﺎن‬‫اﻟﺮﯾﺢ‬ ‫اﺗﺠﺎه‬ ‫ﻋﻜﺲ‬ ‫ﻓﻲ‬ ‫وﻟﻤﺎذا؟؟‬ . ‫اﻛﺜﺮ‬ ‫ﻟﻮﻗﻮد‬ ‫ﺗﺤﺘﺎج‬ ‫أﯾﮭﻤﺎ‬ ‫اﻟﮭﻮاء‬ ‫ﻣﻘﺎوﻣﺔ‬ ‫ﻓﺘﺰداد‬ ‫اﻟﺮﯾﺎح‬ ‫اﺗﺠﺎه‬ ‫ﻋﻜﺲ‬ ‫ﻓﻲ‬ ‫اﺗﺠﺎھﺎ‬ ‫اﻛﺜﺮﻻن‬ ‫ﻟﻮﻗﻮد‬ ‫ﺗﺤﺘﺎج‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫اﻟﻄﺎﺋﺮة‬‫ﻟﮭﺎ‬‫ﻣﻦ‬ ‫اﻛﺜﺮ‬ ‫وﻗﻮد‬ ‫ﻛﻤﯿﺔ‬ ‫ﻓﺘﺤﺘﺎج‬ ‫ﻓﻲ‬ ‫ﺗﺴﯿﺮ‬ ‫اﻟﺘﻲ‬ ‫اﻻوﻟﻰ‬ ‫اﻟﻄﺎﺋﺮة‬‫ﻧﻔﺲ‬‫اﻟﺮﯾﺢ‬ ‫اﺗﺠﺎه‬ ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﻜﻨﻮﻟﻮﺟﻰ‬ ‫ﺗﻄﺒﯿﻖ‬
  10. 10. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٠ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |١٠ : ‫اﻟﻀﻮء‬‫اﻹ‬ ‫ﺣﺎﺳﺔ‬ ‫ﯾﺜﯿﺮ‬ ‫ﺧﺎرﺟﻰ‬ ‫ﻣﺆﺛﺮ‬ ‫ھﻮ‬.‫اﻟﺴﻠﯿﻤﺔ‬ ‫اﻟﻌﯿﻦ‬ ‫ﻓﻰ‬ ‫ﺑﺼﺎر‬ ‫اﻟﻀﻮء‬.‫اﻟﻔﺮاغ‬ ‫ﻓﻰ‬ ‫اﻻﻧﺘﻘﺎل‬ ‫ﯾﻤﻜﻨﮭﺎ‬ ‫ﻛﮭﺮوﻣﻐﻨﺎﻃﯿﺴﯿﺔ‬ ‫ﻣﻮﺟﺎت‬ ‫ﻋﻦ‬ ‫ﻋﺒﺎرة‬ ‫وھﻮ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫أﺷﻜﺎل‬ ‫أﺣﺪ‬ : ‫اﻟﻀﻮء‬ ‫اﻧﻌﻜﺎس‬‫ھﻮ‬‫ارﺗﺪاد‬‫اﻟﻤﻮﺟﺎت‬‫اﻟﻀﻮﺋﯿﺔ‬‫ﺳﻘﻮﻃﮭﺎ‬ ‫ﺟﮭﺔ‬ ‫ﻧﻔﺲ‬ ‫اﻟﻰ‬‫ﻋﻨﺪﻣﺎ‬‫ﺗﻘﺎﺑﻞ‬‫ﺳﻄﺤﺎ‬‫ﻋﺎﻛﺴﺎ‬ ‫اﻟﻀﻮء؟‬ ‫ﻓﻰ‬ ‫اﻻﻧﻌﻜﺎس‬ ‫ﻗﺎﻧﻮﻧﺎ‬ ‫اﺳﺘﻨﺘﺎج‬ ‫ﺑﺎﻟﺘﺠﺮﺑﺔ‬ ‫وﺿﺤﻰ‬ ‫اﻟﺘﺠﺮﺑﺔ‬ ١-‫اﻟﻤﻨﻘﻠﺔ‬ ‫و‬ ‫اﻟﻮرﻗﺔ‬ ‫ﻣﻦ‬ ‫ﻛﻼ‬ ‫ﻋﻠﻰ‬ ‫ﻋﻤﻮدﯾﺎ‬ ‫اﻟﻤﺮاة‬ ‫ﻣﺴﺘﻮى‬ ‫ﯾﻜﻮن‬ ‫ﺑﺤﯿﺚ‬ ‫ﺑﯿﻀﺎء‬ ‫ورﻗﺔ‬ ‫ﺳﻄﺢ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺴﺘﻮﯾﺔ‬ ‫ﻣﺮاة‬ ‫ﻧﺜﺒﺖ‬ ٢‫اﻟﻤﺮاة‬ ‫ﺳﻄﺢ‬ ‫ﻋﻠﻰ‬ ‫اﻻﺳﻘﺎط‬ ‫ﺟﮭﺎز‬ ‫ﻣﻦ‬ ‫ﺿﻮﺋﻰ‬ ‫ﺷﻌﺎع‬ ‫ﻧﺴﻘﻂ‬ ٣‫زاوﯾﺔ‬ ‫و‬ ‫اﻟﺴﻘﻮط‬ ‫زاوﯾﺔ‬ ‫ﻣﻦ‬ ‫ﻛﻼ‬ ‫ﻧﻌﯿﻦ‬‫اﻻﻧﻌﻜﺎس‬ ‫اﻟﻤﻼﺣﻈﺔ‬ ‫اﻻﻧﻌﻜﺎس‬ ‫زاوﯾﺔ‬ = ‫اﻟﺴﻘﻮط‬ ‫زاوﯾﺔ‬ ‫ان‬ ‫ﻧﻼﺣﻆ‬ ٤-‫اﻟﺴﻘﻮط‬ ‫زاوﯾﺔ‬ ‫ﻧﻌﯿﻦ‬ ‫ﻣﺮة‬ ‫ﻛﻞ‬ ‫ﻓﻰ‬ ‫و‬ ‫ﻣﺮات‬ ‫ﻋﺪة‬ ‫اﻟﺴﻘﻮط‬ ‫زاوﯾﺔ‬ ‫ﻧﻐﯿﺮ‬ ‫اﻻﻧﻌﻜﺎس‬ ‫زاوﯾﺔ‬ ‫و‬ ‫اﻟﻤﻼﺣﻈﺔ‬‫ﻧﻼﺣﻆ‬‫ان‬‫اﻻﻧﻌﻜﺎس‬ ‫زاوﯾﺔ‬ = ‫اﻟﺴﻘﻮط‬ ‫زاوﯾﺔ‬‫ﻣﺮة‬ ‫ﻛﻞ‬ ‫ﻓﻰ‬ ٥-‫اﻟﺒﯿﻀﺎء‬ ‫اﻟﻮرﻗﺔ‬ ‫ﻣﺴﺘﻮى‬ ‫ﻋﻠﻰ‬ ‫ﯾﻤﯿﻞ‬ ‫اﻟﻤﺮاة‬ ‫ﻣﺴﺘﻮى‬ ‫ﻧﺠﻌﻞ‬ ‫اﻟ‬‫ﻤﻼﺣﻈﺔ‬‫اﻟﻤﻨﻌﻜﺲ‬ ‫اﻟﺸﻌﺎع‬ ‫رؤﯾﺔ‬ ‫ﻋﺪم‬ : ‫ﻧﻼﺣﻆ‬ ‫ا‬‫ﻻﺳﺘﻨﺘﺎج‬‫ھﻤﺎ‬ ‫ﻟﻘﺎﻧﻮﻧﯿﻦ‬ ‫وﻓﻘﺎ‬ ‫ﯾﺘﻢ‬ ‫اﻟﻀﻮء‬ ‫اﻧﻌﻜﺎس‬ : ‫اﻻول‬ ‫اﻟﻘﺎﻧﻮن‬‫اﻻﻧﻌﻜﺎس‬ ‫زاوﯾﺔ‬ = ‫اﻟﺴﻘﻮط‬ ‫زاوﯾﺔ‬ ‫اﻟﻤﻔﮭﻮم‬‫ﺗﻌﺮﯾﻔﮫ‬ ‫اﻟﻀﻮء‬ ‫اﻧﻌﻜﺎس‬‫اﻟﻀﻮ‬ ‫اﻻﺷﻌﺔ‬ ‫ارﺗﺪاد‬ ‫ھﻮ‬‫ﻋﺎﻛﺲ‬ ‫ﺗﻘﺎﺑﻠﺴﻄﺢ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ﺳﻘﻮﻃﮭﺎ‬ ‫ﺟﮭﺔ‬ ‫ﻧﻔﺲ‬ ‫إﻟﻲ‬ ‫ﺋﯿﺔ‬ ‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬.ً‫ﺎ‬‫ﻛﺮﯾ‬ ‫أو‬ ً‫ﺎ‬‫ﻣﺴﺘﻮﯾ‬ ‫ﯾﻜﻮن‬ ‫ﻗﺪ‬ ‫ﻣﺼﻘﻮل‬ ‫ﻧﺼﻒ‬ ‫أو‬ ‫ﻣﺼﻘﻮل‬ ‫ﺳﻄﺢ‬ ‫ھﻮ‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﺸﻌﺎع‬.‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﻋﻠﻰ‬ ‫ﯾﺴﻘﻂ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺑﺨﻂ‬ ‫ﺗﻤﺜﻞ‬ ‫رﻓﯿﻌﺔ‬ ‫ﺿﻮﺋﯿﺔ‬ ‫ھﻮﺣﺰﻣﺔ‬ ‫ھﻮ‬ ‫اﻟﻤﻨﻌﻜﺲ‬ ‫اﻟﺸﻌﺎع‬‫ﺗﻤﺜ‬ ‫رﻓﯿﻌﺔ‬ ‫ﺿﻮﺋﯿﺔ‬ ‫ﺣﺰﻣﺔ‬ ‫ھﻮ‬.‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﻋﻦ‬ ‫ارﺗﺪ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺑﺨﻂ‬ ‫ﻞ‬ ‫اﻻﻧﻌﻜﺎس‬ ‫ﻋﻤﻮد‬.‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺴﻘﻮط‬ ‫ﻧﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻌﻤﻮداﻟﻤﻘﺎم‬ ‫ھﻮ‬ ‫اﻟﺴﻘﻮط‬ ‫زاوﯾﺔ‬.‫اﻻﻧﻌﻜﺎس‬ ‫وﻋﻤﻮد‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﺸﻌﺎع‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺤﺼﻮرة‬ ‫اﻟﺰاوﯾﺔ‬ ‫ھﻰ‬ ‫اﻻﻧﻌﻜﺎس‬ ‫زاوﯾﺔ‬‫و‬ ‫اﻟﻤﻨﻌﻜﺲ‬ ‫اﻟﺸﻌﺎع‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺤﺼﻮرة‬ ‫اﻟﺰاوﯾﺔ‬ ‫ھﻰ‬.‫اﻻﻧﻌﻜﺎس‬ ‫ﻋﻤﻮد‬ ‫اﻟﻀﻮﺋﯿﺔ‬ ‫اﻟﻄﺎﻗﺔ‬ ‫اﻟﻀﻮء‬ ‫ﻓﻰ‬ ‫اﻻﻧﻌﻜﺎس‬ ‫ﻗﺎﻧﻮﻧﺎ‬ ‫ﺑﺎﻧ‬ ‫ﻣﺮﺗﺒﻄﺔ‬ ‫ﻣﻔﺎھﯿﻢ‬‫اﻟﻀﻮء‬ ‫ﻌﻜﺎس‬
  11. 11. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١١ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |١١ : ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻘﺎﻧﻮن‬‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﻋﻠﻲ‬ ‫اﻟﺴﻘﻮط‬ ‫ﻧﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻤﻘﺎم‬ ‫اﻟﻌﻤﻮد‬ ‫و‬ ‫اﻟﻤﻨﻌﻜﺲ‬ ‫اﻟﻀﻮﺋﻰ‬ ‫اﻟﺸﻌﺎع‬ ‫و‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﻀﻮﺋﻲ‬ ‫اﻟﺸﻌﺎع‬ ‫ﺟﻤ‬ ‫ﺗﻘﻊ‬‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﻋﻠﻲ‬ ‫ﻋﻤﻮدي‬ ‫واﺣﺪ‬ ‫ﻣﺴﺘﻮي‬ ‫ﻓﻲ‬ ‫ﯿﻌﺎ‬ (‫ﻞ‬‫)ﻋﻠ‬‫ﻲ‬‫ﻋﻠ‬ ‫ﺎ‬‫ﻋﻤﻮدﯾ‬ ‫ﺎﻗﻂ‬‫اﻟﺴ‬ ‫ﻮﺋﻲ‬‫اﻟﻀ‬ ‫ﻌﺎع‬‫اﻟﺸ‬ ‫ﻧﻔﺴﮫ‬ ‫ﻋﻠﻲ‬ ‫ﯾﻨﻌﻜﺲ‬ ‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﺎس‬ ‫اﻻﻧﻌﻜ‬ ‫ﺔ‬ ‫زاوﯾ‬ ‫ﺎوي‬ ‫ﺗﺴ‬ ‫ﻘﻮط‬ ‫اﻟﺴ‬ ‫ﺔ‬ ‫زاوﯾ‬ ‫ﻻن‬ (‫ـ‬ ‫)ﺟ‬ ‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬ : ‫اﻟﻌﺪﺳﺎت‬ ‫و‬ ‫اﻟﻤﺮاﯾﺎ‬‫اﻟ‬ ‫و‬ ‫اﻟﻤﯿﻜﺮوﺳﻜﻮﺑﺎت‬ ‫ﻣﺜﻞ‬ ‫اﻟﺒﺼﺮﯾﺔ‬ ‫اﻻﺣﮭﺰة‬ ‫ﻓﻰ‬ ‫ﺗﺴﺘﺨﺪم‬ ‫ﺿﻮﺋﯿﺔ‬ ‫ﻗﻄﻊ‬ ‫ھﻰ‬‫اﻟﻄﺒﯿﺔ‬ ‫اﻟﻨﻈﺎرات‬ ‫و‬ ‫ﺘﻠﺴﻜﻮﺑﺎت‬ : ‫اﻟﻌﺪﺳﺎت‬ ‫و‬ ‫اﻟﻤﺮاﯾﺎ‬ ‫وﻇﯿﻔﺔ‬‫او‬ ‫ﻣﻜﺒﺮة‬ ‫اﻟﺼﻮرة‬ ‫ھﺬة‬ ‫ﺗﻜﻮن‬ ‫ﻗﺪ‬ ‫و‬ ‫اﻣﺎﻣﮭﺎ‬ ‫ﺗﻘﻊ‬ ‫اﻟﺘﻰ‬ ‫ﻟﻼﺟﺴﺎم‬ ‫ﺗﻘﺪﯾﺮﯾﺔ‬ ‫او‬ ‫ﺣﻘﯿﻘﯿﺔ‬ ‫ﺻﻮرة‬ ‫ﺗﻜﻮﯾﻦ‬ ‫اﻻﺻﻠﻰ‬ ‫ﻟﻠﺠﺴﻢ‬ ‫ﻣﺴﺎوﯾﺔ‬ ‫او‬ ‫ﻣﺼﻐﺮة‬ :‫واﻟﺘﻘﺪﯾﺮﯾﺔ‬ ‫اﻟﺤﻘﯿﻘﯿﺔ‬ ‫اﻟﺼﻮرة‬- ‫اﻟﺤﻘﯿﻘﯿﺔ‬ ‫اﻟﺼﻮرة‬‫اﻟﺘﻘﺪﯾﺮﯾﺔ‬ ‫اﻟﺼﻮرة‬ ‫اﻷﺷﻌﺔ‬ ‫ﺗﻼﻗﻰ‬ ‫ﻧﺘﯿﺠﺔ‬ ‫ﺗﺘﻜﻮن‬‫ا‬‫اﻟﻤﻨﻜﺴﺮة‬ ‫او‬ ‫ﻟﻤﻨﻌﻜﺴﺔ‬‫اﻟﻤﻨﻜﺴﺮة‬ ‫او‬ ‫اﻟﻤﻨﻌﻜﺴﺔ‬ ‫اﻷﺷﻌﺔ‬ ‫اﻣﺘﺪادات‬ ‫ﺗﻼﻗﻰ‬ ‫ﻧﺘﯿﺠﺔ‬ ‫ﺗﺘﻜﻮن‬ ‫ﺣﺎﺋﻞ‬ ‫ﻋﻠﻰ‬ ‫اﺳﺘﻘﺒﻠﮭﺎ‬ ‫وﯾﻤﻜﻦ‬.‫ﺣﺎﺋﻞ‬ ‫ﻋﻠﻰ‬ ‫اﺳﺘﻘﺒﻠﮭﺎ‬ ‫ﯾﻤﻜﻦ‬ ‫وﻻ‬ :‫اﻟﻤﺮاﯾﺎ‬-{‫ﻣﺤﺪﺑﺔ‬ ‫او‬ ‫}ﻣﻘﻌﺮة‬ ‫ﻛﺮﯾﺔ‬ ‫او‬ ‫ﻣﺴﺘﻮﯾﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻗﺪ‬ .‫ﻟﻠﻀﻮء‬ ‫ﻋﺎﻛﺴﺔ‬ ‫أﺳﻄﺢ‬ ‫ھﻰ‬ ١.‫ﺗﻘﺎس‬‫ﻣﺪى‬‫ﺟﻮدة‬‫اﻟﻤﺮأة‬‫ﺑﻤﺪى‬‫ﻣﻄﺎﺑﻘﺔ‬‫اﻟﺼﻮر‬‫ﻟﻸﺻﻞ‬ ‫ا‬‫ﻻﺳﺘ‬‫ﺨﺪام‬‫ﺗﺴﺘﺨﺪم‬‫ﻓﻰ‬‫ﺟﻤﯿﻊ‬‫اﻷﺟﮭﺰة‬‫اﻟﺒﺼﺮﯾﺔ‬‫ﻣﺜﻞ‬‫اﻟﻤﯿﻜﺮوﺳﻜﻮب‬‫واﻟﺘﻠﺴﻜﻮب‬‫واﻟﻨﻈﺎرات‬ ) ‫ﻧﺸﺎط‬١‫اﻟﻤﺴﺘﻮﯾﺔ‬ ‫ﺑﺎﻟﻤﺮآة‬ ‫اﻟﻤﺘﻜﻮﻧﺔ‬ ‫اﻟﺼﻮر‬ ‫ﺧﻮاص‬ ‫ﺑﺎﻟﺘﺠﺮﺑﺔ‬ ‫وﺿﺤﻰ‬ :( ١-.‫ﻣﺴﺘﻮﯾﺔ‬ ‫ﻣﺮآة‬ ً‫ﺎ‬‫رأﺳﯿ‬ ‫ﻋﻠﯿﮫ‬ ‫ﻧﻀﻊ‬ ‫ﺛﻢ‬ ‫ﺑﯿﻀﺎء‬ ‫ورﻗﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ﻧﺮﺳﻢ‬ ٢-‫دﺑﻮﺳﯿﻦ‬ ‫ﻧﺜﺒﺖ‬ ‫ﺛﻢ‬ ‫اﻟﻤﺴﺘﻮﯾﺔ‬ ‫اﻟﻤﺮآة‬ ‫أﻣﺎم‬ (‫)أ‬ ‫دﺑﻮس‬ ‫ﻧﻀﻊ‬‫ﺟﺎﻧﺒﻰ‬ ‫أﺣﺪ‬ ‫ﻋﻠﻰ‬ (‫و)ﺣـ‬ (‫)ب‬ .‫اﻟﻤﺮآة‬ ‫ﻓﻰ‬ (/‫)أ‬ ‫اﻟﺪﺑﻮس‬ ‫ﺻﻮرة‬ ‫ﻣﻊ‬ ‫واﺣﺪة‬ ‫اﺳﺘﻘﺎﻣﺔ‬ ‫ﻋﻠﻰ‬ ‫ﯾﻜﻮﻧﺎ‬ ‫ﺑﺤﯿﺚ‬ (‫)أ‬ ‫اﻟﺪﺑﻮس‬ ٣-‫ﯾﻜﻮﻧﺎن‬ ‫ﺑﺤﯿﺚ‬ (‫)د(،)ھـ‬ ‫آﺧﺮﯾﻦ‬ ‫دﺑﻮﺳﯿﻦ‬ (‫)أ‬ ‫اﻟﺪﺑﻮس‬ ‫ﻣﻦ‬ ‫اﻷﺧﺮى‬ ‫اﻟﺠﮭﺔ‬ ‫ﻓﻰ‬ ‫ﻧﺜﺒﺖ‬ ‫)أ‬ ‫اﻟﺪﺑﻮس‬ ‫ﺻﻮرة‬ ‫ﻣﻊ‬ ‫واﺣﺪة‬ ‫اﺳﺘﻘﺎﻣﺔ‬ ‫ﻋﻠﻰ‬ ً‫ﺎ‬‫أﯾﻀ‬.(/ ٤-‫ﻓﻰ‬ ‫ﻓﯿﺘﻘﺒﻼن‬ ‫اﺳﺘﻘﺎﻣﺘﯿﮭﻤﺎ‬ ‫ﻋﻠﻰ‬ (‫ھـ‬ ‫)د‬ ، (‫ﺣـ‬ ‫)ب‬ ‫ﻧﺼﻞ‬ ‫ﺛﻢ‬ ‫واﻟﺪﺑﺎﺑﯿﺲ‬ ‫اﻟﻤﺮآة‬ ‫ﻧﺮﻓﻊ‬ .(‫)أ‬ ‫اﻟﺪﺑﻮس‬ ‫ﺻﻮرة‬ ‫ﻣﻮﺿﻊ‬ ‫ھﻰ‬ ‫ﻓﺘﻜﻮن‬ (/‫)أ‬ ‫اﻟﻨﻘﻄﺔ‬ .(‫)م‬ ‫ﻓﻰ‬ ‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﻟﯿﻘﺎﺑﻞ‬ (/‫أ‬ ‫)أ‬ ‫ﻧﺼﻞ‬ ٥-.(‫م‬ /‫)أ‬ ، (‫م‬ ‫)أ‬ ‫ﻧﻘﯿﺲ‬ :‫اﻟﻤﻼﺣﻈﺔ‬‫ان‬]١.(‫م‬ /‫)أ‬ = (‫م‬ ‫)أ‬ [٢.‫اﻟﻤﺮآة‬ ‫ﺳﻄﺢ‬ ‫ﻋﻠﻰ‬ ‫ﻣﻮدى‬ /‫أ‬ ‫أ‬ [ ‫اﻻ‬:‫ﺳﺘﻨﺘﺎج‬- ]١‫ﻋﻠﻰ‬ ‫ﻋﻤﻮدى‬ ‫ﯾﻜﻮن‬ ‫واﻟﺼﻮرة‬ ‫اﻟﺠﺴﻢ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻮاﺻﻞ‬ ‫اﻟﻤﺴﺘﻘﯿﻢ‬ [‫اﻟ‬‫ﺴﻄﺢ‬‫ﻟ‬ ‫اﻟﻌﺎﻛﺲ‬.‫ﻠﻤﺮآة‬ ]٢‫ﻋﻦ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺑﻌﺪ‬ [‫اﻟﻤﺮاة‬‫ﻋﻦ‬ ‫اﻟﺼﻮرة‬ ‫ﺑﻌﺪ‬ =‫اﻟﻤﺮاة‬ ١-‫اﻟﻤﺴﺘﻮﯾﺔ‬ ‫اﻟﻤﺮاة‬ ‫ﺍﻻﻨﻌﻜﺎﺱ‬‫ﺯﺍﻭﻴﺔ‬ ‫ﻤﺴﺘﻭﻴﺔ‬ ‫ﻤﺭﺁﺓ‬ ‫ﺍﻟﻤﻨﻌﻜﺱ‬ ‫ﺍﻟﺸﻌﺎﻉ‬‫ﺍﻟﺴﺎﻗﻁ‬ ‫ﺍﻟﺸﻌﺎﻉ‬ ‫ﺍﻟﺴﻘﻭﻁ‬‫ﺯﺍﻭﻴﺔ‬ ‫اﻟﻤﺮاﯾﺎ‬ ‫اوﻻ‬:- ‫أ‬ ‫أ‬/ ‫م‬ ‫ھـ‬ ‫د‬‫ب‬ ‫ﺣـ‬ == ==
  12. 12. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٢ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |١٢ :‫اﻟﻤﺴﺘﻮﯾﺔ‬ ‫ﺑﺎﻟﻤﺮآة‬ ‫اﻟﻤﺘﻜﻮﻧﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﺧﻮاص‬- ]١.‫ﻣﻌﺘﺪﻟﺔ‬ ‫ﺻﻮرة‬ [ ]٢.‫ﺗﻘﺪﯾﺮﯾﺔ‬ ‫ﺻﻮرة‬ [ ]٣. ‫ﻟﻠﺠﺴﻢ‬ ‫ﻣﺴﺎوﯾﺔ‬ [ ]٤‫ﻟﻠﺠﺴﻢ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫اﻟﻮﺿﻊ‬ ‫ﻣﻌﻜﻮﺳﺔ‬ [}‫ھﻮ‬ ‫اﻟﺠﺴﻢ‬ ‫ﯾﻤﯿﻦ‬ .{‫اﻟﺼﻮرة‬ ‫ﯾﻤﯿﻦ‬ ‫اﻟﺠﺴﻢ‬ ‫ﯾﺴﺎر‬ ‫و‬ ‫اﻟﺼﻮرة‬ ‫ﯾﺴﺎر‬ ]٥.‫اﻟﻤﺮآة‬ ‫ﻣﻦ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺑﻌﺪ‬ ‫ﯾﺴﺎوى‬ ‫اﻟﻤﺮآة‬ ‫ﻋﻦ‬ ‫اﻟﺼﻮرة‬ ‫ﺑﻌﺪ‬ [ ]٦ً‫ﺎ‬‫ﻋﻤﻮدﯾ‬ ‫ﯾﻜﻮن‬ ‫وﺻﻮرﺗﮫ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻮاﺻﻞ‬ ‫اﻟﻤﺴﺘﻘﯿﻢ‬ [ ‫اﻟﻤﺮآ‬ ‫ﺳﻄﺢ‬ ‫ﻋﻠﻰ‬.‫ة‬ ‫اﻟﻌﻤﻠﯿﺔ‬ ‫اﻟﺤﯿﺎة‬ ‫ﻓﻰ‬ ‫اﻟﻤﺴﺘﻮﯾﺔ‬ ‫ﻟﻠﻤﺮاة‬ ‫ﺗﺴﺘﺨﺪم‬ ‫ﺗﻄﺒﯿﻘﺎت‬ : ‫ﻋﻠﻞ‬‫ﺳﯿﺎرة‬ ‫ﻋﻠﻰ‬ ‫اﺳﻌﺎف‬ ‫ﻛﻠﻤﺔ‬ ‫ﺗﻜﺘﺐ‬‫؟‬ ‫ﻣﻌﻜﻮﺳﺔ‬ ‫اﻻﺳﻌﺎف‬ ‫اﻻﺳﻌﺎف‬ ‫ﻟﺴﯿﺎرة‬ ‫اﻟﻄﺮﯾﻖ‬ ‫ﺑﺎﺧﻼء‬ ‫ﻓﯿﺴﺮﻋﻮ‬ ‫ﻣﻀﺒﻮﻃﺔ‬ ‫اﻟﻤﺮاة‬ ‫ﻓﻰ‬ ‫اﻟﺴﯿﺎرات‬ ‫ﻗﺎﺋﺪى‬ ‫ﯾﺮاھﺎ‬ ‫ﺣﺘﻰ‬ ‫ﻋﻠﻞ‬‫ان‬ ‫اﻟﻌﯿﻮن‬ ‫ﻃﺒﯿﺐ‬ ‫:ﯾﺴﺘﻄﯿﻊ‬‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻨﻈﺮ‬ ‫ﻓﺤﺺ‬ ‫ﯾﺠﺮى‬٦‫ﻃﻮﻟﮭﺎ‬ ‫ﺣﺠﺮة‬ ‫ﻓﻰ‬ ‫ﻣﺘﺮ‬٣‫؟‬ ‫ﻓﻘﻂ‬ ‫ﻣﺘﺮ‬ ‫اﻟﺠﺴ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﺗﺼﺒﺢ‬ ‫ﻟﺬﻟﻚ‬ ‫اﻟﻤﺮآة‬ ‫ﻣﻦ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺑﻌﺪ‬ = ‫اﻟﻤﺮآة‬ ‫ﻋﻦ‬ ‫اﻟﺼﻮرة‬ ‫ﺑﻌﺪ‬ ‫ﻻن‬‫ﺻﻮرﺗﺔ‬ ‫و‬ ‫ﻢ‬٦‫وھﻮ‬ ‫ﻣﺘﺮ‬ ‫ا‬‫اﻻﻧﺴﺎن‬ ‫ﻟﺮؤﯾﺔ‬ ‫اﻟﻄﺒﯿﻌﻰ‬ ‫اﻟﻤﺪى‬ ‫اﻟﻨﻈﺮ‬ ‫ﺑﻤﺠﺮد‬ ‫اﻟﺜﻼﺛﺔ‬ ‫اﻟﻤﺮاﯾﺎ‬ ‫اﻧﻮاع‬ ‫ﺑﯿﻦ‬ ‫ﻧﻔﺮق‬ ‫ﻛﯿﻒ‬ :‫اﻟﻜﺮﯾﺔ‬ ‫اﻟﻤﺮآة‬- ١.. ‫ﺟﻮﻓﺎء‬ ‫ﻛﺮة‬ ‫ﺳﻄﺢ‬ ‫ﻣﻦ‬ ‫ﺟﺰء‬ ‫اﻟﻌﺎﻛﺲ‬ ‫ﺳﻄﺤﮭﺎ‬ ‫ﻣﺮآة‬ ‫ھﻰ‬ ٢.‫ﻓﺪ‬‫ﺗﻜﻮن‬‫ﻣﺤﺪﺑﺔ‬‫أو‬‫ﻣﻘﻌﺮة‬ ٣.‫ھﻰ‬ ‫اﻟﻤﻌﻠﻘﺔ‬‫أﻗﺮب‬‫ﻣﺜﺎل‬‫ﻟﻠﻤﺮاﯾﺎ‬‫وﺟﮭﮭﺎ‬ ‫اﻟﻜﺮﯾﺔ‬‫ﻣﻘﻌﺮة‬ ‫ﻣﺮاة‬ ‫اﻟﺪاﺧﻠﻰ‬‫و‬‫وﺟ‬‫ﮭﮭﺎ‬‫ﻣﺤﺪﺑﺔ‬ ‫ﻣﺮاة‬ ‫اﻟﺨﺎرﺟﻰ‬ : ‫اﻟﻜﺮﯾﺔ‬ ‫اﻟﻤﺮاﯾﺎ‬ ‫أﻧﻮاع‬ ]١(‫)ﻣﺠﻤﻌﺔ‬ ‫ﻣﻘﻌﺮة‬ ‫ﻣﺮآة‬ []٢(‫)ﻣﻔﺮﻗﺔ‬ ‫ﻣﺤﺪﺑﺔ‬ ‫ﻣﺮآة‬ [ ‫ﺗﻌﺘﺒﺮ‬ ‫اﻟﺘﻰ‬ ‫ﻟﻠﻜﺮة‬ ‫اﻟﺪاﺧﻠﻰ‬ ‫اﻟﺴﻄﺢ‬ ‫ھﻮ‬ ‫اﻟﻌﺎﻛﺲ‬ ‫ﺳﻄﺤﮭﺎ‬ . ‫ﻣﻨﮭﺎ‬ ‫ﺟﺰء‬ ‫اﻟﻤﺮاة‬ ‫ﻟﻠﻜﺮة‬ ‫اﻟﺨﺎرﺟﻰ‬ ‫اﻟﺴﻄﺢ‬ ‫ھﻮ‬ ‫اﻟﻌﺎﻛﺲ‬ ‫ﺳﻄﺤﮭﺎ‬ .‫ﻣﻨﮭﺎ‬ ‫ﺟﺰء‬ ‫اﻟﻤﺮاة‬ ‫ﺗﻌﺘﺒﺮ‬ ‫اﻟﺘﻰ‬ ‫إﻟﯿ‬ ‫اﻟﻨﻈﺮ‬ ‫ﻋﻨﺪ‬ ‫ﻣﻜﺒﺮة‬ ‫ﺻﻮرة‬ ‫ﺗﻜﻮن‬‫ﮭﺎ‬‫إﻟﯿﮭﺎ‬ ‫اﻟﻨﻈﺮ‬ ‫ﻋﻨﺪ‬ ‫ﻣﺼﻐﺮة‬ ‫ﺻﻮرة‬ ‫ﺗﻜﻮن‬ ‫ﻟﻠﻤﻠﻌﻘﺔ‬ ‫اﻟﺪاﺧﻠﻰ‬ ‫اﻟﺴﻄﺢ‬ :‫ﻟﮭﺎ‬ ‫ﻣﺜﺎل‬‫ﻟﻠﻤﻠﻌﻘﺔ‬ ‫اﻟﺨﺎرﺟﻰ‬ ‫اﻟﺴﻄﺢ‬ :‫ﻟﮭﺎ‬ ‫ﻣﺜﺎل‬ ‫اﻟﻜﺮﯾﺔ‬ ‫اﻟﻤﺮآة‬ ‫ﻋﻦ‬ ‫أﺳﺎﺳﯿﺔ‬ ‫ﻣﻔﺎھﯿﻢ‬ ‫م‬ ‫م‬ ‫ق‬‫ق‬ ‫أﺻ‬ ‫ﻣﺤﻮر‬‫ﻠﻰ‬ ‫ﺛﺎﻧﻮى‬ ‫ﻣﺤﻮر‬ ‫ﻣﻘﻌﺮة‬ ‫ﻣﺮآة‬‫ﻣﺤﺪﺑﺔ‬ ‫ﻣﺮآة‬ ‫ﻧﻖ‬‫ﻧﻖ‬ ٢-‫اﻟﻜﺮﯾﺔ‬ ‫اﻟﻤﺮاﯾﺎ‬
  13. 13. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٣ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |١٣ : ‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮاة‬ ‫ﺑﺆرة‬ ‫ﺗﻌﯿﯿﻦ‬ ‫ﯾﻤﻜﻦ‬ ‫ﻛﯿﻒ‬ ‫ﺑﺎﻟﺘﺠﺮﺑﺔ‬ ‫ﺿﺤﻰ‬ ‫اﻟﺴﻄﺢ‬ ‫اﻣﺎم‬ ‫اﻟﺤﺎﺋﻞ‬ ‫ﻧﺤﺮك‬ ‫ﺟﺪا‬ ‫ﺑﻌﯿﺪ‬ ‫ﺟﺴﻢ‬ ‫او‬ ‫اﻟﺸﻤﺲ‬ ‫ﻻﺷﻌﺔ‬ ‫ﻣﻮاﺟﮭﺔ‬ ‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮاة‬ ‫ﻧﻀﻊ‬‫اوﺿﺢ‬ ‫ﻋﻠﻰ‬ ‫ﻧﺤﺼﻞ‬ ‫ﺣﺘﻰ‬ ‫ﻟﻠﻤﺮاة‬ ‫اﻟﻌﻜﺲ‬ ‫اﻟﺒﺆرة‬ ‫ھﻰ‬ ‫(ﻓﺘﻜﻮن‬ ‫ﻣﻀﯿﺌﺔ‬ ‫ﻧﻘﻄﺔ‬ ) ‫ﺻﻮرة‬ ‫اﺻﻐﺮ‬ ‫و‬ ‫اﻟﻤﻘﻌﺮة‬ ‫ﻟﻠﻤﺮاة‬ (‫)ع‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫ھﻰ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﺬة‬ ‫ﻓﺘﻜﻮن‬ ‫اﻟﻤﺮاة‬ ‫ﻗﻄﺐ‬ ‫و‬ ‫اﻟﻤﻀﯿﺌﺔ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻧﻘﯿﺲ‬ : ‫اﻻﺳﺘﻨﺘﺎج‬‫اﻟﺒ‬ ‫ﺗﺴﻤﻰ‬ ‫ﺣﺎﺋﻞ‬ ‫ﻋﻠﻰ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻓﻰ‬ ‫ﺗﺘﺠﻤﻊ‬ ‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮاة‬ ‫ﻣﻦ‬ ‫اﻟﻤﻨﻌﻜﺴﺔ‬ ‫اﻻﺷﻌﺔ‬ ‫ان‬‫ﺆرة‬ :‫اﻟﺒﺆرى‬ ‫واﻟﺒﻌﺪ‬ ‫اﻟﺘﻜﻮر‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﻼﻗﺔ‬-= ‫ﻧﻖ‬ ‫او‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫ﺿﻌﻒ‬ = ‫اﻟﺘﻜﻮر‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬٢‫ع‬ :‫اﻟﻜﺮﯾﺔ‬ ‫ﻟﻠﻤﺮآة‬ ‫اﻟﺘﻘﺪﯾﺮﯾﺔ‬ ‫واﻟﺒﺆرة‬ ‫اﻟﺤﻘﯿﻘﯿﺔ‬ ‫اﻟﺒﺆرة‬- ‫اﻟﺤﻘﯿﻘﯿﺔ‬ ‫اﻟﺒﺆرة‬‫اﻟﺘﻘﺪﯾﺮﯾﺔ‬ ‫اﻟﺒﺆرة‬ .‫اﻟﻤﻨﻌﻜﺴﺔ‬ ‫اﻷﺷﻌﺔ‬ ‫ﺗﻼﻗﻰ‬ ‫ﻧﻘﻄﺔ‬ ‫ھﻰ‬‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮاة‬ ‫ﻓﻰ‬‫اﻣﺘﺪاد‬ ‫ﺗﻼﻗﻰ‬ ‫ﻣﻦ‬ ‫ﺗﺘﻜﻮن‬‫اﻷﺷﻌﺔ‬‫اﻟﻤﻨﻌﻜﺴﺔ‬‫اﻟﻤﺤﺪﺑﺔ‬ ‫اﻟﻤﺮاة‬ ‫ﻓﻰ‬ .‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮآة‬ ‫أﻣﺎم‬ ‫ﺗﻘﻊ‬ ‫و‬. ‫اﻟﻤﺤﺪﺑﺔ‬ ‫اﻟﻤﺮآة‬ ‫ﺧﻠﻒ‬ ‫ﺗﻘﻊ‬ .‫ﺣﺎﺋﻞ‬ ‫ﻋﻠﻰ‬ ‫اﺳﺘﻘﺒﺎﻟﮭﺎ‬ ‫ﯾﻤﻜﻦ‬ ‫و‬.‫ﺣﺎﺋﻞ‬ ‫ﻋﻠﻰ‬ ‫اﺳﺘﻘﺒﺎﻟﮭﺎ‬ ‫ﯾﻤﻜﻦ‬ ‫ﻻ‬ ‫اﻟﻤﻔﮭﻮم‬‫ﺗﻌﺮﯾﻔﮫ‬ (‫)م‬ ‫اﻟﻤﺮآة‬ ‫ﺗﻜﻮر‬ ‫ﻣﺮﻛﺰ‬.‫ﻣﻨﮭﺎ‬ ً‫ا‬‫ﺟﺰء‬ ‫اﻟﻤﺮآة‬ ‫ﺗﻌﺘﺒﺮ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻜﺮة‬ ‫ﻣﺮﻛﺰ‬ ‫ھﻮ‬ (‫)ق‬ ‫اﻟﻤﺮآة‬ ‫ﻗﻄﺐ‬‫ھﻰ‬.‫اﻟﻜﺮﯾﺔ‬ ‫ﻟﻠﻤﺮآة‬ ‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﺗﺘﻮﺳﻂ‬ ‫وھﻤﯿﺔ‬ ‫ﻧﻘﻄﺔ‬ (‫)ﻧﻖ‬ ‫اﻟﻤﺮآة‬ ‫ﺗﻜﻮر‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬ ‫اﻟﻜﺮة‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬ ‫ھﻮ‬ ‫ﺳﻄﺤﮭﺎاو‬ ‫ﻋﻠﻰ‬ ‫ﻧﻘﻄﺔ‬ ‫وأى‬ ‫اﻟﻤﺮآة‬ ‫ﺗﻜﻮر‬ ‫ﻣﺮﻛﺰ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﻮ‬ ‫ﻣﻨﮭﺎ‬ ‫ﺟﺰء‬ ‫اﻟﻤﺮاة‬ ‫ﺗﻌﺘﺒﺮ‬ ‫اﻟﺘﻰ‬ ‫ﻟﻠﻤﺮآة‬ ‫اﻷﺻﻠﻰ‬ ‫اﻟﻤﺤﻮر‬‫وﻗﻄﺒﮭ‬ ‫اﻟﻤﺮآة‬ ‫ﺗﻜﻮر‬ ‫ﺑﻤﺮﻛﺰ‬ ‫اﻟﻤﺎر‬ ‫اﻟﻤﺴﺘﻘﯿﻢ‬ ‫ھﻮ‬.‫ﺎ‬ ‫ﻟﻠﻤﺮآة‬ ‫اﻟﺜﺎﻧﻮى‬ ‫اﻟﻤﺤﻮر‬ ‫ﻗﻄﺒﮭﺎ‬ ‫ﻋﺪا‬ ‫ﻣﺎ‬ ‫ﺳﻄﺤﮭﺎ‬ ‫ﻋﻠﻲ‬ ‫ﻧﻘﻄﺔ‬ ‫أي‬ ‫و‬ ‫اﻟﻤﺮآة‬ ‫ﺗﻜﻮر‬ ‫ﺑﻤﺮﻛﺰ‬ ‫ﯾﻤﺮ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫أي‬ ‫ھﻮ‬ (‫)ب‬ ‫اﻟﻜﺮﯾﺔ‬ ‫اﻟﻤﺮآة‬ ‫ﺑﺆرة‬‫اﻣﺘﺪادھﺎ‬ ‫أو‬ ‫ھﻰ‬ ‫اﻟﻤﻨﻌﻜﺴﺔ‬ ‫اﻷﺷﻌﺔ‬ ‫ﺗﻼﻗﻰ‬ ‫ﻧﻘﻄﺔ‬ ‫ھﻰ‬ ‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮآة‬ ‫ﺑﺆرة‬‫ﺗ‬ ‫ﻧﻘﻄﺔ‬ ‫ھﻲ‬‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮآة‬ ‫ﻋﻠﻲ‬ ‫اﻟﻤﻨﻌﻜﺴﺔ‬ ‫اﻷﺷﻌﺔ‬ ‫ﻼﻗﻰ‬ (‫ع‬ ‫ﻟﻠﻤﺮآة‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬.‫اﻟﻤﺮآة‬ ‫وﻗﻄﺐ‬ ‫اﻻﺻﻠﯿﺔ‬ ‫اﻟﺒﺆرة‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﻮ‬ ‫ب‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫ب‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬
  14. 14. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٤ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |١٤ :‫ﻋﻨﮭﺎ‬ ‫اﻧﻌﻜﺎﺳﮭﺎ‬ ‫واﺗﺠﺎه‬ ‫ﻛﺮﯾﺔ‬ ‫ﻣﺮآة‬ ‫ﺳﻄﺢ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺴﺎﻗﻄﺔ‬ ‫اﻷﺷﻌﺔ‬ ‫ﺑﻌﺾ‬ ‫ﻣﺴﺎر‬- ١-‫ﻠﻰ‬ ‫اﻷﺻ‬ ‫ﻮر‬ ‫ﻟﻠﻤﺤ‬ ‫ﻮازى‬ ‫ﻣ‬ ‫ﺎﻗﻂ‬ ‫اﻟﺴ‬ ‫ﻌﺎع‬ ‫اﻟﺸ‬ً‫ا‬‫ﺎر‬ ‫ﻣ‬ ‫ﻨﻌﻜﺲ‬ ‫ﯾ‬ .‫ﺑﺎﻟﺒﺆرة‬ ٢-‫ﻮر‬ ‫ﻟﻠﻤﺤ‬ ً‫ﺎ‬ ‫ﻣﻮازﯾ‬ ‫ﻨﻌﻜﺲ‬ ‫ﯾ‬ ‫ﺎﻟﺒﺆرة‬ ‫ﺑ‬ ً‫ا‬‫ﺎر‬ ‫ﻣ‬ ‫ﺎﻗﻂ‬ ‫اﻟﺴ‬ ‫ﻌﺎع‬ ‫اﻟﺸ‬ .‫اﻷﺻﻠﻰ‬ ٣-‫ﻷﻧﮫ‬ ‫ﻧﻔﺴﮫ‬ ‫ﻋﻠﻰ‬ ‫ﯾﻨﻌﻜﺲ‬ ‫اﻟﺘﻜﻮر‬ ‫ﺑﻤﺮﻛﺰ‬ ً‫ا‬‫ﻣﺎر‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﺸﻌﺎع‬ .‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﻋﻠﻰ‬ ‫ﻋﻤﻮدى‬ ‫ﯾﻜﻮن‬ ‫اﻟﺠﺴﻢ‬ ‫ﻣﻮﺿﻊ‬‫اﻟﺮﺳﻢ‬‫اﻟﺼﻮرة‬ ‫ﺧﻮاص‬ ]١‫ﻣﻦ‬ ‫أﻛﺒﺮ‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﺴﻢ‬ [ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫ﺿﻌﻒ‬‫ﺻﻮ‬‫رة‬‫ﻣﺼﻐﺮة‬ / ‫ﻣﻘﻠﻮﺑﺔ‬ / ‫ﺣﻘﯿﻘﯿﺔ‬ ‫اﻟﺘﻜﻮر‬ ‫وﻣﺮﻛﺰ‬ ‫اﻟﺒﺆرة‬ ‫ﺑﯿﻦ‬ ]٢‫ﯾﺴﺎوى‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﺴﻢ‬ [ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫ﺿﻌﻒ‬ (‫اﻟﺘﻜﻮر‬ ‫ﻣﺮﻛﺰ‬ ‫)ﻋﻨﺪ‬ ‫ﺻﻮرة‬‫ﻣﺴﺎوﯾﺔ‬ / ‫ﻣﻘﻠﻮﺑﺔ‬ / ‫ﺣﻘﯿﻘﯿﺔ‬ ‫اﻟﺘﻜﻮر‬ ‫ﻣﺮﻛﺰ‬ ‫ﻋﻨﺪ‬ ‫ﻟﻠﺠﺴﻢ‬ ]٣‫ﻣﻦ‬ ‫أﻛﺒﺮ‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﺴﻢ‬ [ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫اﻟﺒﻌﺪ‬ ‫ﺿﻌﻒ‬ ‫ﻣﻦ‬ ‫وأﺻﻐﺮ‬ .‫اﻟﺒﺆرى‬ ‫ﺻﻮرة‬‫ﻣ‬ / ‫ﺣﻘﯿﻘﯿﺔ‬‫ﻣﻜﺒﺮة‬ / ‫ﻘﻠﻮﺑﺔ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺘﻜﻮر‬ ‫ﻣﺮﻛﺰ‬ ‫ﻣﻦ‬ ‫أﺑﻌﺪ‬ ]٤‫ﻣﻦ‬ ‫أﻗﻞ‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﺴﻢ‬ [ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫ﺻﻮرة‬‫ﻣﻜﺒﺮة‬ / ‫ﻣﻌﺘﺪﻟﺔ‬ / ‫ﺗﻘﺪﯾﺮﯾﺔ‬ ‫اﻟﻤﺮآة‬ ‫داﺧﻞ‬ ‫ﺗﺮى‬ :‫اﻟﻤﺤﺪﺑﺔ‬ ‫اﻟﻤﺮآة‬ ‫ﻓﻰ‬ ‫اﻟﻤﺘﻜﻮﻧﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﺧﻮاص‬ ‫ﺻﻮرة‬‫ﻣﻌﺘﺪﻟﺔ‬ / ‫ﺗﻘﺪﯾﺮﯾﺔ‬/‫ﻣﺼﻐﺮة‬ ‫م‬ ‫ب‬ ‫م‬ ‫ب‬ ‫م‬ ‫ب‬ ‫م‬‫ب‬ ‫اﻟﻜﺮﯾﺔ‬ ‫ﺑﺎﻟﻤﺮاﯾﺎ‬ ‫اﻟﺼﻮر‬ ‫ﺗﻜﻮن‬ ‫ب‬ ‫ب‬ ‫ب‬ ‫م‬
  15. 15. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٥ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |١٥ : ‫اﻟﻌﺪﺳﺎت‬-‫ﻟ‬ ‫ﻛﺎﺳﺮ‬ ‫ﺷﻔﺎف‬ ‫وﺳﻂ‬ ‫ھﻰ‬‫ﻣﺴﺘﻮى‬ ‫وآﺧﺮ‬ ‫ﻛﺮى‬ ‫ﺳﻄﺢ‬ ‫أو‬ ‫ﻛﺮﯾﺎن‬ ‫ﺳﻄﺤﺎن‬ ‫ﯾﺤﺪه‬ ‫ﻠﻀﻮء‬ :‫اﻟﻌﺪﺳﺎت‬ ‫أﻧﻮاع‬- ]١(‫)ﻣﺠﻤﻌﺔ‬ ‫ﻣﺤﺪﺑﺔ‬ ‫ﻋﺪﺳﺔ‬ []٢(‫)ﻣﻔﺮﻗﺔ‬ ‫ﻣﻘﻌﺮة‬ ‫ﻋﺪﺳﺔ‬ [ .‫اﻟﺤﺎﻓﺔ‬ ‫ﻋﻨﺪ‬ ‫ورﻗﯿﻘﺔ‬ ‫اﻟﻤﻨﺘﺼﻒ‬ ‫ﻣﻦ‬ ‫ﺳﻤﯿﻜﺔ‬.‫اﻟﺤﺎﻓﺔ‬ ‫ﻋﻨﺪ‬ ‫وﺳﻤﯿﻜﺔ‬ ‫اﻟﻤﻨﺘﺼﻒ‬ ‫ﻣﻦ‬ ‫رﻗﯿﻘﺔ‬ ‫ﻣﺘﻮازﯾﺔ‬ ‫ﻋﻠﯿﮭﺎ‬ ‫ﺗﺴﻘﻂ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻷﺷﻌﺔ‬ ‫ﺗﺠﻤﻊ‬‫ﻣﺘ‬ ‫ﻋﻠﯿﮭﺎ‬ ‫ﺗﺴﻘﻂ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻟﻀﻮﺋﯿﺔ‬ ‫اﻷﺷﻌﺔ‬ ‫ﺗﻔﺮق‬.‫ﻮازﯾﺔ‬ ‫اﻟﻤﻔﮭﻮم‬‫ﺗﻌﺮﯾﻔﮫ‬ (‫)م‬ ‫اﻟﻌﺪﺳﺔ‬ ‫وﺟﮫ‬ ‫ﺗﻜﻮر‬ ‫ﻣﺮﻛﺰ‬‫ھﻮ‬‫اﻟﻜﺮة‬ ‫ﻣﺮﻛﺰ‬‫ﯾﻌﺘﺒﺮ‬ ‫اﻟﺬى‬.‫ﻣﻨﮭﺎ‬ ً‫ا‬‫ﺟﺰء‬ ‫اﻟﻮﺟﮫ‬ ‫ھﺬا‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻷﺻﻠﻰ‬ ‫اﻟﻤﺤﻮر‬‫ھﻮ‬.‫اﻟﻌﺪﺳﺔ‬ ‫وﺟﮭﻰ‬ ‫ﺗﻜﻮر‬ ‫ﺑﻤﺮﻛﺰى‬ ‫اﻟﻤﺎر‬ ‫اﻟﻤﺴﺘﻘﯿﻢ‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺒﺼﺮى‬ ‫اﻟﻤﺮﻛﺰ‬ ‫ھﻮ‬‫ﺗﻘﻊ‬ ‫اﻟﻌﺪﺳﺔ‬ ‫ﺑﺎﻃﻦ‬ ‫ﻓﻰ‬ ‫وھﻤﯿﺔ‬ ‫ﻧﻘﻄﺔ‬.‫اﻷﺻﻠﻰ‬ ‫اﻟﻤﺤﻮر‬ ‫ﻋﻠﻰ‬‫اﻟﻤﺎر‬ ‫اﻟﻤﺴﺘﻘﯿﻢ‬ ‫و‬ ‫اﻧﻜﺴﺎر‬ ‫اى‬ ‫ﯾﻌﺎﻧﻰ‬ ‫ان‬ ‫دون‬ ‫ﯾﻨﻔﺬ‬ ‫ﺑﮭﺎ‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺜﺎﻧﻮى‬ ‫اﻟﻤﺤﻮر‬‫ھﻮ‬.‫اﻷﺻﻠﻰ‬ ‫ﻣﺤﻮرھﺎ‬ ‫ﻏﯿﺮ‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺒﺼﺮى‬ ‫ﺑﺎﻟﻤﺮﻛﺰ‬ ‫ﯾﻤﺮ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫أى‬ ‫ﺑﺆرة‬‫ا‬(‫)ب‬ ‫ﻟﻌﺪﺳﺔ‬‫ﻧﻘﻄﺔ‬ ‫ھﻰ‬ ‫ن‬‫اﻷﺷﻌﺔ‬ ‫ﺗﻼﻗﻰ‬‫اﻟﻤﻨﻜﺴﺮة‬‫ھﻰ‬.‫اﻣﺘﺪادھﺎ‬ ‫أو‬ ‫ﻟ‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬(‫)ع‬ ‫ﻠﻌﺪﺳﺔ‬‫ھﻮ‬.‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺒﺼﺮى‬ ‫واﻟﻤﺮﻛﺰ‬ ‫اﻷﺻﻠﯿﺔ‬ ‫اﻟﺒﺆرة‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﻟﻌﺪﺳﺔ‬ ‫وﺟﺔ‬ ‫ﺗﻜﻮر‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬‫ﻣﻨﮭﺎ‬ ‫ﺟﺰءا‬ ‫اﻟﻮﺟﺔ‬ ‫ھﺬا‬ ‫ﯾﻌﺘﺒﺮ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻜﺮة‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬ ‫ھﻮ‬ :‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺘﻘﺪﯾﺮﯾﺔ‬ ‫واﻟﺒﺆرة‬ ‫اﻟﺤﻘﯿﻘﯿﺔ‬ ‫اﻟﺒﺆرة‬- ‫اﻟﺤﻘﯿﻘﯿﺔ‬ ‫اﻟﺒﺆرة‬‫اﻟﺘﻘﺪﯾﺮﯾﺔ‬ ‫اﻟﺒﺆرة‬ ‫ﻧﻘﻄﺔ‬ ‫ھﻰ‬‫اﻷﺷﻌ‬ ‫ﺗﻼﻗﻰ‬‫ﺔ‬‫اﻟﻤﻨﻜﺴﺮة‬‫ﻓﻰ‬.‫اﻟﻌﺪﺳﺔ‬‫اﻟﻤﺤﺪﺑﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ھﻰ‬‫اﻷﺷﻌﺔ‬ ‫اﻣﺘﺪاد‬ ‫ﺗﻼﻗﻰ‬‫اﻟﻤﻨﻜﺴﺮة‬ ‫ﻓﻰ‬.‫اﻟﻌﺪﺳﺔ‬‫اﻟﻤﻘﻌﺮة‬ ‫و‬.‫ﺣﺎﺋﻞ‬ ‫ﻋﻠﻰ‬ ‫اﺳﺘﻘﺒﺎﻟﮭﺎ‬ ‫ﯾﻤﻜﻦ‬‫و‬.‫ﺣﺎﺋﻞ‬ ‫ﻋﻠﻰ‬ ‫اﺳﺘﻘﺒﺎﻟﮭﺎ‬ ‫ﯾﻤﻜﻦ‬ ‫ﻻ‬ ‫اﻟﻌﺪﺳﺎت‬ ‫ﻋﻦ‬ ‫أﺳﺎﺳﯿﺔ‬ ‫ﻣﻔﺎھﯿﻢ‬ ‫ب‬ ‫ب‬ ‫اﻟﻌﺪﺳﺎت‬ :ً‫ﺎ‬‫ﺛﺎﻧﯿ‬
  16. 16. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٦ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |١٦ : ‫اﻟﻤﺤﺪﺑﺔ‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫ﺗﻌﯿﯿﻦ‬ : ‫اﻻدوات‬‫ﻣﺤﺪﺑﺔ‬ ‫ﻋﺪﺳﺔ‬-‫ﺣﺎﺋﻞ‬-‫اﻟﻌﺪﺳﺔ‬ ‫ﺣﺎﻣﻞ‬-‫ﻟﯿﻜ‬ ‫و‬ ‫ﺑﻌﯿﺪ‬ ‫ﺿﻮﺋﻰ‬ ‫ﻣﺼﺪر‬‫اﻟﺸﻤﺲ‬ ‫اﺷﻌﺔ‬ ‫ﻦ‬ : ‫اﻟﺨﻄﻮات‬‫ﺐ‬‫اﻟﺠﺎﻧ‬ ‫ﻰ‬‫ﻋﻠ‬ ‫ﯿﺎ‬‫راﺳ‬ ‫ﻞ‬‫اﻟﺤﺎﺋ‬ ‫ﻊ‬‫ﻧﻀ‬ ‫و‬ ‫ﺪ‬‫اﻟﺒﻌﯿ‬ ‫ﻮﺋﻰ‬‫اﻟﻀ‬ ‫ﺪر‬‫اﻟﻤﺼ‬ ‫ﺟﮭﯿﮭﺎ‬ ‫و‬ ‫اﺣﺪ‬ ‫ﯾﻘﺎﺑﻞ‬ ‫ﺑﺤﯿﺚ‬ ‫اﻟﺤﺎﻣﻞ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﺪﺳﺔ‬ ‫ﻧﻀﻊ‬ ‫اﻟﻌﺪﺳﺔ‬ ‫ﺑﺆرة‬ ‫ھﻰ‬ ‫ﻓﺘﻜﻮن‬ ‫ﻣﻀﯿﺌﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫اوﺿﺢ‬ ‫ﻋﻠﻰ‬ ‫ﻧﺤﺼﻞ‬ ‫ﺣﺘﻰ‬ ‫اﻟﻌﺪﺳﺔ‬ ‫ﻣﻦ‬ ‫ﺑﻌﺪا‬ ‫و‬ ‫ﻗﺮﺑﺎ‬ ‫ﻧﺤﺮﻛﺔ‬ ‫و‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻻﺧﺮ‬ ‫اﻟﺒﺼ‬ ‫اﻟﻤﺮﻛﺰ‬ ‫و‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ھﺬة‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻧﻘﯿﺲ‬‫اﻟﻤﺤﺪﺑﺔ‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫ھﻮ‬ ‫ﻓﯿﻜﻮن‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫ﺮى‬ :‫ﻣﻨﮭﺎ‬ ‫وﻧﻔﺎذھﺎ‬ ‫اﻟﻌﺪﺳﺔ‬ ‫وﺟﮭﻰ‬ ‫أﺣﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺴﺎﻗﻄﺔ‬ ‫اﻷﺷﻌﺔ‬ ‫ﺑﻌﺾ‬ ‫ﻣﺴﺎر‬- ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﺸﻌﺎع‬ ‫اﻷﺻﻠﻰ‬ ‫ﻟﻠﻤﺤﻮر‬ ً‫ﺎ‬‫ﻣﻮازﯾ‬ ً‫ا‬‫ﻣﻨﻜﺴﺮ‬ ‫ﯾﻨﻔﺬ‬ .‫ﺑﺎﻟﺒﺆرة‬ ‫ﻣﺎرا‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﺸﻌﺎع‬ ‫ﺑﺎﻟﺒﺆرة‬ ً‫ا‬‫ﻣﺎر‬ ً‫ﺎ‬‫ﻣﻮازﯾ‬ ‫ﯾﻨﻔﺬ‬ .‫اﻷﺻﻠﻰ‬ ‫ﻟﻠﻤﺤﻮر‬ ً‫ا‬‫ﻣﺎر‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﺸﻌﺎع‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺒﺼﺮى‬ ‫ﺑﺎﻟﻤﺮﻛﺰ‬ .‫اﺳﺘﻘﺎﻣﺘﮫ‬ ‫ﻋﻠﻰ‬ ‫ﯾﻨﻔﺬ‬ ‫اﻟﺠﺴﻢ‬ ‫ﻣﻮﺿﻊ‬‫اﻟﺮﺳﻢ‬‫اﻟﺼﻮرة‬ ‫ﺧﻮاص‬ ‫أﻛﺒﺮ‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﺴﻢ‬ .‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫ﺿﻌﻒ‬ ‫ﻣﻦ‬ ‫ﺣﻘﯿﻘﯿﺔ‬ ‫ﺻﻮرة‬ ‫ﻣﺼﻐﺮة‬ ‫ﻣﻘﻠﻮﺑﺔ‬ ‫اﻟﺘﻜﻮر‬ ‫وﻣﺮﻛﺰ‬ ‫اﻟﺒﺆرة‬ ‫ﺑﯿﻦ‬ ‫ﺗﻘﻊ‬ ‫ﯾﺴﺎوى‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﺴﻢ‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫ﺿﻌﻒ‬ (‫اﻟﺘﻜﻮر‬ ‫ﻣﺮﻛﺰ‬ ‫)ﻓﻰ‬ ‫ﺣﻘﯿﻘﺔ‬ ‫ﺻﻮرة‬ ‫ﻣﺴﺎو‬ ‫ﻣﻘﻠﻮﺑﺔ‬‫ﻟﻠﺠﺴﻢ‬ ‫ﯾﺔ‬ ‫اﻟﺘﻜﻮر‬ ‫ﻣﺮﻛﺰ‬ ‫ﻋﻨﺪ‬ ‫ﺗﻘﻊ‬ ‫ب‬ ‫م‬ ‫ب‬‫م‬ ‫ﺑﺎﻟﻌﺪﺳﺎت‬ ‫اﻟﺼﻮر‬ ‫ﺗﻜﻮن‬ ‫ب‬ ‫م‬ ‫ب‬‫م‬ ‫ب‬ ‫ب‬
  17. 17. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٧ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |١٧ ‫أﻛﺒﺮ‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﺴﻢ‬ ‫ﻣﻦ‬‫اﻟﺒﻌﺪ‬ ‫اﻟﺒﻌﺪ‬ ‫ﺿﻌﻒ‬ ‫ﻣﻦ‬ ‫وأﺻﻐﺮ‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫اﻟﺒﺆرى‬ ‫ﺣﻘﯿﻘﯿﺔ‬ ‫ﺻﻮرة‬ ‫ﻣﻜﺒﺮة‬ ‫ﻣﻘﻠﻮﺑﺔ‬ ‫اﻟﺘﻜﻮر‬ ‫ﻣﺮﻛﺰ‬ ‫ﺑﻌﺪ‬ ‫ﺗﻘﻊ‬ ‫اﻟﺒﺆرة‬ ‫ﻋﻨﺪ‬ ‫اﻟﺠﺴﻢ‬ ‫ﻻ‬‫ﺗﺘﻜﻮن‬‫ﺻﻮرة‬‫ﺗﻨﻔﺬ‬ ‫اﻻﺷﻌﺔ‬ ‫ﻻن‬ ‫اﻟﻰ‬ ‫ﻣﺘﻮازﯾﺔ‬‫ﻻﻧﮭﺎﯾﺔ‬ ‫ﻣﺎ‬ ‫ﻣﻦ‬ ‫اﻗﻞ‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﺴﻢ‬ ‫اﻟﺒﻌ‬‫اﻟﺒﺆرى‬ ‫ﺪ‬ ‫ﻣﻜﺒﺮة‬ ‫ﻣﻌﺘﺪﻟﺔ‬ ‫ﺗﻘﺪﯾﺮﯾﺔ‬ ‫ﺻﻮرة‬ ‫اﻟﺠﺴﻢ‬ ‫ﺟﮭﺔ‬ ‫ﻧﻔﺲ‬ ‫وﻓﻰ‬ ‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻌﺪﺳﺔ‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬:‫ﻣﺼﻐﺮة‬ ‫ﻣﻌﺘﺪﻟﺔ‬ ‫ﺗﻘﺪﯾﺮﯾﺔ‬ ‫ﺻﻮرة‬ ‫ﺗﺘﻜﻮن‬ ‫اﻻﺑﺼﺎر‬ ‫ﻋﯿﻮب‬ ‫ﻋﻼج‬ ‫ﻓﻰ‬ ‫اﻟﻌﺪﺳﺎت‬ ‫اﺳﺘﺨﺪام‬ : ‫اﻻﺑﺼﺎر‬ ‫ﻋﯿﻮب‬ ‫اھﻢ‬‫اﻟﻨﻈﺮ‬ ‫ﻃﻮل‬ ‫و‬ ‫اﻟﻨﻈﺮ‬ ‫ﻗﺼﺮ‬ ‫اﻟﻨﻈﺮ؟‬ ‫ﻃﻮل‬ ‫و‬ ‫اﻟﻨﻈﺮ‬ ‫ﻗﺼﺮ‬ ‫ﺣﺪوث‬ ‫ﺳﺒﺐ‬ ‫ھﻮ‬ ‫ﻣﺎ‬ ١-‫ﺗﺤﺪب‬ ‫إﻧﺘﻈﺎم‬ ‫ﻋﺪم‬‫اﻟﻌﯿﻦ‬ ‫ﻗﺮﻧﯿﺔ‬٢-‫اﻟﻌﯿﻦ‬ ‫ﻛﺮوﯾﺔ‬ ‫إﻧﺘﻈﺎم‬ ‫ﻋﺪم‬ :‫اﻟﺴﻠﯿﻤﺔ‬ ‫اﻟﻌﯿﻦ‬ ‫ﺻﻔﺎت‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺒﻌﯿﺪة‬ ‫اﻻﺟﺴﺎم‬ ‫ﺗﺮى‬٦‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻘﺮﯾﺒﺔ‬ ‫اﻻﺟﺴﺎم‬ ‫وﺗﺮى‬ ‫واﺿﺤﺔ‬ ‫ﻣﺘﺮ‬٢٥‫واﺿﺤﺔ‬ ‫ﺳﻢ‬ ‫اﻟﻨﻈﺮ‬ ‫ﻗﺼﺮ‬‫اﻟﻨﻈﺮ‬ ‫ﻃﻮل‬ ‫اﻟﻌﯿﻦ‬ ‫ﺗﺮى‬‫اﻷﺟﺴﺎم‬‫اﻟﻘﺮﯾﺒﺔ‬‫واﺿﺤﺔ‬ ‫و‬‫اﻷﺟﺴﺎم‬‫اﻟﺒﻌﯿﺪة‬‫واﺿﺤ‬ ‫ﻏﯿﺮ‬‫ﺔ‬ ‫ﻻن‬‫اﻟﺼﻮرة‬‫ﺗﻘﻊ‬‫اﻟﺸﺒﻜﯿﺔ‬ ‫اﻣﺎم‬ ‫اﻷﺟﺴﺎم‬ ‫اﻟﻌﯿﻦ‬ ‫ﺗﺮى‬‫واﺿﺤﺔ‬ ‫اﻟﺒﻌﯿﺪة‬ ‫و‬‫اﻷﺟﺴﺎم‬‫اﻟﻘﺮﯾﺒﺔ‬‫واﺿﺤﺔ‬ ‫ﻏﯿﺮ‬ ‫اﻟﺼﻮرة‬ ‫ﺣﯿﺚ‬‫ﺗﻘﻊ‬‫اﻟﺸﺒﻜﯿﺔ‬ ‫ﺧﻠﻒ‬ : ‫اﻟﻨﻈﺮ‬ ‫ﻗﺼﺮ‬ ‫ﺣﺪوث‬ ‫اﺳﺒﺎب‬ ١-‫ﻗﻄﺮ‬‫ﻛﺮة‬‫ا‬ ‫اﻟﻌﯿﻦ‬‫ﻛﺒﺮ‬‫اﻟﻼزم‬ ‫ﻣﻦ‬‫ﻓﺘﺰ‬‫داد‬‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﻟﻌﯿﻦ‬ ‫وﻋﺪﺳﺔ‬ ‫اﻟﺸﺒﻜﯿﺔ‬ ‫ﺑﯿﻦ‬ ٢-‫اﻛﺜﺮ‬ ‫اﻟﻌﯿﻦ‬ ‫ﻋﺪﺳﺔ‬‫ﺗﺤﺪﺑﺎ‬‫ﺑﻌﺪھﺎ‬ ‫ﻓﯿﻘﻞ‬‫اﻟﺒﺆ‬‫رى‬ ‫اﻟﺸﺒﻜﯿﺔ‬ ‫أﻣﺎم‬ ‫اﻟﺠﺴﻢ‬ ‫ﻣﻦ‬ ‫اﻟﻘﺎدﻣﺔ‬ ‫اﻷﺷﻌﺔ‬ ‫ﻓﺘﺘﺠﻤﻊ‬ : ‫اﻟﻨﻈﺮ‬ ‫ﻃﻮل‬ ‫ﺣﺪوث‬ ‫اﺳﺒﺎب‬ ١.١-‫ﻗﻄﺮ‬‫ﻛﺮة‬‫اﻟﻼزم‬ ‫ﻣﻦ‬ ‫اﺻﻐﺮ‬ ‫اﻟﻌﯿﻦ‬‫ﻓﺘﻘﻞ‬‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﻟﻌﯿﻦ‬ ‫وﻋﺪﺳﺔ‬ ‫اﻟﺸﺒﻜﯿﺔ‬ ‫ﺑﯿﻦ‬ ٢-‫ﻓﯿﺰداد‬ ‫ﺗﺤﺪﺑﺎ‬ ‫اﻗﻞ‬ ‫اﻟﻌﯿﻦ‬ ‫ﻋﺪﺳﺔ‬‫ﺑﻌﺪ‬‫ھﺎ‬‫اﻟﺒﺆرى‬ ‫اﻟﺸﺒﻜﯿﺔ‬ ‫ﺧﻠﻒ‬ ‫اﻟﺠﺴﻢ‬ ‫ﻣﻦ‬ ‫اﻟﻘﺎدﻣﺔ‬ ‫اﻷﺷﻌﺔ‬ ‫ﻓﺘﺘﺠﻤﻊ‬ ‫ب‬ ‫ب‬‫م‬ ‫ب‬ ‫م‬ ‫ب‬ ‫ب‬ ‫ب‬‫ب‬
  18. 18. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٨ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |١٨ : ‫اﻟﻌﻼج‬ ‫ﺗﻌﻤﻞ‬ ‫ﻣﻘﻌﺮة‬ ‫ﻋﺪﺳﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻷﺷﻌﺔ‬ ‫ﺗﻔﺮﯾﻖ‬ ‫ﻋﻠﻰ‬‫اﻟﻌﯿﻦ‬ ‫اﻟﻰ‬ ‫دﺧﻮﻟﮭﺎ‬ ‫ﻗﺒﻞ‬ ‫اﻟﺸﺒﻜﯿﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺼﻮرة‬ ‫ﻓﺘﺘﻜﻮن‬ : ‫اﻟﻌﻼج‬ ‫ﻋﻠﻰ‬ ‫ﺗﻌﻤﻞ‬ ‫ﻣﺤﺪﺑﺔ‬ ‫ﻋﺪﺳﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬ ‫اﻟﻌﯿﻦ‬ ‫اﻟﻰ‬ ‫دﺧﻮﻟﮭﺎ‬ ‫ﻗﺒﻞ‬ ‫اﻷﺷﻌﺔ‬ ‫ﺗﺠﻤﯿﻊ‬ ‫اﻟﺸﺒﻜﯿﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺼﻮرة‬ ‫ﻓﺘﺘﻜﻮن‬ :‫اﻟﻼﺻﻘﺔ‬ ‫اﻟﻌﺪﺳﺎت‬‫ﻣﺼﻨﻮﻋﺔ‬ ‫ﺟﺪا‬ ‫رﻗﯿﻘﺔ‬ ‫ﻋﺪﺳﺎت‬ ‫ھﻰ‬‫ﺑﺴﮭﻮﻟﺔ‬ ‫وﻧﺰﻋﮭﺎ‬ ‫اﻟﻌﯿﻦ‬ ‫ﻋﺪﺳﺔ‬ ‫ﻋﻠﻰ‬ ‫وﺿﻌﮭﺎ‬ ‫وﯾﻤﻜﻦ‬ ‫اﻟﺒﻼﺳﺘﯿﻚ‬ ‫ﻣﻦ‬. :‫اﺳﺘﺨﺪاﻣﮭﺎ‬‫اﻟﻄﺒﯿﺔ‬ ‫اﻟﻨﻈﺎرات‬ ‫ﻣﻦ‬ ‫ﺑﺪﻻ‬ ‫ﺗﺴﺘﺨﺪم‬ ١-‫اﻻراﺿﻰ‬ ‫ﻣﺴﺎﺣﺔ‬ ‫ﻗﯿﺎس‬ ‫ﻋﻠﻤﺎء‬ ‫ﯾﺴﺘﺨﺪم‬‫اﻟﻄﺒﻮﻏﺮاﻓﯿﺎ‬‫اﻟﻤﺮاﯾﺎ‬‫اﻟﺘﻰ‬‫ﺗﺤﺘﻮى‬‫ﻋﻠﻰ‬‫اﻟﯿﺰر‬ ‫أﺷﻌﺔ‬‫ﻟﻘﯿﺎس‬‫ﻣﺴﺎﺣﺔ‬‫اﻷراﺿﻰ‬‫اﻟﺰراﻋﯿﺔ‬ ‫إﺳ‬‫ﺘﺨﺪم‬‫أرﺷﯿﻤﯿﺪس‬‫ﺿﻮء‬‫اﻟﺸﻤﺲ‬‫ﻛﺴﻼح‬‫ﺿﺪ‬‫اﻷﺳﻄﻮل‬‫اﻟﺮوﻣﺎﻧﻰ‬‫ﺑﻮﺿﻊ‬‫ﻣﺮاﯾﺎ‬‫ﻣﻘﻌﺮة‬‫ﺿﺨﻤﺔ‬‫ﻟﺘﺠﻤﯿﻊ‬‫أﺷﻌﺔ‬‫وﺗﻮﺟﯿﮭﮭﺎ‬ ‫اﻟﺸﻤﺲ‬ ‫ﻧﺤﻮ‬‫اﻟﺴﻔﻦ‬‫ﻓﺄﺣﺮﻗﺘﮭﺎ‬‫ﺑﺎﻟﻜﺎﻣﻞ‬ ‫اﻟﺒﯿﻀﺎء‬ ‫اﻟﻤﯿﺎة‬ ‫او‬ ‫اﻟﻜﺘﺎرﻛﺘﺎ‬ ‫ﻣﺮض‬‫ھﻰ‬‫ﻋﺒﺎر‬‫اﻟﺮؤﯾﺔ‬ ‫ﺿﻌﻒ‬ ‫اﻟﻰ‬ ‫ﺗﺆدى‬ ‫اﻟﻌﯿﻦ‬ ‫ﻋﺪﺳﺔ‬ ‫ﻋﻠﻰ‬ ‫ﺳﺤﺎﺑﺔ‬ ‫ﻋﻦ‬ ‫اﺳﺒﺎب‬‫اﻟﻤﺮض‬١-‫اﻟﺴﻦ‬ ‫ﻛﺒﺮ‬٢-‫اﻵ‬ ‫و‬‫ﺛﺎر‬‫اﻟﺠﺎﻧﺒﯿﺔ‬‫ﻟﻠﻌﻘﺎﻗﯿﺮ‬‫اﻟﻄﺒﯿﺔ‬٣-‫اﻷﻣﺮاض‬ ‫و‬‫اﻟﻮراﺛﯿﺔ‬ : ‫اﻟﻌﻼج‬‫اﻟﺘﺪﺧﻞ‬‫اﻟﺠﺮاﺣﻰ‬‫ﺑﺈﺳﺘﺒﺪال‬‫ﻋﺪﺳﺔ‬‫اﻟﻌﯿﻦ‬‫ﺑﻌﺪﺳﺔ‬‫ﺑﻼﺳﺘﯿﻜﯿﺔ‬ ‫اﻟﺸﺎﺳﻊ‬ ‫اﻟﻔﻀﺎء‬ ‫ھﻮ‬‫اﻟﻤﻤﺘﺪ‬. ‫ﺷﺊ‬ ‫وﻛﻞ‬ ‫اﻟﺤﯿﺔ‬ ‫واﻟﻜﺎﺋﻨﺎت‬ ‫واﻷﻗﻤﺎر‬ ‫واﻟﻜﻮاﻛﺐ‬ ‫واﻟﻨﺠﻮم‬ ‫اﻟﻤﺠﺮات‬ ‫ﺟﻤﯿﻊ‬ ‫ﻓﯿﺔ‬ ‫ﯾﺴﺒﺢ‬ ‫اﻟﺬى‬ ‫ﯾﺤﺘﻮى‬ ‫و‬‫ﻋﻠﻰ‬١٠٠.٠٠٠‫ﻣﺠﺮة‬ ‫ﻣﻠﯿﻮن‬ ‫اﻟﻜﻮن‬ ‫ﻣﻨﮭﺎ‬ ‫ﯾﺘﻜﻮن‬ ‫اﻟﺘﻰ‬ ‫اﻟﻌﻈﻤﻰ‬ ‫اﻟﻜﻮن‬ ‫وﺣﺪة‬ ‫ھﻰ‬ ‫اﻟﻤﺠﺮة‬ ‫و‬ : ‫اﻟﻤﺠﺮات‬‫اﻟﻨﺠﻮم‬ ‫ﻣﻦ‬ ‫اﻟﻤﻼﯾﯿﻦ‬ ‫اﻻف‬ ‫ﻣﻦ‬ ‫ﺗﺘﻜﻮن‬ ( ‫ﻋﻠﻞ‬ ) ‫ﻟﮭﺎ‬ ‫ﻣﻤﯿﺰا‬ ‫ﺷﻜﻼ‬ ‫ﺗﺎﺧﺬ‬ ‫ﻣﺠﺮة‬ ‫ﻛﻞ‬‫ﺑﮭﺎ‬ ‫اﻟﻨﺠﻮم‬ ‫ﺗﺮﺗﯿﺐ‬ ‫و‬ ‫ﺗﻨﺎﺳﻖ‬ ‫ﺣﺴﺐ‬ ‫وذﻟﻚ‬ ‫ﻧﺠ‬ ‫ﻋﻠﻰ‬ ‫ﺗﺤﺘﻮى‬ ‫اﻟﺘﻰ‬ ‫اﻟﺘﺒﺎﻧﺔ‬ ‫درب‬ ‫ﻣﺠﺮة‬ ‫ﺑﯿﻨﮭﺎ‬ ‫ﻣﻦ‬ ‫ﻋﻨﺎﻗﯿﺪ‬ ‫ﻓﻰ‬ ‫اﻟﻤﺠﺮات‬ ‫ﺗﻮﺟﺪ‬ ‫و‬‫اﻟﺸﻤﺲ‬ ‫ﻢ‬ ‫اﻟﻜﻮن‬ : ‫اﻻول‬ ‫اﻟﺪرس‬ ‫اﻟﻜﻮن‬ : ‫اوﻻ‬ ‫ﺗﻜﻨﻮﻟﻮﺟﻰ‬ ‫ﺗﻄﺒﯿﻖ‬
  19. 19. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٩ ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬ Page |١٩ : ‫ﺷﻜﻠﮭﺎ‬‫اﻟﺸﻜﻞ‬ ‫ﺣﻠﺰوﻧﯿﺔ‬ ‫او‬ ‫ﻟﻮﻟﺒﯿﺔ‬ : ‫ﺗﺮﻛﯿﺒﮭﺎ‬ ‫اﻟﻘﺪﯾﻤﺔ‬ ‫اﻟﻨﺠﻮم‬ ‫ﻣﻦ‬ ‫اﻟﻌﺪﯾﺪ‬ ‫ﻣﺮﻛﺰاﻟﻤﺠﺮة‬ ‫ﻓﻰ‬ ‫ﯾﺘﺠﻤﻊ‬ ‫ا‬ ‫اﻻذرع‬ ‫ﻓﻰ‬ ‫اﻟﻮاﻗﻌﺔ‬ ‫اﻟﺼﻐﯿﺮة‬ ‫اﻟﻨﺠﻮم‬ ‫ﻣﻦ‬ ‫ﺑﮭﺎﻟﺔ‬ ‫ﻣﺤﺎﻃﺔ‬‫اﻟﺤﻠﺰوﻧﯿﺔ‬‫ﻟﻠﻤﺠﺮة‬ ‫اﻟﻤﺠﺮة‬ ‫ھﺬة‬ ‫ﻓﻰ‬ ‫اﻟﻨﺠﻮم‬ ‫ﻣﻼﯾﯿﻦ‬ ‫ﻣﻦ‬ ‫ﻣﻦ‬ ‫ﻧﺠﻢ‬ ‫اﻟﺸﻤﺲ‬ ‫و‬ ‫ﻋﻠ‬ ‫ﺗﺤﺘﻮى‬ ‫و‬‫اﻟﺸﻤﺴﻰ‬ ‫اﻟﻨﻈﺎم‬ ‫و‬ ‫اﻟﺸﻤﺲ‬ ‫ﻰ‬ ‫اﻟﺘﺒﺎﻧﺔ‬ ‫درب‬ ‫ﺑﻤﺠﺮة‬ ‫ﺳﻤﯿﺖ‬‫اﻻرض‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﻨﺜﻮر‬ ‫اﻟﺘﺒﻦ‬ ‫ﺗﺸﺒﺔ‬ ‫ﻻﻧﮭﺎ‬ ‫اﻟﻠﺒﻨﻰ‬ ‫ﻃﺮﯾﻖ‬ ‫أو‬ ‫ﺗﺸﺒﺔ‬ ‫او‬‫اﻻرض‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺴﻜﻮب‬ ‫اﻟﻠﺒﻦ‬ ١.‫و‬ ‫اﻟﺸﻤﺲ‬ ‫ﻋﻠﻰ‬ ‫ﺗﺤﺘﻮى‬ : ‫اﻟﺸﻤﺴﻰ‬ ‫اﻟﻨﻈﺎم‬ ‫او‬٨‫ﻛﻮاﻛﺐ‬ ٢.‫ﺗﺪور‬‫اﻟﻜﻮاﻛﺐ‬‫ﺣﻮل‬‫اﻟﺸﻤﺲ‬‫اﻟﻔﻀﺎﺋﯿﺔ‬ ‫واﻻﺟﺴﺎم‬ ‫اﻻﻗﻤﺎر‬ ‫ﻛﺬﻟﻚ‬ ‫و‬ ٣.‫ﻣﺮ‬ ‫ﺣﻮل‬ ‫اﻟﺸﻤﺲ‬ ‫ﺗﺪور‬ ‫و‬‫اﻟﻤﺠﺮة‬ ‫ﻛﺰ‬ ٤.‫ﻓﻰ‬ ‫اﻟﻤﺠﺮة‬ ‫ﻣﺮﻛﺰ‬ ‫ﺣﻮل‬ ‫ﻛﺎﻣﻠﺔ‬ ‫دورة‬ ‫اﻟﺸﻤﺲ‬ ‫وﺗﻌﻤﻞ‬٢٢٠‫ﺳﻨﺔ‬ ‫ﻣﻠﯿﻮن‬ ٥.‫اﻟﺸﻤﺴﯿﺔ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﻣﻜﺎن‬: ‫اﻟﺸﻤﺴﯿﺔ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﺗﻘﻊ‬‫ﻋﻠﻰ‬‫اﻟﺤﻠﺰوﻧﯿﺔ‬ ‫اﻷذرع‬ ‫أﺣﺪ‬‫ﻟﻤﺠﺮة‬‫اﻟﺘﺒﺎﻧﺔ‬ ‫درب‬‫اﻟﻤﺠﺮة‬ ‫ﺣﺎﻓﺔ‬ ‫ﻋﻠﻰ‬ : ‫اﻟﻀﻮﺋﯿﺔ‬ ‫اﻟﺴﻨﺔ‬= ‫ﺗﺴﺎوى‬ ‫و‬ ‫ﺳﻨﺔ‬ ‫ﻓﻰ‬ ‫اﻟﻀﻮء‬ ‫ﯾﻘﻄﻌﮭﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﻰ‬٩٤٦٠.٠٠٠‫ﻛﻢ‬ ‫ﻣﻠﯿﻮن‬‫او‬9.46×1012 ‫اﻟﻀﻮء‬ ‫ﺳﺮﻋﺔ‬‫اﻟ‬ ‫ﯾﻘﻄﻌﮭﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﻰ‬= ‫ھﻰ‬ ‫و‬ ‫اﻟﻮاﺣﺪة‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫ﻓﻰ‬ ‫ﻀﻮء‬٣٠٠.٠٠٠‫او‬ ‫ﻛﻢ/اﻟﺜﺎﻧﯿﺔ‬٣×١٠٨ ‫م/ث‬ : ‫ﻧﻮﻋﺎن‬ ‫ﻓﮭﻰ‬ ‫اﻟﻜﻮن‬ ‫ﻧﺸﺎة‬ ‫ﻛﯿﻔﯿﺔ‬ ‫ﺣﻮل‬ ‫اﻻﻗﺎوﯾﻞ‬ ‫اﺧﺘﻠﻔﺖ‬ ١.‫اﻟﻜﻮن‬ ‫وواﺟﺪ‬ ‫ﺧﺎﻟﻖ‬ ‫ھﻮ‬ ‫ﺗﻌﺎﻟﻰ‬ ‫و‬ ‫ﺳﺒﺤﺎﻧﮫ‬ ‫اﷲ‬ ‫ان‬ ٢.‫ﺑﻨﻔﺴﺔ‬ ‫ﺧﻠﻖ‬ ‫ﻗﺪ‬ ‫اﻟﻜﻮن‬ ‫ان‬ :‫اﻟﻜﻮن‬ ‫ﻟﻨﺸﺎة‬ ‫اﻻﻧﺴﺎن‬ ‫ﺗﺼﻮرات‬ ١.: ‫اﻟﻘﺪﯾﻤﺔ‬ ‫اﻟﻌﺼﻮر‬‫ﻋ‬ ‫اﻟﺨﺮاﻓﺎت‬ ‫ﺳﯿﻄﺮت‬‫اﻻﻧﺴﺎن‬ ‫ﺧﯿﺎل‬ ‫ﻠﻰ‬ ٢.: ‫اﻟﺮوﻣﺎن‬ ‫و‬ ‫اﻻﻏﺮﯾﻖ‬‫ﻟﻠﻈﻮاھﺮاﻟﻜﻮﻧﯿﺔ‬ ‫ﻧﻈﺮﯾﺎت‬ ‫وﺿﻊ‬ ‫اﻻﻏﺮﯾﻖ‬ ‫ﻓﻼﺳﻔﺔ‬ ‫ﺣﺎوﻟﺖ‬ ٣.‫اﻟﺼﯿﻨﯿﺔ‬ ‫و‬ ‫اﻟﮭﻨﺪﯾﺔ‬ ‫اﻟﺤﻀﺎرة‬:‫اﻟﺘﻨﺠﯿﻢ‬ ‫ﻋﻠﻢ‬ ‫ﻋﻨﺪھﻢ‬ ‫ﺳﺎد‬ ٤.: ‫اﻟﺒﺎﺑﻠﯿﯿﻦ‬ ‫و‬ ‫اﻟﻤﺼﺮﯾﯿﻦ‬ ‫ﻗﺪﻣﺎء‬‫اﻟﻤﺴﯿﻄﺮة‬ ‫اﻻﻟﺔاﻟﻤﺘﻌﺪدة‬ ‫و‬ ‫اﻟﻜﻮن‬ ‫أزﻟﯿﺔ‬ ‫ﺑﯿﻦ‬ ‫ﻗﺪﯾﻤﺎ‬ ‫اﻟﻜﻮن‬ ‫ﻧﺸﺄة‬ ‫ارﺗﺒﻂ‬ ‫ﻋﻠﯿﺔ‬ ‫اﻟﻠﺒﻨﻰ‬ ‫اﻟﻄﺮﯾﻖ‬ ‫او‬ ‫اﻟﺘﺒﺎﻧﺔ‬ ‫درب‬ ‫ﻣﺠﺮة‬ : ‫ﺛﺎﻧﯿﺎ‬ ‫اﻟﺸﻤﺴﯿﺔ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬ : ‫ﺛﺎﻟﺜﺎ‬ ‫اﻟﻜﻮن‬ ‫ﻧﺸﺄة‬ : ‫راﺑﻌﺎ‬ ‫ﻣﻌﻠﻮﻣﺔ‬: ‫اﺿﺎﻓﯿﺔ‬ ‫ﻗﺪﯾﻤﺎ‬ ‫اﻟﻜﻮن‬ ‫ﻧﺸﺎة‬

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