1. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫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. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٢
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫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. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٣
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫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. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٤
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫؟‬ ‫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. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٥
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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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. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٦
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫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. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٧
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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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. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٨
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫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. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٩
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫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. ‫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. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١١
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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: ‫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. ‫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. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٣
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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: ‫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. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٤
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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:‫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. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٥
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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: ‫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. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٦
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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: ‫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. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٧
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫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. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٨
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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: ‫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. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٩
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2015‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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: ‫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