Ch3

Page 1

‫ﺍﻟﻔﺼل ﺍﻟﺜﺎﻟﺙ‪ :‬ﺍﻟﺤﺭﻜﺔ ﻓﻲ ﻤﺴﺘﻭ‬

‫ﺍﻟﻔﺼﻞ ﺍﻟﺜﺎﻟﺚ‬

‫ﺍﻟﺤﺮﻛﺔ ﻓﻲ ﻣﺴﺘﻮ‬ ‫)‪(Plane Motion‬‬

‫‪ 1-3‬ﺘﻤﻬﻴﺩ‬ ‫ﺩﺭﺴﻨﺎ ﻓﻲ ﺍﻟﻔﺼل ﺍﻟﺴﺎﺒﻕ ﺤﺭﻜﺔ ﺍﻷﺠﺴﺎﻡ ﺒﺸﻜل ﻋﺎﻡ ﻭﺍﺴﺘﺨﺭﺠﻨﺎ ﺍﻟﻤﻌﺎﺩﻻﺕ ﺍﻟﺘﻲ ﺘﻌﻁﻲ ﻤﺘﻐﻴﺭﺍﺘﻬﺎ‬ ‫ﻓﻲ ﺍﻟﻔﻀﺎﺀ‪ ،‬ﺜﻡ ﺍﻨﺘﻘﻠﻨﺎ ﻟﺤﺭﻜﺔ ﺠﺴﻡ ﻋﻠﻰ ﺨﻁ ﻤﺴﺘﻘﻴﻡ ﻭﺒﺨﺎﺼﺔ ﺍﻟﺴﻘﻭﻁ ﺍﻟﺤﺭ‪ .‬ﺇﻻ ﺃﻥ ﺃﻫﻡ ﺍﻟﺤﺭﻜﺎﺕ‬

‫ﺍﻟﺸﺎﺌﻌﺔ ﻓﻲ ﺍﻟﻁﺒﻴﻌﺔ‪ ،‬ﻜﺎﻟﻘﻤﺭ ﺤﻭل ﺍﻷﺭﺽ ﺃﻭ ﺍﻟﻜﻭﺍﻜﺏ ﺤﻭل ﺍﻟﺸﻤﺱ‪ ،‬ﺘﺘﻡ ﻓﻲ ﻤﺴﺘﻭ‪ .‬ﻟﺫﺍ ﻨﺩﺭﺱ ﻓﻲ‬ ‫ﻫﺫﺍ ﺍﻟﻔﺼل ﺍﻟﺤﺭﻜﺔ ﺍﻟﻤﺴﺘﻭﻴﺔ ﻟﻸﺠﺴﺎﻡ‪ ،‬ﺜﻡ ﻨﺩﺭﺱ ﺤﺎﻟﺔ ﺨﺎﺼﺔ ﻫﻲ ﺍﻟﻤﻘﺫﻭﻓﺎﺕ ﻷﻨﻬﺎ ﺴﻬﻠﺔ ﻭﻟﻬﺎ‬ ‫ﺘﻁﺒﻴﻘﺎﺕ ﻴﻭﻤﻴﺔ ﻜﺜﻴﺭﺓ‪ .‬ﻓﻨﺼﻔﻬﺎ ﻭﻨﺤﻠﻠﻬﺎ ﻟﻤﺭﻜﺒﺘﻴﻥ ﻋﻠﻰ ﻤﺤﻭﺭﻴﻥ ﻤﻨﺎﺴﺒﻴﻥ‪ ،‬ﻭﻨﺴﺘﺨﻠﺹ ﻤﻌﺎﺩﻻﺕ‬

‫ﺍﻟﺤﺭﻜﺔ ﻭﺍﻟﻤﺴﺎﺭ ﻟﻬﺎ‪ .‬ﺜﻡ ﻨﺩﺭﺱ ﺍﻟﺤﺭﻜﺔ ﺍﻟﺩﺍﺌﺭﻴﺔ ﺍﻟﻤﻨﺘﻅﻤﺔ ﺍﻟﺘﻲ ﺘﺘﻡ ﺒﺴﺭﻋﺔ ﺜﺎﺒﺘﺔ ﺒﺎﻟﻘﻴﻤﺔ ﻭﻨﺴﺘﺨﺭﺝ‬ ‫ﺘﺴﺎﺭﻋﻬﺎ ﺍﻟﻤﺭﻜﺯﻱ ﻭﺩﻭﺭﻫﺎ ﻭﺘﺭﺩﺩﻫﺎ‪ .‬ﻭﻨﺩﺭﺱ ﺃﺨﻴﺭﺍ ﻤﻔﻬﻭﻡ ﺍﻟﺴﺭﻋﺔ ﺍﻟﻨﺴﺒﻴﺔ ﻭﺒﻌﺽ ﺘﻁﺒﻴﻘﺎﺘﻬﺎ‪.‬‬

‫‪ 2-3‬ﺍﻟﺤﺭﻜﺔ ﻓﻲ ﻤﺴﺘﻭ‬

‫‪y‬‬

‫ﺇﺫﺍ ﺘﺎﺒﻌﻨﺎ ﺤﺭﻜﺔ ﻜﺭﺓ ﺘﺘﺩﺤﺭﺝ ﻋﻠﻰ ﺃﺭﺽ ﺍﻟﻐﺭﻓﺔ‪ ،‬ﻜﻤﺎ ﻓﻲ‬ ‫ﺍﻟﺸﻜل )‪ ،(1-3‬ﻟﻼﺤﻅﻨﺎ ﺃﻨﻬﺎ ﺘﺒﻘﻰ ﺩﺍﺌﻤﺎ ﻋﻨﺩ ﻨﻔﺱ ﺍﻻﺭﺘﻔﺎﻉ‬

‫‪v‬‬

‫ﻟﻜﻨﻬﺎ ﺘﺘﺤﺭﻙ ﻓﻲ ﻤﺴﺘﻭ ﺃﺭﺽ ﺍﻟﻐﺭﻓﺔ ﻭﻟﺫﺍ ﻨﻘﻭل ﺇﻥ ﺤﺭﻜﺘﻬﺎ‬ ‫ﻤﺴﺘﻭﻴﺔ‪ .‬ﻭﺘﺘﺤﺩﺩ ﻤﺘﻐﻴﺭﺍﺕ ﺤﺭﻜﺔ ﺍﻟﻜﺭﺓ ﻓﻲ ﺃﻱ ﻟﺤﻅﺔ‬

‫ﺒﻤﺘﺠﻪ ﻤﻭﻀﻌﻬﺎ ‪ r‬ﻭﺴﺭﻋﺘﻬﺎ ‪ v‬ﻭﺘﺴﺎﺭﻋﻬﺎ ‪ a‬ﺤﻴﺙ ﻴﻜﻭﻥ‬

‫‪a‬‬ ‫‪x‬‬

‫‪r‬‬

‫ﺍﻟﺸﻜل )‪(1-3‬‬

‫ﻟﻜل ﻤﻨﻬﺎ ﻤﺭﻜﺒﺘﻴﻥ ﻓﻘﻁ ﻋﻠﻰ ﺍﻟﻤﺤﻭﺭﻴﻥ ‪) ox‬ﻁﻭل ﺍﻟﻐﺭﻓﺔ( ﻭ‪) oy‬ﻋﺭﻀﻬﺎ( ﻤﺜﻼ‪.‬‬ ‫‪67‬‬


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