1. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫اﻟﻮﺣﺪة‬ ‫ﻣﻘﺪﻣﺔ‬
‫اﻟﻄﻠﻘﺔ‬ ‫اﻟﻘﻄﺎر‬‫اﻟﯿﺎﺑﺎن‬ ‫اﻧﺘﺠﺘﮫ‬
) ‫اﻟﻰ‬ ‫ﺳﺮﻋﺘﺔ‬ ‫ﺗﺼﻞ‬ ‫ﺳﺮﯾﻊ‬ ‫ﻛﮭﺮﺑﺎﺋﻲ‬ ‫ﻗﻄﺎر‬ ‫اول‬ ‫ھﻮ‬٢٠٠) ‫ﺳﺮﻋﺘﮫ‬ ‫ﺑﻠﻐﺖ‬ ‫ﺣﺘﻲ‬ ‫اﻟﻘﻄﺎر‬ ‫ھﺬا‬ ‫ﱢر‬‫ﻮ‬‫ﻃ‬ ‫ﺛﻢ‬ ، ( ‫ﻛﻢ/ﺳﺎﻋﺔ‬٢٧٠( ‫ﻛﻢ/ﺳﺎﻋﺔ‬
‫؟‬ ‫اﻟﻤﻌﺘﺎد‬ ‫اﻟﻘﻄﺎر‬ ‫ﻋﻦ‬ ‫اﻟﻄﻠﻘﺔ‬ ‫اﻟﻘﻄﺎر‬ ‫ﯾﺨﺘﻠﻒ‬ ‫ﻋﻠﻞ‬
‫ﻋﺮﺑﺎﺗﺔ‬ ‫ﻣﻦ‬ ‫ﻋﺮﺑﺔ‬ ‫ﻛﻞ‬ ‫ﻻن‬‫ﻟﮭﺎ‬‫ﺧﺎص‬ ‫ﻣﻮﺗﻮر‬‫ﺑﮭﺎ‬‫وﻟﺬﻟﻚ‬‫ﯾﻤﻜﻦ‬‫ﯾﺘﺤﺮك‬ ‫ان‬‫اﻟﻘﻄﺎر‬‫ﺑﺴﺮﻋ‬‫ﺔ‬‫ﻛﺒﯿﺮة‬‫ﺟﺪا‬
‫آﺧﺮ‬ ‫ﻟﺠﺴﻢ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫اﻟﺠﺴﻢ‬ ‫ﻣﻮﺿﻊ‬ ‫ﺗﻐﯿﺮ‬ ‫ھﻲ‬‫ﺛﺎﺑﺖ‬. ‫اﻟﺰﻣﻦ‬ ‫ﺑﻤﺮور‬
‫اﻟﺴﺎﻛﻦ‬ ‫اﻟﺠﺴﻢ‬‫اﻟﺰﻣﻦ‬ ‫ﺑﻤﺮور‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ﻟﻨﻘﻄﺔ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﻣﻮﺿﻌﺔ‬ ‫ﯾﺘﻐﯿﺮ‬ ‫ﻻ‬ ‫اﻟﺬى‬ ‫اﻟﺠﺴﻢ‬ ‫ھﻮ‬
‫اﻟﻤﺘﺤﺮك‬ ‫اﻟﺠﺴﻢ‬‫اﻟﺰﻣﻦ‬ ‫ﺑﻤﺮور‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ﻟﻨﻘﻄﺔ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﻣﻮﺿﻌﺔ‬ ‫ﯾﺘﻐﯿﺮ‬ ‫اﻟﺬى‬ ‫اﻟﺠﺴﻢ‬ ‫ھﻮ‬
‫ﺣﺮﻛﺔ‬ ‫ھﻰ‬‫اﻟﺠﺴﻢ‬‫ﻟ‬‫أو‬ ‫ﻸﻣﺎم‬‫ﻷﺳﻔﻞ‬ ‫أو‬ ‫ﻷﻋﻠﻲ‬ ‫ﯾﺘﺤﺮك‬ ‫وﻻ‬ ‫ﻟﻠﺨﻠﻒ‬
‫و‬‫ﻣﻨﮭﻤﺎ‬ ً‫ﺎ‬‫ﺗﺮﻛﯿﺒ‬ ‫أو‬ ً‫ﺎ‬‫ﻣﻨﺤﻨﯿ‬ ‫أو‬ ً‫ﺎ‬‫ﻣﺴﺘﻘﯿﻤ‬ ‫ﺧﻂ‬ ‫ﻓﻲ‬ ‫ﻣﺴﺎره‬ ‫ﯾﻜﻮن‬ ‫ﻗﺪ‬
‫واﺣﺪ‬ ‫اﺗﺠﺎه‬ ‫ﻓﻲ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫أﻣﺜﻠﺔ‬‫اﻟﻘﻀﺒﺎن‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺘﺮو‬ ‫اﻟﻘﻄﺎراو‬ ‫ﺣﺮﻛﺔ‬
: ‫اﻟﺤﺮﻛﺔ‬ ‫أﻧﻮاع‬ ‫أﺑﺴﻂ‬‫ھﻰ‬‫واﺣﺪ‬ ‫اﺗﺠﺎه‬ ‫وﻓﻲ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ﻓﻲ‬ ‫اﻟﺤﺮﻛﺔ‬
‫ھﻰ‬‫اﻟﻤﺴﺎﻓﺔ‬‫اﻟﻤﻘﻄ‬‫ﻮﻋﺔ‬. ‫اﻟﺰﻣﻦ‬ ‫وﺣﺪة‬ ‫ﺧﻼل‬
‫ﺣﺮﻛﺔ‬ ‫وﺻﻒ‬ ‫ﻓﻰ‬ ‫ﺗﺴﺘﺨﺪم‬ ‫اﻟﺘﻰ‬ ‫اﻻﺳﺎﺳﯿﺔ‬ ‫اﻟﻌﻮاﻣﻞ‬‫ﺟﺴﻢ‬
‫ﺣﺮﻛﺔ‬‫ﺑﻌﺾ‬‫اﻻﺟﺴﺎم‬‫ﺗﻮﺻﻒ‬‫ﺳﺮﯾﻌﺔ‬ ‫ﺑﺎﻧﮭﺎ‬‫اﻻﺧﺮ‬ ‫واﻟﺒﻌﺾ‬‫ﺗﻮﺻﻒ‬‫ﺑﻄﯿﺌﺔ‬ ‫ﺑﺎﻧﮭﺎ‬.
‫ﻧﺴﺘﻨﺘﺞ‬‫ﻣ‬‫ﺳﺒﻖ‬ ‫ﻤﺎ‬:
‫ان‬‫ﻋﺎﻣﻼن‬ ‫ھﻨﺎك‬‫اﺳﺎﺳﯿﺎن‬‫ﻓﻰ‬ ‫ﺗﺴﺘﺨﺪم‬‫اﻟﺤﺮﻛﺔ‬ ‫وﺻﻒ‬‫ھﻤﺎ‬:
١-. ‫اﻟﺠﺴﻢ‬ ‫ﯾﻘﻄﻌﮭﺎ‬ ‫اﻟﺘﻲ‬ ‫اﻟﻤﺴﺎﻓﺔ‬
٢-‫و‬‫ﯾﺴﺘﻐﺮﻗﮫ‬ ‫اﻟﺬي‬ ‫اﻟﺰﻣﻦ‬‫ﻟ‬ ‫اﻟﺠﺴﻢ‬‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﺬه‬ ‫ﻘﻄﻊ‬
‫و‬‫ھﺬ‬ ‫ﻣﻦ‬‫ان‬‫اﻟﻌ‬‫ﺎﻣﻼن‬‫ﺗﻌﺮﯾﻒ‬ ‫ﯾﻤﻜﻦ‬‫ﻓﯿﺰﯾﺎﺋ‬ ‫ﻛﻤﯿﺔ‬‫ﯿﺔ‬‫ﺗﺴﻤﻰ‬" ‫اﻟﺴﺮﻋﺔ‬ "

2. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٢
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫ھﻰ‬‫اﻟﻤﺴﺎﻓﺔ‬‫اﻟﻤﻘﻄﻮﻋﺔ‬‫ﺧﻼل‬‫وﺣﺪة‬‫اﻟﺰﻣﻦ‬
:‫س‬‫اﻟﻤﻘﻄﻮﻋﺔ؟‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻣﻊ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﺗﺘﺴﺎوى‬ ‫ﻣﺘﻰ‬
‫ﻛﺎن‬ ‫اذا‬‫ھﻰ‬ ‫و‬ ‫اﻟﺰﻣﻦ‬ ‫وﺣﺪة‬ ‫ﺧﻼل‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﺬة‬ ‫ﯾﻘﻄﻊ‬ ‫اﻟﺠﺴﻢ‬١‫او‬ ‫ث‬١‫او‬ ‫دﻗﯿﻘﺔ‬١‫ﺳﺎﻋﺔ‬
‫و‬:‫اﻟﺴﺮﻋﺔ‬ ‫ﻗﯿﺎس‬ ‫ﺣﺪة‬
١-: ‫ﺛﺎﻧﯿﺔ‬ / ‫ﻣﺘﺮ‬‫ﻋﻨﺪﻣﺎ‬‫ﺗﻘﺎس‬‫اﻟﻤﺴﺎﻓﺔ‬‫ﺑﺎﻟﻤﺘﺮ‬‫واﻟ‬‫ﺰﻣﻦ‬‫ﺑﺎﻟﺜﺎﻧﯿﺔ‬.
٢-: ‫اﻟﺴﺎﻋﺔ‬ / ‫ﻣﺘﺮ‬ ‫ﻛﯿﻠﻮ‬‫ﻋﻨﺪﻣﺎ‬‫ﺗﻘﺎس‬‫اﻟﻤﺴﺎﻓﺔ‬‫ﺑﺎﻟﻜﯿﻠﻮﻣﺘﺮ‬‫واﻟﺰﻣﻦ‬‫ﺑﺎﻟﺴﺎﻋﺔ‬‫ﻛﻤﺎ‬‫ﻓﻰ‬‫ﺣﺎﻟﺔ‬‫اﻟﻄﺎﺋﺮات‬ ‫و‬ ‫اﻟﻘﻄﺎرات‬ ‫و‬ ‫اﻟﺴﯿﺎرات‬
‫ﻟﻠﺘﺤﻮﯾﻞ‬‫اﻟﻮﺣﺪات‬ ‫ﺑﯿﻦ‬
١-‫ﺳ‬‫اﻻوﻟ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ﻓﻰ‬ ‫ﺗﺘﺤﺮﻛﺎن‬ ‫ﯿﺎرﺗﺎن‬‫ﻰ‬‫ﻣﺴﺎﻓﺔ‬ ‫ﻗﻄﻌﺖ‬٥٠٠‫ﺧﻼل‬ ‫م‬٥‫ﻣﺴﺎﻓﺔ‬ ‫ﻗﻄﻌﺖ‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫و‬ ‫ﺛﻮاﻧﻰ‬٢٥٠‫ﺧﻼل‬ ‫م‬٢.٥‫ﺛﺎﻧﯿﺔ‬
‫اﻟﺴﯿﺎرﺗﯿﻦ‬ ‫ﻣﻦ‬ ‫ﻛﻼ‬ ‫ﺳﺮﻋﺔ‬ ‫اﺣﺴﺐ‬
٢-‫ﺳﯿﺎرة‬‫ﺗﺘﺤﺮك‬‫ﺑﺴﺮﻋﺔ‬٧٠‫ﺳﺎﻋﺔ‬ /‫ﻛﻢ‬‫ﺳﺎﻋﺘﯿﻦ‬ ‫ﺧﻼل‬ ‫ﺗﻘﻄﻌﮭﺎ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﺣﺴﺐ‬
٣-‫ﺳﯿﺎرة‬‫ﺗﺘﺤﺮك‬‫ﺑﺴﺮﻋﺔ‬٨٠‫ﺳﺎﻋﺔ‬ /‫ﻛﻢ‬‫اﻟﻼزم‬ ‫اﻟﺰﻣﻦ‬ ‫ﻓﻤﺎ‬‫ﻟ‬‫ﻘﻄﻊ‬‫ﻣﺴﺎﻓﺔ‬٢٠٠. ‫ﻛﯿﻠﻮﻣﺘﺮ‬
١-‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﺴﺮﻋﺔ‬٢-‫ﻣﻨﺘﻈﻤﺔ‬ ‫اﻟﻐﯿﺮ‬ ‫اﻟﺴﺮﻋﺔ‬
‫ﯾﻘﻄﻊ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ﻓﻰ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺑﮭﺎ‬ ‫ﯾﺘﺤﺮك‬ ‫اﻟﺘﻲ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ھﻲ‬
‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ازﻣﻨﺔ‬ ‫ﻓﻲ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ﻣﺴﺎﻓﺎت‬
‫ﯾﻘﻄﻊ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺑﮭﺎ‬ ‫ﯾﺘﺤﺮك‬ ‫اﻟﺘﻰ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ھﻰ‬
‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ازﻣﻨﺔ‬ ‫ﻓﻰ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ﻏﯿﺮ‬ ‫ﻣﺴﺎﻓﺎت‬
‫ﻣﺘﺴﺎو‬ ‫ﻣﺴﺎﻓﺎت‬ ‫او‬‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ﻏﯿﺮ‬ ‫ازﻣﻨﺔ‬ ‫ﻓﻰ‬ ‫ﯾﺔ‬
‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺑﺨﻂ‬ ‫ﺗﻤﺜﻞ‬‫ﻣﻨﺤﻨﻰ‬ ‫ﺑﺨﻂ‬ ‫ﺗﻤﺜﻞ‬
‫ﺟﻤﯿﻊ‬‫اﻟﻜﮭﺮوﻣﻐﻨﺎﻃﯿﺴﯿﺔ‬ ‫اﻟﻤﻮﺟﺎت‬‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﺗﺴﯿﺮ‬
‫ﺑﺴﺮﻋﺔ‬ ‫اﻟﻔﺮاغ‬ ‫ﻓﻰ‬ ‫ﯾﺴﯿﺮ‬ ‫اﻟﺬى‬ ‫اﻟﻀﻮء‬ ‫ﻣﺜﻞ‬٣×١٠8
‫م/ث‬
‫اﻟﻄﺮﯾﻖ‬ ‫اﺣﻮال‬ ‫ﺣﺴﺐ‬ ‫ﺳﺮﻋﺘﮭﺎ‬ ‫ﺗﺘﻐﯿﺮ‬ ‫اﻟﺘﻰ‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺣﺮﻛﺔ‬
‫اﻟﺴﺮﻋﺔ‬ ‫اﻧﻮاع‬

3. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٣
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫ﻋﺪادات‬ ‫ﺑﻤﺠﻤﻮﻋﺔ‬ ‫اﻟﺴﯿﺎرات‬ ‫و‬ ‫اﻟﻄﺎﺋﺮات‬ ‫ﺗﺰود‬‫و‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻋﺪاد‬ ‫ﻣﺜﻞ‬‫ﻋﺪاد‬‫اﻟﻤﺴﺎﻓﺔ‬
‫اﻟﺴﺮﻋﺔ‬ ‫ﻋﺪاد‬‫ھﻮ‬‫ﯾﺴﺎﻋﺪ‬ ‫ﺟﮭﺎز‬‫ﻋﻠﻰ‬‫ﻣﻌﺮﻓﺔ‬‫ﺳﺮﻋﺔ‬‫اﻟﺴﯿﺎرة‬‫ﻣﺒﺎﺷﺮة‬
‫؟‬ ‫اﻟﻔﺮاغ‬ ‫ﻓﻰ‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﯾﻨﺘﻘﻞ‬ ‫اﻟﺬى‬ ‫اﻟﺸﺊ‬ ‫ھﻮ‬ ‫ﻣﺎ‬ ‫س‬
‫ﺟﻤﯿﻊ‬‫اﻟﻜﮭﺮوﻣﻐﻨﺎﻃﯿﺴﯿﺔ‬ ‫اﻟﻤﻮﺟﺎت‬‫ﻛ‬‫ﺎﻟﻀﻮء‬‫ﺗﻨﺘﻘﻞ‬‫ﻣﻘﺪارھﺎ‬ ‫ﺛﺎﺑﺘﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫اﻟﻔﺮاغ‬ ‫ﻓﻰ‬٣×١٠8‫م/ث‬
‫ﯾﻌ‬ ‫ﻣﺎذا‬‫ان‬ ‫ﻨﻰ‬
١-‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﺗﺴﯿﺮ‬ ‫ﺳﯿﺎرة‬٧٠‫ﻛﻢ‬/‫س‬‫؟‬‫ﻣﺴﺎﻓﺔ‬ ‫ﺗﻘﻄﻊ‬ ‫اﻟﺴﯿﺎرة‬ ‫ان‬ ‫اى‬٧٠‫ﻛ‬‫ﻛﻞ‬ ‫ﻢ‬‫ﺳﺎﻋﺔ‬‫ﺑﺎﻧﺘﻈﺎم‬
٢-‫ﻣﻨﺘﻈﻤﺔ؟‬ ‫ﻏﯿﺮ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫اﻻﻧﻔﺎق‬ ‫ﻣﺘﺮو‬
‫اى‬‫ﯾﻘﻄﻊ‬ ‫اﻻﻧﻔﺎق‬ ‫ﻣﺘﺮو‬ ‫ان‬‫ﻣ‬‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ازﻣﻨﺔ‬ ‫ﻓﻰ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ﻏﯿﺮ‬ ‫ﺴﺎﻓﺎت‬‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ﻏﯿﺮ‬ ‫ازﻣﻨﺔ‬ ‫ﻓﻰ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ﻣﺴﺎﻓﺎت‬ ‫او‬
‫ﻋﻠﻞ‬‫ﯾ‬‫ﻋﻤﻠﯿﺎ؟‬ ‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﺤﻘﯿﻖ‬ ‫ﺼﻌﺐ‬‫اﺧﺮى‬ ‫ﺣﯿﺎﻧﺎ‬ ‫وﺗﻘﻞ‬ ‫اﺣﯿﺎﻧﺎ‬ ‫ﺗﺰداد‬ ‫ﻓﮭﻰ‬ ‫اﻟﻄﺮﯾﻖ‬ ‫اﺣﻮال‬ ‫ﺣﺴﺐ‬ ‫ﺗﺘﻐﯿﺮ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﻻن‬
(/‫ع‬ ) ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﺴﺮﻋﺔ‬‫ھﻰ‬‫اﻟﻤﺴﺎﻓﺔ‬‫اﻟﻜﻠﯿﺔ‬‫اﻟﺘﻲ‬‫ﯾﻘﻄﻌﮭﺎ‬‫اﻟﺠﺴﻢ‬‫اﻟﻤﺘﺤﺮك‬‫ﻣﻘﺴﻮﻣﺔ‬‫ﻋﻠﻰ‬‫اﻟﺰﻣﻦ‬‫اﻟﻤﺴﺘﻐﺮ‬ ‫اﻟﻜﻠﻰ‬‫ق‬‫ﻟﻘﻄﻊ‬‫ھﺬه‬‫اﻟﻤﺴﺎﻓﺔ‬.
( /‫)ع‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﺴﺮﻋﺔ‬‫ﻟﻮ‬ ‫اﻟﺘﻲ‬ ‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ھﻲ‬‫ﺗﺤﺮك‬‫ا‬ ‫ﻧﻔﺲ‬ ‫ﻓﻲ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻧﻔﺲ‬ ‫ﻟﻘﻄﻊ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺑﮭﺎ‬‫ﻟﺰﻣﻦ‬
‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﻐﯿﺮ‬ ‫واﻟﺤﺮﻛﺔ‬ ‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﺑﯿﻦ‬ ‫ﻗﺎرن‬
‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﺤﺮﻛﺔ‬‫ﻣﻨﺘﻈﻤﺔ‬ ‫اﻟﻐﯿﺮ‬ ‫اﻟﺤﺮﻛﺔ‬
‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﺴﺎوي‬ ‫ﻟﻠﺠﺴﻢ‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬
‫ع‬ = /‫ع‬ )‫اﻟﻤﻨﺘﻈﻤﺔ‬‫ﻣﻨﺘﻈﻤﺔ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺣﺮﻛﺔ‬ ‫ﺗﻜﻮن‬ (
‫ﺗﺴﺎوي‬ ‫ﻻ‬ ‫ﻟﻠﺠﺴﻢ‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻋﻨﺪﻣﺎ‬‫اﻟﺴﺮﻋﺔاﻟﻤﻨﺘﻈﻤﺔ‬
)/‫ع‬≠‫ع‬‫اﻟﻤﻨﺘﻈﻤﺔ‬‫ﻣﻨﺘﻈﻤﺔ‬ ‫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-‫ذاھﺐ‬ ‫وھﻮ‬ ‫ﻟﻠﻌﺪاء‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﺴﺮﻋﺔ‬‫؟‬
٢-‫؟‬ ‫ﻋﺎﺋﺪ‬ ‫وھﻮ‬ ‫ﻟﻠﻌﺪاء‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﺴﺮﻋﺔ‬
٣-‫؟‬ ‫اﻟﺮﺣﻠﺔ‬ ‫ﺧﻼل‬ ‫ﻟﻠﻌﺪاء‬ ‫اﻟﻤﺘﻮﺳﻄﺔ‬ ‫اﻟﺴﺮﻋﺔ‬
‫ﺳﺮﻋﺔ‬ ‫ھﻰ‬‫ﺟﺴﻢ‬‫ﻣﺘﺤﺮك‬‫ﺑﺎﻟﻨﺴﺒﺔ‬‫ﻟﻤﺮاﻗﺐ‬‫ﻣﺘ‬ ‫او‬ ‫ﺳﺎﻛﻦ‬‫ﺤﺮك‬
:‫اﻟﻤﺮاﻗﺐ‬‫اﻟﻤﺘﺤﺮﻛﺔ‬ ‫ﻟﻼﺟﺴﺎم‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﻘﺪﯾﺮ‬ ‫و‬ ‫ﺑﻤﺮاﻗﺒﺔ‬ ‫ﯾﻘﻮم‬ ‫ﻣﺘﺤﺮك‬ ‫او‬ ‫ﺳﺎﻛﻦ‬ ‫ﺷﺨﺺ‬ ‫ھﻮ‬
‫ﺳﯿﺎرة‬ ‫ﻟﯿﻜﻦ‬ ‫و‬ ‫ﻣﺘﺤﺮك‬ ‫ﻟﺠﺴﻢ‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺣﺴﺎب‬
‫اى‬‫أن‬‫ﺗﺨﺘﻠﻒ‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬‫ﺣﺴﺐ‬‫ﺣﺎﻟﺔ‬‫اﻟﻤﺮاﻗﺐ‬‫ﻣﺘﺤﺮك‬ ‫او‬ ‫ﺳﺎﻛﻦ‬ ‫ﻛﺎن‬ ‫اذا‬‫اﻟﻤﺮاﻗﺐ‬ ‫ﺣﺮﻛﺔ‬ ‫اﺗﺠﺎة‬ ‫و‬
١‫؟‬ ‫ﺻﻔﺮ‬ = ‫ﻣﺘﺤﺮك‬ ‫ﻟﺠﺴﻢ‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻣﺘﻰ‬ : ‫س‬‫اﻟﻤﺮاﻗﺐ‬ ‫ﺳﺮﻋﺔ‬ ‫ﺑﻨﻔﺲ‬ ‫و‬ ‫اﻻﺗﺠﺎة‬ ‫ﻧﻔﺲ‬ ‫ﻓﻰ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬
: ‫س‬‫ﻋﻠﻞ‬‫ﯾﺘﺤﺮ‬ ‫ﻟﻤﺮاﻗﺐ‬ ‫ﻣﺎ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫اﻟﻤﺘﺤﺮﻛﺔ‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺗﺒﺪو‬‫؟‬ ‫ﺳﺎﻛﻨﺔ‬ ‫ﻛﺎﻧﮭﺎ‬ ‫و‬ ‫اﺗﺠﺎھﮭﺎ‬ ‫ﻧﻔﺲ‬ ‫ﻓﻰ‬ ‫و‬ ‫ﺳﺮﻋﺘﮭﺎ‬ ‫ﺑﻨﻔﺲ‬ ‫ك‬
١-‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻻن‬‫ﻟﮭﺎ‬‫ﺳﺎﻛﻨﺔ‬ ‫ﻛﺎﻧﮭﺎ‬ ‫و‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺗﺒﺪو‬ ‫ﺑﺎﻟﺘﺎﻟﻰ‬ ‫و‬ ‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوى‬
‫ﺳﺎﻛﻦ‬ ‫اﻟﻤﺮاﻗﺐ‬‫اﻻﺗﺠﺎة‬ ‫ﻧﻔﺲ‬ ‫ﻓﻰ‬ ‫ﻣﺘﺤﺮك‬ ‫اﻟﻤﺮاﻗﺐ‬‫اﻻﺗﺠﺎة‬ ‫ﻋﻜﺲ‬ ‫ﻓﻰ‬ ‫ﻣﺘﺤﺮك‬ ‫اﻟﻤﺮاﻗﺐ‬
‫اﻟﻔﻌﻠﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ = ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬‫اﻟﻨﺴﺒﯿ‬ ‫اﻟﺴﺮﻋﺔ‬‫ﺔ‬=‫اﻟﺴﺮﻋﺘﯿﻦ‬ ‫ﻓﺮق‬
‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬=‫اﻟﻔﻌﻠﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬–
‫اﻟﻤﺮاﻗﺐ‬ ‫ﺳﺮﻋﺔ‬
‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬=‫ﻣﺠﻤﻮع‬‫اﻟﺴﺮﻋﺘﯿﻦ‬
‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬=‫اﻟﻔﻌﻠﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬+
‫اﻟﻤﺮاﻗﺐ‬ ‫ﺳﺮﻋﺔ‬
‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬‫ﻣﻦ‬ ‫اﻗﻞ‬‫اﻟﻔﻌﻠﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬‫ﻣﻦ‬ ‫اﻛﺒﺮ‬‫اﻟ‬‫اﻟﻔﻌﻠﯿﺔ‬ ‫ﺴﺮﻋﺔ‬

4. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٤
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺴﺎﺋﻞ‬
‫ﻣﺜﺎل‬١-‫اﻻوﻟﻰ‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺳﺮﻋﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫ﻓﺎذا‬ ‫اﻻﺗﺠﺎة‬ ‫ﻧﻔﺲ‬ ‫ﻓﻰ‬ ‫اﻟﻄﺮﯾﻖ‬ ‫ﻋﻠﻰ‬ ‫ﺗﺘﺤﺮﻛﺎن‬ ‫ﺳﯿﺎرﺗﺎن‬٤٠‫ﻛﻢ/س‬‫اﻟﺴﯿﺎرة‬ ‫ﺳﺮﻋﺔ‬ ‫و‬
‫اﻟﺜﺎﻧﯿﺔ‬٧٠‫اﻟﺜﺎﻧﯿﺔ‬ ‫ﻟﻠﺴﯿﺎرة‬ ‫اﻟﻨﺴﺒﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻓﻜﻢ‬ ‫ﻛﻢ/س‬
١-‫اﻻرض‬ ‫ﻋﻠﻰ‬ ‫ﯾﻘﻒ‬ ‫ﻟﻤﺮاﻗﺐ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬
٢-‫ﺑﺎﻟﻨﺴﺒﺔ‬‫ﻓﻰ‬ ‫ﻟﻤﺮاﻗﺐ‬‫اﻻوﻟﻰ‬ ‫اﻟﺴﯿﺎرة‬
٣-‫اﻟﺴﯿﺎرة‬ ‫ﻧﻔﺲ‬ ‫ﻓﻰ‬ ‫ﻟﻤﺮاﻗﺐ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬
‫ﻣﺜﺎل‬٢‫اﺣﺴﺒﻰ‬‫اﻟﻨﺴﺒﯿﺔ‬ ‫ﺳﺮﻋﺘﮭﺎ‬ ‫ﻟﺴﯿﺎرة‬ ‫اﻟﻔﻌﻠﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬٨٠‫ﺑﺴﺮﻋﺔ‬ ‫اﺗﺠﺎھﮭﺎ‬ ‫ﻧﻔﺲ‬ ‫ﻓﻰ‬ ‫ﯾﺘﺤﺮك‬ ‫ﻟﻤﺮاﻗﺐ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫ﻛﻢ/س‬٤٠‫ﻛﻢ/س‬
‫ﻣﺜﺎل‬٣–‫ﻣﺴﺎﻓﺔ‬ ‫ﻋﻠﻰ‬ ‫اﺻﺒﺤﺖ‬ ‫ﻟﻤﺎ‬ ‫و‬ ‫اﻟﻘﺎھﺮة‬ ‫ﺑﺮج‬ ‫اﺗﺠﺎة‬ ‫ﻓﻰ‬ ‫ﺗﺘﺤﺮك‬ ‫ﺳﯿﺎرة‬٥٠‫ﺑﺴﺮﻋﺔ‬ ‫ﺗﺴﯿﺮ‬ ‫ﺧﺎﺻﺔ‬ ‫ﺣﺮاﺳﺔ‬ ‫ﻃﺎﺋﺮة‬ ‫رﺻﺪﺗﮭﺎ‬ ‫ﻛﻢ‬
٢٥٥‫ﺑﺴﺮﻋﺔ‬ ‫ﺗﺴﯿﺮ‬ ‫ﻛﺎﻧﮭﺎ‬ ‫اﻟﺴﯿﺎرة‬ ‫ﻓﺒﺪت‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺣﺮﻛﺔ‬ ‫ﻋﻜﺲ‬ ‫اﺗﺠﺎة‬ ‫ﻓﻰ‬ ‫ﻛﻢ/س‬٢٧٠‫اﻟﻘﺎھﺮة‬ ‫ﺑﺮج‬ ‫اﻟﻰ‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺗﺼﻞ‬ ‫ﻓﻤﺘﻰ‬ ‫ﻛﻢ/س‬
‫اﻷدوات‬:‫ﺳﯿﺎ‬‫ﺑ‬ ‫ﺗﻌﻤﻞ‬ ‫أﻃﻔﺎل‬ ‫ﻟﻌﺐ‬ ‫رة‬‫ﻛﻨﺘﺮول‬ ‫ﺎﻟﺮﯾﻤﻮت‬–‫ﺧﺸﺒﻲ‬ ‫ﻟﻮح‬‫اﻣﻠﺲ‬‫ﻃﻮﻟﺔ‬٢‫ﻣﺘﺮ‬
–‫ﻣﺘﺮﯾﺔ‬ ‫ﻣﺴﻄﺮة‬–‫إﯾﻘﺎف‬ ‫ﺳﺎﻋﺔ‬–‫ﻣﻠﻮن‬ ‫ﻗﻠﻢ‬
: ‫اﻟﻌﻤﻞ‬ ‫ﺧﻄﻮات‬١-‫ﻧ‬‫ﺛﻢ‬ ‫أﻓﻘﻲ‬ ‫ﺿﻊ‬ ‫و‬ ‫ﻓﻲ‬ ‫اﻟﺨﺸﺒﻲ‬ ‫اﻟﻠﻮح‬ ‫ﻀﻊ‬‫ﻧ‬‫ﻋﻼﻣﺘﯿﻦ‬ ‫ﻀﻊ‬‫اﻟﻠﻮح‬ ‫ﻋﻠﻰ‬‫اﻟﺨﺸﺒﻰ‬‫و‬‫ﻧ‬‫ﻘ‬‫ﯿ‬‫ﺑﯿﻨ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﺲ‬‫ﮭﻤﺎ‬(‫)ف‬
٢-‫ﻧ‬‫اﻟﺴﯿﺎرة‬ ‫ﺸﻐﻞ‬‫و‬‫ﻧ‬‫اﻟﺰﻣﻦ‬ ‫ﻌﯿﻦ‬(‫)ز‬‫ﻟﻘﻄﻊ‬ ‫اﻟﻼزم‬‫ھﺬة‬‫اﻟﻤﺴﺎﻓﺔ‬(‫)ف‬
٣-‫ﻧ‬‫ﻣﺮات‬ ‫ﻋﺪة‬ ‫اﻟﺴﺎﺑﻘﺔ‬ ‫ﻜﺮراﻟﺨﻄﻮة‬‫ﻛﻞ‬ ‫ﻓﻰ‬ ‫و‬‫ﻧﻌﯿﻦ‬ ‫ﻣﺮة‬‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺳﺮﻋﺔ‬‫ف/ز‬ = (‫)ع‬
‫و‬‫ﻧ‬‫اﻟﻘﺮا‬ ‫ﺴﺠﻞ‬‫ء‬‫ا‬‫ﺟﺪول‬ ‫ﻓﻰ‬ ‫ت‬
٤-‫ﻧ‬‫ﺑﯿﻦ‬ ‫ﺑﯿﺎﻧﯿﺔ‬ ‫ﻋﻼﻗﺔ‬ ‫ﺮﺳﻢ‬‫اﻟﻤﺴﺎﻓﺔ‬(‫)ف‬‫ﻧﺤﺼﻞ‬ (‫)ز‬ ‫واﻟﺰﻣﻦ‬‫اﻻﺻﻞ‬ ‫ﺑﻨﻘﻄﺔ‬ ‫ﯾﻤﺮ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ﻋﻠﻰ‬
٥-‫ﻧ‬‫ﺑﯿﻦ‬ ‫ﺑﯿﺎﻧﯿﺔ‬ ‫ﻋﻼﻗﺔ‬ ‫ﺮﺳﻢ‬‫اﻟﺴﺮﻋﺔ‬)‫ع‬‫ﻧﺤﺼﻞ‬ (‫(واﻟﺰﻣﻦ)ز‬‫ﻋﻠ‬‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ﻰ‬‫ﯾﻮازىﻤﺤﻮراﻟﺰﻣﻦ‬ ‫اﻓﻘﻰ‬
: ‫اﻻﺳﺘﻨﺘﺎج‬ ‫و‬ ‫اﻟﻤﻼﺣﻈﺔ‬
‫اﻟﻔﯿﺰﯾﺎء‬ ‫ﻋﻠﻤﺎء‬‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﻋﻠﻤﺎء‬
‫ﯾﺴﺘﺨﺪﻣ‬‫و‬ ‫ﻮا‬‫اﻟﺮﯾﺎﺿﯿﺎت‬ ‫ﺳﺎﺋﻞ‬‫اﻟﺒﯿﺎﻧﯿﺔ‬ ‫اﻟﺮﺳﻮم‬ ‫و‬ ‫ﻛﺎﻟﺠﺪاول‬‫ﻋﻠﻞ‬
‫ﺑﺎﻟﻌﻼﻗ‬ ‫واﻟﺘﻨﺒﺆ‬ ‫أﺳﮭﻞ‬ ‫ﺑﻄﺮﯾﻘﺔ‬ ‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻈﻮاھﺮ‬ ‫ﻟﻮﺻﻒ‬‫ﺔ‬‫ﺑﯿﻦ‬
‫اﻟﻤﺨﺘﻠﻔﺔ‬ ‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻜﻤﯿﺎت‬
‫اﻟﻤﺨﺘﻠﻔﺔ‬ ‫اﻟﻤﺘﻐﯿﺮات‬ ‫ﺑﯿﻦ‬ ‫اﻟﺮﯾﺎﺿﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﯾﺴﺘﺨﺪﻣﻮا‬‫ﻋﻠﻞ‬
‫ﻟﻮﺻﻒ‬‫ﻓﮭﻢ‬ ‫و‬‫أﺳﮭﻞ‬ ‫ﺑﻄﺮﯾﻘﺔ‬ ‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻈﻮاھﺮ‬
١-( ‫اﻟﺰﻣﻦ‬ ‫و‬ ‫)اﻟﻤﺴﺎﻓﺔ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﯿﺎﻧﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬
(‫ﺛﺎﺑﺘﺔ‬ ) ‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﻟﻠﺤﺮﻛﺔ‬
٢-( ‫ﻟﺰﻣﻦ‬ ‫و‬ ‫)اﻟﺴﺮﻋﺔ‬ ‫ﺑﯿﻦ‬ ‫اﻟﺒﯿﺎﻧﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬
(‫)ﺛﺎﺑﺘﺔ‬ ‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﻟﻠﺤﺮﻛﺔ‬
٣-‫و‬ ‫ﺑﯿﻦ)اﻟﻤﺴﺎﻓﺔ‬ ‫اﻟﺒﯿﺎﻧﯿﺔ‬ ‫اﻟﻌﻼﻗﺔ‬
‫ﻟﺴﺎﻛﻦ‬ ‫ا‬ ‫ﻟﻠﺠﺴﻢ‬ (‫اﻟﺰﻣﻦ‬
‫اﻷﺻﻞ‬ ‫ﺑﻨﻘﻄﺔ‬ ‫ﯾﻤﺮ‬ ‫ﻣﺎﺋﻞ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺑﺨﻂ‬ ‫ﺗﻤﺜﻞ‬‫اﻟﺰﻣﻦ‬ ‫ﻣﺤﻮر‬ ‫ﯾﻮازي‬ ‫اﻓﻘﻰ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺑﺨﻂ‬ ‫ﺗﻤﺜﻞ‬‫اﻟﺰﻣﻦ‬ ‫ﻣﺤﻮر‬ ‫ﯾﻮازي‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺑﺨﻂ‬ ‫ﺗﻤﺜﻞ‬
‫اﻟﻤﺴﺎﻓﺔ‬
‫اﻟﺰﻣﻦ‬
‫اﻟﺴﺮﻋﺔ‬
‫اﻟﺰﻣﻦ‬
‫اﻟﻤﺴﺎﻓﺔ‬
‫اﻟﺰﻣﻦ‬

5. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٥
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫ﺳﺮﻋﺔ‬ ‫ﻓﻲ‬ ‫اﻟﺘﻐﯿﺮ‬ ‫ﻣﻘﺪار‬ ‫ھﻲ‬‫اﻟ‬‫اﻟﻮاﺣﺪة‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫ﻓﻲ‬ ‫ﺠﺴﻢ‬‫او‬‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﻓﻲ‬ ‫اﻟﺘﻐﯿﺮ‬ ‫ﻣﻘﺪار‬ ‫ھﻲ‬‫ﺧﻼل‬‫اﻟﺰﻣﻦ‬ ‫وﺣﺪة‬
‫اﻟﺰﻣﻨﻰ‬ ‫اﻟﻤﻌﺪل‬ ‫ھﻰ‬ ‫او‬‫اﻟﺴﺮﻋﺔ‬ ‫ﻓﻰ‬ ‫ﻟﻠﺘﻐﯿﺮ‬
: ‫اﻟﻤﻌﺠﻠﺔ‬ ‫اﻟﺤﺮﻛﺔ‬‫اﻟﺰﻣﻦ‬ ‫ﺑﻤﺮور‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﻓﯿﮭﺎ‬ ‫ﺗﺘﻐﯿﺮ‬ ‫اﻟﺘﻰ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ھﻰ‬
‫اﻟﻌﺠﻠﺔ‬: ‫اﻟﻤﻨﺘﻈﻤﺔ‬‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ازﻣﻨﺔ‬ ‫ﻓﻰ‬ ‫ﻣﺘﺴﺎوﯾﺔ‬ ‫ﺑﻤﻘﺎدﯾﺮ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﻓﯿﮭﺎ‬ ‫ﺗﺘﻐﯿﺮ‬
:‫اﻟﻤﻨﺘﻈﻤﺔ‬ ‫اﻟﻌﺠﻠﺔ‬ ‫أﻧﻮاع‬-
١-(+ ) ‫ﺗﺰﯾﺎدﯾﺔ‬ ‫ﻋﺠﻠﺔ‬-‫ﺗﻨ‬ ‫ﻋﺠﻠﺔ‬) ‫ﺎﻗﺼﯿﺔ‬-: (
‫ﺛﺎﺑﺖ‬ ‫ﺑﻤﻘﺪار‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﻓﯿﮭﺎ‬ ‫ﺗﺰداد‬‫اﻟﺰﻣﻦ‬ ‫ﺑﻤﺮور‬‫ﺛﺎﺑﺖ‬ ‫ﺑﻤﻘﺪار‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ﻓﯿﮭﺎ‬ ‫ﺗﺘﻨﺎﻗﺺ‬‫اﻟﺰﻣﻦ‬ ‫ﺑﻤﺮور‬
‫ع‬ ‫ﻓﯿﮭﺎ‬ ‫ﺗﻜﻮن‬٢‫ع‬ <١‫ع‬ ‫ﻓﯿﮭﺎ‬ ‫ﺗﻜﻮن‬ ‫و‬١‫ع‬ <٢
‫ﻣﻮﺟﺒﺔ‬ ‫ﻗﯿﻤﺘﮭﺎ‬ ‫و‬‫ﺳﺎﻟﺒﺔ‬ ‫ﻗﯿﻤﺘﮭﺎ‬ ‫و‬
‫ﯾﺒ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫ﺗﺤﺪث‬‫اﻟﺴﻜﻮن‬ ‫ﻣﻦ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺪأ‬‫اﻟﻔﺮاﻣﻞ‬ ‫اﺳﺘﺨﺪام‬ ‫ﺣﺎﻟﺔ‬ ‫ﻓﻰ‬ ‫ﺗﺤﺪث‬
‫س‬١‫ﻋﻠﻞ‬‫ﻋﺠﻠﺔ‬ ‫ﻟﺔ‬ ‫ﻟﯿﺲ‬ ‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫اﻟﺬى‬ ‫اﻟﺠﺴﻢ‬
‫ﻻن‬‫اﻟﺰﻣﻦ‬ ‫ﺑﻤﺮور‬ ‫ﺗﺘﻐﯿﺮ‬ ‫ﻻ‬ ‫اﻟﺴﺮﻋﺔ‬‫و‬‫ﻻن‬‫ع‬٢=‫ع‬١‫ﺑﺎﻟﺘﺎﻟﻰ‬ ‫و‬‫اﻟﻌﺠﻠﺔ‬‫ﺻﻔﺮ‬ =
‫س‬٢‫ﯾﻌﻨﻰ‬ ‫ﻣﺎذا‬‫أن‬
١-‫ﺻﻔﺮ؟‬ = ‫ﺑﻌﺠﻠﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫ﺟﺴﻢ‬‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫اﻟﺠﺴﻢ‬ ‫ان‬ ‫اى‬( ‫)ﺛﺎﺑﺘﺔ‬
٢-‫ﻣﻘﺪارھﺎ‬ ‫ﺑﻌﺠﻠﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫ﺟﺴﻢ‬٥‫م/ث‬٢‫ان‬ ‫؟اى‬‫ﺳﺮﻋ‬‫اﻟﺠﺴﻢ‬ ‫ﺔ‬‫ﺑﻤﻘﺪار‬ ‫ﺗﺰداد‬٥‫ﺛﺎﻧﯿﺔ‬ ‫ﻛﻞ‬ ‫ﻓﻰ‬ ‫م/ث‬
٣-= ‫ﺑﻌﺠﻠﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫ﺟﺴﻢ‬-٢‫م/ث‬٢‫؟‬‫ﺑﻤﻘﺪار‬ ‫ﺗﻘﻞ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ان‬ ‫اى‬٢‫ﺛﺎﻧﯿﺔ‬ ‫ﻛﻞ‬ ‫ﻓﻰ‬ ‫م/ث‬
٤-= ‫ﺑﺘﻘﺼﯿﺮ‬ ‫ﯾﺘﺤﺮك‬ ‫ﺟﺴﻢ‬٢‫م/ث‬٢‫؟‬‫ﺑﻤﻘﺪار‬ ‫ﺗﻘﻞ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺳﺮﻋﺔ‬ ‫ان‬ ‫اى‬٢‫ﺛﺎﻧﯿﺔ‬ ‫ﻛﻞ‬ ‫ﻓﻰ‬ ‫م/ث‬

6. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٦
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫اﻟﻌﺠﻠﺔ‬ ‫ﻣﺴﺎﺋﻞ‬ ‫ﺣﻞ‬ ‫اﺳﺎﺳﯿﺎت‬
١-‫اﻟﺴﻜﻮن‬ ‫ﻣﻦ‬ ‫ﺣﺮﻛﺘﺔ‬ ‫ﺑﺪا‬ ‫ﺟﺴﻢ‬‫ع‬١‫ﺻﻔﺮ‬ =
٢-‫اﻟﺴﯿﺎرة‬ ‫ﻓﺘﻮﻗﻔﺖ‬ ‫اﻟﻔﺮاﻣﻞ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺴﺎﺋﻖ‬ ‫ﺿﻐﻂ‬‫ع‬٢‫ﺻﻔﺮ‬ =
٣-‫ﻣﻨﺘﻈﻤﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫ﺟﺴﻢ‬‫اى‬‫)ع‬٢‫ع‬ =١(‫اﻟﻌﺠﻠﺔ‬‫ﺻﻔﺮ‬ =
)‫ﻣﺴـــــــــــــــــﺎﺋﻞ‬(
)١-(‫إﻟﻰ‬ ‫ﺳﺮﻋﺘﮫ‬ ‫وﺻﻠﺖ‬ ‫ﺳﺎﻛﻦ‬ ‫ﻗﺎرب‬ ‫ﺗﺸﻐﯿﻞ‬ ‫ﻋﻨﺪ‬٢.٥‫زﻣﻨﯿ‬ ‫ﻓﺘﺮة‬ ‫ﺧﻼل‬ ‫م/ث‬‫ﻣﻘﺪارھﺎ‬ ‫ﺔ‬٣٠: ‫أوﺟﺪ‬ ‫ث‬
١-‫؟‬ ‫اﻟﻘﺎرب‬ ‫ﺑﮭﺎ‬ ‫ﯾﺘﺤﺮك‬ ‫اﻟﺘﻰ‬ ‫اﻟﻌﺠﻠﺔ‬ ‫ﻣﻘﺪار‬٢-‫؟‬ ‫اﻟﺴﺒﺐ‬ ‫ذﻛﺮ‬ ‫ﻣﻊ‬ ‫اﻟﻌﺠﻠﺔ‬ ‫ﻧﻮع‬
)٢-(‫ﺑﺴﺮﻋﺔ‬ ‫ﺳﯿﺎرة‬ ‫ﺗﺘﺤﺮك‬٣٠‫ﻗﺪرة‬ ‫زﻣﻦ‬ ‫ﺧﻼل‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺗﻮﻗﻔﺖ‬ ‫اﻟﻔﺮاﻣﻞ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺴﺎﺋﻖ‬ ‫ﺿﻐﻂ‬ ‫وﻋﻨﺪﻣﺎ‬ ‫م/ث‬١٥‫ث‬
: ‫أوﺟﺪ‬١-‫اﻟﺘﻰ‬ ‫اﻟﻌﺠﻠﺔ‬ ‫ﻣﻘﺪار‬‫؟‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺑﮭﺎ‬ ‫ﺗﺘﺤﺮك‬٢-‫؟‬ ‫اﻟﺴﺒﺐ‬ ‫ذﻛﺮ‬ ‫ﻣﻊ‬ ‫اﻟﻌﺠﻠﺔ‬ ‫ﻧﻮع‬
)٣-(‫ﻣﻘﺪارھﺎ‬ ‫اﺑﺘﺪاﺋﯿﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫ﻗﻄﺎر‬٧.٥‫ﻣﻘﺪارھﺎ‬ ‫ﺑﻌﺠﻠﺔ‬ ‫و‬ ‫م/ث‬١٠‫م/ث‬٢‫ﺑﻌﺪھﺎ‬ ‫ﺗﺼﺒﺢ‬ ‫اﻟﺘﻰ‬ ‫اﻟﺰﻣﻨﯿﺔ‬ ‫اﻟﻔﺘﺮة‬ ‫ﻣﻘﺪار‬ ‫اﺣﺴﺐ‬
‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﻘﻄﺎر‬ ‫ﺳﺮﻋﺔ‬٤‫اﻻﺑﺘﺪاﺋﯿﺔ‬ ‫ﺳﺮﻋﺘﺔ‬ ‫اﻣﺜﺎل‬
٤-)٤-(‫اﻟﺴﻜﻮن‬ ‫ﻣﻦ‬ ‫ﺣﺮﻛﺘﮭﻤﺎ‬ ‫ﺑﺪات‬ ( ‫ب‬ ) ‫و‬ ( ‫أ‬ ) ‫ﺳﯿﺎرﺗﺎن‬‫اﻻوﻟﻰ‬ ‫ﺳﺮﻋﺔ‬ ‫ﻓﺎﺻﺒﺤﺖ‬٦٠‫ﻣﺮور‬ ‫ﺑﻌﺪ‬ ‫ث‬ / ‫م‬٥‫اﻟﺜﺎﻧﯿﺔ‬ ‫ﺳﺮﻋﺔ‬ ‫و‬ ‫ﺛﻮاﻧﻰ‬
٨٠‫ﻣﺮور‬ ‫ﺑﻌﺪ‬ ‫م/ث‬١٠‫ﺛﻮاﻧﻰ‬‫اﻛﺒﺮ‬ ‫ﺑﻌﺠﻠﺔ‬ ‫ﺗﺘﺤﺮك‬ ‫اﻟﺴﯿﺎرﺗﯿﻦ‬ ‫ﻓﺎى‬
)٥-(‫ﻣﻘﺪارھﺎ‬ ‫اﺑﺘﺪاﺋﯿﺔ‬ ‫ﺑﺴﺮﻋﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫ﻗﻄﺎر‬٦٠‫ﻣﺮور‬ ‫ﺑﻌﺪ‬ ‫اﻟﻨﮭﺎﺋﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻣﻘﺪار‬ ‫اﺣﺴﺐ‬ ‫ﻛﻢ/س‬٤٢‫ﺑﻌﺠﻠﺔ‬ ‫ﯾﺘﺤﺮك‬ ‫ﺑﺎﻧﺔ‬ ‫ﻋﻠﻤﺎ‬ ‫دﻗﯿﻘﺔ‬
٥٠‫ﻛﻢ/س‬٢
)٦-(‫ﺗﺴﯿ‬ ‫ﺳﯿﺎرة‬‫ﺑﺴﺮﻋﺔ‬ ‫ﺮ‬٩٠‫ﺑﻤﻌﺪل‬ ‫ﻓﺘﻨﺎﻗﺼﺖ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻟﺘﻘﻠﯿﻞ‬ ‫اﻟﻔﺮاﻣﻞ‬ ‫اﻟﺴﺎﺋﻖ‬ ‫اﺳﺘﺨﺪم‬ ‫س‬ / ‫ﻛﻢ‬٢‫ث‬ / ‫م‬٢
‫ﺑﻌﺪ‬ ‫ﺳﺮﻋﺘﮭﺎ‬ ‫اﺣﺴﺒﻰ‬
‫ﻣﺮور‬١٠‫اﻟﻔﺮاﻣﻞ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻀﻐﻂ‬ ‫ﻟﺤﻈﺔ‬ ‫ﻣﻦ‬ ‫ﺛﻮاﻧﻰ‬
‫اﻟﺒﯿﺎﻧﯿﺔ‬ ‫اﻟﺮﺳﻮﻣﺎت‬ ‫اھﻢ‬

7. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٧
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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: ‫اﻟﻔﯿﺰﯾﺎء‬ ‫ﻋﻠﻢ‬‫اﻟﺬى‬ ‫اﻟﻌﻠﻢ‬ ‫ھﻮ‬‫ﺑﻮﺻﻒ‬ ‫ﯾﮭﺘﻢ‬‫ﺗﻔﺴﯿﺮ‬ ‫و‬‫اﻟﻈﻮاھﺮ‬‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬)‫اﻟﻄﺒﯿﻌﯿﺔ‬(
‫اﻟﺮﯾﺎﺿﯿﺔ‬ ‫اﻟﻌﻼﻗﺎت‬ ‫ﻋﻠﻰ‬ ‫ﺗﻔﺴﯿﺮة‬ ‫ﻓﻰ‬ ‫ﯾﻌﺘﻤﺪ‬ ‫و‬‫ﺑﯿﻦ‬‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻜﻤﯿﺎت‬
: ‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻜﻤﯿﺎت‬‫ﻣﺜﻞ‬‫اﻟﻤﺴﺎﻓﺔ‬‫و‬‫اﻟﺰﻣﻦ‬‫و‬‫و‬ ‫اﻟﺴﺮﻋﺔ‬‫اﻟﻜﺘﻠﺔ‬‫و‬‫و‬ ‫اﻟﺤﺠﻢ‬‫اﻟﻌﺠﻠﺔ‬
‫ﻋﻠﻞ‬ ‫س‬: ‫ﯾﺎﺗﻰ‬ ‫ﻟﻤﺎ‬
١-‫ﻣﺘﺠﮭﺔ؟‬ ‫ﻛﻤﯿﺔ‬ ‫اﻻزاﺣﺔ‬ ‫ﺑﯿﻨﻤﺎ‬ ‫ﻗﯿﺎﺳﯿﺔ‬ ‫ﻛﻤﯿﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬
‫ﻣﻘﺪار‬ ‫ﻣﻌﺮﻓﺔ‬ ً‫ﺎ‬‫ﺗﺎﻣ‬ ً‫ﺎ‬‫ﺗﻌﺮﯾﻔ‬ ‫ﻟﺘﻌﺮﯾﻔﮭﺎ‬ ‫ﯾﻠﺰم‬ ‫ﻷﻧﮫ‬ ‫ﻗﯿﺎﺳﯿﺔ‬ ‫ﻛﻤﯿﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬‫ھﺎ‬‫ﻗﯿﺎﺳﮭﺎ‬ ‫ووﺣﺪة‬‫ﻓﻘﻂ‬
‫ﻣﻘﺪارھﺎ‬ ‫ﻣﻌﺮﻓﺔ‬ ً‫ﺎ‬‫ﺗﺎﻣ‬ ً‫ﺎ‬‫ﺗﻌﺮﯾﻔ‬ ‫ﻟﺘﻌﺮﯾﻔﮭﺎ‬ ‫ﯾﻠﺰم‬ ‫ﻷﻧﮫ‬ ‫ﻣﺘﺠﮭﺔ‬ ‫ﻛﻤﯿﺔ‬ ‫اﻻزاﺣﺔ‬ ‫اﻣﺎ‬‫ﻗﯿﺎﺳﮭﺎ‬ ‫ووﺣﺪة‬‫واﺗﺠﺎھﮭﺎ‬
٢-‫زﻣﻦ؟‬ ‫إﻟﻰ‬ ‫ﻛﺘﻠﺔ‬ ‫إﺿﺎﻓﺔ‬ ‫ﯾﻤﻜﻦ‬ ‫ﻻ‬‫ﻷن‬‫ﻟﯿﺲ‬ ‫اﻟﺰﻣﻦ‬ ‫و‬ ‫اﻟﻜﺘﻠﺔ‬‫اﻟﻮﺣﺪة‬ ‫ﻧﻔﺲ‬ ‫ﻟﮭﻤﺎ‬
٣-‫ﻛﺘﻠﺔ؟‬ ‫إﻟﻰ‬ ‫ﻛﺘﻠﺔ‬ ‫إﺿﺎﻓﺔ‬ ‫ﯾﻤﻜﻦ‬‫اﻟﻮﺣﺪة‬ ‫ﻧﻔﺲ‬ ‫ﻟﮭﻤﺎ‬ ‫ﻷن‬
= ‫ﺟﺴﻢ‬ ‫ازاﺣﺔ‬ : ‫ان‬ ‫ﯾﻌﻨﻰ‬ ‫ﻣﺎذا‬١٠‫؟‬ ‫ﻣﺘﺮ‬‫ان‬ ‫اى‬‫ﻃﻮل‬‫اﻗﺼﺮ‬‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬= ‫ﺣﺮﻛﺘﺔ‬ ‫ﻧﮭﺎﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫و‬ ‫اﻟﺠﺴﻢ‬ ‫ﺣﺮﻛﺔ‬ ‫ﺑﺪاﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﺑﯿﻦ‬١٠
‫ﻣﺘﺮ‬‫ﻣﺘﺮ‬
‫س‬١‫ﯾﺄﺗﻲ‬ ‫ﻣﺎ‬ ‫أﻛﻤﻞ‬
.......... ‫......................ووﺣﺪةﻗﯿﺎﺳﮭﺎ‬ ‫ﻛﻤﯿﺔ‬ ‫اﻻزاﺣﺔ‬‫ا‬....... ‫ﻗﯿﺎﺳﮭﺎ‬ ‫ووﺣﺪة‬ ............ ‫ﻛﻤﯿﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻣﺎ‬......
‫س‬٢‫واﻟﻤﺴﺎﻓﺔ‬ ‫اﻻزاﺣﺔ‬ ‫ﺑﯿﻦ‬ ‫ﻗﺎرن‬‫اﻟﻤﻔﮭﻮم‬ ) ‫ﺣﯿﺚ‬ ‫ﻣﻦ‬–( ‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻜﻤﯿﺔ‬ ‫ﻧﻮع‬
‫اﻟﻤﻘﺎرﻧﺔ‬ ‫وﺟﺔ‬‫اﻟﻘﯿﺎﺳﯿﺔ‬ ‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻜﻤﯿﺎت‬‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﻔﯿﺰﯾﺎﺋﯿﺔ‬ ‫اﻟﻜﻤﯿﺎت‬
‫اﻟﺘﻌﺮﯾﻒ‬
‫ﻣﻌﺮﻓﺔ‬ ً‫ﺗﺎﻣﺎ‬ ً‫ﺎ‬‫ﺗﻌﺮﯾﻔ‬ ‫ﻟﺘﻌﺮﯾﻔﮭﺎ‬ ‫ﯾﻠﺰم‬ ‫اﻟﺘﻰ‬ ‫اﻟﻜﻤﯿﺔ‬ ‫ھﻰ‬
‫ﻓﻘﻂ‬ ‫ﻗﯿﺎﺳﮭﺎ‬ ‫ووﺣﺪة‬ ‫ﻣﻘﺪارھﺎ‬
‫اﻟﻮﺣﺪة‬ ‫ﻧﻔﺲ‬ ‫ﻟﮭﺎ‬ ‫ﻛﺎن‬ ‫اذا‬ ‫ﺗﻄﺮح‬ ‫و‬ ‫ﺗﺠﻤﻊ‬
‫اﻟﻜ‬ ‫ھﻰ‬ً‫ﺎ‬‫ﺗﺎﻣ‬ ً‫ﺎ‬‫ﺗﻌﺮﯾﻔ‬ ‫ﻟﺘﻌﺮﯾﻔﮭﺎ‬ ‫ﯾﻠﺰم‬ ‫اﻟﺘﻰ‬ ‫ﻤﯿﺔ‬
‫واﺗﺠﺎھﮭﺎ‬ ‫ﻗﯿﺎﺳﮭﺎ‬ ‫ووﺣﺪة‬ ‫ﻣﻘﺪارھﺎ‬ ‫ﻣﻌﺮﻓﺔ‬
‫اﻣﺜﻠﺔ‬
١-‫اﻟﻤﺴﺎﻓﺔ‬: ‫اﻟﻄﻮل‬ ‫و‬‫ﻗﯿﺎﺳﮭ‬ ‫وﺣﺪة‬‫ﻤ‬‫ﺎ‬( ‫)م‬ ‫اﻟﻤﺘﺮ‬
٢-‫اﻟﺰﻣﻦ‬:‫ﻗﯿﺎﺳﮭﺎ‬ ‫وﺣﺪة‬( ‫)ث‬ ‫اﻟﺜﺎﻧﯿﺔ‬
٣-‫ا‬‫اﻟﻘﯿﺎﺳﯿﺔ‬ ‫ﻟﺴﺮﻋﺔ‬:‫ﻗﯿﺎﺳﮭﺎ‬ ‫وﺣﺪة‬‫م/ث‬
٤-‫اﻟﻜﺘﻠﺔ‬:‫ﻗﯿﺎﺳﮭﺎ‬ ‫وﺣﺪة‬( ‫)ﻛﺠﻢ‬ ‫ﺟﺮام‬ ‫اﻟﻜﯿﻠﻮ‬
١-‫اﻹزاﺣﺔ‬:‫ﻗﯿﺎﺳﮭﺎ‬ ‫وﺣﺪة‬(‫)م‬ ‫اﻟﻤﺘﺮ‬
٢-‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬:‫ﻗﯿﺎﺳﮭﺎ‬ ‫وﺣﺪة‬‫م/ث‬
٣-‫اﻟﻌﺠﻠﺔ‬:‫م/ث‬٢
٤-‫اﻟﻘﻮة‬:‫ﻗﯿﺎﺳﮭﺎ‬ ‫وﺣﺪة‬‫اﻟﻨﯿﻮﺗﻦ‬
‫اﻟﻤﺴ‬‫ﺎﻓﺔ‬‫اﻻزاﺣﺔ‬
‫ﻧﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫اﻟﺠﺴﻢ‬ ‫ﯾﻘﻄﻌﮭﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻔﻌﻠﯿﺔ‬ ‫اﻟﻤﺴﺎﻓﺎت‬ ‫ﻣﺠﻤﻮع‬ ‫ھﻰ‬‫اﻟ‬‫ﺒﺪاﯾﺔ‬
‫ﻧﻘﻄﺔ‬ ‫اﻟﻰ‬‫اﻟ‬‫ﻨﮭﺎﯾﺔ‬
‫اﻟﻤﺘﺤﺮك‬ ‫اﻟﺠﺴﻢ‬ ‫ﯾﺴﻠﻜﮫ‬ ‫اﻟﺬي‬ ‫اﻟﻔﻌﻠﻰ‬ ‫اﻟﻤﺴﺎر‬ ‫ﻃﻮل‬ ‫اوھﻰ‬‫ﻧﻘﻄﺔ‬ ‫ﻣﻦ‬
‫اﻟ‬‫ﺒﺪاﯾﺔ‬‫اﻟﻰ‬‫ﻧﻘﻄﺔ‬‫اﻟ‬‫ﻨﮭﺎﯾﺔ‬
‫ھﻰ‬‫ﺛ‬ ‫اﺗﺠﺎه‬ ‫ﻓﻲ‬ ‫اﻟﻤﻘﻄﻮﻋﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬‫ﺎﺑﺖ‬‫ﻧﻘﻄﺔ‬ ‫ﻣﻦ‬‫اﻟ‬‫ﺒﺪاﯾﺔ‬
‫ﻧﻘﻄﺔ‬ ‫اﻟﻰ‬‫اﻟ‬‫ﻨﮭﺎﯾﺔ‬
‫اﻻزاﺣﺔ‬ ‫ﻣﻘﺪار‬‫ﻣﻮﺿﻌﯿﻦ‬ ‫ﺑﯿﻦ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫أﻗﺼﺮ‬ ‫ﻃﻮل‬ ‫ھﻰ‬
‫اﻟﺒﺪاﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺘﻘﯿﻤﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﻰ‬ ‫أو‬‫اﻟﻨﮭﺎﯾﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫و‬
‫اﻟﻤﺘﺮ‬ ‫ﻗﯿﺎﺳﮭﺎ‬ ‫وﺣﺪة‬ ‫ﻗﯿﺎﺳﯿﺔ‬ ‫ﻓﯿﺰﯾﺎﺋﯿﺔ‬ ‫ﻛﻤﯿﺔ‬‫ﻗﯿﺎﺳﮭﺎ‬ ‫وﺣﺪة‬ ‫ﻣﺘﺠﮭﺔ‬ ‫ﻓﯿﺰﯾﺎﺋﯿﺔ‬ ‫ﻛﻤﯿﺔ‬‫اﻟﻤﺘﺮ‬

8. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٨
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫ﺗﻄﺒﯿﻖ‬
‫ﻃﻨﻄﺎ‬ ‫اﻟﻰ‬ ‫اﻟﻘﺎھﺮة‬ ‫ﻣﻦ‬ ‫ﺑﺎﻟﺴﯿﺎرة‬ ‫ﺑﺮﺣﻠﺔ‬ ‫اﻟﻘﯿﺎم‬ ‫ﺷﺨﺺ‬ ‫اراد‬ ‫اذا‬
‫ﺛﺎﺑﺘﺔ‬ ‫اﻻزاﺣﺔ‬ ‫اﻣﺎ‬ ‫اﻟﺮﺣﻠﺔ‬ ‫ﻣﺴﺎر‬ ‫ﺑﺎﺧﺘﻼف‬ ‫ﺗﺨﺘﻠﻒ‬ ‫ﻃﻨﻄﺎ‬ ‫اﻟﻰ‬ ‫اﻟﻘﺎھﺮة‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻓﺎن‬
‫ﻣﺘﻰ‬ ‫س‬‫؟‬ ‫اﻹزاﺣﺔ‬ ‫ﻣﻘﺪار‬ ‫ﻣﻊ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﺗﺘﺴﺎوى‬‫ﻓﻰ‬ ‫و‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ﻓﻰ‬ ‫اﻟﺤﺮﻛﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫اذا‬ :‫ج‬‫اﺗﺠﺎة‬‫ﺛﺎﺑﺖ‬
‫ھﺎﻣﺔ‬ ‫ﻣﻠﺤﻮﻇﺔ‬:-
١-‫ا‬ (‫أ‬ )‫ﻣﻦ‬ ‫ﺛﺎﺑﺖ‬ ‫اﺗﺠﺎه‬ ‫ﻓﻰ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺗﺤﺮك‬ ‫إذا‬(‫ب‬ )‫ﻟﻰ‬‫أ‬ ) ‫اﻟﺤﺎدﺛﺔ‬ ‫اﻻزاﺣﺔ‬ ‫ﻓﺈن‬(‫ب‬=‫اﻟﻤﻘﻄﻮﻋﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ً‫ﺎ‬‫ﻋﺪدﯾ‬
(‫)أ‬ ‫اﻟﻰ‬ ‫أﺧﺮى‬ ‫ﻣﺮة‬ ‫ﻋﺎد‬ ‫ﺛﻢ‬ (‫)ب‬ ‫)أ(اﻟﻰ‬ ‫ﻣﻦ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺗﺤﺮك‬ ‫إذا‬‫ﺻﻔﺮ‬ = ‫اﻟﺤﺎدﺛﺔ‬ ‫اﻻزاﺣﺔ‬ ‫ﻓﺈن‬‫اﻣﺎ‬= ‫اﻟﻤﻘﻄﻮﻋﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬٢x‫أب‬ ‫ﻃﻮل‬
٢-‫ﺟﺴﻢ‬ ‫ﺗﺤﺮك‬ ‫اذا‬: ‫اﻻزاﺣﺔ‬ ‫و‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﺗﺤﺴﺐ‬ ‫ﻛﯿﻒ‬ ‫داﺋﺮى‬ ‫ﻣﺴﺎر‬ ‫ﻓﻰ‬
‫أ‬-‫اﻟﺪورات‬ ‫ﻋﺪد‬ = ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﻜﺬا‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﺗﺤﺴﺐ‬x) ‫اﻟﺪاﺋﺮة‬ ‫ﻣﺤﯿﻂ‬٢( ‫ﻧﻖ‬ ‫ط‬
‫ب‬–‫اﻻزاﺣﺔ‬ ‫ﺗﺤﺴﺐ‬
‫اﻟﻨﮭﺎﯾﺔ‬ ‫ھﻰ‬ ‫اﻟﺒﺪاﯾﺔ‬ ‫ﻻن‬ ‫ﺻﻔﺮ‬ = ‫اﻻزاﺣﺔ‬ ‫ﻓﺎن‬ ‫ﻛﺎﻣﻠﺔ‬ ‫دورات‬ ‫ﻋﺪد‬ ‫ﺗﺤﺮك‬ ‫ﻟﻮ‬ :
‫ﯾﻌﻨﻰ‬ ‫ﻧﺼﻒ‬ ‫و‬ ‫اﻟﺪورات‬ ‫ﻣﻦ‬ ‫ﻋﺪد‬ ‫اى‬ ‫او‬ ‫دورة‬ ‫ﻧﺼﻒ‬ ‫ﺗﺤﺮك‬ ‫ﻟﻮ‬ :٢‫ﻧﺼ‬ ‫و‬‫ﻣﺜﻼ‬ ‫دورة‬ ‫ﻒ‬= ‫اﻻزاﺣﺔ‬ ‫ﻓﺎن‬٢‫ﻧﻖ‬
‫او‬ ‫دورة‬ ‫رﺑﻊ‬ ‫ﺗﺤﺮك‬ ‫ﻟﻮ‬ :٣/٤‫ﻓﯿﺜﺎﻏﻮرث‬ ‫ﻣﻦ‬ ‫ﺗﺤﺴﺐ‬ ‫اﻻزاﺣﺔ‬ ‫ﻓﺎن‬ ‫دورة‬
‫ﻣﺴﺎﺋﻞ‬
١-‫ﻣﺤﯿﻄﮭﺎ‬ ‫داﺋﺮة‬ ‫ﻋﻠﻰ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫ﺣﺮﻛﺘﺔ‬ ‫ﺟﺴﻢ‬ ‫ﺑﺪا‬٥‫ﻣﻨﮭﺎ‬ ‫ﺑﺪا‬ ‫اﻟﺘﻰ‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻟﻨﻔﺲ‬ ‫ﻋﺎد‬ ‫ﺛﻢ‬ ‫دورﺗﯿﻦ‬ ‫ﺑﻌﻤﻞ‬ ‫ﻓﻘﺎم‬ ‫ﻣﺘﺮ‬‫اﻟﺤﺮﻛﺔ‬
‫اﺣﺴﺒ‬‫ﻰ‬‫اﻟﺠﺴﻢ‬ ‫ﺑﮭﺎ‬ ‫ﺗﺤﺮك‬ ‫اﻟﺘﻰ‬ ‫اﻻزاﺣﺔ‬ ‫و‬ ‫اﻟﻤﺴﺎﻓﺔ‬
٢-‫ﯾﺘﺤ‬‫ﻗﻄﺮھﺎ‬ ‫داﺋﺮة‬ ‫ﻣﺤﯿﻂ‬ ‫ﻋﻠﻰ‬ ‫ﺟﺴﻢ‬ ‫ﺮك‬٤‫اﻟﺠﺴﻢ‬ ‫ﯾﻜﻤﻞ‬ ‫ﻋﻨﺪﻣﺎ‬ ‫اﻻزاﺣﺔ‬ ‫و‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﺣﺴﺒﻰ‬ ‫م‬١.٧٥‫دورة‬
٣-‫ﻣﻦ‬ ‫ﺣﺠﺮ‬ ‫ﺷﺨﺺ‬ ‫ﻗﺬف‬‫ﻋﻠﻰ‬ ‫ﻣﺒﻨﻰ‬‫ارﺗﻔﺎع‬٢‫اﻻرض‬ ‫ﺳﻄﺢ‬ ‫ﻣﻦ‬ ‫ﻣﺘﺮ‬‫ﻣﻘﺪارھﺎ‬ ‫راﺳﯿﺔ‬ ‫ﻣﺴﺎﻓﺔ‬ ‫ﻻﻋﻠﻰ‬١٠‫ﻣﺘﺮ‬‫اﻟﻤﺒﻨﻰ‬ ‫ﺳﻄﺢ‬ ‫ﻣﻦ‬‫ﻓﺴﻘﻂ‬
‫اﻟﺤﺠﺮ‬ ‫ﺗﺤﺮﻛﮭﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻻزاﺣﺔ‬ ‫و‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﺣﺴﺒﻰ‬ ‫ﻓﺘﺮة‬ ‫ﺑﻌﺪ‬ ‫اﻻرض‬ ‫ﻋﻠﻰ‬
٤-‫ﻋﻘﺮب‬‫ﻃﻮﻟﺔ‬ ‫ﺛﻮاﻧﻰ‬٧‫م‬‫اﻟﺜﻮاﻧﻰ‬ ‫ﻋﻘﺮب‬ ‫ﻗﻄﻌﮭﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻻزاﺣﺔ‬ ‫و‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﺣﺴﺒﻰ‬ ‫دﻗﯿﻘﺔ‬ ‫ﻧﺼﻒ‬ ‫ﺗﺤﺮك‬
‫اﻟﻘﯿﺎﺳﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬
‫اﻟﺰﻣﻦ‬ ‫وﺣﺪة‬ ‫ﺧﻼل‬ ‫اﻟﻤﻘﻄﻮﻋﺔ‬ ‫اﻟﻜﻠﯿﺔ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﻰ‬‫اﻟﺰﻣﻦ‬ ‫وﺣﺪة‬ ‫ﺧﻼل‬ ‫اﻟﻤﻘﻄﻮﻋﺔ‬ ‫اﻻزاﺣﺔ‬ ‫ھﻰ‬
‫ﻗﯿﺎﺳﯿﺔ‬ ‫ﻛﻤﯿﺔ‬‫ﻻﻧﺔ‬‫ﻣﻌﺮﻓﺔ‬ ً‫ﺗﺎﻣﺎ‬ ً‫ﺎ‬‫ﺗﻌﺮﯾﻔ‬ ‫ﻟﺘﻌﺮﯾﻔﮭﺎ‬ ‫ﯾﻠﺰم‬
‫ﻓﻘﻂ‬ ‫ﻗﯿﺎﺳﮭﺎ‬ ‫ووﺣﺪة‬ ‫ﻣﻘﺪارھﺎ‬
‫ﻣﻘﺪارھﺎ‬ ‫ﻣﻌﺮﻓﺔ‬ ً‫ﺎ‬‫ﺗﺎﻣ‬ ً‫ﺎ‬‫ﺗﻌﺮﯾﻔ‬ ‫ﻟﺘﻌﺮﯾﻔﮭﺎ‬ ‫ﯾﻠﺰم‬ ‫ﻷﻧﮫ‬ ‫ﻣﺘﺠﮭﺔ‬ ‫ﻛﻤﯿﺔ‬
‫واﺗﺠﺎھﮭﺎ‬ ‫ﻗﯿﺎﺳﮭﺎ‬ ‫ووﺣﺪة‬
( ‫ﻛﻢ/ﺳﺎﻋﺔ‬ ‫او‬ ‫م/ث‬ ) ‫وھـــــــﻰ‬ ‫اﻟﻘﯿﺎﺳﯿﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻗﯿﺎس‬ ‫وﺣﺪة‬ ‫ﻧﻔﺲ‬ ‫ھﻰ‬ ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ﻗﯿﺎس‬ ‫وﺣﺪة‬
‫اﻟﺴﺮﻋﺔ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻔﺮق‬ ‫ﻣﺎ‬‫اﻟﻘﯿﺎﺳﯿﺔ‬‫اﻟ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫و‬‫؟‬ ‫ﻤﺘﺠﮭﺔ‬‫ﻣﺤﺪد‬ ‫اﺗﺠﺎة‬ ‫ﻓﻰ‬ ‫ﻟﻜﻦ‬ ‫ﻗﯿﺎﺳﯿﺔ‬ ‫ﺳﺮﻋﺔ‬ ‫ھﻰ‬ ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬
‫ان‬ ‫ﯾﻌﻨﻰ‬ ‫ﻣﺎذا‬‫ﺑﺴﺮﻋﺔ‬ ‫ﺗﺘﺤﺮك‬ ‫ﺳﯿﺎرة‬٥٠‫؟‬ ‫ﺷﻤﺎﻻ‬ ‫ث‬ / ‫م‬= ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫ان‬ ‫اى‬٥٠‫ث‬ / ‫م‬
‫ﻣﺜﺎل‬‫ﯾﻌﺘﺒﺮ‬‫ﺣﯿﻮان‬‫اﻟﻔﮭﺪ‬‫اﻟﻤﻔﺘﺮس‬( ‫اﻟﺸﯿﺘﺎ‬ )‫اﻟﺤﯿﻮاﻧﺎت‬ ‫اﺳﺮع‬ ‫ﻣﻦ‬‫ﺣﯿﺚ‬‫ﺳﺮﻋﺘﮫ‬ ‫ﺗﺒﻠﻎ‬٢٧‫ﺳﺮﻋﺘﮫ‬ ‫اﻟﺘﻌﺒﯿﺮﻋﻦ‬ ‫أردﻧﺎ‬ ‫ﻓﺈذا‬ ‫م/ث‬
‫اﻟﻤﺘﺠﮭ‬‫ﺔ‬‫ﻧﻘﻮل‬‫ان‬‫ﻟﻠﺸﯿﺘﺎ‬ ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬٢٧‫اﻟﺸﺮق‬ ‫اﺗﺠﺎه‬ ‫ﻓﻰ‬ ‫م/ث‬‫اﻟﻤﺜﺎل‬ ‫ﺳﺒﯿﻞ‬ ‫ﻋﻠﻰ‬
‫ﺑﺎﻟﺴﯿﺎرة‬ ‫اﻟﺮﺣﻠﺔ‬ ‫ﻣﺴﺎر‬‫اﻟﻤﺴﺎﻓﺔ‬‫اﻻزاﺣ‬‫ﺔ‬
‫اﻟﻘﺎھﺮة‬–‫ﺑﻨﮭﺎ‬-‫ﻃﻨﻄﺎ‬٤٥+٦٠=١٠٥‫ﻛﻢ‬٩٣‫اﻟﺸﻤﺎل‬ ‫اﺗﺠﺎه‬ ‫ﻓﻰ‬ ‫ﻛﻢ‬
‫اﻟﻘﺎھﺮة‬–‫اﻟﺰﻗﺎزﯾﻖ‬-‫ﻃﻨﻄﺎ‬٨٠+٨٥=١٦٥‫ﻛﻢ‬٩٣‫اﻟﺸﻤﺎل‬ ‫اﺗﺠﺎه‬ ‫ﻓﻰ‬ ‫ﻛﻢ‬
‫اﻟﻘﺎھﺮة‬–‫ﻃﻨﻄﺎ‬٩٣‫ﻛﻢ‬٩٣‫اﻟﺸﻤﺎل‬ ‫اﺗﺠﺎه‬ ‫ﻓﻰ‬ ‫ﻛﻢ‬

9. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٩
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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10. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٠
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‫اﻻزاﺣﺔ‬ ‫و‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫اﺣﺴﺒﻰ‬ ‫اﻟﻤﻘﺎﺑﻞ‬ ‫اﻟﺸﻜﻞ‬ ‫ﻓﻰ‬
‫ﻋﻠﻞ‬‫ﻟﻠﺮﯾﺎح‬ ‫اﻟﻤﺘﺠﮭﺔ‬ ‫اﻟﺴﺮﻋﺔ‬ ‫اﻟﻄﯿﺎرون‬ ‫ﯾﺮاﻋﻲ‬‫اﻟﻄﯿﺮان‬ ‫ﻋﻨﺪ‬‫و‬ ‫اﻟﺮﺣﻠﺔ‬ ‫زﻣﻦ‬ ‫ﻻن‬‫ﻛﻤﯿﺔ‬‫اﻟﺮﯾﺎح‬ ‫اﺗﺠﺎة‬ ‫ﻋﻠﻰ‬ ‫ﯾﺘﻮﻗﻔﺎن‬ ‫اﻟﻮﻗﻮد‬
‫ﻋﻠﻞ‬‫اﻟﻤﺴﺘﮭ‬ ‫اﻟﻮﻗﻮد‬ ‫ﻛﻤﯿﺔ‬‫ﻠﻜﺔ‬‫ﺗﺨﺘﻠﻒ‬‫ﺑﺎﺧﺘﻼف‬‫ﺣﺴﺐ‬‫اﻟﺮﯾﺎح‬ ‫اﺗﺠﺎة‬‫ﻻﻧﺔ‬‫ﺗﺤﺮﻛ‬ ‫اذا‬‫ﺖ‬‫اﻟﻄﺎﺋﺮة‬‫ﻓﻰ‬‫ﻧﻔﺲ‬‫اﻟﺮﯾﺎح‬ ‫اﺗﺠﺎة‬‫ﺳﺮﻋﺘﮭﺎ‬ ‫ﺗﺰداد‬
‫اﻟﻤﺘﺠﮭﺔ‬‫اﻟﻤﺴﺘﮭﻠﻜﺔ‬ ‫اﻟﻮﻗﻮد‬ ‫ﻛﻤﯿﺔ‬ ‫ﻛﺬﻟﻚ‬ ‫و‬ ‫اﻟﺮﺣﻠﺔ‬ ‫زﻣﻦ‬ ‫ﯾﻘﻞ‬ ‫ﺑﺎﻟﺘﺎﻟﻰ‬ ‫و‬‫ﺻﺤﯿﺢ‬ ‫اﻟﻌﻜﺲ‬ ‫و‬
‫س‬:‫أﯾ‬ ‫اﻟﺮﯾﺢ‬ ‫اﺗﺠﺎه‬ ‫ﻋﻜﺲ‬ ‫ﻓﻲ‬ ‫واﻻﺧﺮى‬ ‫اﻟﺮﯾﺎح‬ ‫اﺗﺠﺎه‬ ‫ﻓﻲ‬ ‫اﻻوﻟﻰ‬ ‫وﻟﻜﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻧﻔﺲ‬ ‫ﺗﻘﻄﻌﺎن‬ ‫ﻃﺎﺋﺮﺗﺎن‬‫وﻟﻤﺎذا؟؟‬ ‫اﻛﺜﺮ‬ ‫ﻟﻮﻗﻮد‬ ‫ﺗﺤﺘﺎج‬ ‫ﮭﻤﺎ‬
‫اﻛﺜﺮ‬ ‫ﻟﻮﻗﻮد‬ ‫ﺗﺤﺘﺎج‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫اﻟﻄﺎﺋﺮة‬‫اﺗﺠﺎھ‬ ‫ﻻن‬‫ﮭ‬‫اﻟﺮﯾﺎح‬ ‫اﺗﺠﺎه‬ ‫ﻋﻜﺲ‬ ‫ﻓﻲ‬ ‫ﺎ‬‫ﻓ‬‫ﻛﺬﻟﻚ‬ ‫و‬ ‫اﻟﺮﺣﻠﺔ‬ ‫زﻣﻦ‬ ‫ﯾﺰداد‬ ‫ﺑﺎﻟﺘﺎﻟﻰ‬ ‫و‬ ‫اﻟﻤﺘﺠﮭﺔ‬ ‫ﺳﺮﻋﺘﮭﺎ‬ ‫ﺘﻘﻞ‬
‫اﻟﻤﺴﺘﮭﻠﻜﺔ‬ ‫اﻟﻮﻗﻮد‬ ‫ﻛﻤﯿﺔ‬
‫ا‬‫ا‬: ‫اﻟﻀﻮء‬ ‫ﻧﻌﻜﺎس‬‫ھﻮ‬‫ارﺗﺪاد‬‫اﻟﻤﻮﺟﺎت‬‫اﻟﻀﻮﺋﯿﺔ‬‫ﺳﻘﻮﻃﮭﺎ‬ ‫ﺟﮭﺔ‬ ‫ﻧﻔﺲ‬ ‫اﻟﻰ‬‫ﻋﻨﺪﻣﺎ‬‫ﺗﻘﺎﺑﻞ‬‫ﺳﻄﺤ‬‫ﺎ‬‫ﻋﺎﻛﺴﺎ‬
‫ا‬‫ا‬‫اﻟﻌﺎﻛﺲ‬ ‫ﻟﺴﻄﺢ‬ً‫ﺎ‬‫ﻛﺮﯾ‬ ‫أو‬ ً‫ﺎ‬‫ﻣﺴﺘﻮﯾ‬ ‫ﯾﻜﻮن‬ ‫ﻗﺪ‬ ‫ﻣﺼﻘﻮل‬ ‫ﻧﺼﻒ‬ ‫أو‬ ‫ﻣﺼﻘﻮل‬ ‫ﺳﻄﺢ‬ ‫ھﻮ‬
‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﺸﻌﺎع‬‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﻋﻠﻰ‬ ‫ﯾﺴﻘﻂ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺑﺨﻂ‬ ‫ﺗﻤﺜﻞ‬ ‫رﻓﯿﻌﺔ‬ ‫ﺿﻮﺋﯿﺔ‬ ‫ھﻮﺣﺰﻣﺔ‬
‫اﻟﻤﻨﻌﻜﺲ‬ ‫اﻟﺸﻌﺎع‬‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﻋﻦ‬ ‫ارﺗﺪ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺑﺨﻂ‬ ‫ﺗﻤﺜﻞ‬ ‫رﻓﯿﻌﺔ‬ ‫ﺿﻮﺋﯿﺔ‬ ‫ﺣﺰﻣﺔ‬ ‫ھﻮ‬
‫اﻻﻧﻌﻜﺎس‬ ‫ﻋﻤﻮد‬‫ﻣﻦ‬ ‫اﻟﻌﻤﻮداﻟﻤﻘﺎم‬ ‫ھﻮ‬‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺴﻘﻮط‬ ‫ﻧﻘﻄﺔ‬
‫اﻟﺴﻘﻮط‬ ‫زاوﯾﺔ‬‫اﻻﻧﻌﻜﺎس‬ ‫وﻋﻤﻮد‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﺸﻌﺎع‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺤﺼﻮرة‬ ‫اﻟﺰاوﯾﺔ‬ ‫ھﻰ‬
‫اﻻﻧﻌﻜﺎس‬ ‫زاوﯾﺔ‬‫اﻻﻧﻌﻜﺎس‬ ‫وﻋﻤﻮد‬ ‫اﻟﻤﻨﻌﻜﺲ‬ ‫اﻟﺸﻌﺎع‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺤﺼﻮرة‬ ‫اﻟﺰاوﯾﺔ‬ ‫ھﻰ‬
‫ﺿﻮﺋﻰ‬ ‫ﺷﻌﺎع‬ ‫ﺳﻘﻮط‬ ‫زاوﯾﺔ‬ ‫ان‬ ‫ﯾﻌﻨﻰ‬ ‫ﻣﺎذا‬٤٠0
‫؟‬
‫ان‬ ‫اى‬‫اﻻ‬ ‫وﻋﻤﻮد‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﺸﻌﺎع‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺤﺼﻮرة‬ ‫اﻟﺰاوﯾﺔ‬‫ﻧﻌﻜﺎس‬=٤٠o
‫ﺗﻜﻨﻮﻟﻮﺟﻰ‬ ‫ﺗﻄﺒﯿﻖ‬
‫ﻣﻔﺎھﯿﻢ‬‫ﺧﺎﺻﺔ‬‫اﻟﻀﻮء‬ ‫ﺑﺎﻧﻌﻜﺎس‬

11. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١١
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫اﻟﻀﻮء؟‬ ‫ﻓﻰ‬ ‫اﻻﻧﻌﻜﺎس‬ ‫ﻗﺎﻧﻮﻧﺎ‬ ‫اﺳﺘﻨﺘﺎج‬ ‫ﺑﺎﻟﺘﺠﺮﺑﺔ‬ ‫وﺿﺤﻰ‬
: ‫اﻻدوات‬‫ﻣﺴﺘﻮﯾﺔ‬ ‫ﻣﺮاة‬–‫ﺑﯿﻀﺎء‬ ‫ورﻗﺔ‬–‫دﺑﺎﺑﯿﺲ‬ ‫ﻣﺠﻤﻮﻋﺔ‬–‫ﻣﻨﻘﻞ‬–‫ﻣﺴﻄﺮة‬
: ‫اﻟﺨﻄﻮات‬
١-‫ﻧﺜﺒﺖ‬‫اﻟ‬‫ﻤﺮاة‬‫اﻟ‬‫ﻤﺴﺘﻮﯾﺔ‬‫اﻟ‬ ‫ﻋﻠﻰ‬ ‫ﻋﻤﻮدﯾﺎ‬‫ﻮرﻗﺔ‬‫اﻟ‬‫ﺒﯿﻀﺎء‬(‫ص‬ ‫)س‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ارﺳﻢ‬ ‫ﺛﻢ‬
٢-‫ص‬ ‫)س‬ ‫اﻟﺨﻂ‬ ‫(ﻋﻠﻰ‬ ‫م‬ ‫)ن‬ ‫اﻟﻌﻤﻮد‬ ‫ﻧﻘﯿﻢ‬(
٣-‫م‬ ‫)ا‬ ‫ﻣﺎﺋﻞ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫ﺧﻂ‬ ‫ﻧﺮﺳﻢ‬‫اﻟﻤﺮاة‬ ‫ﻋﻠﻰ‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﻀﻮﺋﻰ‬ ‫اﻟﺸﻌﺎع‬ ‫ﯾﻤﺜﻞ‬ (
‫د‬ ‫دﺑﻮﺳﯿﻦ‬ ‫ﻧﺜﺒﺖ‬ ‫و‬ ( ‫اﻟﺴﻘﻮط‬ ‫)زاوﯾﺔ‬ ‫اﻟﻌﻤﻮد‬ ‫ﻣﻊ‬ ‫زاوﯾﺔ‬ ‫ﯾﺼﻨﻊ‬١‫د‬٢
(‫م‬ ‫)ا‬ ‫اﻟﻤﺴﺘﻘﯿﻢ‬ ‫اﻟﺨﻂ‬ ‫ﻋﻠﻰ‬
٤-‫د‬ ‫اﻟﺪﺑﻮﺳﯿﻦ‬ ‫ﺻﻮرﺗﻰ‬ ‫ﻟﺘﺸﺎھﺪ‬ ‫اﻻﺧﺮ‬ ‫اﻟﺠﺎﻧﺐ‬ ‫ﻣﻦ‬ ‫اﻟﻤﺮاة‬ ‫ﻓﻰ‬ ‫اﻧﻈﺮ‬١‫د‬٢
‫د‬ ‫دﺑﻮﺳﯿﻦ‬ ‫ﻧﺜﺒﺖ‬ ‫و‬٣‫د‬٤‫اﺳﺘﻘﺎﻣﺔ‬ ‫ﻋﻠﻰ‬ ‫ﯾﻜﻮﻧﺎ‬ ‫ﺑﺤﯿﺚ‬‫د‬ ‫ﺻﻮرة‬١‫د‬٢
٥-‫د‬ ‫اﻟﺪﺑﻮﺳﯿﻦ‬ ‫ارﻓﻊ‬٣‫د‬٤‫اﺳﺘﻘﺎﻣﺘﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺪة‬ ‫و‬ ‫ﺑﻤﺴﺘﻘﯿﻢ‬ ‫ﺑﯿﻨﮭﻤﺎ‬ ‫ﺻﻞ‬ ‫ﺛﻢ‬
‫ھﺬ‬ ‫م‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ﻋﻨﺪ‬ ‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﻟﯿﻘﺎﺑﻞ‬‫ا‬‫اﻟﺨﻂ‬)‫م‬ ‫ب‬(‫اﻟﻤﻨﻌﻜﺲ‬ ‫اﻟﺸﻌﺎع‬ ‫ﯾﻤﺜﻞ‬
٦-‫اﻻﻧﻌﻜﺎس‬ ‫زاوﯾﺔ‬ ‫ھﻰ‬ ‫ﻓﺘﻜﻮن‬ ‫اﻟﻌﻤﻮد‬ ‫ﻣﻊ‬ ‫م‬ ‫ب‬ ‫ﯾﺼﻨﻌﮭﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻟﺰاوﯾﺔ‬ ‫ﻧﻘﯿﺲ‬
٧-‫اﻟﻤﻨﻘﻠﺔ‬ ‫ﺑﻮاﺳﻄﺔ‬ ‫ﻣﺮات‬ ‫ﻋﺪة‬ ‫اﻟﺴﻘﻮط‬ ‫زاوﯾﺔ‬ ‫ﻧﻐﯿﺮ‬‫ﻛﻞ‬ ‫ﻓﻰ‬ ‫و‬‫اﻻﻧﻌﻜﺎس‬ ‫زاوﯾﺔ‬ ‫ﻧﻌﯿﻦ‬ ‫ﻣﺮة‬
‫اﻟﻤﻼﺣﻈﺔ‬١-‫ﻟﮭﺎ‬ ‫ﻣﺴﺎوﯾﺔ‬ ‫ﺗﻜﻮن‬ ‫ﺑﺤﯿﺚ‬ ‫اﻟﺴﻘﻮط‬ ‫زاوﯾﺔ‬ ‫ﻟﺘﻐﯿﺮ‬ ‫ﺗﺒﻌﺎ‬ ‫اﻻﻧﻌﻜﺎس‬ ‫زاوﯾﺔ‬ ‫ﺗﺘﻐﯿﺮ‬‫داﺋﻤﺎ‬
‫اﻻﺳﺘﻨﺘﺎج‬‫ﯾﻌﺮﻓ‬ ‫ﻟﻘﺎﻧﻮﻧﯿﻦ‬ ‫اﻧﻌﻜﺎﺳﺔ‬ ‫ﻓﻰ‬ ‫اﻟﻀﻮء‬ ‫ﯾﺨﻀﻊ‬‫ﺑﺎﺳﻢ‬ ‫ﺎ‬‫اﻻ‬ ‫ﻗﺎﻧﻮﻧﺎ‬‫ﻧﻌﻜﺎس‬‫ﻓﻰ‬‫اﻟﻀﻮء‬‫و‬‫ھﻤﺎ‬:-
: ‫اﻻول‬ ‫اﻟﻘﺎﻧﻮن‬‫اﻻﻧﻌﻜﺎ‬ ‫زاوﯾﺔ‬ = ‫اﻟﺴﻘﻮط‬ ‫زاوﯾﺔ‬‫س‬
: ‫اﻟﺜﺎﻧﻰ‬ ‫اﻟﻘﺎﻧﻮن‬‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﻋﻠﻲ‬ ‫اﻟﺴﻘﻮط‬ ‫ﻧﻘﻄﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻤﻘﺎم‬ ‫اﻟﻌﻤﻮد‬ ‫و‬ ‫اﻟﻤﻨﻌﻜﺲ‬ ‫اﻟﻀﻮﺋﻰ‬ ‫اﻟﺸﻌﺎع‬ ‫و‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﻀﻮﺋﻲ‬ ‫اﻟﺸﻌﺎع‬
‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﻋﻠﻲ‬ ‫ﻋﻤﻮدي‬ ‫واﺣﺪ‬ ‫ﻣﺴﺘﻮي‬ ‫ﻓﻲ‬ ‫ﺟﻤﯿﻌﺎ‬ ‫ﺗﻘﻊ‬
(‫)ﻋﻠﻞ‬‫ﻧﻔﺴﮫ‬ ‫ﻋﻠﻲ‬ ‫ﯾﻨﻌﻜﺲ‬ ‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﻋﻠﻲ‬ ‫ﻋﻤﻮدﯾﺎ‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﻀﻮﺋﻲ‬ ‫اﻟﺸﻌﺎع‬
‫ﺗﺴﺎو‬ ‫اﻟﺴﻘﻮط‬ ‫زاوﯾﺔ‬ ‫ﻻن‬ (‫)ﺟـ‬‫ﺻﻔﺮ‬ ‫ﺗﺴﺎوي‬ ‫اﻻﻧﻌﻜﺎس‬ ‫زاوﯾﺔ‬ ‫ي‬
:‫اﻟﻤﺮاﯾﺎ‬-{‫ﻣﺤﺪﺑﺔ‬ ‫او‬ ‫}ﻣﻘﻌﺮة‬ ‫ﻛﺮﯾﺔ‬ ‫او‬ ‫ﻣﺴﺘﻮﯾﺔ‬ ‫ﺗﻜﻮن‬ ‫ﻗﺪ‬ .‫ﻟﻠﻀﻮء‬ ‫ﻋﺎﻛﺴﺔ‬ ‫أﺳﻄﺢ‬ ‫ھﻰ‬
‫ﺗﻘﺪﯾﺮﯾﺔ‬ ‫او‬ ‫ﺣﻘﯿﻘﯿﺔ‬ ‫ﻛﺎﻧﺖ‬ ‫ﺳﻮاء‬ ‫اﻟﺼﻮر‬ ‫ﺗﻜﻮﯾﻦ‬ ‫ﻓﻰ‬ ‫ھﺎﻣﺎ‬ ‫دورا‬ ‫ﻟﺔ‬ ‫اﻟﻀﻮء‬ ‫اﻧﻌﻜﺎس‬
) ‫ﻧﺸﺎط‬١‫ﺧﻮاص‬ ‫ﺑﺎﻟﺘﺠﺮﺑﺔ‬ ‫وﺿﺤﻰ‬ :(‫اﻟﻤﺴﺘﻮﯾﺔ‬ ‫ﺑﺎﻟﻤﺮآة‬ ‫اﻟﻤﺘﻜﻮﻧﺔ‬ ‫اﻟﺼﻮر‬
: ‫اﻻدوات‬‫ﻣﺴﺘﻮﯾﺔ‬ ‫ﻣﺮاة‬-‫اﻟﺤﺮف‬ ‫ﺑﻌﺾ‬ ‫ﻋﻠﯿﮭﺎ‬ ‫ﻣﻜﺘﻮب‬ ‫ﺑﻄﺎﻗﺔ‬
٢: ‫اﻟﺨﻄﻮات‬‫ﺑﺎﻟﺸﻜﻞ‬ ‫ﻛﻤﺎ‬ ‫اﻟﻤﺮاة‬ ‫اﻣﺎم‬ ‫اﻟﺒﻄﺎﻗﺔ‬ ‫ﻧﻀﻊ‬ ‫و‬ ‫راﺳﯿﺎ‬ ‫اﻟﻤﺮاة‬ ‫ﻧﺜﺒﺖ‬
‫و‬ ‫اﻟﻤﻼﺣﻈﺔ‬:‫اﻻﺳﺘﻨﺘﺎج‬-
:‫اﻟﻤﺴﺘﻮﯾﺔ‬ ‫ﺑﺎﻟﻤﺮآة‬ ‫اﻟﻤﺘﻜﻮﻧﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﺧﻮاص‬-
]١‫ﺻﻮرة‬ [‫ﺗﻘﺪﯾﺮﯾﺔ‬.]٢.‫ﺻﻮرة‬ [‫ﻣﻌﺘﺪﻟﺔ‬]٣‫ﻟﻠﺠﺴﻢ‬ ‫ﻣﺴﺎوﯾﺔ‬ [
].٤‫ﻟﻠﺠﺴﻢ‬ ‫ﺑﺎﻟﻨﺴﺒﺔ‬ ‫اﻟﻮﺿﻊ‬ ‫ﻣﻌﻜﻮﺳﺔ‬ [.
]٥‫ا‬ ‫ﺑﻌﺪ‬ [‫اﻟﺠﺴﻢ‬‫اﻟﻤﺮآة‬ ‫ﻋﻦ‬=‫ﺑﻌﺪ‬‫اﻟﺼﻮرة‬.‫اﻟﻤﺮآة‬ ‫ﻣﻦ‬
]٦‫ﻋﻠﻰ‬ ً‫ﺎ‬‫ﻋﻤﻮدﯾ‬ ‫ﯾﻜﻮن‬ ‫وﺻﻮرﺗﮫ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻮاﺻﻞ‬ ‫اﻟﻤﺴﺘﻘﯿﻢ‬ [
‫ﻟﻠﻤﺮاة‬ ‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬
‫اﻟﺤﻘﯿﻘﯿﺔ‬ ‫اﻟﺼﻮرة‬‫اﻟﺘﻘﺪﯾﺮﯾﺔ‬ ‫اﻟﺼﻮرة‬
‫ﯾﻤﻜﻦ‬ ‫اﻟﺘﻰ‬ ‫اﻟﺼﻮرة‬ ‫ھﻰ‬‫ﺣﺎﺋﻞ‬ ‫ﻋﻠﻰ‬ ‫اﺳﺘﻘﺒﻠﮭﺎ‬‫ﻻﯾﻤﻜﻦ‬ ‫اﻟﺘﻰ‬ ‫اﻟﺼﻮرة‬ ‫ھﻰ‬‫ﺣﺎﺋﻞ‬ ‫ﻋﻠﻰ‬ ‫اﺳﺘﻘﺒﻠﮭﺎ‬
‫وﺗﻨﺸﺎ‬‫اﻟﻤﻨﻌﻜﺴﺔ‬ ‫اﻷﺷﻌﺔ‬ ‫ﺗﻼﻗﻰ‬ ‫ﻧﺘﯿﺠﺔ‬‫ﻓ‬‫اﻟﻤﺮاﯾﺎ‬ ‫ﻰ‬‫وﺗﻨﺸﺎ‬‫اﻟﻤﻨﻌﻜﺴﺔ‬ ‫اﻷﺷﻌﺔ‬ ‫اﻣﺘﺪادات‬ ‫ﺗﻼﻗﻰ‬ ‫ﻧﺘﯿﺠﺔ‬‫اﻟﻤﺮاﯾﺎ‬ ‫ﻓﻰ‬.
‫داﺋﻤﺎ‬ ‫ﻣﻘﻠﻮﺑﺔ‬ ‫ﺗﻜﻮن‬ ‫ﺑﺎﻟﺘﺎﻟﻰ‬ ‫و‬‫اﻟﻤﺮاة‬ ‫اﻣﺎم‬‫داﺋﻤﺎ‬ ‫ﻣﻌﺘﺪﻟﺔ‬ ‫ﺗﻜﻮن‬ ‫ﺑﺎﻟﺘﺎﻟﻰ‬ ‫و‬‫اﻟﻤﺮاة‬ ‫ﺧﻠﻒ‬
‫اﻟﻀﻮء‬ ‫ﻓﻰ‬ ‫اﻻﻧﻌﻜﺎس‬ ‫ﻗﺎﻧﻮﻧﺎ‬

12. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٢
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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١-: ‫ﻋﻠﻞ‬‫؟‬ ‫ﻣﻌﻜﻮﺳﺔ‬ ‫اﻻﺳﻌﺎف‬ ‫ﺳﯿﺎرة‬ ‫ﻋﻠﻰ‬ ‫اﺳﻌﺎف‬ ‫ﻛﻠﻤﺔ‬ ‫ﺗﻜﺘﺐ‬
‫اﻟﺴﯿ‬ ‫ﻗﺎﺋﺪى‬ ‫ﯾﺮاھﺎ‬ ‫ﺣﺘﻰ‬‫اﻻﺳﻌﺎف‬ ‫ﻟﺴﯿﺎرة‬ ‫اﻟﻄﺮﯾﻖ‬ ‫ﺑﺎﺧﻼء‬ ‫ﻓﯿﺴﺮﻋﻮ‬ ‫ﻣﻀﺒﻮﻃﺔ‬ ‫اﻟﻤﺮاة‬ ‫ﻓﻰ‬ ‫ﺎرات‬
٢-‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻨﻈﺮ‬ ‫ﻓﺤﺺ‬ ‫اﻟﻌﯿﻮن‬ ‫ﻃﺒﯿﺐ‬ ‫ﻋﻠﻞ:ﯾﺴﺘﻄﯿﻊ‬٦‫ﺣﺠﺮة‬ ‫ﻓﻰ‬ ‫ﻣﺘﺮ‬٣‫؟‬ ‫ﻣﺘﺮ‬
‫ﺻﻮرﺗﺔ‬ ‫و‬ ‫اﻟﺠﺴﻢ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﺗﺼﺒﺢ‬ ‫ﻟﺬﻟﻚ‬ ‫اﻟﻤﺮآة‬ ‫ﻣﻦ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺑﻌﺪ‬ = ‫اﻟﻤﺮآة‬ ‫ﻋﻦ‬ ‫اﻟﺼﻮرة‬ ‫ﺑﻌﺪ‬ ‫ﻻن‬٦‫وھﻮ‬ ‫ﻣﺘﺮ‬‫ا‬‫اﻻﻧﺴﺎن‬ ‫ﻟﺮؤﯾﺔ‬ ‫اﻟﻄﺒﯿﻌﻰ‬ ‫اﻟﻤﺪى‬
٣-‫ﻣﺴﺘﻮﯾﺔ‬ ‫ﻣﺮاة‬ ‫ﺧﻼل‬ ‫ﻣﻦ‬ ‫اﻟﺼﻔﺤﺔ‬ ‫اﻟﻰ‬ ‫ﯾﻨﻈﺮون‬ ‫ھﻢ‬ ‫و‬ ‫ﺻﺤﯿﺤﺔ‬ ‫ﺑﻄﺮﯾﻘﺔ‬ ‫اﻟﻜﺘﺎﺑﺔ‬ ‫اﻟﻨﺎس‬ ‫ﻣﻦ‬ ‫اﻟﻜﺜﯿﺮ‬ ‫ﯾﺴﺘﻄﯿﻊ‬ ‫ﻻ‬ ‫ﻋﻠﻞ‬‫؟‬
‫اﻟﻮﺿﻊ‬ ‫ﻣﻌﻜﻮﺳﺔ‬ ‫ﺗﻜﻮن‬ ‫اﻟﻤﺮاة‬ ‫ﻓﻰ‬ ‫اﻟﻤﺘﻜﻮﻧﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﻻن‬
٤-‫ﺣﺎﺋﻞ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺴﺘﻮﯾﺔ‬ ‫اﻟﻤﺮاة‬ ‫ﻓﻰ‬ ‫اﻟﻤﺘﻜﻮﻧﺔ‬ ‫اﻟﺼﻮرة‬ ‫اﺳﺘﻘﺒﺎل‬ ‫ﯾﻤﻜﻦ‬ ‫ﻻ‬ ‫ﻋﻠﻞ‬‫؟‬
‫اﻟﻤﺮاة‬ ‫ﺧﻠﻒ‬ ‫ﺗﺘﻜﻮن‬ ‫ﺗﻘﺪﯾﺮﯾﺔ‬ ‫ﺻﻮرة‬ ‫ﻻﻧﮭﺎ‬‫اﻟﻤﻨﻌﻜﺴﺔ‬ ‫اﻻﺷﻌﺔ‬ ‫اﻣﺘﺪاد‬ ‫ﺗﻼﻗﻰ‬ ‫ﻧﺘﯿﺠﺔ‬
:‫اﻟﻜﺮﯾﺔ‬ ‫اﻟﻤﺮآة‬-‫ﺟﻮﻓﺎء‬ ‫ﻛﺮة‬ ‫ﺳﻄﺢ‬ ‫ﻣﻦ‬ ‫ﺟﺰء‬ ‫اﻟﻌﺎﻛﺲ‬ ‫ﺳﻄﺤﮭﺎ‬ ‫ﻣﺮآة‬ ‫ھﻰ‬‫و‬‫ﻗ‬‫ﺪ‬‫ﺗﻜﻮن‬‫ﻣﺤﺪﺑﺔ‬‫أو‬‫ﻣﻘﻌﺮة‬
: ‫اﻟﻜﺮﯾﺔ‬ ‫اﻟﻤﺮاﯾﺎ‬ ‫أﻧﻮاع‬
]١(‫)ﻣﺠﻤﻌﺔ‬ ‫ﻣﻘﻌﺮة‬ ‫ﻣﺮآة‬ []٢(‫)ﻣﻔﺮﻗﺔ‬ ‫ﻣﺤﺪﺑﺔ‬ ‫ﻣﺮآة‬ [
‫ﺳﻄﺤﮭﺎ‬‫ﻟﻠﻜﺮة‬ ‫اﻟﺪاﺧﻠﻰ‬ ‫اﻟﺴﻄﺢ‬ ‫ھﻮ‬ ‫اﻟﻌﺎﻛﺲ‬.
‫ا‬ ‫اﻟﺴﻄﺢ‬ ‫ھﻮ‬ ‫اﻟﻌﺎﻛﺲ‬ ‫ﺳﻄﺤﮭﺎ‬‫ﻟﻠﻜﺮة‬ ‫ﻟﺨﺎرﺟﻰ‬
‫ﻋﻠﯿﮭﺎ‬ ‫اﻟﺴﺎﻗﻄﺔ‬ ‫اﻻﺷﻌﺔ‬ ‫ﺗﺠﻤﻊ‬ ‫ﻻﻧﮭﺎ‬ ‫ﻻﻣﺔ‬ ‫او‬ ‫ﻣﺠﻤﻌﺔ‬‫ﻋﻠﯿﮭﺎ‬ ‫اﻟﺴﺎﻗﻄﺔ‬ ‫اﻻﺷﻌﺔ‬ ‫ﺗﺠﻤﻊ‬ ‫ﻻﻧﮭﺎ‬ ‫ﻣﻔﺮﻗﺔ‬
‫؟‬ ‫ﻛﺮﯾﺔ‬ ‫ﻣﺮاة‬ ‫اﻟﻔﻀﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻤﺼﻨﻮﻋﺔ‬ ‫اﻟﻤﻌﻠﻘﺔ‬ ‫ﺗﻌﺘﺒﺮ‬ ‫ﻋﻠﻞ‬‫وﺟﮭﮭﺎ‬‫اﻟﺪاﺧﻠﻰ‬‫ﻛ‬ ‫ﯾﻌﻤﻞ‬‫وﺟﮭﮭﺎ‬ ‫و‬ ‫ﻣﻘﻌﺮة‬ ‫ﻤﺮاة‬‫اﻟﺨﺎرﺟﻰ‬‫ﻛ‬‫ﻣﺤﺪﺑﺔ‬ ‫ﻤﺮاة‬
‫اﻟﻨﻈﺮ‬ ‫ﺑﻤﺠﺮد‬ ‫اﻟﺜﻼﺛﺔ‬ ‫اﻟﻤﺮاﯾﺎ‬ ‫اﻧﻮاع‬ ‫ﺑﯿﻦ‬ ‫ﻧﻔﺮق‬ ‫ﻛﯿﻒ‬
:‫اﻟﻜﺮﯾﺔ‬ ‫ﻟﻠﻤﺮآة‬ ‫اﻟﺘﻘﺪﯾﺮﯾﺔ‬ ‫واﻟﺒﺆرة‬ ‫اﻟﺤﻘﯿﻘﯿﺔ‬ ‫اﻟﺒﺆرة‬-
١-(‫)م‬ ‫اﻟﻤﺮآة‬ ‫ﺗﻜﻮر‬ ‫ﻣﺮﻛﺰ‬‫ﻣﻨﮭﺎ‬ ً‫ا‬‫ﺟﺰء‬ ‫اﻟﻤﺮآة‬ ‫ﺗﻌﺘﺒﺮ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻜﺮة‬ ‫ﻣﺮﻛﺰ‬ ‫ھﻮ‬
٢-(‫)ق‬ ‫اﻟﻤﺮآة‬ ‫ﻗﻄﺐ‬‫ﻟﻠﻤﺮآة‬ ‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫ﺗﺘﻮﺳﻂ‬ ‫وھﻤﯿﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ھﻰ‬
٣-‫ﻧﺼﻒ‬‫)ﻧﻖ‬ ‫اﻟﻤﺮآة‬ ‫ﺗﻜﻮر‬ ‫ﻗﻄﺮ‬(
‫ﻗﻄ‬ ‫ﻧﺼﻒ‬ ‫ھﻮ‬‫اﻟﻜﺮة‬ ‫ﺮ‬‫ﻣﻨﮭﺎ‬ ‫ﺟﺰء‬ ‫اﻟﻤﺮاة‬ ‫ﺗﻌﺘﺒﺮ‬ ‫اﻟﺘﻰ‬
‫ھﻮ‬ ‫او‬‫ﺳﻄﺤﮭﺎ‬ ‫ﻋﻠﻰ‬ ‫ﻧﻘﻄﺔ‬ ‫وأى‬ ‫اﻟﻤﺮآة‬ ‫ﺗﻜﻮر‬ ‫ﻣﺮﻛﺰ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬
٤‫ﻟﻠﻤﺮآة‬ ‫اﻷﺻﻠﻰ‬ ‫اﻟﻤﺤﻮر‬‫وﻗﻄﺒﮭﺎ‬ ‫اﻟﻤﺮآة‬ ‫ﺗﻜﻮر‬ ‫ﺑﻤﺮﻛﺰ‬ ‫اﻟﻤﺎر‬ ‫اﻟﻤﺴﺘﻘﯿﻢ‬ ‫ھﻮ‬
٥-‫ﻟﻠﻤﺮآة‬ ‫اﻟﺜﺎﻧﻮى‬ ‫اﻟﻤﺤﻮر‬‫ﻗﻄﺒﮭﺎ‬ ‫ﻋﺪا‬ ‫ﻣﺎ‬ ‫ﺳﻄﺤﮭﺎ‬ ‫ﻋﻠﻲ‬ ‫ﻧﻘﻄﺔ‬ ‫أي‬ ‫و‬ ‫اﻟﻤﺮآة‬ ‫ﺗﻜﻮر‬ ‫ﺑﻤﺮﻛﺰ‬ ‫ﯾﻤﺮ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫أي‬ ‫ھﻮ‬
٦-‫اﻟ‬‫ﺒ‬‫ﺆرة‬‫ﻟ‬ ‫اﻻﺻﻠﯿﺔ‬(‫)ب‬ ‫ﻠﻤﺮآة‬‫اﻣﺘﺪادھﺎ‬ ‫أو‬ ‫ھﻰ‬ ‫اﻟﻤﻨﻌﻜﺴﺔ‬ ‫اﻷﺷﻌﺔ‬ ‫ﺗﻼﻗﻰ‬ ‫ﻧﻘﻄﺔ‬ ‫ھﻰ‬
٧-‫ﻟﻠﻤﺮآة‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬)(‫ع‬‫اﻟﻤﺮآة‬ ‫وﻗﻄﺐ‬ ‫اﻻﺻﻠﯿﺔ‬ ‫اﻟﺒﺆرة‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﻮ‬
‫اﻟﺤﻘﯿﻘﯿﺔ‬ ‫اﻟﺒﺆرة‬‫اﻟﺘﻘﺪﯾﺮﯾﺔ‬ ‫اﻟﺒﺆرة‬
‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮاة‬ ‫اﻟﻤﻨﻌﻜﺴﺔ.ﻓﻰ‬ ‫اﻷﺷﻌﺔ‬ ‫ﺗﻼﻗﻰ‬ ‫ﻧﻘﻄﺔ‬ ‫ھﻰ‬‫اﻟﻤﺤﺪﺑﺔ‬ ‫اﻟﻤﺮاة‬ ‫ﻓﻰ‬ ‫اﻟﻤﻨﻌﻜﺴﺔ‬ ‫اﻷﺷﻌﺔ‬ ‫اﻣﺘﺪاد‬ ‫ﺗﻼﻗﻰ‬ ‫ﻧﻘﻄﺔ‬ ‫ھﻰ‬
‫أﻣﺎم‬ ‫ﺗﻘﻊ‬ ‫و‬‫ﻓﻰ‬ ‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬.‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮآة‬‫ﺧﻠﻒ‬ ‫ﺗﻘﻊ‬‫ﻓ‬ ‫اﻟﻌﺎﻛﺲ‬ ‫اﻟﺴﻄﺢ‬‫ﻰ‬. ‫اﻟﻤﺤﺪﺑﺔ‬ ‫اﻟﻤﺮآة‬
.‫ﺣﺎﺋﻞ‬ ‫ﻋﻠﻰ‬ ‫اﺳﺘﻘﺒﺎﻟﮭﺎ‬ ‫ﯾﻤﻜﻦ‬ ‫و‬.‫ﺣﺎﺋﻞ‬ ‫ﻋﻠﻰ‬ ‫اﺳﺘﻘﺒﺎﻟﮭﺎ‬ ‫ﯾﻤﻜﻦ‬ ‫ﻻ‬
‫ب‬
‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬
‫ب‬
‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬

13. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٣
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫ﺗﻌﯿﯿﻦ‬ ‫ﯾﻤﻜﻦ‬ ‫ﻛﯿﻒ‬ ‫ﺑﺎﻟﺘﺠﺮﺑﺔ‬ ‫وﺿﺤﻰ‬‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬: ‫ﻣﻘﻌﺮة‬ ‫ﻟﻤﺮاة‬
‫اﻻدوات‬‫ﻣﻘﻌﺮة‬ ‫ﻣﺮاة‬-‫ﺣﺎﺋﻞ‬
‫اﻟﺨﻄﻮات‬١-‫ﻣﻮا‬ ‫ﻣﻘﻌﺮة‬ ‫ﻣﺮاة‬ ‫ﻧﻀﻊ‬‫ﺟﺪا‬ ‫ﺑﻌﯿﺪ‬ ‫ﺟﺴﻢ‬ ‫او‬ ‫اﻟﺸﻤﺲ‬ ‫ﻻﺷﻌﺔ‬ ‫ﺟﮭﺔ‬
٢-‫ﻧﺤﺮك‬‫اﻟ‬‫ﺤﺎﺋﻞ‬‫ﺑﻌﺪا‬ ‫و‬ ‫ﻗﺮﺑﺎ‬‫ﻋﻠﻰ‬ ‫ﻧﺤﺼﻞ‬ ‫ﺣﺘﻰ‬ ‫ﻟﻠﻤﺮاة‬ ‫اﻟﻌﻜﺲ‬ ‫اﻟﺴﻄﺢ‬ ‫اﻣﺎم‬‫أ‬‫وﺿﺢ‬‫ﻣﻀﯿﺌﺔ‬ ‫ﻧﻘﻄﺔ‬
‫ﻋﻠﯿﺔ‬‫ﺑﺆرة‬ ‫ھﻰ‬ ‫ﻓﺘﻜﻮن‬‫اﻟﻤﺮاة‬
‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻧﻘﯿﺲ‬‫اﻟﺤﺎﺋﻞ‬ ‫و‬ ‫اﻟﻤﺮاة‬‫اﻟﻤﻘﻌﺮة‬ ‫ﻟﻠﻤﺮاة‬ (‫)ع‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﺬة‬ ‫ﻓﺘﻜﻮن‬
‫و‬ ‫اﻟﻤﻼﺣﻈﺔ‬: ‫اﻻﺳﺘﻨﺘﺎج‬
١-‫ھﻰ‬ ‫ﻟﻠﻤﺮاة‬ ‫اﻻﺻﻠﯿﺔ‬ ‫اﻟﺒﺆرة‬‫اﻟﻤﻨﻌﻜﺴﺔ‬ ‫اﻷﺷﻌﺔ‬ ‫ﺗﻼﻗﻰ‬ ‫ﻧﻘﻄﺔ‬‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮاة‬ ‫ﻋﻠﻰ‬
٢-‫اﻟﻤﺮاة‬ ‫ﻗﻄﺐ‬ ‫و‬ ‫اﻻﺻﻠﯿﺔ‬ ‫اﻟﺒﺆرة‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﻮ‬ ‫ﻟﻠﻤﺮاة‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬
‫ﺗﻜﻮر‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻌﻼﻗﺔ‬‫اﻟﻤﺮاة‬‫وﺑﻌﺪ‬‫ھﺎ‬:‫اﻟﺒﺆرى‬-
‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫ﺿﻌﻒ‬ = ‫اﻟﺘﻜﻮر‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬= ‫ﻧﻖ‬ ‫او‬٢‫ع‬
‫ﻣﺴﺎر‬‫ات‬‫ﻷ‬‫ﻋﻠﻰ‬ ‫اﻟﺴﺎﻗﻄﺔ‬ ‫ﺷﻌﺔ‬‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮاة‬:-
١-‫اﻷﺻﻠﻰ‬ ‫ﻟﻠﻤﺤﻮر‬ ‫ﻣﻮازى‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﺸﻌﺎع‬٢-‫ﺑﺎﻟﺒﺆرة‬ ً‫ا‬‫ﻣﺎر‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﺸﻌﺎع‬٣-‫اﻟﺘﻜﻮر‬ ‫ﺑﻤﺮﻛﺰ‬ ً‫ا‬‫ﻣﺎر‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﺸﻌﺎع‬
‫ﺑﺎﻟﺒﺆرة‬ ً‫ا‬‫ﻣﺎر‬ ‫ﯾﻨﻌﻜﺲ‬‫اﻷﺻﻠﻰ‬ ‫ﻟﻠﻤﺤﻮر‬ ً‫ﺎ‬‫ﻣﻮازﯾ‬ ‫ﯾﻨﻌﻜﺲ‬‫ﻧﻔﺴﮫ‬ ‫ﻋﻠﻰ‬ ‫ﯾﻨﻌﻜﺲ‬
‫اﻟﺠﺴﻢ‬ ‫ﻣﻮﺿﻊ‬‫اﻟﺮﺳﻢ‬‫اﻟﺼﻮرة‬ ‫ﺧﻮاص‬
]١[‫اﻟﺠ‬‫ﺟﺪا‬ ‫ﺑﻌﯿﺪ‬ ‫ﺴﻢ‬
‫ﻣﻮازﯾﺔ‬ ‫و‬ ‫ﻣﺘﻮازﯾﺔ‬ ‫اﻻﺷﻌﺔ‬ ‫ﺗﺴﻘﻂ‬
‫اﻻﺻﻠﻰ‬ ‫ﻟﻠﻤﺤﻮر‬
‫ﺟﺪا‬ ‫ﺻﻐﯿﺮة‬ ‫ﺣﻘﯿﻘﺔ‬ ‫ﺻﻮرة‬‫ﻋﻦ‬ ‫ﻋﺒﺎرة‬
(‫)ب‬ ‫اﻟﺒﺆرة‬ ‫ﻋﻨﺪ‬ ‫ﻣﻀﯿﺌﺔ‬ ‫ﻧﻘﻄﺔ‬
]٢[‫ﻣﻦ‬ ‫أﻛﺒﺮ‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﺴﻢ‬
‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫ﺿﻌﻒ‬
‫ﻣﻦ‬ ‫اﺑﻌﺪ‬‫اﻟﺘﻜﻮر‬ ‫ﻣﺮﻛﺰ‬(‫)م‬
‫ﺻﻮرة‬‫ﻣﺼﻐﺮة‬ / ‫ﻣﻘﻠﻮﺑﺔ‬ / ‫ﺣﻘﯿﻘﯿﺔ‬
‫اﻟﺒﺆرة‬ ‫ﺑﯿﻦ‬(‫)ب‬‫اﻟﺘﻜﻮر‬ ‫وﻣﺮﻛﺰ‬(‫)م‬
]٣[‫ﯾﺴﺎوى‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﺴﻢ‬
‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫ﺿﻌﻒ‬
‫ﻋﻨﺪ‬‫اﻟﺘﻜﻮر‬ ‫ﻣﺮﻛﺰ‬)‫م‬(
‫ﺻﻮرة‬‫ﻣﺴﺎوﯾﺔ‬ / ‫ﻣﻘﻠﻮﺑﺔ‬ / ‫ﺣﻘﯿﻘﯿﺔ‬
‫ﻋﻨﺪ‬ ‫ﻟﻠﺠﺴﻢ‬‫اﻟﺘﻜﻮر‬ ‫ﻣﺮﻛﺰ‬)‫م‬(
‫ا‬ ‫اﻟﺼﻮرة‬ ‫ﺧﻮاص‬‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮاة‬ ‫ﺑﻮاﺳﻄﺔ‬ ‫ﻟﻤﺘﻜﻮﻧﺔ‬

14. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٤
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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]٤[‫ﻣﻦ‬ ‫أﻛﺒﺮ‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﺴﻢ‬
‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬(‫)ب‬
‫اﻟﺒﻌﺪ‬ ‫ﺿﻌﻒ‬ ‫ﻣﻦ‬ ‫وأﺻﻐﺮ‬
.‫اﻟﺒﺆرى‬
‫ﺻﻮرة‬‫ﻣﻜﺒﺮة‬ / ‫ﻣﻘﻠﻮﺑﺔ‬ / ‫ﺣﻘﯿﻘﯿﺔ‬
‫ﻣﺴﺎﻓﺔ‬ ‫ﻋﻠﻰ‬
‫ﻣﺮﻛﺰ‬ ‫ﻣﻦ‬ ‫أﺑﻌﺪ‬‫اﻟﺘﻜﻮر‬)‫م‬(
]٥[‫ﻣﻦ‬ ‫أﻗﻞ‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﺴﻢ‬
‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬
‫ﺻﻮرة‬‫ﻣﻜﺒﺮة‬ / ‫ﻣﻌﺘﺪﻟﺔ‬ / ‫ﺗﻘﺪﯾﺮﯾﺔ‬
‫ﺧﻠﻒ‬ ‫ﺗﺘﻜﻮن‬‫اﻟﻤﺮآة‬
: ‫ﻣﻠﺤﻮﻇﺔ‬‫؟‬ ‫ﺻﻮرة‬ ‫ﻟﺔ‬ ‫ﺗﺘﻜﻮن‬ ‫ﻻ‬ ‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮاة‬ ‫ﺑﺆرة‬ ‫ﻋﻨﺪ‬ ‫ﺟﺴﻢ‬ ‫وﺿﻊ‬ ‫ﻋﻨﺪ‬
‫ﻻﻧﮭﺎﯾﺔ‬ ‫ﻣﺎ‬ ‫اﻟﻰ‬ ‫ﻣﺘﻮازﯾﺔ‬ ‫ﺗﻨﻌﻜﺲ‬ ‫اﻻﺷﻌﺔ‬ ‫ﻻن‬
‫ﺑﺎﻟﺘﺠ‬ ‫وﺿﺤﻰ‬‫ﺗﻌﯿﯿﻦ‬ ‫ﯾﻤﻜﻦ‬ ‫ﻛﯿﻒ‬ ‫ﺮﺑﺔ‬‫ا‬ ‫ﺗﻜﻮر‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬‫ﻟﻤﺮاة‬‫اﻟ‬: ‫ﻤﻘﻌﺮة‬( ‫ﻧﻖ‬ )
‫اﻻدوات‬:١-‫ﻣﻘﻌﺮة‬ ‫ﻣﺮاة‬
٢-‫ﻟﻠﻤﺮاة‬ ‫ﺣﺎﻣﻞ‬
٣-‫ﺛﻘﺐ‬ ‫ﺑﺔ‬ ‫ﺿﻮﺋﻰ‬ ‫ﺻﻨﺪوق‬
٤-‫ﻣﺴﻄﺮة‬
: ‫اﻟﺨﻄﻮات‬١-‫اﻟﺜﻘﺐ‬ ‫اﻟﻀﻮﺋﻰ‬ ‫اﻟﻤﺼﺪر‬ ‫اﻣﺎم‬ ‫اﻟﺤﺎﻣﻞ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﺮاة‬ ‫ﻧﻀﻊ‬
٢-‫ﻣﻦ‬ ‫ﺑﻌﺪا‬ ‫و‬ ‫ﻗﺮﺑﺎ‬ ‫اﻟﻤﺮاة‬ ‫ﻧﺤﺮك‬‫وﺑﺠﻮارة‬ ‫ﻟﻠﺜﻘﺐ‬ ‫ﻣﺴﺎوﯾﺔ‬ ‫ﺻﻮرة‬ ‫ﻋﻠﻰ‬ ‫ﻧﺤﺼﻞ‬ ‫ﺣﺘﻰ‬
٣-‫اﻟﺜﻘﺐ‬ ‫و‬ ‫اﻟﻤﺮاة‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻧﻘﯿﺲ‬
‫اﻻﺳﺘﻨﺘﺎج‬ ‫و‬ ‫اﻟﻤﻼﺣﻈﺔ‬
‫ان‬‫ا‬ ‫ﺗﻜﻮر‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬‫ﻟﻤﺮاة‬‫اﻟ‬‫ﻤﻘﻌﺮة‬( ‫ﻧﻖ‬ )‫ھﻰ‬ ‫اﻟﺜﻘﺐ‬ ‫و‬ ‫اﻟﻤﺮاة‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﻮ‬
‫اﺳﺘﺨﺪاﻣﺎت‬‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮاة‬‫؟‬
١-‫اﻟﻀﻮء‬ ‫ﻟﻌﻜﺲ‬ ‫اﻟﺠﯿﺐ‬ ‫ﻛﺸﺎف‬ ‫ﻓﻰ‬ ‫ﺗﺴﺘﺨﺪم‬
٢-‫اﻟﻤﺼﺎﺑﯿ‬ ‫ﻓﻰ‬ ‫ﺗﺴﺘﺨﺪم‬‫اﻟﻀﻮء‬ ‫ﻟﻌﻜﺲ‬ ‫ﻟﻠﺴﯿﺎرات‬ ‫اﻻﻣﺎﻣﯿﺔ‬ ‫ﺢ‬
٣-‫ﻓﻰ‬ ‫ﺗﺴﺘﺨﺪم‬‫اﻟﺴﻔﻦ‬ ‫ﻻرﺷﺎد‬ ‫اﻟﻤﻮاﻧﻰ‬ ‫ﻓﻰ‬ ‫اﻟﺒﺤﺮﯾﺔ‬ ‫اﻟﻔﻨﺎرات‬
٤-‫اﻟﻄﺎﺋﺮات‬ ‫ﻻرﺷﺎد‬ ‫اﻟﻄﺎﺋﺮات‬ ‫ھﺒﻮط‬ ‫ﺑﻤﻤﺮ‬ ‫اﻟﻤﻮﺟﻮدة‬ ‫اﻟﻜﺸﺎﻓﺎت‬ ‫ﻓﻰ‬ ‫ﺗﺴﺘﺨﺪم‬
٥-‫ﻓﻰ‬ ‫ﺗﺴﺘﺨﺪم‬‫ﻣﻜﺒﺮا‬ ‫ﻓﯿﮭﺎ‬ ‫اﻟﻮﺟﺔ‬ ‫ﯾﺮى‬ ‫ﺣﯿﺚ‬ ‫اﻟﺬﻗﻦ‬ ‫ﺣﻼﻗﺔ‬
‫ﻓﻰ‬ ‫اﻟﻤﺘﻜﻮﻧﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﺧﻮاص‬:‫اﻟﻤﺤﺪﺑﺔ‬ ‫اﻟﻤﺮآة‬
‫ﻓﻰ‬ ‫اﻟﺼﻮرة‬‫اﻟﻤﺮاة‬‫اﻟﻤﺤﺪﺑﺔ‬‫ﺗﻜﻮن‬‫ﺻﻮرة‬ ‫داﺋﻤﺎ‬‫ﻣﻌﺘﺪﻟﺔ‬ / ‫ﺗﻘﺪﯾﺮﯾﺔ‬/‫ﻣﺼﻐﺮة‬
‫اﻟﻤﺮاة‬ ‫ﻋﻦ‬ ‫اﻟﺠﺴﻢ‬ ‫ﺑﻌﺪ‬ ‫ﻛﺎن‬ ‫ﻣﮭﻤﺎ‬
‫اﺳﺘﺨﺪاﻣﺎت‬‫اﻟﻤ‬ ‫اﻟﻤﺮاة‬‫؟‬ ‫ﺤﺪﺑﺔ‬
‫؟‬ ‫اﻟﺴﯿﺎرة‬ ‫ﺳﺎﺋﻖ‬ ‫ﯾﺴﺎر‬ ‫ﻋﻠﻰ‬ ‫ﻣﺤﺪﺑﺔ‬ ‫ﻣﺮاة‬ ‫ﺗﺴﺘﺨﺪم‬ ‫ﻋﻠﻞ‬
‫ﻣﺼﻐ‬ ‫ﻣﻌﺘﺪﻟﺔ‬ ‫ﺗﻘﺪﯾﺮﯾﺔ‬ ‫ﺻﻮرة‬ ‫ﺗﻜﻮن‬ ‫ﺣﺘﻰ‬‫اﻟﺴﺎﺋﻖ‬ ‫ﺧﻠﻒ‬ ‫ﻟﻠﻄﺮﯾﻖ‬ ‫ﺮة‬‫ﻛﺸﻒ‬ ‫ﻋﻠﻰ‬ ‫ﻓﯿﺴﺎﻋﺪ‬‫اﻟﻄﺮﯾﻖ‬‫ﺧﻠﻔﺔ‬
‫اﻟﻤﺮاﯾﺎ‬ ‫ﻋﻠﻰ‬ ‫ﻣﺴﺎﺋﻞ‬
١-‫ﻃﻮﻟﺔ‬ ‫ﺟﺴﻢ‬٥‫ﻣﺴﺎﻓﺔ‬ ‫ﻋﻠﻰ‬ ‫وﺿﻊ‬ ‫ﺳﻢ‬٦‫اﻟﺒﺆرى‬ ‫ﺑﻌﺪھﺎ‬ ‫ﻣﻘﻌﺮة‬ ‫ﻣﺮاة‬ ‫ﻣﻦ‬ ‫ﺳﻢ‬٣‫ﺳﻢ‬
‫ﺑﺎﻟﻤﺮاة‬ ‫اﻟﻤﺘﻜﻮﻧﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﺧﻮاص‬ ‫ﺑﺎﻟﺮﺳﻢ‬ ‫وﺿﺤﻰ‬‫اﻟﺼﻮرة‬ ‫ﻃﻮل‬ ‫ﻣﺎ‬ ‫و‬

15. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٥
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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٢-‫ﻣﺴﺎﻓﺔ‬ ‫ﻋﻠﻰ‬ ‫ﺟﺴﻢ‬ ‫وﺿﻊ‬١٥‫ﻛﺮ‬ ‫ﻣﺮاة‬ ‫ﻣﻦ‬ ‫ﺳﻢ‬‫اﻟﺼﻮرة‬ ‫ﻃﻮل‬ = ‫اﻟﺠﺴﻢ‬ ‫ﻃﻮل‬ ‫ﻛﺎن‬ ‫و‬ ‫ﺣﺎﺋﻞ‬ ‫ﻋﻠﻰ‬ ‫ﺻﻮرة‬ ‫ﻟﺔ‬ ‫ﻓﺘﻜﻮﻧﺖ‬ ‫ﯾﺔ‬
‫اﻟﻤﺮاة‬ ‫ﻧﻮع‬ ‫ﻣﺎ‬–‫ﻟﻠﻤﺮاة‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫اﺣﺴﺒﻰ‬-‫ﺑﺎﻟﻤﺮاة‬ ‫اﻟﻤﺘﻜﻮﻧﺔ‬ ‫اﻟﺼﻮرة‬ ‫ﺧﻮاص‬ ‫و‬
٣-‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫ﺟﺴﻢ‬ ‫وﺿﻊ‬٨‫ﻣﺼﻐﺮة‬ ‫ﻣﻘﻠﻮﺑﺔ‬ ‫ﺣﻘﯿﻘﯿﺔ‬ ‫ﺻﻮرة‬ ‫ﻟﺔ‬ ‫ﻓﺘﻜﻮﻧﺖ‬ ‫ﻣﺮاة‬ ‫ﻗﻄﺐ‬ ‫ﻣﻦ‬ ‫ﺳﻢ‬
‫اﻟﺠﺴﻢ‬ ‫ﺗﺤﺮك‬ ‫واذا‬٢‫ﺻﻮر‬ ‫ﻟﺔ‬ ‫ﻓﺘﻜﻮﻧﺖ‬ ‫اﻟﻤﺮاة‬ ‫ﺟﮭﺔ‬ ‫ﺳﻢ‬‫ﻟﻠﺠﺴﻢ‬ ‫ﻣﺴﺎوﯾﺔ‬ ‫ة‬
‫اﻟﻤﺮاة‬ ‫ﻧﻮع‬ ‫ﻣﺎ‬–‫اﻟﺒﺆرى‬ ‫ﺑﻌﺪھﺎ‬ ‫ﻣﺎ‬–‫اﻟﺜﺎﻧﯿﺔ‬ ‫و‬ ‫اﻻوﻟﻰ‬ ‫اﻟﺼﻮرة‬ ‫ارﺳﻤﻰ‬
: ‫اﻟﻌﺪﺳﺎت‬-‫ﻣﺴﺘﻮى‬ ‫وآﺧﺮ‬ ‫ﻛﺮى‬ ‫ﺳﻄﺢ‬ ‫أو‬ ‫ﻛﺮﯾﺎن‬ ‫ﺳﻄﺤﺎن‬ ‫ﯾﺤﺪه‬ ‫ﻟﻠﻀﻮء‬ ‫ﻛﺎﺳﺮ‬ ‫ﺷﻔﺎف‬ ‫وﺳﻂ‬ ‫ھﻰ‬
‫اﻟﻌﺪﺳﺎت‬ ‫اﺳﺴﺘﺨﺪام‬ ‫و‬ ‫اھﻤﯿﺔ‬:
١-‫اﻟﻨﻈﺎرات‬ ‫ﻓﻰ‬ ‫ﺗﺴﺘﺨﺪم‬‫ﺗﺴﺘﺨﺪم‬ ‫اﻟﺘﻰ‬ ‫اﻟﻄﺒﯿﺔ‬‫ﻟﻠﻤﺸﻰ‬ ‫او‬ ‫ﻟﻠﻘﺮاءة‬
٢-‫اﻟﺴﺎﻋﺎت‬ ‫اﺻﻼح‬ ‫ﻓﻰ‬ ‫ﺗﺴﺘﺨﺪم‬‫ﻓﯿﮭﺎ‬ ‫اﻟﺪﻗﯿﻘﺔ‬ ‫اﻻﺟﺰاء‬ ‫ﻟﺮؤﯾﺔ‬
٣-‫ﻓﻰ‬ ‫ﺗﺴﺘﺨﺪم‬‫اﻟﺤﺮوب‬ ‫ﻓﻰ‬ ‫اﻟﻤﺴﺘﺨﺪﻣﺔ‬ ‫اﻟﻤﻨﺎﻇﯿﺮ‬
:‫اﻟﻌﺪﺳﺎت‬ ‫أﻧﻮاع‬-
]١(‫)ﻣﺠﻤﻌﺔ‬ ‫ﻣﺤﺪﺑﺔ‬ ‫ﻋﺪﺳﺔ‬ []٢(‫)ﻣﻔﺮﻗﺔ‬ ‫ﻣﻘﻌﺮة‬ ‫ﻋﺪﺳﺔ‬ [
‫ﺳﻤﯿﻜﺔ‬‫ﻋﻨﺪ‬‫اﻟ‬‫ﻤﻨﺘﺼﻒ‬‫ﻋﻨﺪ‬ ‫ورﻗﯿﻘﺔ‬‫اﻟ‬‫ﺤﺎﻓﮫ‬‫رﻗﯿﻘﺔ‬‫ﻋﻨﺪ‬‫اﻟ‬‫ﻤﻨﺘﺼﻒ‬‫و‬‫ﺳﻤﯿﻜﺔ‬‫ﻋﻨﺪ‬‫اﻟ‬‫ﺤﺎﻓﮫ‬.
‫ﻻﻧﮭﺎ‬ ‫اﻟﻼﻣﺔ‬ ‫ﺑﺎﻟﻌﺪﺳﺔ‬ ‫ﺗﺴﻤﻰ‬‫اﻷﺷﻌﺔ‬ ‫ﺗﺠﻤﻊ‬‫اﻟﺴﺎ‬‫ﻗﻄ‬‫ﺔ‬‫ﻣﺘﻮازﯾﺔ‬ ‫ﻋﻠﯿﮭﺎ‬‫ﺗﻔﺮق‬ ‫ﻻﻧﮭﺎ‬ ‫اﻟﻤﻔﺮﻗﺔ‬ ‫ﺑﺎﻟﻌﺪﺳﺔ‬ ‫ﺗﺴﻤﻰ‬‫اﻷﺷﻌﺔ‬‫اﻟﺴﺎ‬‫ﻗﻄ‬‫ﺔ‬‫ﻣﺘﻮازﯾﺔ‬ ‫ﻋﻠﯿﮭﺎ‬
‫ﺣﻘﯿﻘﯿﺔ‬ ‫اﻻﺻﻠﯿﺔ‬ ‫ﺑﺆرﺗﮭﺎ‬‫ﺗﻘﺪﯾﺮﯾﺔ‬ ‫اﻻﺻﻠﯿﺔ‬ ‫ﺑﺆرﺗﮭﺎ‬
‫ﺣﻘﯿﻘﯿﺔ‬ ‫ﺗﻜﻮن‬ ‫ﺗﻜﻮﻧﮭﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻟﺼﻮر‬ ‫اﻏﻠﺐ‬
‫ﺗﻘﺪﯾﺮﯾﺔ‬ ‫ﺗﻜﻮﻧﮭﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻟﺼﻮر‬ ‫ﻛﻞ‬
‫اﻟﻤﻔﮭﻮم‬‫ﺗﻌﺮﯾﻔﮫ‬
(‫)م‬ ‫اﻟﻌﺪﺳﺔ‬ ‫وﺟﮫ‬ ‫ﺗﻜﻮر‬ ‫ﻣﺮﻛﺰ‬‫ھﻮ‬‫اﻟﻜﺮة‬ ‫ﻣﺮﻛﺰ‬‫ﯾﻌﺘﺒﺮ‬ ‫اﻟﺬى‬.‫ﻣﻨﮭﺎ‬ ً‫ا‬‫ﺟﺰء‬ ‫اﻟﻮﺟﮫ‬ ‫ھﺬا‬
‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻷﺻﻠﻰ‬ ‫اﻟﻤﺤﻮر‬)‫م‬ ‫م‬(‫ھﻮ‬.‫اﻟﻌﺪﺳﺔ‬ ‫وﺟﮭﻰ‬ ‫ﺗﻜﻮر‬ ‫ﺑﻤﺮﻛﺰى‬ ‫اﻟﻤﺎر‬ ‫اﻟﻤﺴﺘﻘﯿﻢ‬
‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺒﺼﺮى‬ ‫اﻟﻤﺮﻛﺰ‬)‫ص‬(‫ھﻮ‬.‫اﻷﺻﻠﻰ‬ ‫اﻟﻤﺤﻮر‬ ‫ﻋﻠﻰ‬ ‫ﺗﻘﻊ‬ ‫اﻟﻌﺪﺳﺔ‬ ‫ﺑﺎﻃﻦ‬ ‫ﻓﻰ‬ ‫وھﻤﯿﺔ‬ ‫ﻧﻘﻄﺔ‬‫وﺟﮭﯿﮭﺎ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻣﻨﺘﺼﻒ‬ ‫ﻓﻰ‬
‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺜﺎﻧﻮى‬ ‫اﻟﻤﺤﻮر‬‫ھﻮ‬.‫اﻷﺻﻠﻰ‬ ‫ﻣﺤﻮرھﺎ‬ ‫ﻏﯿﺮ‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺒﺼﺮى‬ ‫ﺑﺎﻟﻤﺮﻛﺰ‬ ‫ﯾﻤﺮ‬ ‫ﻣﺴﺘﻘﯿﻢ‬ ‫أى‬
‫اﻟ‬‫ﺒﺆرة‬‫ﻟ‬ ‫اﻻﺻﻠﯿﺔ‬(‫)ب‬ ‫ﻠﻌﺪﺳﺔ‬‫ﻧﻘﻄﺔ‬ ‫ھﻰ‬ ‫ن‬‫اﻷﺷﻌﺔ‬ ‫ﺗﻼﻗﻰ‬‫اﻟﻤﻨﻜﺴﺮة‬‫ھﻰ‬.‫اﻣﺘﺪادھﺎ‬ ‫أو‬
(‫)ع‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬‫ھﻮ‬‫اﻟﺒ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬.‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺒﺼﺮى‬ ‫واﻟﻤﺮﻛﺰ‬ ‫اﻷﺻﻠﯿﺔ‬ ‫ﺆرة‬
‫اﻟﻌﺪﺳﺔ‬ ‫وﺟﺔ‬ ‫ﺗﻜﻮر‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬)‫ﻧﻖ‬(‫ﻣﻨﮭﺎ‬ ‫ﺟﺰءا‬ ‫اﻟﻮﺟﺔ‬ ‫ھﺬا‬ ‫ﯾﻌﺘﺒﺮ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻜﺮة‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬ ‫ھﻮ‬

16. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٦
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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:‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺘﻘﺪﯾﺮﯾﺔ‬ ‫واﻟﺒﺆرة‬ ‫اﻟﺤﻘﯿﻘﯿﺔ‬ ‫اﻟﺒﺆرة‬-
‫اﻟﺤﻘﯿﻘﯿﺔ‬ ‫اﻟﺒﺆرة‬‫اﻟﺘﻘﺪﯾﺮﯾﺔ‬ ‫اﻟﺒﺆرة‬
‫ﻧﻘﻄﺔ‬ ‫ھﻰ‬‫اﻷﺷﻌﺔ‬ ‫ﺗﻼﻗﻰ‬‫اﻟﻤﻨﻜﺴﺮة‬‫ﻓﻰ‬.‫اﻟﻌﺪﺳﺔ‬‫اﻟﻤ‬‫ﺤﺪﺑﺔ‬
‫ﻧﻘﻄﺔ‬ ‫ھﻰ‬‫اﻷﺷﻌﺔ‬ ‫اﻣﺘﺪاد‬ ‫ﺗﻼﻗﻰ‬‫اﻟﻤﻨﻜﺴﺮة‬‫اﻟﻌﺪﺳﺔ.اﻟﻤﻘﻌﺮة‬ ‫ﻓﻰ‬
‫و‬.‫ﺣﺎﺋﻞ‬ ‫ﻋﻠﻰ‬ ‫اﺳﺘﻘﺒﺎﻟﮭﺎ‬ ‫ﯾﻤﻜﻦ‬‫و‬.‫ﺣﺎﺋﻞ‬ ‫ﻋﻠﻰ‬ ‫اﺳﺘﻘﺒﺎﻟﮭﺎ‬ ‫ﯾﻤﻜﻦ‬ ‫ﻻ‬
‫اﻟﻤﺤﺪﺑﺔ‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫ﺗﻌﯿﯿﻦ‬( ‫ع‬ ):
: ‫اﻻدوات‬‫ﻣﺤﺪﺑﺔ‬ ‫ﻋﺪﺳﺔ‬-‫ﺣﺎﺋﻞ‬-‫اﻟﻌﺪﺳﺔ‬ ‫ﺣﺎﻣﻞ‬-‫ﺑﻌﯿﺪ‬ ‫ﺿﻮﺋﻰ‬ ‫ﻣﺼﺪر‬
: ‫اﻟﺨﻄﻮات‬
١-‫ﻧﻀﻊ‬‫اﻟﺒﻌﯿﺪ‬ ‫اﻟﻀﻮﺋﻰ‬ ‫اﻟﻤﺼﺪر‬ ‫ﺟﮭﯿﮭﺎ‬ ‫و‬ ‫اﺣﺪ‬ ‫ﯾﻘﺎﺑﻞ‬ ‫ﺑﺤﯿﺚ‬ ‫اﻟﺤﺎﻣﻞ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻌﺪﺳﺔ‬
٢-‫اﻟﻌﺪﺳﺔ‬ ‫ﻣﻦ‬ ‫ﺑﻌﺪا‬ ‫و‬ ‫ﻗﺮﺑﺎ‬ ‫ﻧﺤﺮﻛﺔ‬ ‫و‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻻﺧﺮ‬ ‫اﻟﺠﺎﻧﺐ‬ ‫ﻋﻠﻰ‬ ‫راﺳﯿﺎ‬ ‫اﻟﺤﺎﺋﻞ‬ ‫ﻧﻀﻊ‬
‫ﺑﺆرة‬ ‫ھﻰ‬ ‫ﻓﺘﻜﻮن‬ ‫ﻣﻀﯿﺌﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫اوﺿﺢ‬ ‫ﻋﻠﻰ‬ ‫ﻧﺤﺼﻞ‬ ‫ﺣﺘﻰ‬‫ا‬‫ﻟﻌﺪﺳﺔ‬
٣-‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺒﺼﺮى‬ ‫اﻟﻤﺮﻛﺰ‬ ‫و‬ ‫اﻟﻨﻘﻄﺔ‬ ‫ھﺬة‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﻧﻘﯿﺲ‬
‫اﻟﻤﻼﺣﻈﺔ‬‫ﺗ‬‫ﻧﻘﻄﺔ‬ ‫ﻓﻰ‬ ‫ﻣﺘﺠﻤﻌﺔ‬ ‫اﻟﻤﺤﺪﺑﺔ‬ ‫اﻟﻌﺪﺳﺔ‬ ‫ﻣﻦ‬ ‫اﻻﺷﻌﺔ‬ ‫ﻨﻔﺬ‬‫ﺑﺆرة‬‫ا‬‫ﻟﻌﺪﺳﺔ‬
‫اﻻﺳﺘﻨﺘﺎج‬‫ﺗﻤﺜﻞ‬ ‫اﻟﺤﺎﺋﻞ‬ ‫و‬ ‫اﻟﻌﺪﺳﺔ‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬‫اﻟﻤﺤﺪﺑﺔ‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬( ‫ع‬ )
‫ﻋﻠﻰ‬ ‫اﻟﺴﺎﻗﻄﺔ‬ ‫ﻣﺴﺎراﻷﺷﻌﺔ‬‫ﺳﻄﺢ‬‫ﻋﺪﺳﺔ‬‫ﻣﺤﺪﺑﺔ‬:-
‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﺸﻌﺎع‬‫اﻷﺻﻠﻰ‬ ‫ﻟﻠﻤﺤﻮر‬ ً‫ﺎ‬‫ﻣﻮازﯾ‬‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﺸﻌﺎع‬‫ﺑﺎﻟﺒﺆرة‬ ً‫ا‬‫ﻣﺎر‬ً‫ا‬‫ﻣﺎر‬ ‫اﻟﺴﺎﻗﻂ‬ ‫اﻟﺸﻌﺎع‬‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺒﺼﺮى‬ ‫ﺑﺎﻟﻤﺮﻛﺰ‬
‫ﺑﺎﻟﺒﺆرة‬ ‫ﻣﺎرا‬ ً‫ا‬‫ﻣﻨﻜﺴﺮ‬ ‫ﯾﻨﻔﺬ‬ً‫ﺎ‬‫ﻣﻮازﯾ‬ ‫ﯾﻨﻔﺬ‬‫اﻷﺻﻠﻰ‬ ‫ﻟﻠﻤﺤﻮر‬‫اﺳﺘﻘﺎﻣﺘﮫ‬ ‫ﻋﻠﻰ‬ ‫ﯾﻨﻔﺬ‬
‫ب‬ ‫ب‬

17. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٧
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫اﻟﺠﺴﻢ‬ ‫ﻣﻮﺿﻊ‬‫اﻟﺮﺳﻢ‬‫اﻟﺼﻮرة‬ ‫ﺧﻮاص‬
‫اﻟﺴﺎﻗﻄﺔ‬ ‫اﻻﺷﻌﺔ‬ ‫ﺟﺪا‬ ‫ﺑﻌﯿﺪ‬ ‫اﻟﺠﺴﻢ‬
‫اﻟﺮاﺳﻰ‬ ‫ﻟﻠﻤﺤﻮر‬ ‫ﻣﻮازﯾﺔ‬ ‫و‬ ‫ﻣﺘﻮازﯾﺔ‬
‫ﺣﻘﯿﻘﯿﺔ‬ ‫ﺻﻮرة‬‫ﻋﺒﺎرة‬ ‫ﺟﺪا‬ ‫ﺻﻐﯿﺮة‬
‫اﻟﺒﻮرة‬ ‫ﻋﻨﺪ‬ ‫ﻣﻀﯿﺌﺔ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻋﻦ‬(‫ب‬ )
‫ﺿﻌﻒ‬ ‫ﻣﻦ‬ ‫أﻛﺒﺮ‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﺴﻢ‬
‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬‫ﻣﻦ‬ ‫اﺑﻌﺪ‬
‫اﻟﺘﻜﻮر‬ ‫ﻣﺮﻛﺰ‬‫م‬ )(.
‫ﺣﻘﯿﻘﯿﺔ‬ ‫ﺻﻮرة‬‫ﻣﺼﻐﺮة‬ ‫ﻣﻘﻠﻮﺑﺔ‬
‫اﻟﺘﻜﻮر‬ ‫وﻣﺮﻛﺰ‬ ‫اﻟﺒﺆرة‬ ‫ﺑﯿﻦ‬ ‫ﺗﻘﻊ‬
( ‫م‬ )‫و‬ (‫ب‬ )‫ﺑﯿﻦ‬
‫ﯾﺴﺎوى‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﺴﻢ‬
‫اﻟﺒﻌﺪ‬ ‫ﺿﻌﻒ‬‫اﻟﺒﺆرى‬‫ﻋﻨﺪ‬
‫اﻟﺘﻜﻮر‬ ‫ﻣﺮﻛﺰ‬( ‫م‬ )
‫ﺣﻘﯿﻘﺔ‬ ‫ﺻﻮرة‬‫ﻟﻠﺠﺴﻢ‬ ‫ﻣﺴﺎوﯾﺔ‬ ‫ﻣﻘﻠﻮﺑﺔ‬
‫ﻋﻨﺪ‬ ‫ﺗﻘﻊ‬‫اﻟﺘﻜﻮر‬ ‫ﻣﺮﻛﺰ‬( ‫م‬ )
‫ﻣﻦ‬ ‫أﻛﺒﺮ‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﺴﻢ‬‫اﻟﺒﻌﺪ‬
‫اﻟﺒﻌﺪ‬ ‫ﺿﻌﻒ‬ ‫ﻣﻦ‬ ‫وأﺻﻐﺮ‬ ‫اﻟﺒﺆرى‬
‫اﻟﺒﺆرى‬( ‫م‬ )‫و‬ (‫ب‬ )‫ﺑﯿﻦ‬‫ﺣﻘﯿﻘﯿﺔ‬ ‫ﺻﻮرة‬‫ﻣﻜﺒﺮة‬ ‫ﻣﻘﻠﻮﺑﺔ‬‫ﺑﻌﺪ‬ ‫ﺗﻘﻊ‬
‫اﻟﺘﻜﻮر‬ ‫ﻣﺮﻛﺰ‬( ‫م‬ )
‫اﻟﺒﺆرة‬ ‫ﻋﻨﺪ‬ ‫اﻟﺠﺴﻢ‬(‫ب‬ )
‫ﻻ‬‫ﺗﺘﻜﻮن‬‫ﺻﻮرة‬‫ﺗﻨ‬ ‫اﻻﺷﻌﺔ‬ ‫ﻻن‬‫ﻔﺬ‬
‫اﻟﻰ‬ ‫ﻣﺘﻮازﯾﺔ‬‫ﻻﻧﮭﺎﯾﺔ‬ ‫ﻣﺎ‬
‫ﻣﻦ‬ ‫اﻗﻞ‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺠﺴﻢ‬
‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬(‫ب‬ )
‫ﻣﻜﺒﺮة‬ ‫ﻣﻌﺘﺪﻟﺔ‬ ‫ﺗﻘﺪﯾﺮﯾﺔ‬ ‫ﺻﻮرة‬
‫اﻟﺠﺴﻢ‬ ‫ﺟﮭﺔ‬ ‫ﻧﻔﺲ‬ ‫وﻓﻰ‬
١-‫ﻣﺤﺪﺑﺔ‬ ‫ﻋﺪﺳﺔ‬ ‫ﺑﺆرة‬ ‫ﻋﻨﺪ‬ ‫وﺿﻌﮭﺎ‬ ‫ﻋﻨﺪ‬ ‫رﻗﯿﻘﺔ‬ ‫ورﻗﺔ‬ ‫اﺣﺘﺮاق‬ ‫ﻋﻠﻞ‬
‫اﻟﻰ‬ ‫ﯾﺆدى‬ ‫ﻣﻤﺎ‬ ‫اﻟﺒﺆرة‬ ‫ﺗﺴﻤﻰ‬ ‫ﻧﻘﻄﺔ‬ ‫ﻓﻰ‬ ‫اﻧﻜﺴﺎرھﺎ‬ ‫ﺑﻌﺪ‬ ‫اﻻﺷﻌﺔ‬ ‫ﺗﺠﻤﻊ‬ ‫اﻟﻤﺤﺪﺑﺔ‬ ‫اﻟﻌﺪﺳﺔ‬ ‫ﻻن‬‫ﻓﺘﺤﺘﺮق‬ ‫ﻋﻨﺪھﺎ‬ ‫اﻟﺸﻤﺲ‬ ‫اﺷﻌﺔ‬ ‫ﺗﺮﻛﯿﺰ‬
٢-‫اﻟﻤﺤﺪﺑﺔ‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫ﻋﻠﻞ‬‫اﻟﺮﻓﯿﻌﺔ‬‫اﻛﺒﺮ‬‫اﻟﻤﺤﺪﺑﺔ‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫اﻟﺒﺆرى‬ ‫اﻟﺒﻌﺪ‬ ‫ﻣﻦ‬‫اﻟﺴﻤﯿﻜﺔ‬
‫ﺗﻜﻮر‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬ ‫ﻻن‬‫اﻟﻤﺤﺪﺑﺔ‬ ‫اﻟﻌﺪﺳﺔ‬‫ﺗﻜﻮر‬ ‫ﻗﻄﺮ‬ ‫ﻧﺼﻒ‬ ‫ﻣﻦ‬ ‫اﻛﺒﺮ‬ ‫اﻟﺮﻓﯿﻌﺔ‬‫اﻟﺴﻤﯿﻜﺔ‬ ‫اﻟﻤﺤﺪﺑﺔ‬ ‫اﻟﻌﺪﺳﺔ‬
٣-‫ﺗﻜﻮر‬ ‫ﻣﺮﻛﺰ‬ ‫ﻟﮭﺎ‬ ‫اﻟﻤﺮاة‬ ‫اﻣﺎ‬ ‫ﺗﻜﻮر‬ ‫ﻣﺮﻛﺰﯾﻦ‬ ‫ﻟﻠﻌﺪﺳﺔ‬ ‫ﻋﻠﻞ‬‫واﺣﺪ‬
‫واﺣﺪ‬ ‫ﻛﺮى‬ ‫ﺳﻄﺢ‬ ‫ﻟﮭﺎ‬ ‫اﻟﻤﺮاة‬ ‫اﻣﺎ‬ ‫ﻛﺮﯾﺎن‬ ‫ﺳﻄﺤﺎن‬ ‫ﻟﮭﺎ‬ ‫اﻟﻌﺪﺳﺔ‬ ‫ﻻن‬
‫ﺧﻮاص‬‫اﻟﺼﻮر‬‫ﺑﺎﻟﻌﺪﺳﺔ‬ ‫اﻟﻤﺘﻜﻮﻧﺔ‬ ‫ة‬‫اﻟﻤﺤﺪﺑﺔ‬

18. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٨
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫ﺑﺎﻟ‬ ‫اﻟﺼﻮرة‬ ‫ﺧﻮاص‬‫اﻟﻤﻘﻌﺮة‬ ‫ﻌﺪﺳﺔ‬:
‫ﻣﻮﺿﻊ‬ ‫اى‬ ‫ﻋﻨﺪ‬ ‫اﻟﻌﺪﺳﺔ‬ ‫اﻣﺎم‬ ‫اﻟﺠﺴﻢ‬‫ﻣﺼﻐﺮة‬ ‫ﻣﻌﺘﺪﻟﺔ‬ ‫ﺗﻘﺪﯾﺮﯾﺔ‬ ‫ﺻﻮرة‬ ‫داﺋﻤﺎ‬
‫اﻟﺠﺴﻢ‬ ‫ﺟﮭﺔ‬ ‫ﻧﻔﺲ‬
: ‫اﻻﺑﺼﺎر‬ ‫ﻋﯿﻮب‬ ‫اھﻢ‬‫اﻟﻨﻈﺮ‬ ‫ﻃﻮل‬ ‫و‬ ‫اﻟﻨﻈﺮ‬ ‫ﻗﺼﺮ‬
‫ﻃﻮ‬ ‫و‬ ‫اﻟﻨﻈﺮ‬ ‫ﻗﺼﺮ‬ ‫ﺣﺪوث‬ ‫ﺳﺒﺐ‬ ‫ھﻮ‬ ‫ﻣﺎ‬‫اﻟﻨﻈﺮ؟‬ ‫ل‬١-‫اﻟﻌﯿﻦ‬ ‫ﻛﺮوﯾﺔ‬ ‫إﻧﺘﻈﺎم‬ ‫ﻋﺪم‬٢-‫ﺗﺤﺪب‬ ‫إﻧﺘﻈﺎم‬ ‫ﻋﺪم‬‫ﻋﺪﺳﺔ‬ ‫ﺳﻄﺤﻰ‬‫اﻟﻌﯿﻦ‬
‫اﻟﺸﺨﺺ‬:‫اﻟﺴﻠﯿﻢ‬‫ﯾ‬‫اﻻﺟﺴﺎم‬ ‫ﺮى‬) ‫ﻣﻦ‬ ‫ﯾﺘﺮاوح‬ ‫ﺑﻌﺪ‬ ‫ﻋﻠﻰ‬ ‫واﺿﺤﺔ‬٢٥‫ﺳﻢ‬:٦‫ﻣﺘﺮ‬(
‫اﻟﻤﺮض‬‫اﻟﻨﻈﺮ‬ ‫ﻗﺼﺮ‬‫اﻟﻨﻈﺮ‬ ‫ﻃﻮل‬
‫اﻟﺘﻌﺮﯾﻒ‬
‫رؤﯾﺔ‬ ‫ھﻮ‬‫اﻷﺟﺴﺎم‬‫اﻟﻘﺮﯾﺒﺔ‬‫واﺿﺤﺔ‬‫و‬‫اﻷﺟﺴﺎم‬
‫اﻟﺒﻌﯿﺪة‬‫ﻣﺸﻮھﺔ‬
‫رؤﯾﺔ‬ ‫ھﻮ‬‫اﻷﺟﺴﺎم‬‫واﺿﺤﺔ‬ ‫اﻟﺒﻌﯿﺪة‬‫و‬‫اﻷﺟﺴﺎم‬
‫اﻟﻘﺮﯾﺒﺔ‬‫ﻣﺸﻮھﺔ‬
‫ﺗﻜﻮن‬ ‫ﻣﻜﺎن‬
‫اﻟﺼﻮرة‬
‫ﺗﻘﻊ‬‫اﻟﺼﻮ‬‫رة‬‫اﻟﺸﺒﻜﯿﺔ‬ ‫اﻣﺎم‬‫ﺗﻘﻊ‬‫اﻟﺼﻮرة‬‫اﻟﺸﺒﻜﯿﺔ‬ ‫ﺧﻠﻒ‬
‫اﺳﺒﺎب‬
‫اﻟﻤﺮض‬
١-‫زﯾﺎدة‬‫ﻗﻄﺮ‬‫ﻛﺮة‬‫اﻟﻌﯿﻦ‬‫ﻓﺘﻜﻮن‬‫اﻟﺸﺒﻜﯿﺔ‬‫ﻋﻦ‬ ‫ﺑﻌﯿﺪة‬
‫اﻟﻌﯿﻦ‬ ‫ﻋﺪﺳﺔ‬
٢-‫اﻟﻌﯿﻦ‬ ‫ﻋﺪﺳﺔ‬ ‫ﺳﻄﺤﻰ‬ ‫ﺗﺤﺪب‬ ‫زﯾﺎدة‬‫ﺑﻌﺪھﺎ‬ ‫ﻓﯿﻘﻞ‬‫اﻟﺒﺆرى‬
١-‫ﻧﻘﺺ‬‫ﻗﻄﺮ‬‫ﻛﺮة‬‫اﻟﻌﯿﻦ‬‫ﻓﺘﻜﻮن‬‫اﻟﺸﺒﻜﯿﺔ‬‫ﻣﻦ‬ ‫ﻗﺮﯾﺒﺔ‬
‫اﻟﻌﯿﻦ‬ ‫ﻋﺪﺳﺔ‬
٢-‫ﻓﯿﺰداد‬ ‫اﻟﻌﯿﻦ‬ ‫ﻋﺪﺳﺔ‬ ‫ﺳﻄﺤﻰ‬ ‫ﺗﺤﺪب‬ ‫ﻧﻘﺺ‬‫ﺑﻌﺪھﺎ‬‫اﻟﺒﺆرى‬
‫ﺗﻌﻤﻞ‬ ‫ﻣﻘﻌﺮة‬ ‫ﻋﺪﺳﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬‫اﻷﺷﻌﺔ‬ ‫ﺗﻔﺮﯾﻖ‬ ‫ﻋﻠﻰ‬
‫اﻟﻌﯿﻦ‬ ‫اﻟﻰ‬ ‫دﺧﻮﻟﮭﺎ‬ ‫ﻗﺒﻞ‬‫اﻟﺸﺒﻜﯿﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺼﻮرة‬ ‫ﻓﺘﺘﻜﻮن‬
‫ﻋﻠﻰ‬ ‫ﺗﻌﻤﻞ‬ ‫ﻣﺤﺪﺑﺔ‬ ‫ﻋﺪﺳﺔ‬ ‫ﺑﺎﺳﺘﺨﺪام‬‫اﻷﺷﻌﺔ‬ ‫ﺗﺠﻤﯿﻊ‬
‫اﻟﻌﯿﻦ‬ ‫اﻟﻰ‬ ‫دﺧﻮﻟﮭﺎ‬ ‫ﻗﺒﻞ‬‫اﻟﺸﺒﻜﯿﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺼﻮرة‬ ‫ﻓﺘﺘﻜﻮن‬

19. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ١٩
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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‫اﻟﻌﺪﺳﺎت‬ ‫اﺳﺘﺨﺪام‬
١-‫اﻟﻤﻨﺎﻇﯿﺮ‬ ‫و‬ ‫اﻟﺘﻠﯿﺴﻜﻮب‬ ‫و‬ ‫اﻟﻤﯿﻜﺮوﺳﻜﻮب‬ ‫ﻣﺜﻞ‬ ‫اﻟﺒﺼﺮﯾﺔ‬ ‫اﻻﺟﮭﺰة‬ ‫ﻓﻰ‬ ‫اﻟﻌﺪﺳﺎت‬ ‫ﺗﺴﺘﺨﺪم‬
٢-‫اﻟﻄﺒﯿﺔ‬ ‫اﻟﻨﻈﺎرات‬ ‫ﺻﻨﺎﻋﺔ‬ ‫ﻓﻰ‬ ‫ﺗﺴﺘﺘﺨﺪم‬
:‫اﻟﻼﺻﻘﺔ‬ ‫اﻟﻌﺪﺳﺎت‬‫رﻗﯿﻘ‬ ‫ﻋﺪﺳﺎت‬ ‫ھﻰ‬‫ﻋﻠﻰ‬ ‫وﺿﻌﮭﺎ‬ ‫وﯾﻤﻜﻦ‬ ‫اﻟﺒﻼﺳﺘﯿﻚ‬ ‫ﻣﻦ‬ ‫ﻣﺼﻨﻮﻋﺔ‬ ‫ﺟﺪا‬ ‫ﺔ‬‫ﻗﺮﻧﯿﺔ‬‫ﺑﺴﮭﻮﻟﺔ‬ ‫وﻧﺰﻋﮭﺎ‬ ‫اﻟﻌﯿﻦ‬.
:‫اﺳﺘﺨﺪاﻣﮭﺎ‬‫اﻟﻄﺒﯿﺔ‬ ‫اﻟﻨﻈﺎرات‬ ‫ﻣﻦ‬ ‫ﺑﺪﻻ‬ ‫ﺗﺴﺘﺨﺪم‬
١‫اﻟﺒﯿﻀﺎء‬ ‫اﻟﻤﯿﺎة‬ ‫او‬ ‫اﻟﻜﺘﺎرﻛﺘﺎ‬ ‫ﻣﺮض‬٢-‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮاﯾﺎ‬‫ﻣﺴﺎﺣ‬ ‫ﻗﯿﺎس‬‫ﺔ‬‫اﻻراﺿﻰ‬
‫ﻋﺪ‬ ‫ﻋﻠﻰ‬ ‫ﺳﺤﺎﺑﺔ‬ ‫ﻋﻦ‬ ‫ﻋﺒﺎر‬ ‫ھﻰ‬‫ﺗﺆدى‬ ‫اﻟﻌﯿﻦ‬ ‫ﺳﺔ‬
‫اﻟﺮؤﯾﺔ‬ ‫ﺿﻌﻒ‬ ‫اﻟﻰ‬
‫اﻟﻤﺮض‬ ‫اﺳﺒﺎب‬
١-‫اﻟﺴﻦ‬ ‫ﻛﺒﺮ‬
٢-‫اﻵﺛﺎر‬ ‫و‬‫اﻟﺠﺎﻧﺒﯿﺔ‬‫ﻟﻠﻌﻘﺎﻗﯿﺮ‬‫اﻟﻄﺒﯿﺔ‬
٣-‫اﻷﻣﺮاض‬ ‫و‬‫اﻟﻮراﺛﯿﺔ‬
: ‫اﻟﻌﻼج‬
‫اﻟﺘﺪﺧﻞ‬‫اﻟﺠﺮاﺣﻰ‬‫ﺑﺈﺳﺘﺒﺪال‬‫ﻋﺪﺳﺔ‬‫اﻟﻌﯿﻦ‬‫ﺑﻌﺪﺳﺔ‬
‫ﺑﻼﺳﺘﯿﻜﯿﺔ‬
‫إﺳﺘﺨﺪم‬‫أرﺷﯿﻤﯿﺪس‬‫اﻟﻤﻘﻌﺮة‬ ‫اﻟﻤﺮاﯾﺎ‬
‫ﻛﺴﻼح‬‫ﺿﺪ‬‫اﻷﺳﻄﻮل‬‫اﻟﺮوﻣﺎﻧﻰ‬
‫ﺣﯿﺚ‬‫و‬‫ﺿﻊ‬‫ﻋﺪة‬‫ﻣﺮاﯾﺎ‬‫ﻣﻘﻌﺮة‬‫ﻓﻰ‬
‫اﻟﺸﻤﺲ‬ ‫اﺷﻌﺔ‬ ‫ﻣﻮاﺟﮭﺔ‬‫ﻓﺘﺠﻤﻌﺖ‬
‫واﺣﺪة‬ ‫ﻧﻘﻄﺔ‬ ‫ﻓﻰ‬ ‫اﻟﻤﻨﻌﻜﺴﺔ‬ ‫اﻻﺷﻌﺔ‬
‫ﻓﺘﻮﻟﺪت‬ ‫اﻟﺴﻔﻦ‬ ‫اﺷﺮﻋﺔ‬ ‫ﻋﻠﻰ‬‫ﺣﺮارة‬
‫ﺷﺪﯾﺪة‬‫اﺣﺘﺮاﻗﮭﺎ‬ ‫اﻟﻰ‬ ‫ادت‬‫ﺑﻜﺎﻣﻞ‬
‫اﻟﺴﻔﻦ‬ ‫ﻏﺮق‬ ‫ﺑﺎﻟﺘﺎﻟﻰ‬ ‫و‬
١-‫ﯾﺴﺘﺨﺪم‬‫و‬ ‫اﻻراﺿﻰ‬ ‫ﻣﺴﺎﺣﻮ‬‫ﻋﻠﻤﺎء‬
‫اﻟﻄﺒﻮﻏﺮاﻓﯿﺎ‬‫ﺗﺤﺪﯾﺪ‬ ‫ﻓﻰ‬ ‫ﺧﺎﺻﺔ‬ ‫اﺟﮭﺰة‬
‫اﻻﺟ‬ ‫ھﺬة‬ ‫اﻟﻤﺴﺎﻓﺎت‬ ‫و‬ ‫اﻻرﺗﻔﺎﻋﺎت‬‫ﮭﺰة‬
‫ﻋﺪﺳﺎت‬ ‫و‬ ‫ﺑﻤﺮاﯾﺎ‬ ‫ﻣﺰودة‬
٢-‫ﻋﻠﻰ‬ ‫اﻻﺟﮭﺰة‬ ‫ھﺬة‬ ‫ﻋﻤﻞ‬ ‫ﻓﻜﺮة‬ ‫ﺗﻌﺘﻤﺪ‬ ‫و‬
‫اﺳﺘﻘﺒﺎﻟﮭﺎ‬ ‫ﺛﻢ‬ ‫اﻟﻠﯿﺰر‬ ‫اﺷﻌﺔ‬ ‫ﻣﻦ‬ ‫ﺣﺰﻣﺔ‬ ‫ارﺳﺎل‬
‫اﻟﻤﺮاﯾﺎ‬ ‫ﺑﻮاﺳﻄﺔ‬‫واﻟﻌﺪﺳﺎت‬
‫اﻟﻌﻼﻗﺔ‬ ‫ﻣﻦ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ﺣﺴﺎب‬ ‫ﯾﻤﻜﻦ‬ ‫ﺑﺎﻟﺘﺎﻟﻰ‬ ‫و‬
‫ف‬ = ‫ع‬×‫ز‬
‫ھﻮ‬‫اﻟﺸﺎﺳﻊ‬ ‫اﻟﻔﻀﺎء‬‫اﻟﻤﻤﺘﺪ‬‫اﻟﺬى‬‫ﻋﻠﻰ‬ ‫ﯾﺤﺘﻮى‬‫اﻟﻤﺠﺮات‬. ‫ﺷﺊ‬ ‫وﻛﻞ‬ ‫اﻟﺤﯿﺔ‬ ‫واﻟﻜﺎﺋﻨﺎت‬ ‫واﻷﻗﻤﺎر‬ ‫واﻟﻜﻮاﻛﺐ‬ ‫واﻟﻨﺠﻮم‬
‫و‬
١-‫اﻟﺠﺎذﺑﯿﺔ‬ ‫ﺑﺘﺎﺛﯿﺮ‬ ‫اﻟﻔﻀﺎء‬ ‫ﻓﻰ‬ ‫ﻣﻌﺎ‬ ‫ﺗﺪور‬ ‫اﻟﻨﺠﻮم‬ ‫ﻣﻦ‬ ‫ﻣﺠﻤﻮﻋﺎت‬ ‫ھﻰ‬
٢٢-‫ﻓﻰ‬ ‫اﻟﻤﺠﺮات‬ ‫ﻋﺪد‬‫اﻟﻜﻮن‬‫ﺣﻮاﻟﻰ‬١٠٠.٠٠٠‫ﻣﺠﺮة‬ ‫ﻣﻠﯿﻮن‬
٣-‫ﺗﻌﺘﺒﺮ‬ ‫و‬‫وﺣﺪة‬ ‫اﻟﻤﺠﺮة‬‫ﺑﻨﺎء‬‫اﻟﻜﻮن‬
٤-‫ﻣﺠﺮة‬ ‫ﻛﻞ‬‫ﺗ‬( ‫ﻋﻠﻞ‬ ) ‫ﻣﻤﯿﺰا‬ ‫ﺷﻜﻼ‬ ‫ﺘﺨﺬ‬‫ﺗ‬ ‫ﺣﺴﺐ‬ ‫وذﻟﻚ‬‫ﺮﺗﯿﺐ‬‫و‬‫ﺗﻨﺎﺳﻖ‬‫ﻣﺠﻤﻮﻋﺎت‬‫اﻟﻨﺠﻮم‬‫ﻓﯿﮭﺎ‬
٥-‫ﺗﺘﺠﻤﻊ‬‫اﻟﻤﺠﺮات‬‫ﻣﻜﻮﻧﺔ‬ ‫ﻣﻌﺎ‬‫ﻋﻨﺎﻗﯿﺪ‬‫اﻟﻤﺠﺮات‬
٦-: ‫اﻟﻤﺠﺮات‬ ‫ﻋﻨﺎﻗﯿﺪ‬‫ھﻰ‬‫ﻣﺠﻤﻮﻋﺔ‬‫اﻟﺠﺎذﺑﯿﺔ‬ ‫ﺑﻔﻌﻞ‬ ‫اﻟﻔﻀﺎء‬ ‫ﻓﻰ‬ ‫ﻣﻌﺎ‬ ‫ﺗﺪور‬ ‫اﻟﻤﺠﺮات‬ ‫ﻣﻦ‬
١-‫ﻣﺠﺮة‬ ‫ھﻰ‬‫اﻟﺸﻜﻞ‬ ‫ﺣﻠﺰوﻧﯿﺔ‬ ‫او‬ ‫ﻟﻮﻟﺒﯿﺔ‬
٢-‫اﻟﻨﺠﻮم‬ ‫ﻣﻼﯾﯿﻦ‬ ‫ﻋﻠﻰ‬ ‫ﺗﺤﺘﻮى‬‫وﺗﻌﺘﺒﺮاﻟﺸﻤﺲ‬‫اﻟﻨﺠﻮم‬ ‫ھﺬة‬ ‫اﺣﺪ‬
٣-‫ا‬‫ﻟﻨﺠﻮم‬‫ﻋﻤﺮا‬ ‫اﻻﻗﺪم‬‫ﺗﻘﻊ‬‫ﻣﺮﻛﺰاﻟﻤﺠﺮة‬ ‫ﻓﻰ‬‫ﻣ‬‫اﻟﺼﻐﯿﺮة‬ ‫اﻟﻨﺠﻮم‬ ‫ﻣﻦ‬ ‫ﺑﮭﺎﻟﺔ‬ ‫ﺤﺎﻃﺔ‬(‫ﻋﻤﺮا‬ ‫)اﻻﺣﺪث‬‫اﻟﺼﻐﯿﺮة‬ ‫اﻟﻨﺠﻮم‬ ‫ھﺬة‬‫ﺗ‬‫ﻓﻰ‬ ‫ﻘﻊ‬
‫اﻻذرع‬‫اﻟﺤﻠﺰوﻧﯿﺔ‬‫ﻟﻠﻤﺠﺮة‬
٤-‫اﻟﺘﺒﺎﻧﺔ‬ ‫درب‬ ‫ﺑﻤﺠﺮة‬ ‫ﺳﻤﯿﺖ‬‫ﻻن‬‫ﯾ‬ ‫ﺑﮭﺎ‬ ‫اﻟﻨﺠﻮم‬ ‫ﺗﺠﻤﻊ‬‫اﻻرض‬ ‫ﻋﻠﻰ‬ ‫اﻟﻤﻨﺜﻮر‬ ‫اﻟﺘﺒﻦ‬ ‫ﺸﺒﺔ‬
‫ﺗﻜﻨﻮﻟﻮﺟﻰ‬ ‫ﺗﻄﺒﯿﻖ‬

20. ‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬٠١١٤٠٢٣٧٩٩ ٢٠
‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﻣﺬﻛﺮة‬2017‫اﻟﻤﻈﺎﻟﻰ‬ ‫ﺑﻜﺮ‬ ‫اﺑﻮ‬ ‫ﺧﺎﻟﺪ‬
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١-: ‫اﻟﺸﻤﺴﻰ‬ ‫اﻟﻨﻈﺎم‬ ‫او‬‫اﻟﺸﻤﺴ‬ ‫اﻟﻨﻈﺎم‬ ‫ﯾﺘﻜﻮن‬‫اﻟﺸﻤﺲ‬ ‫ھﻮ‬ ‫و‬ ‫واﺣﺪ‬ ‫ﻧﺠﻢ‬ ‫ﻣﻦ‬ ‫ﻰ‬‫ﯾ‬‫ﺣﻮﻟﺔ‬ ‫ﺪور‬٨‫ﻛﻮاﻛﺐ‬
٢-‫ﺗﺪور‬‫اﻟﻜﻮاﻛﺐ‬‫ﺣﻮل‬‫اﻟﺸﻤﺲ‬
٣-‫ﻓﻰ‬ ‫اﻟﻤﺠﺮة‬ ‫ﻣﺮﻛﺰ‬ ‫ﺣﻮل‬ ‫ﻛﺎﻣﻠﺔ‬ ‫دورة‬ ‫وﺗﻌﻤﻞ‬ ‫اﻟﻤﺠﺮة‬ ‫ﻣﺮﻛﺰ‬ ‫ﺣﻮل‬ ‫اﻟﺸﻤﺲ‬ ‫ﺗﺪور‬ ‫و‬٢٢٠‫ﺳﻨﺔ‬ ‫ﻣﻠﯿﻮن‬
٤-‫اﻟﺸﻤﺴﯿﺔ‬ ‫اﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﺗﻘﻊ‬‫ﻋﻠﻰ‬‫اﻟﺤﻠﺰوﻧﯿﺔ‬ ‫اﻷذرع‬ ‫أﺣﺪ‬‫ﻟﻤﺠﺮة‬‫اﻟﺘﺒﺎﻧﺔ‬ ‫درب‬‫اﻟﻤﺠﺮة‬ ‫ﺣﺎﻓﺔ‬ ‫ﻋﻠﻰ‬
‫اﻟﻜﻮن‬ ‫ﻓﻰ‬ ‫اﻟﺴﻤﺎوﯾﺔ‬ ‫اﻻﺟﺮام‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺎت‬ ‫ﻗﯿﺎس‬
‫اﻟﻀﻮﺋﯿﺔ‬ ‫اﻟﺴﻨﺔ‬ ‫ﺗﺴﺘﺨﺪم‬‫ﻻ‬ ‫و‬ ‫اﻟﺴﻤﺎوﯾﺔ‬ ‫اﻻﺟﺮام‬ ‫ﺑﯿﻦ‬ ‫اﻟﻤﺴﺎﻓﺎت‬ ‫ﻗﯿﺎس‬ ‫ﻓﻰ‬‫ﯾ‬‫ﻣﺘﺮ‬ ‫اﻟﻜﯿﻠﻮ‬ ‫ﺴﺘﺨﺪم‬‫ﺟﺪا‬ ‫ﻛﺒﯿﺮة‬ ‫ﺑﯿﻨﮭﺎ‬ ‫اﻟﻤﺴﺎﻓﺎت‬ ‫ﻻن‬ ‫؟‬
: ‫اﻟﻀﻮﺋﯿﺔ‬ ‫اﻟﺴﻨﺔ‬= ‫ﺗﺴﺎوى‬ ‫و‬ ‫ﺳﻨﺔ‬ ‫ﻓﻰ‬ ‫اﻟﻀﻮء‬ ‫ﯾﻘﻄﻌﮭﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﻰ‬٩٤٦٠.٠٠٠‫ﻛﻢ‬ ‫ﻣﻠﯿﻮن‬‫او‬٩.٤٦×١٢
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‫اﻟﻀﻮء‬ ‫ﺳﺮﻋﺔ‬= ‫ھﻰ‬ ‫و‬ ‫اﻟﻮاﺣﺪة‬ ‫اﻟﺜﺎﻧﯿﺔ‬ ‫ﻓﻰ‬ ‫اﻟﻀﻮء‬ ‫ﯾﻘﻄﻌﮭﺎ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻤﺴﺎﻓﺔ‬ ‫ھﻰ‬٣×١٠٨
‫م/ث‬
‫اﻟﻜﻮن‬ ‫ﺗﻤﺪد‬‫اﻟﻤﺠﺮات‬ ‫ﺗﺒﺎﻋﺪ‬ ‫ھﻮ‬‫ﺑﻌﻀﮭﺎ‬ ‫ﻋﻦ‬‫ﻧﺘﯿﺠﺔ‬‫ﺣﺮﻛ‬‫ﺘﮭﺎ‬‫اﻟﻤﻨﺘﻈﻤﺔ‬
‫؟‬ ‫اﻟﻜﻮﻧﻰ‬ ‫ﻟﻠﻔﻀﺎء‬ ‫اﻟﻤﺴﺘﻤﺮ‬ ‫اﻻﺗﺴﺎع‬ ‫ﻋﻠﻞ‬‫ﺑﺴﺒﺐ‬‫اﻟﻤﺠﺮات‬ ‫ﺗﺒﺎﻋﺪ‬‫ﺑﻌﻀﮭﺎ‬ ‫ﻋﻦ‬‫ﻧﺘﯿﺠﺔ‬‫ﺣﺮﻛ‬‫ﺘﮭﺎ‬‫اﻟﻤﻨﺘﻈﻤﺔ‬
‫ﺑﻌﻀﮭﺎ‬ ‫ﻋﻦ‬ ‫ﺗﺘﺒﺎﻋﺪ‬ ‫اﻟﻤﺠﺮات‬ ‫و‬ ‫ﻣﺴﺘﻤﺮ‬ ‫ﺗﻤﺪد‬ ‫ﻓﻰ‬ ‫اﻟﻜﻮن‬ ‫ان‬ ‫ﺑﺎﻟﺘﺠﺮﺑﺔ‬ ‫وﺿﺤﻰ‬
: ‫اﻻدوات‬‫ﻣﺎء‬–‫دﻗﯿﻖ‬–‫ﺧﻤﯿﺮة‬–‫ذﺑﯿﺐ‬–‫زﺟﺎﺟﻰ‬ ‫اﻧﺎء‬
: ‫اﻟﺨﻄﻮات‬‫ﻣﺘﻤﺎﺳﻜﺔ‬ ‫ﻋﺠﯿﻨﺔ‬ ‫ﻟﻌﻤﻞ‬ ‫اﻟﺪاﻓﺊ‬ ‫ﺑﺎﻟﻤﺎء‬ ‫اﻟﺨﻤﯿﺮة‬ ‫و‬ ‫اﻟﺪﻗﯿﻖ‬ ‫ﻧﺨﻠﻂ‬
‫اﻟﻌﺠﯿﻦ‬ ‫ﺳﻄﺢ‬ ‫ﻋﻠﻰ‬ ‫اﻟﺬﺑﯿﺐ‬ ‫ﺣﺒﺎت‬ ‫ﻧﻐﺮس‬
‫ﯾﺘﺨﻤﺮ‬ ‫ﺣﺘﻰ‬ ‫داﻓﺊ‬ ‫ﻣﻜﺎن‬ ‫ﻓﻰ‬ ‫اﻟﻌﺠﯿﻦ‬ ‫ﻧﺘﺮك‬
: ‫اﻟﻤﻼﺣﻈﺔ‬‫ﺑﻌﻀﮭﺎ‬ ‫ﻋﻦ‬ ‫اﻟﺬﺑﯿﺐ‬ ‫ﺣﺒﺎت‬ ‫ﺗﺒﺎﻋﺪ‬ ‫و‬ ‫اﻟﻌﺠﯿﻦ‬ ( ‫)ﺗﻤﺪد‬ ‫اﻧﺘﻔﺎخ‬
‫اﻻﺳﺘﻨﺘ‬: ‫ﺎج‬‫اﻟﻌﺠﯿﻦ‬ ‫اﻧﺘﻔﺎخ‬ ‫ﻣﺜﻞ‬ ‫ﻣﺴﺘﻤﺮ‬ ‫ﺗﻤﺪد‬ ‫ﻓﻰ‬ ‫اﻟﻜﻮن‬ ‫ان‬
‫اﻟﺬﺑﯿﺐ‬ ‫ﺣﺒﺎت‬ ‫ﻣﺜﻞ‬ ‫ﺑﻌﻀﮭﺎ‬ ‫ﻋﻦ‬ ‫ﺗﺘﺒﺎﻋﺪ‬ ‫اﻟﻤﺠﺮات‬ ‫و‬
‫اﻟﻜﻮن‬ ‫ﻟﻨﺸﺎة‬ ‫اﻻﻧﺴﺎن‬ ‫ﺗﺼﻮرات‬‫ﻗﺪﯾﻤﺎ‬:
‫اﻟﻜﻮن‬ ‫ﺗﺼﻮر‬ ‫ﻋﻠﻞ‬‫ﻓﻰ‬‫ﻧﻈﺮﯾﺎت‬ ‫ﺑﻮﺿﻊ‬ ‫ﯾﺴﻤﺢ‬ ‫ﻟﻢ‬ ‫اﻟﻘﺪﯾﻤﺔ‬ ‫اﻟﻌﺼﻮر‬‫اﻟﻜﻮن‬ ‫ﻧﺸﺎة‬ ‫ﻋﻦ‬‫؟‬
‫اﻻﻋ‬ ‫و‬ ‫اﻟﻤﺘﻌﺪدة‬ ‫اﻻﻟﺔ‬ ‫ﺑﻌﺎﻟﻢ‬ ‫ارﺗﺒﻄﺖ‬ ‫اﻟﺘﺼﻮرات‬ ‫ھﺬة‬ ‫ﻻن‬‫اﻻرض‬ ‫و‬ ‫اﻟﺴﻤﺎء‬ ‫ﺑﯿﻦ‬ ‫اﺳﺎﺳﻰ‬ ‫اﺧﺘﻼف‬ ‫ﺑﻮﺟﻮد‬ ‫ﺘﻘﺎد‬
‫اﺣﺪ‬ ‫وﺟﻮد‬ ‫ﻋﺪم‬ ‫ﻣﻦ‬ ‫ﺑﺎﻟﺮﻏﻢ‬ ‫اﻟﻜﻮن‬ ‫ﻧﺸﺎة‬ ‫ﺗﻔﺴﯿﺮ‬ ‫ﺗﺤﺎول‬ ‫اﻟﺘﻰ‬ ‫اﻟﻨﻈﺮﯾﺎت‬ ‫ﺗﻌﺪد‬ ‫ﻋﻠﻞ‬‫اﻟﻜﻮن‬ ‫ﻧﺸﺎة‬ ‫ﻋﻨﺪ‬‫ﻟ‬‫ﻧﺸ‬ ‫ﻛﯿﻒ‬ ‫ﻟﻨﺎ‬ ‫ﯿﺮوى‬‫ﺄ؟‬
‫ﻣﻦ‬ ‫اﻟﻌﻠﻤﺎء‬ ‫ﻣﻜﻨﺖ‬ ‫اﻟﺘﻰ‬ ‫اﻟﻔﻠﻚ‬ ‫و‬ ‫اﻟﻔﯿﺰﯾﺎء‬ ‫ﻋﻠﻢ‬ ‫ﻓﻰ‬ ‫اﻟﺤﺪﯾﺜﺔ‬ ‫اﻻﻛﺘﺸﺎﻓﺎت‬ ‫ﺑﺴﺒﺐ‬‫اﻗﺘﻔﺎء‬‫اﻻو‬ ‫اﻟﻠﺤﻈﺎت‬ ‫ﻣﻨﺬ‬ ‫اﻟﻜﻮن‬ ‫ﺗﺎرﯾﺦ‬‫ﻟﻨﺸﺄﺗﺔ‬ ‫ﻟﻰ‬
‫اﻟﻌﻈﯿﻢ‬ ‫اﻻﻧﻔﺠﺎر‬ ‫ﻧﻈﺮﯾﺔ‬ ‫ھﻰ‬ ‫اﻟﻜﻮن‬ ‫ﻟﻨﺸﺄة‬ ‫اﻟﺤﺪﯾﺜﺔ‬ ‫اﻟﻨﻈﺮﯾﺎت‬ ‫اھﻢ‬
‫اﻟﻌﺼﺮ‬‫اﻟﺤﺠﺮى‬‫ﻋﻠﻰ‬ ‫اﻟﺨﺮاﻓﺎت‬ ‫ﺳﯿﻄﺮت‬‫ﺧﯿﺎل‬‫اﻻﻧﺴﺎن‬
‫اﻟﺼﯿﻨﯿﺔ‬ ‫و‬ ‫اﻟﮭﻨﺪﯾﺔ‬ ‫اﻟﺤﻀﺎرة‬‫اﻟﺘﻨﺠﯿﻢ‬ ‫ﻋﻠﻢ‬ ‫ﺳﺎد‬
‫اﻟﺮوﻣﺎن‬ ‫و‬ ‫اﻻﻏﺮﯾﻖ‬‫ﻧﻈﺮﯾﺎت‬ ‫وﺿﻊ‬ ‫اﻻﻏﺮﯾﻖ‬ ‫ﻓﻼﺳﻔﺔ‬ ‫ﺣﺎوﻟﺖ‬‫ﺗ‬‫ا‬ ‫ﻔﺴﺮ‬‫ﻟﻈﻮاھﺮاﻟﻜﻮﻧﯿﺔ‬
‫اﻟﺒﺎﺑﻠﯿﯿﻦ‬ ‫و‬ ‫اﻟﻤﺼﺮﯾﯿﻦ‬ ‫ﻗﺪﻣﺎء‬‫رﺑﻄﻮا‬‫ﻋﻠﯿﺔ‬ ‫اﻟﻤﺴﯿﻄﺮة‬ ‫واﻻﻟﺔاﻟﻤﺘﻌﺪدة‬ ‫اﻟﻜﻮن‬ ‫أزﻟﯿﺔ‬ ‫ﺑﯿﻦ‬