Ch1 physics and measurements

‫ﻭﺍﻟﻘﻴﺎﺱ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬
2
‫ﺘﻭﺜﻴــﻕ‬
‫اﻟﺒﯿﺎن‬
Physics for Scientists and Engineers
By
Raymond A. Serway & John W. Jewett
6th Edition
‫اﻟﻤﯿﻜﺎﻧﯿﻜﺎ‬ ‫اﻷول‬ ‫اﻟﺠﺰء‬
‫اﻷوﻟﻰ‬ ‫اﻟﻮﺣﺪة‬‫واﻟﻘﯿﺎس‬ ‫اﻟﻔﯿﺰﯾﺎء‬
‫د‬/.‫ﺳﻜﯿﻚ‬ ‫ﻓﻼح‬ ‫ﺣﺎزم‬
‫ﻓﯿﺰﯾﺎء‬
‫ﻛﺘﺎب‬
5-1-2009
‫ﺍﻷﻭﻟﻰ‬ ‫ﺍﻟﻭﺤﺩﺓ‬
‫د‬.‫ﺳﻛﯾك‬ ‫ﻓﻼح‬ ‫ﺣﺎزم‬
www.trgma.com
‫م‬‫اﻟﺒﻨﺪ‬
1‫اﻟﻤﺼﺪر‬Physics for Scientists and Engineers
Raymond A. Serway & John W. Jewett
2‫اﻟﻤﻮﺿﻮع‬
3‫اﻟﻤﺘﺮﺟﻢ‬
4‫اﻟﻌﻠﻤﯿﺔ‬ ‫اﻟﻤﺮاﺟﻌﺔ‬
5‫اﻟﻠﻐﻮﯾﺔ‬ ‫اﻟﻤﺮاﺟﻌﺔ‬
6‫اﻟﺘﺼﻨﯿﻒ‬
7‫اﻟﻔﺌﺔ‬
11‫اﻟﺘﺎرﯾﺦ‬

3
‫ﺒﺄﺴﺎﺴﻴﺎﺕ‬‫ﺍﻟﻜﻭﻥ‬.‫ﻴﺸﻜل‬
‫ﺍﻟﻔﻠﻙ‬ ‫ﻤﺜل‬ ‫ﺍﻟﻌﻠﻭﻡ‬ ‫ﻤﻥ‬ ‫ﻟﻠﻜﺜﻴﺭ‬
‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬ ‫ﻋﻠﻡ‬ ‫ﺘﻘﺴﻴﻡ‬ ‫ﻭﻴﻤﻜﻥ‬
‫ﺤﺭﻜﺔ‬ ‫ﺒﺩﺭﺍﺴﺔ‬ ‫ﺘﻬﺘﻡ‬ ‫ﻭﺍﻟﺘﻲ‬‫ﺍﻷﺠﺴﺎﻡ‬‫ﻤﻊ‬ ‫ﺒﺎﻟﻤﻘﺎﺭﻨﺔ‬ ‫ﺍﻟﻜﺒﻴﺭﺓ‬‫ﺍﻷﺠﺴﺎﻡ‬‫ﺘﺘﺤﺭﻙ‬ ‫ﻭﺍﻟﺘﻲ‬ ‫ﺍﻟﺫﺭﻴﺔ‬
‫ﺍﻟﻀﻭﺀ‬ ‫ﺴﺭﻋﺔ‬ ‫ﻤﻥ‬ ‫ﺒﻜﺜﻴﺭ‬ ‫ﺍﻗل‬ ‫ﺒﺴﺭﻋﺎﺕ‬.
‫ﺍﻷﺠﺴﺎﻡ‬‫ﺍﻟﻀﻭﺀ‬ ‫ﺴﺭﻋﺔ‬ ‫ﻤﻥ‬ ‫ﻗﺭﻴﺒﺔ‬ ‫ﺒﺴﺭﻋﺎﺕ‬ ‫ﺘﺘﺤﺭﻙ‬ ‫ﺍﻟﺘﻲ‬.
‫ﺍﻟﺴﻠﻭﻙ‬ ‫ﻭﺩﺭﺍﺴﺔ‬ ‫ﺍﻟﺤﺭﺍﺭﺓ‬ ‫ﻭﺩﺭﺠﺔ‬ ‫ﻭﺍﻟﺸﻐل‬ ‫ﺍﻟﺤﺭﺍﺭﺓ‬ ‫ﻤﻊ‬ ‫ﺘﺘﻌﺎﻤل‬ ‫ﻭﺍﻟﺘﻲ‬‫ﺍﻹﺤﺼﺎﺌﻲ‬‫ﻷﻨﻅﻤﺔ‬
‫ﺍﻟﺠﺴﻴﻤﺎﺕ‬ ‫ﻤﻥ‬ ‫ﻜﺒﻴﺭ‬ ‫ﻋﺩﺩ‬ ‫ﻋﻠﻰ‬ ‫ﺘﺤﺘﻭﻱ‬.
‫ﻭﺍﻟﻤﺠﻼﺕ‬ ‫ﻭﺍﻟﻤﻐﻨﺎﻁﻴﺴﻴﺔ‬ ‫ﺍﻟﻜﻬﺭﺒﻴﺔ‬ ‫ﺒﺩﺭﺍﺴﺔ‬ ‫ﺘﻬﺘﻡ‬ ‫ﻭﺍﻟﺘﻲ‬‫ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ‬.
‫ﺍﻷﺨﺭﻯ‬ ‫ﺍﻟﻤﻭﺍﺩ‬ ‫ﻤﻊ‬ ‫ﻭﺘﻔﺎﻋﻠﻪ‬ ‫ﺍﻟﻀﻭﺀ‬ ‫ﺴﻠﻭﻙ‬ ‫ﺒﺩﺭﺍﺴﺔ‬ ‫ﻴﻬﺘﻡ‬ ‫ﻭﺍﻟﺫﻱ‬.
‫ﺩﻗﻴﻘﺔ‬ ‫ﺠﺴﻴﻤﺎﺕ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻤﻜﻭﻨﺔ‬ ‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﺴﻠﻭﻙ‬ ‫ﺒﺩﺭﺍﺴﺔ‬ ‫ﺘﺘﻌﻠﻕ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﻨﻅﺭﻴﺎﺕ‬ ‫ﻭﻴﺸﻤل‬.
www.trgma.com
‫ﺍﻟﻌﻠﻭﻡ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬‫ﺍﻷﺴﺎﺴﻴﺔ‬‫ﺘﻬﺘﻡ‬ ‫ﺍﻟﺘﻲ‬‫ﺒﺄﺴﺎﺴﻴﺎﺕ‬
‫ﺍﻟﻘﺎﻋﺩﺓ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬ ‫ﻋﻠﻡ‬‫ﺍﻷﺴﺎﺴﻴﺔ‬‫ﺍﻟﻔﻠﻙ‬ ‫ﻤﺜل‬ ‫ﺍﻟﻌﻠﻭﻡ‬ ‫ﻤﻥ‬ ‫ﻟﻠﻜﺜﻴﺭ‬
‫ﻭﺍﻟﺠﻴﻭﻟﻭﺠﻴﺎ‬ ‫ﻭﺍﻟﻜﻴﻤﻴﺎﺀ‬ ‫ﻭﺍﻟﺒﻴﻭﻟﻭﺠﻲ‬.‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬ ‫ﻋﻠﻡ‬ ‫ﺘﻘﺴﻴﻡ‬ ‫ﻭﻴﻤﻜﻥ‬
‫ﺴﺘﺔ‬ ‫ﺇﻟﻰ‬‫ﺃﻗﺴﺎﻡ‬
1.‫ﺍﻟﻜﻼﺴﻴﻜﻴﺔ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬،‫ﺤﺭﻜﺔ‬ ‫ﺒﺩﺭﺍﺴﺔ‬ ‫ﺘﻬﺘﻡ‬ ‫ﻭﺍﻟﺘﻲ‬
‫ﺍﻟﻀﻭﺀ‬ ‫ﺴﺭﻋﺔ‬ ‫ﻤﻥ‬ ‫ﺒﻜﺜﻴﺭ‬ ‫ﺍﻗل‬ ‫ﺒﺴﺭﻋﺎﺕ‬
2.‫ﺍﻟﻨﺴﺒﻴﺔ‬،‫ﺘﺼﻑ‬ ‫ﻨﻅﺭﻴﺔ‬ ‫ﻭﻫﻲ‬‫ﺍﻷﺠﺴﺎﻡ‬
3.‫ﺍﻟﺤﺭﺍﺭﻴﺔ‬ ‫ﺍﻟﺩﻴﻨﺎﻤﻴﻜﺎ‬،‫ﺍﻟﺴﻠﻭﻙ‬ ‫ﻭﺩﺭﺍﺴﺔ‬ ‫ﺍﻟﺤﺭﺍﺭﺓ‬ ‫ﻭﺩﺭﺠﺔ‬ ‫ﻭﺍﻟﺸﻐل‬ ‫ﺍﻟﺤﺭﺍﺭﺓ‬ ‫ﻤﻊ‬ ‫ﺘﺘﻌﺎﻤل‬ ‫ﻭﺍﻟﺘﻲ‬
‫ﺍﻟﺠﺴﻴﻤﺎﺕ‬ ‫ﻤﻥ‬ ‫ﻜﺒﻴﺭ‬ ‫ﻋﺩﺩ‬ ‫ﻋﻠﻰ‬ ‫ﺘﺤﺘﻭﻱ‬
4.‫ﺍﻟﻜﻬﺭﻭﻤﻐﻨﺎﻁﻴﺴﻴﺔ‬،‫ﻭﺍﻟﻤﺠﻼﺕ‬ ‫ﻭﺍﻟﻤﻐﻨﺎﻁﻴﺴﻴﺔ‬ ‫ﺍﻟﻜﻬﺭﺒﻴﺔ‬ ‫ﺒﺩﺭﺍﺴﺔ‬ ‫ﺘﻬﺘﻡ‬ ‫ﻭﺍﻟﺘﻲ‬
5.‫ﺍﻟﻀﻭﺀ‬،‫ﺍﻷﺨﺭﻯ‬ ‫ﺍﻟﻤﻭﺍﺩ‬ ‫ﻤﻊ‬ ‫ﻭﺘﻔﺎﻋﻠﻪ‬ ‫ﺍﻟﻀﻭﺀ‬ ‫ﺴﻠﻭﻙ‬ ‫ﺒﺩﺭﺍﺴﺔ‬ ‫ﻴﻬﺘﻡ‬ ‫ﻭﺍﻟﺫﻱ‬
6.‫ﺍﻟﻜﻡ‬ ‫ﻤﻴﻜﺎﻨﻴﻜﺎ‬،‫ﺩﻗﻴﻘﺔ‬ ‫ﺠﺴﻴﻤﺎﺕ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻤﻜﻭﻨﺔ‬ ‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﺴﻠﻭﻙ‬ ‫ﺒﺩﺭﺍﺴﺔ‬ ‫ﺘﺘﻌﻠﻕ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﻨﻅﺭﻴﺎﺕ‬ ‫ﻭﻴﺸﻤل‬

4
‫ﺍﻷﻭﻟﻰ‬ ‫ﺍﻟﻭﺤﺩﺓ‬:‫ﻭﺍﻟﻘﻴﺎﺱ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬
v‫ﻭﺍﻟﺯﻤﻥ‬ ‫ﻭﺍﻟﻜﺘﻠﺔ‬ ‫ﺍﻟﻁﻭل‬
v‫ﺍﻟﻨﻤﺎﺫﺝ‬ ‫ﻭﺒﻨﺎﺀ‬ ‫ﺍﻟﻤﺎﺩﺓ‬
v‫ﻭﻜﺘﻠﺔ‬ ‫ﺍﻟﻜﺜﺎﻓﺔ‬‫ﺍﻟﺫﺭﺓ‬
v‫ﺘﺤﻠﻴ‬‫ـ‬‫ﺍﻷﺒﻌ‬ ‫ل‬‫ــ‬‫ﺎﺩ‬
v‫ﺘﺤﻭﻴ‬‫ـ‬‫ﺍﻟﻭﺤﺩﺍﺕ‬ ‫ل‬
v‫ﻭﺍﻷﺭﻗﺎﻡ‬ ‫ﺍﻟﺘﻘﺩﻴﺭﺍﺕ‬
v‫ﺍﻷﺭﻗﺎﻡ‬‫ﺍﻟﻤﻌﻨﻭﻴـﺔ‬
www.trgma.com

5
 
‫ﺍﻟﻜﻤﻴﺔ‬ ‫ﻭﺍﻟﻘﻴﺎﺴﺎﺕ‬ ‫ﺍﻟﻌﻤﻠﻴﺔ‬ ‫ﺍﻟﻤﻼﺤﻅﺎﺕ‬ ‫ﻋﻠﻰ‬ ‫ﺘﻌﺘﻤﺩ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬ ،‫ﺍﻟﻌﻠﻭﻡ‬.‫ﻭ‬‫ﺍﻟﻬﺩﻑ‬‫ﺍﻷﺴﺎﺴﻲ‬‫ﻫﻭ‬ ‫ﻟﻠﻔﻴﺯﻴﺎﺀ‬‫ﺇﻴﺠﺎﺩ‬
‫ﺍﻟﻘﻭﺍﻨﻴﻥ‬ ‫ﻫﺫﻩ‬ ‫ﻟﺘﺴﺘﺨﺩﻡ‬ ‫ﺍﻟﻁﺒﻴﻌﻴﺔ‬ ‫ﺍﻟﻅﻭﺍﻫﺭ‬ ‫ﺘﺤﻜﻡ‬ ‫ﺍﻟﺘﻲ‬‫ﻓﻲ‬‫ﻤﺴﺘﻘﺒﻠﻴﺔ‬ ‫ﻟﺘﺠﺎﺭﺏ‬ ‫ﻨﺘﺎﺌﺞ‬ ‫ﺘﺘﻭﻗﻊ‬ ‫ﻨﻅﺭﻴﺎﺕ‬ ‫ﺘﻁﻭﻴﺭ‬.
‫ﺍﻟﻨﻅﺭﻴﺔ‬ ‫ﺒﻴﻥ‬ ‫ﺍﻟﺠﺴﺭ‬ ‫ﺍﻟﺭﻴﺎﻀﻴﺎﺕ‬ ‫ﻭﺘﻌﺘﺒﺭ‬ ،‫ﺍﻟﺭﻴﺎﻀﻴﺎﺕ‬ ‫ﺒﻠﻐﺔ‬ ‫ﻋﻨﻬﺎ‬ ‫ﻴﻌﺒﺭ‬ ‫ﻨﻅﺭﻴﺎﺕ‬ ‫ﻟﺘﻁﻭﻴﺭ‬ ‫ﺍﻟﻤﺴﺘﺨﺩﻤﺔ‬
‫ﻴﺠﺏ‬ ‫ﺠﺩﻴﺩﺓ‬ ‫ﻨﻅﺭﻴﺎﺕ‬ ‫ﻓﺎﻥ‬ ‫ﻭﺍﻟﻨﻅﺭﻴﺔ‬ ‫ﺍﻟﻌﻤﻠﻴﺔ‬ ‫ﺍﻟﻨﺘﺎﺌﺞ‬ ‫ﺒﻴﻥ‬ ‫ﺘﻌﺎﺭﺽ‬ ‫ﻫﻨﺎﻙ‬ ‫ﻴﻜﻭﻥ‬ ‫ﻋﻨﺩﻤﺎ‬‫ﺃﻥ‬‫ﺘﻜﺘﺸﻑ‬‫ﻹﺯﺍﻟﺔ‬‫ﺍﻟﺘﻌﺎﺭ‬ ‫ﻫﺫﺍ‬‫ﺽ‬.‫ﻓﻲ‬
‫ﻤﺤﺩﺩﺓ‬ ‫ﻅﺭﻭﻑ‬ ‫ﻓﻲ‬ ‫ﻓﻘﻁ‬ ‫ﺼﺎﻟﺤﺔ‬ ‫ﺍﻟﻨﻅﺭﻴﺔ‬.‫ﺍﻟﻌﺎﻤﺔ‬ ‫ﻭﺍﻟﻨﻅﺭﻴﺔ‬‫ﺘﻁﺒﻴﻕ‬ ‫ﺒﺩﻭﻥ‬ ‫ﺘﺘﺤﻘﻕ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺘﻠﻙ‬
‫ﺍﻟﻌﺎﻤل‬ ‫ﺍﻜﺘﺸﻔﻬﺎ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﺤﺭﻜﺔ‬ ‫ﻗﻭﺍﻨﻴﻥ‬‫ﺇﺴﺤﺎﻕ‬‫ﻨﻴﻭﺘﻥ‬)1642-1727(‫ﺍﻟﺴﺎﺒﻊ‬ ‫ﺍﻟﻘﺭﻥ‬ ‫ﻓﻲ‬
‫ﻋﺎﺩﻴﺔ‬ ‫ﺴﺭﻋﺎﺕ‬ ‫ﻋﻨﺩ‬،‫ﺘﺼﺒﺢ‬ ‫ﻋﻨﺩﻤﺎ‬ ‫ﺘﻁﺒﻕ‬ ‫ﻻ‬ ‫ﺍﻟﻘﻭﺍﻨﻴﻥ‬ ‫ﺘﻠﻙ‬ ‫ﻭﻟﻜﻥ‬‫ﺍﻷﺠﺴﺎﻡ‬ ‫ﺤﺭﻜﺔ‬
‫ﺍﻟﻌﺎﻟﻡ‬ ‫ﻭﻀﻌﻬﺎ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﻌﺎﻤﺔ‬ ‫ﺍﻟﻨﺴﺒﻴﺔ‬ ‫ﺍﻟﻨﻅﺭﻴﺔ‬‫ﺃﻟﺒﺭﺕ‬‫ﺍﻴﻨﺸﺘﻴﻥ‬)1879-1955(‫ﺒﺩﺍﻴﺔ‬ ‫ﻓﻲ‬
www.trgma.com
‫ﻜل‬ ‫ﻤﺜل‬‫ﺃﻓﺭﻉ‬‫ﺍﻟﻜﻤﻴﺔ‬ ‫ﻭﺍﻟﻘﻴﺎﺴﺎﺕ‬ ‫ﺍﻟﻌﻤﻠﻴﺔ‬ ‫ﺍﻟﻤﻼﺤﻅﺎﺕ‬ ‫ﻋﻠﻰ‬ ‫ﺘﻌﺘﻤﺩ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬ ،‫ﺍﻟﻌﻠﻭﻡ‬
‫ﺍﻟﻘﻭﺍﻨﻴﻥ‬‫ﺍﻷﺴﺎﺴﻴﺔ‬‫ﺍﻟﻘﻭﺍﻨﻴﻥ‬ ‫ﻫﺫﻩ‬ ‫ﻟﺘﺴﺘﺨﺩﻡ‬ ‫ﺍﻟﻁﺒﻴﻌﻴﺔ‬ ‫ﺍﻟﻅﻭﺍﻫﺭ‬ ‫ﺘﺤﻜﻡ‬ ‫ﺍﻟﺘﻲ‬
‫ﺍﻟﻘﻭﺍﻨﻴﻥ‬‫ﺍﻷﺴﺎﺴﻴﺔ‬‫ﺍﻟﻨﻅﺭﻴﺔ‬ ‫ﺒﻴﻥ‬ ‫ﺍﻟﺠﺴﺭ‬ ‫ﺍﻟﺭﻴﺎﻀﻴﺎﺕ‬ ‫ﻭﺘﻌﺘﺒﺭ‬ ،‫ﺍﻟﺭﻴﺎﻀﻴﺎﺕ‬ ‫ﺒﻠﻐﺔ‬ ‫ﻋﻨﻬﺎ‬ ‫ﻴﻌﺒﺭ‬ ‫ﻨﻅﺭﻴﺎﺕ‬ ‫ﻟﺘﻁﻭﻴﺭ‬ ‫ﺍﻟﻤﺴﺘﺨﺩﻤﺔ‬
‫ﻭﺍﻟﺘﺠﺭﺒﺔ‬.
‫ﻴﺠﺏ‬ ‫ﺠﺩﻴﺩﺓ‬ ‫ﻨﻅﺭﻴﺎﺕ‬ ‫ﻓﺎﻥ‬ ‫ﻭﺍﻟﻨﻅﺭﻴﺔ‬ ‫ﺍﻟﻌﻤﻠﻴﺔ‬ ‫ﺍﻟﻨﺘﺎﺌﺞ‬ ‫ﺒﻴﻥ‬ ‫ﺘﻌﺎﺭﺽ‬ ‫ﻫﻨﺎﻙ‬ ‫ﻴﻜﻭﻥ‬ ‫ﻋﻨﺩﻤﺎ‬
‫ﻭﺠﺩﻨﺎ‬ ‫ﺍﻟﺤﺎﻻﺕ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻌﺩﻴﺩ‬‫ﺇﻥ‬‫ﻤﺤﺩﺩﺓ‬ ‫ﻅﺭﻭﻑ‬ ‫ﻓﻲ‬ ‫ﻓﻘﻁ‬ ‫ﺼﺎﻟﺤﺔ‬ ‫ﺍﻟﻨﻅﺭﻴﺔ‬
،‫ﻤﺤﺩﺩﺓ‬ ‫ﻅﺭﻭﻑ‬،‫ﺍﻟﻤﺜﺎل‬ ‫ﺴﺒﻴل‬ ‫ﻋﻠﻰ‬‫ﺍﻟﻌﺎﻤل‬ ‫ﺍﻜﺘﺸﻔﻬﺎ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﺤﺭﻜﺔ‬ ‫ﻗﻭﺍﻨﻴﻥ‬
‫ﺤﺭﻜﺔ‬ ‫ﺒﺩﻗﺔ‬ ‫ﺘﺼﻑ‬ ‫ﻜﺎﻨﺕ‬ ‫ﻋﺸﺭ‬‫ﺍﻷﺠﺴﺎﻡ‬‫ﻋﺎﺩﻴﺔ‬ ‫ﺴﺭﻋﺎﺕ‬ ‫ﻋﻨﺩ‬
‫ﺍﻟﻀﻭﺀ‬ ‫ﺒﺴﺭﻋﺔ‬ ‫ﺘﻘﺎﺭﻥ‬.‫ﺍﻟﻤﻘﺎﺒل‬ ‫ﻓﻲ‬‫ﺍﻟﻌﺎﻟﻡ‬ ‫ﻭﻀﻌﻬﺎ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﻌﺎﻤﺔ‬ ‫ﺍﻟﻨﺴﺒﻴﺔ‬ ‫ﺍﻟﻨﻅﺭﻴﺔ‬

6
‫ﻟﻨﻴﻭﺘﻥ‬ ‫ﺍﻟﺤﺭﻜﺔ‬ ‫ﻤﻌﺎﺩﻻﺕ‬ ‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬ ‫ﻋﻠﻴﻬﺎ‬ ‫ﺤﺼﻠﻨﺎ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﻨﺘﺎﺌﺞ‬ ‫ﻨﻔﺱ‬‫ﺒﺎﻹﻀﺎﻓﺔ‬‫ﺇﻟﻰ‬‫ﻟﻠﺤﺭﻜﺔ‬ ‫ﺩﻗﻴﻕ‬ ‫ﻭﺼﻑ‬
‫ﻟﻠﺤﺭﻜﺔ‬ ‫ﻋﺎﻤﺔ‬ ‫ﻨﻅﺭﻴﺔ‬ ‫ﺍﻴﻨﺸﺘﻴﻥ‬ ‫ﻨﻅﺭﻴﺔ‬ ‫ﺘﻌﺘﺒﺭ‬ ‫ﻭﻟﻬﺫﺍ‬.
‫ﺍﻟﻌﺎﻡ‬ ‫ﻗﺒل‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬ ‫ﻜل‬ ‫ﺘﻌﻨﻲ‬ ،‫ﺍﻟﻜﻼﺴﻴﻜﻴﺔ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬1900‫ﻭﺍﻟﻘﻭﺍﻨﻴﻥ‬ ‫ﻭﺍﻟﻤﺒﺎﺩﺉ‬ ‫ﺍﻟﻨﻅﺭﻴﺎﺕ‬ ‫ﺘﺸﻜل‬ ‫ﻭﺍﻟﺘﻲ‬‫ﻭﺍﻟﺘﺠﺎﺭﺏ‬‫ﻓﻲ‬
‫ﻭﺍﻟﻤﻐﻨﺎﻁﻴﺴﻴﺔ‬ ‫ﻭﺍﻟﻜﻬﺭﺒﻴﺔ‬.
‫ﺍﻟﻤﻴﻜ‬ ‫ﻋﻠﻡ‬ ‫ﻁﻭﺭ‬ ‫ﺍﻨﻪ‬ ‫ﺤﻴﺙ‬ ‫ﺍﻟﻜﻼﺴﻴﻜﻴﺔ‬ ‫ﻟﻠﻔﻴﺯﻴﺎﺀ‬ ‫ﻤﻤﻴﺯﺍ‬ ‫ﺠﻬﺩﺍ‬ ‫ﻨﻴﻭﺘﻥ‬ ‫ﺍﻟﻌﺎﻟﻡ‬ ‫ﻗﺩﻡ‬‫ﻋ‬ ‫ﻤﺅﺴﺴﻲ‬ ‫ﻤﻥ‬ ‫ﻭﻜﺎﻥ‬ ‫ﺍﻟﻜﻼﺴﻴﻜﻴﺔ‬ ‫ﺎﻨﻴﻜﺎ‬‫ﻠﻡ‬
‫ﻋﻠﻡ‬ ‫ﻋﻠﻰ‬ ‫ﻁﺭﺃﺕ‬‫ﺍﻟﻤﻴﻜﺎﻨﻴﻜﺎ‬‫ﺍﻟﺩﻴﻨﺎﻤﻴﻜﺎ‬ ‫ﻤﺠﺎل‬ ‫ﻭﻟﻜﻥ‬ ،‫ﻋﺸﺭ‬ ‫ﺍﻟﺜﺎﻤﻥ‬ ‫ﺍﻟﻘﺭﻥ‬ ‫ﻓﻲ‬ ‫ﺍﺴﺘﻤﺭﺕ‬
‫ﻴﺘﻁﻭﺭ‬ ‫ﻟﻡ‬ ‫ﻨﺎﻁﻴﺴﻴﺔ‬‫ﺇﻻ‬‫ﻴﻌﻭﺩ‬ ‫ﻭﻫﺫﺍ‬ ،‫ﻋﺸﺭ‬ ‫ﺍﻟﺘﺎﺴﻊ‬ ‫ﺍﻟﻘﺭﻥ‬ ‫ﻨﻬﺎﻴﺔ‬ ‫ﻓﻲ‬‫ﺇﻟﻰ‬‫ﺸﺢ‬‫ﺍﻷﺠﻬﺯﺓ‬‫ﻭﺍﻷﺩﻭﺍﺕ‬
‫ﺍﻟﺤﺩﻴﺜﺔ‬ ‫ﺒﺎﻟﻔﻴﺯﻴﺎﺀ‬modern physics‫ﻋﺸﺭ‬ ‫ﺍﻟﺘﺎﺴﻊ‬ ‫ﺍﻟﻘﺭﻥ‬ ‫ﻤﻁﻠﻊ‬ ‫ﻓﻲ‬ ‫ﺒﺩﺃ‬ ،.‫ﺍﻟﺤﺩﻴﺜﺔ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬
‫ﺍﻟﻜﻼﺴﻴﻜﻴﺔ‬ ‫ﺍﻟﻤﻴﻜﺎﻨﻴﻜﺎ‬ ‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬ ‫ﺘﻔﺴﻴﺭﻫﺎ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻌﻠﻤﺎﺀ‬ ‫ﻴﺘﻤﻜﻥ‬ ‫ﻟﻡ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﺍﻟﻅﻭﺍﻫﺭ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻌﺩﻴﺩ‬ ‫ﺍﻜﺘﺸﺎﻑ‬ ‫ﺒﺴﺒﺏ‬ ‫ﺘﻁﻭﺭﺕ‬.‫ﻟﻘﺩ‬
‫ﺍﻟﻜﻡ‬ ‫ﻭﻤﻴﻜﺎﻨﻴﻜﺎ‬ ‫ﺍﻟﻨﺴﺒﻴﺔ‬ ‫ﺍﻟﻨﻅﺭﻴﺔ‬ ‫ﺍﻟﺤﺩﻴﺜﺔ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬ ‫ﻓﻲ‬ ‫ﻨﻅﺭﻴﺘﻴﻥ‬.‫ﻟﻠﻨﺴﺒﻴﺔ‬ ‫ﺍﻴﻨﺸﺘﻴﻥ‬ ‫ﻨﻅﺭﻴﺔ‬‫ﺃﺤ‬‫ﺩﺜﺕ‬‫ﻤﺫﻫﻼ‬ ‫ﺘﻁﻭﺭﺍ‬
‫ﺘ‬ ‫ﻭﺍﻟﺘﻲ‬ ‫ﺍﻟﺩﻗﻴﻘﺔ‬ ‫ﺍﻟﺫﺭﻴﺔ‬ ‫ﺍﻟﺠﺴﻴﻤﺎﺕ‬ ‫ﻋﻠﻰ‬ ‫ﺘﻁﺒﻕ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﻜﻡ‬ ‫ﻤﻴﻜﺎﻨﻴﻜﺎ‬‫ﻟﻭﺼﻑ‬ ‫ﺴﺘﺨﺩﻡ‬
‫ﻋﻠﻰ‬ ‫ﺍﻟﻜﻡ‬ ‫ﻤﻴﻜﺎﻨﻴﻜﺎ‬ ‫ﻨﺸﺄﺕ‬ ‫ﻭﻗﺩ‬ ‫ﺫﺭﻱ‬ ‫ﻤﺴﺘﻭﻯ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﺍﻟﻅﻭﺍﻫﺭ‬ ‫ﻭﺘﻔﺴﻴﺭ‬‫ﺃﻴﺩﻱ‬‫ﺍﻟﻌﻠﻤﺎﺀ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻌﺩﻴﺩ‬.
www.trgma.com
‫ﺍﻟﻌﺎﻡ‬1900‫ﺃﻋﻁﺕ‬‫ﻟﻨﻴﻭﺘﻥ‬ ‫ﺍﻟﺤﺭﻜﺔ‬ ‫ﻤﻌﺎﺩﻻﺕ‬ ‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬ ‫ﻋﻠﻴﻬﺎ‬ ‫ﺤﺼﻠﻨﺎ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﻨﺘﺎﺌﺞ‬ ‫ﻨﻔﺱ‬
‫ﺘﻘﺘﺭﺏ‬ ‫ﻋﻨﺩﻤﺎ‬‫ﺍﻷﺠﺴﺎﻡ‬‫ﺍﻟﻀﻭﺀ‬ ‫ﺴﺭﻋﺔ‬ ‫ﻤﻥ‬.‫ﻟﻠﺤﺭﻜﺔ‬ ‫ﻋﺎﻤﺔ‬ ‫ﻨﻅﺭﻴﺔ‬ ‫ﺍﻴﻨﺸﺘﻴﻥ‬ ‫ﻨﻅﺭﻴﺔ‬ ‫ﺘﻌﺘﺒﺭ‬ ‫ﻭﻟﻬﺫﺍ‬
‫ﺍﻟﻌﺎﻡ‬ ‫ﻗﺒل‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬ ‫ﻜل‬ ‫ﺘﻌﻨﻲ‬ ،‫ﺍﻟﻜﻼﺴﻴﻜﻴﺔ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬
‫ﺍﻟﺤﺭﺍﺭﻴﺔ‬ ‫ﻭﺍﻟﺩﻴﻨﺎﻤﻴﻜﺎ‬ ‫ﺍﻟﻜﻼﺴﻴﻜﻴﺔ‬ ‫ﺍﻟﻤﻴﻜﺎﻨﻴﻜﺎ‬‫ﻭﺍﻟﻤﻐﻨﺎﻁﻴﺴﻴﺔ‬ ‫ﻭﺍﻟﻜﻬﺭﺒﻴﺔ‬
‫ﺍﻟﻤﻴﻜ‬ ‫ﻋﻠﻡ‬ ‫ﻁﻭﺭ‬ ‫ﺍﻨﻪ‬ ‫ﺤﻴﺙ‬ ‫ﺍﻟﻜﻼﺴﻴﻜﻴﺔ‬ ‫ﻟﻠﻔﻴﺯﻴﺎﺀ‬ ‫ﻤﻤﻴﺯﺍ‬ ‫ﺠﻬﺩﺍ‬ ‫ﻨﻴﻭﺘﻥ‬ ‫ﺍﻟﻌﺎﻟﻡ‬ ‫ﻗﺩﻡ‬
‫ﺍﻟﺭﻴﺎﻀﻴﺎﺕ‬.‫ﺍﻟﺘﻁﻭﻴﺭﺍﺕ‬ ‫ﻤﻌﻅﻡ‬‫ﺍﻟﺘﻲ‬‫ﻋﻠﻡ‬ ‫ﻋﻠﻰ‬ ‫ﻁﺭﺃﺕ‬
‫ﻭﺍﻟﻤﻐ‬ ‫ﻭﺍﻟﻜﻬﺭﺒﻴﺔ‬ ‫ﺍﻟﺤﺭﺍﺭﻴﺔ‬‫ﻴﺘﻁﻭﺭ‬ ‫ﻟﻡ‬ ‫ﻨﺎﻁﻴﺴﻴﺔ‬
‫ﺍﻟﻼﺯﻤﺔ‬‫ﻹﺠﺭﺍﺀ‬‫ﺍﻟﻌﻠﻤﻴﺔ‬ ‫ﻭﺍﻟﺒﺤﻭﺙ‬ ‫ﺍﻟﺘﺠﺎﺭﺏ‬.
‫ﻴﺴﻤﻰ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬ ‫ﻓﻲ‬ ‫ﺠﺩﻴﺩ‬ ‫ﻋﺼﺭ‬‫ﺍﻟﺤﺩﻴﺜﺔ‬ ‫ﺒﺎﻟﻔﻴﺯﻴﺎﺀ‬
‫ﺍﻟﻜﻼﺴﻴﻜﻴﺔ‬ ‫ﺍﻟﻤﻴﻜﺎﻨﻴﻜﺎ‬ ‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬ ‫ﺘﻔﺴﻴﺭﻫﺎ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻌﻠﻤﺎﺀ‬ ‫ﻴﺘﻤﻜﻥ‬ ‫ﻟﻡ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﺍﻟﻅﻭﺍﻫﺭ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻌﺩﻴﺩ‬ ‫ﺍﻜﺘﺸﺎﻑ‬ ‫ﺒﺴﺒﺏ‬ ‫ﺘﻁﻭﺭﺕ‬
‫ﻜﺎﻨﺕ‬‫ﺃﻋﻅﻡ‬‫ﺍﻟﻜﻡ‬ ‫ﻭﻤﻴﻜﺎﻨﻴﻜﺎ‬ ‫ﺍﻟﻨﺴﺒﻴﺔ‬ ‫ﺍﻟﻨﻅﺭﻴﺔ‬ ‫ﺍﻟﺤﺩﻴﺜﺔ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬ ‫ﻓﻲ‬ ‫ﻨﻅﺭﻴﺘﻴﻥ‬
،‫ﻭﺍﻟﻁﺎﻗﺔ‬ ‫ﻭﺍﻟﻤﻜﺎﻥ‬ ‫ﺍﻟﺯﻤﺎﻥ‬ ‫ﻤﺒﺎﺩﺉ‬ ‫ﻓﻲ‬‫ﺃﻤﺎ‬‫ﺘ‬ ‫ﻭﺍﻟﺘﻲ‬ ‫ﺍﻟﺩﻗﻴﻘﺔ‬ ‫ﺍﻟﺫﺭﻴﺔ‬ ‫ﺍﻟﺠﺴﻴﻤﺎﺕ‬ ‫ﻋﻠﻰ‬ ‫ﺘﻁﺒﻕ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﻜﻡ‬ ‫ﻤﻴﻜﺎﻨﻴﻜﺎ‬
‫ﻋﻠﻰ‬ ‫ﺍﻟﻜﻡ‬ ‫ﻤﻴﻜﺎﻨﻴﻜﺎ‬ ‫ﻨﺸﺄﺕ‬ ‫ﻭﻗﺩ‬ ‫ﺫﺭﻱ‬ ‫ﻤﺴﺘﻭﻯ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﺍﻟﻅﻭﺍﻫﺭ‬ ‫ﻭﺘﻔﺴﻴﺭ‬

7
‫ﻴﻭﻡ‬ ‫ﻭﻜل‬ ،‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﻭﺍﻟﻘﻭﺍﻨﻴﻥ‬ ‫ﺍﻟﻁﺒﻴﻌﻴﺔ‬ ‫ﺒﺎﻟﻅﻭﺍﻫﺭ‬ ‫ﺍﻟﻤﺘﻌﻠﻘﺔ‬ ‫ﺍﻟﻨﻅﺭﻴﺔ‬ ‫ﺍﻟﻤﻔﺎﻫﻴﻡ‬ ‫ﺘﻁﻭﻴﺭ‬ ‫ﻋﻠﻰ‬ ‫ﻤﺴﺘﻤﺭﺓ‬ ‫ﺒﺼﻭﺭﺓ‬ ‫ﺍﻟﻌﻠﻤﺎﺀ‬ ‫ﻴﻘﻭﻡ‬
‫ﻭﻜﺫﻟﻙ‬ ‫ﻭﺍﻟﺠﻴﻭﻟﻭﺠﻴﺎ‬ ‫ﻭﺍﻟﺒﻴﻭﻟﻭﺠﻲ‬ ‫ﻭﺍﻟﻜﻴﻤﻴﺎﺀ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬ ‫ﺒﻴﻥ‬ ‫ﺘﺩﺍﺨل‬ ‫ﻨﺠﺩ‬ ‫ﺍﻟﺒﺤﻭﺙ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻜﺜﻴﺭ‬ ‫ﻓﻲ‬
‫ﺍﻟﺘﻁﻭﻴﺭﺍﺕ‬‫ﻫﻲ‬ ‫ﺍﻟﻴﻭﻡ‬ ‫ﺍﻟﻌﺎﻟﻡ‬ ‫ﻴﺸﻬﺩﻫﺎ‬ ‫ﺍﻟﺘﻲ‬)1(‫ﺍﻟﻔﻀﺎﺌﻴﺔ‬ ‫ﺍﻟﺭﺤﻼﺕ‬‫ﺇﻟﻰ‬‫ﻭﻫﺒﻭﻁ‬ ‫ﺍﻟﻘﻤﺭ‬
‫ﻭ‬ ،‫ﺍﻟﻜﻤﺒﻴﻭﺘﺭ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻜﺒﻴﺭ‬ ‫ﻭﺍﻟﺘﻁﻭﺭ‬ ‫ﺍﻟﺩﻗﻴﻘﺔ‬ ‫ﺍﻻﻟﻜﺘﺭﻭﻨﻴﺔ‬ ‫ﺍﻟﺩﻭﺍﺌﺭ‬)3(‫ﺍﻟﺘﺼﻭﻴﺭ‬ ‫ﻓﻲ‬ ‫ﺍﻟﺤﺩﻴﺜﺔ‬ ‫ﺍﻟﺘﻘﻨﻴﺎﺕ‬
‫ﺍﻟﻌﻠﻴﻤﺔ‬ ‫ﻭﺍﻟﺒﺤﻭﺙ‬ ‫ﺍﻟﻁﺏ‬ ‫ﻤﺠﺎل‬ ‫ﻓﻲ‬ ‫ﻭﺨﺼﻭﺼﺎ‬.‫ﺇﻥ‬‫ﺤﻴﺎﺘﻨﺎ‬ ‫ﻋﻠﻰ‬ ‫ﻭﺍﻻﻜﺘﺸﺎﻓﺎﺕ‬ ‫ﺍﻟﺘﻁﻭﺭﺍﺕ‬ ‫ﻫﺫﻩ‬ ‫ﺍﺜﺭ‬‫ﺍﻟﻤﺘﻭﻗﻊ‬ ‫ﻭﻤﻥ‬ ،‫ﻋﻅﻴﻡ‬‫ﺃﻥ‬
‫ﺒﺎﻟﻔﺎﺌﺩﺓ‬ ‫ﺤﻴﺎﺘﻪ‬ ‫ﻋﻠﻰ‬ ‫ﺘﻨﻌﻜﺱ‬ ‫ﺴﻭﻑ‬ ‫ﺍﻟﺘﻲ‬ ‫ﻭﺍﻻﻜﺘﺸﺎﻓﺎﺕ‬ ‫ﺍﻟﺘﻁﻭﺭﺍﺕ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻤﺯﻴﺩ‬ ‫ﺍﻟﻌﺎﻟﻡ‬ ‫ﻴﺸﻬﺩ‬‫ﺇﻥ‬‫ﺍﷲ‬ ‫ﺸﺎﺀ‬.
www.trgma.com
‫ﻴﻭﻡ‬ ‫ﻭﻜل‬ ،‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﻭﺍﻟﻘﻭﺍﻨﻴﻥ‬ ‫ﺍﻟﻁﺒﻴﻌﻴﺔ‬ ‫ﺒﺎﻟﻅﻭﺍﻫﺭ‬ ‫ﺍﻟﻤﺘﻌﻠﻘﺔ‬ ‫ﺍﻟﻨﻅﺭﻴﺔ‬ ‫ﺍﻟﻤﻔﺎﻫﻴﻡ‬ ‫ﺘﻁﻭﻴﺭ‬ ‫ﻋﻠﻰ‬ ‫ﻤﺴﺘﻤﺭﺓ‬ ‫ﺒﺼﻭﺭﺓ‬ ‫ﺍﻟﻌﻠﻤﺎﺀ‬ ‫ﻴﻘﻭﻡ‬
‫ﺠﺩﻴﺩﺓ‬ ‫ﺍﻜﺘﺸﺎﻓﺎﺕ‬ ‫ﻟﻨﺎ‬ ‫ﻴﻅﻬﺭ‬.‫ﻭﻜﺫﻟﻙ‬ ‫ﻭﺍﻟﺠﻴﻭﻟﻭﺠﻴﺎ‬ ‫ﻭﺍﻟﺒﻴﻭﻟﻭﺠﻲ‬ ‫ﻭﺍﻟﻜﻴﻤﻴﺎﺀ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬ ‫ﺒﻴﻥ‬ ‫ﺘﺩﺍﺨل‬ ‫ﻨﺠﺩ‬ ‫ﺍﻟﺒﺤﻭﺙ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻜﺜﻴﺭ‬ ‫ﻓﻲ‬
‫ﺍﻟﻬﻨﺩﺴﻴﺔ‬ ‫ﺍﻟﻌﻠﻭﻡ‬ ‫ﻤﻊ‬.‫ﻭﻤﻥ‬‫ﺃﻫﻡ‬‫ﺍﻟﺘﻁﻭﻴﺭﺍﺕ‬
‫ﺍﻹﻨﺴﺎﻥ‬،‫ﻋﻠﻴﻪ‬)2(‫ﻭ‬ ،‫ﺍﻟﻜﻤﺒﻴﻭﺘﺭ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻜﺒﻴﺭ‬ ‫ﻭﺍﻟﺘﻁﻭﺭ‬ ‫ﺍﻟﺩﻗﻴﻘﺔ‬ ‫ﺍﻻﻟﻜﺘﺭﻭﻨﻴﺔ‬ ‫ﺍﻟﺩﻭﺍﺌﺭ‬
‫ﺍﻟﻌﻠﻴﻤﺔ‬ ‫ﻭﺍﻟﺒﺤﻭﺙ‬ ‫ﺍﻟﻁﺏ‬ ‫ﻤﺠﺎل‬ ‫ﻓﻲ‬ ‫ﻭﺨﺼﻭﺼﺎ‬
‫ﺒﺎﻟﻔﺎﺌﺩﺓ‬ ‫ﺤﻴﺎﺘﻪ‬ ‫ﻋﻠﻰ‬ ‫ﺘﻨﻌﻜﺱ‬ ‫ﺴﻭﻑ‬ ‫ﺍﻟﺘﻲ‬ ‫ﻭﺍﻻﻜﺘﺸﺎﻓﺎﺕ‬ ‫ﺍﻟﺘﻁﻭﺭﺍﺕ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻤﺯﻴﺩ‬ ‫ﺍﻟﻌﺎﻟﻡ‬ ‫ﻴﺸﻬﺩ‬

8
‫ﻭﺍﻟﺯﻤﻥ‬ ‫ﻭﺍﻟﻜﺘﻠﺔ‬ ‫ﺍﻟﻁﻭل‬ ‫ﺘﻌﺭﻴﻑ‬
‫ﻤﻨﻬﺎ‬ ‫ﻴﺘﻁﻠﺏ‬ ‫ﻤﺤﺩﺩﺓ‬ ‫ﻓﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﻜﻤﻴﺎﺕ‬ ‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬ ‫ﻗﻭﺍﻨﻴﻥ‬ ‫ﻋﻥ‬ ‫ﻨﻌﺒﺭ‬ ‫ﻨﺤﻥ‬‫ﺃﻥ‬‫ﻭﺒﻭﻀﻭﺡ‬ ‫ﺒﺩﻗﺔ‬ ‫ﻨﻌﺭﻓﻬﺎ‬.‫ﻭ‬‫ﻋﻠﻡ‬ ‫ﻓﻲ‬
‫ﺍﻟﻁﻭل‬ ‫ﻫﻲ‬ ‫ﻓﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﻜﻤﻴﺎﺕ‬ ‫ﺜﻼﺙ‬ ‫ﻫﻨﺎﻙ‬ ،‫ﺍﻟﻤﻴﻜﺎﻨﻴﻜﺎ‬L‫ﻭﺍﻟﻜﺘﻠﺔ‬M‫ﻭﺍﻟﺯﻤﻥ‬T.‫ﻋﻠﻡ‬ ‫ﻓﻲ‬ ‫ﺍﻷﺨﺭﻯ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﺍﻟﻜﻤﻴﺎﺕ‬ ‫ﻭﺠﻤﻴﻊ‬
‫ﺍﻟﺜﻼﺜﺔ‬ ‫ﺍﻷﺴﺎﺴﻴﺔ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﺍﻟﻜﻤﻴﺎﺕ‬ ‫ﻤﻥ‬ ‫ﻋﻠﻴﻬﺎ‬ ‫ﺍﻟﺤﺼﻭل‬ ‫ﻴﺘﻡ‬ ‫ﻤﺸﺘﻘﺔ‬ ‫ﻓﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﻜﻤﻴﺎﺕ‬ ‫ﻫﻲ‬ ‫ﺍﻟﻤﻴﻜﺎﻨﻴﻜﺎ‬)L, M , T.(
‫ﻟﺸﺨﺹ‬ ‫ﻤﺎ‬ ‫ﺸﻲﺀ‬ ‫ﻗﻴﺎﺴﺎﺕ‬ ‫ﻨﺘﺎﺌﺞ‬‫ﺃﺨﺭ‬‫ﻴﺭﻴﺩ‬‫ﺃﻥ‬‫ﺍﻟﻘﻴﺎﺴﺎﺕ‬ ‫ﺘﻠﻙ‬ ‫ﻴﻌﻴﺩ‬،‫ﺍﻟﻀﺭﻭﺭﻱ‬ ‫ﻤﻥ‬ ‫ﻓﺎﻨﻪ‬‫ﺇﻥ‬
.‫ﻜﻭﻜﺏ‬ ‫ﻤﻥ‬ ‫ﺯﺍﺌﺭ‬ ‫ﺯﺍﺭﻨﺎ‬ ‫ﻟﻭ‬ ‫ﻓﻤﺜﻼ‬‫ﺁﺨﺭ‬‫ﻗﺩﺭﻫﺎ‬ ‫ﻤﺴﺎﻓﺔ‬ ‫ﻗﻁﻊ‬ ‫ﺍﻨﻪ‬ ‫ﻟﻨﺎ‬ ‫ﻭﻗﺎل‬ ‫ﻤﺜﻼ‬8
‫ﺍﻟﻤﺴﺎﻓﺔ‬ ‫ﺘﻠﻙ‬ ‫ﺘﻘﺩﻴﺭ‬ ‫ﻨﺴﺘﻁﻴﻊ‬ ‫ﻟﻥ‬‫ﺇﺫﺍ‬‫ﺠﻠ‬ ‫ﻜﻠﻤﺔ‬ ‫ﺘﻌﻨﻲ‬ ‫ﻤﺎﺫﺍ‬ ‫ﻨﻌﺭﻑ‬ ‫ﻨﻜﻥ‬ ‫ﻟﻡ‬‫ﺘﻠﻙ‬ ‫ﺘﺵ‬.‫ﻨﺎﺤﻴﺔ‬ ‫ﻭﻤﻥ‬‫ﺃﺨﺭﻯ‬‫ﺇﺫﺍ‬‫ﻜﺎﻥ‬
‫ﻨﺴﺘﺨﺩﻤﻪ‬ ‫ﺍﻟﺫﻱ‬ ‫ﺍﻟﻘﻴﺎﺴﺎﺕ‬ ‫ﻨﻅﺎﻡ‬ ‫ﻴﻌﺭﻑ‬ ‫ﺸﺨﺹ‬ ‫ﻫﻨﺎﻙ‬‫ﻓﺈﻨﻨﺎ‬‫ﻟﻪ‬ ‫ﻨﻘﻭل‬ ‫ﻋﻨﺩﻤﺎ‬‫ﺇﻥ‬‫ﺍﻟﺠﺩﺍﺭ‬ ‫ﻫﺫﺍ‬ ‫ﻁﻭل‬2‫ﻭﺤﺩﺓ‬ ‫ﺍﺴﺘﺨﺩﻤﻨﺎ‬ ‫ﻭﻫﻨﺎ‬ ‫ﻤﺘﺭ‬
‫ﻴﻌﺎﺩل‬ ‫ﺍﻟﺠﺩﺍﺭ‬ ‫ﻁﻭل‬2‫ﺍﻟﻤﺘﺭ‬ ‫ﺍﻟﻘﻴﺎﺱ‬ ‫ﻭﺤﺩﺓ‬ ‫ﻤﻥ‬.،‫ﻭﺒﺎﻟﻤﺜل‬‫ﺇﺫﺍ‬‫ﺸﺨﺹ‬ ‫ﺍﺨﺒﺭﻨﺎ‬‫ﺁﺨﺭ‬‫ﻜﺘﻠﺘﻪ‬ ‫ﺒﺎﻥ‬75
‫ﻴﻌﻨﻲ‬ ‫ﻫﺫﺍ‬ ‫ﻓﺎﻥ‬ ،‫ﺍﻟﻜﻴﻠﻭﺠﺭﺍﻡ‬ ‫ﻫﻲ‬ ‫ﺍﺴﺘﺨﺩﻤﺕ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﻜﺘﻠﺔ‬ ‫ﻭﺤﺩﺓ‬‫ﺃﻥ‬‫ﻴﻌﺎﺩل‬ ‫ﺍﻟﺸﺨﺹ‬ ‫ﺫﻟﻙ‬75‫ﻤﺭﺓ‬
‫ﻴﺠﺏ‬ ‫ﻓﺈﻨﻪ‬ ‫ﺍﻟﻤﺴﺘﺨﺩﻤﺔ‬ ‫ﺍﻟﻭﺤﺩﺍﺕ‬ ‫ﻜﺎﻨﺕ‬ ‫ﻭﻤﻬﻤﺎ‬‫ﺃﻥ‬‫ﻭﻴﺴﺘﺨﺩﻤﻬﺎ‬ ‫ﺍﻟﺠﻤﻴﻊ‬ ‫ﻋﻠﻰ‬ ‫ﻤﻌﻤﻤﺔ‬ ‫ﺍﻟﻭﺤﺩﺓ‬ ‫ﻫﺫﻩ‬ ‫ﺘﻜﻭﻥ‬
‫ﻤﻜﺎﻨﻨﺎ‬ ‫ﺍﺨﺘﻠﻑ‬ ‫ﻤﻬﻤﺎ‬.
‫ﻓﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﻭﻜﻤﻴﺎﺕ‬ ‫ﻭﺍﻟﻜﺘﻠﺔ‬ ‫ﻟﻠﻁﻭل‬ ‫ﺍﻟﻤﺴﺘﺨﺩﻤﺔ‬ ‫ﺍﻟﻤﻌﺎﻴﻴﺭ‬ ‫ﻟﺘﺄﺴﻴﺱ‬ ‫ﺍﻟﻌﺎﻟﻤﻲ‬ ‫ﺍﻟﻤﺅﺘﻤﺭ‬ ‫ﻋﻘﺩ‬‫ﺃﺨﺭﻯ‬.‫ﻭﻫﺫﻩ‬
‫ﺍﻟﻤﺘﺭﻱ‬ ‫ﺍﻟﻨﻅﺎﻡ‬ ‫ﺒﺎﺴﻡ‬ ‫ﺘﻌﺭﻑ‬ ‫ﺍﻟﻤﺅﺘﻤﺭ‬ ‫ﺫﻟﻙ‬ ‫ﻓﻲ‬ ‫ﻭﻀﻌﺕ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﻤﻌﺎﻴﻴﺭ‬metric system‫ﺒﻨﻅﺎﻡ‬ ‫ﻭﻴﻌﺭﻑ‬ ،SI‫ﺍﺨﺘﺼﺎﺭ‬ ‫ﻭﻫﻲ‬
www.trgma.com
1.1‫ﻭﺍﻟﺯﻤﻥ‬ ‫ﻭﺍﻟﻜﺘﻠﺔ‬ ‫ﺍﻟﻁﻭل‬ ‫ﺘﻌﺭﻴﻑ‬
‫ﻤﻨﻬﺎ‬ ‫ﻴﺘﻁﻠﺏ‬ ‫ﻤﺤﺩﺩﺓ‬ ‫ﻓﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﻜﻤﻴﺎﺕ‬ ‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬ ‫ﻗﻭﺍﻨﻴﻥ‬ ‫ﻋﻥ‬ ‫ﻨﻌﺒﺭ‬ ‫ﻨﺤﻥ‬
‫ﺍﻟﻁﻭل‬ ‫ﻫﻲ‬ ‫ﻓﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﻜﻤﻴﺎﺕ‬ ‫ﺜﻼﺙ‬ ‫ﻫﻨﺎﻙ‬ ،‫ﺍﻟﻤﻴﻜﺎﻨﻴﻜﺎ‬
‫ﺍﻟﺜﻼﺜﺔ‬ ‫ﺍﻷﺴﺎﺴﻴﺔ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﺍﻟﻜﻤﻴﺎﺕ‬ ‫ﻤﻥ‬ ‫ﻋﻠﻴﻬﺎ‬ ‫ﺍﻟﺤﺼﻭل‬ ‫ﻴﺘﻡ‬ ‫ﻤﺸﺘﻘﺔ‬ ‫ﻓﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﻜﻤﻴﺎﺕ‬ ‫ﻫﻲ‬ ‫ﺍﻟﻤﻴﻜﺎﻨﻴﻜﺎ‬
‫ﻓﺈﺫﺍ‬‫ﺃﺭﺩﻨﺎ‬‫ﺃﻥ‬‫ﻨﻘﻭﻡ‬‫ﺒﺈﻋﻁﺎﺀ‬‫ﻟﺸﺨﺹ‬ ‫ﻤﺎ‬ ‫ﺸﻲﺀ‬ ‫ﻗﻴﺎﺴﺎﺕ‬ ‫ﻨﺘﺎﺌﺞ‬
‫ﻤﻌﺎ‬ ‫ﻫﻨﺎﻙ‬ ‫ﻴﻜﻭﻥ‬‫ﻴ‬‫ﻴﺭ‬standard‫ﻋﻠﻴﻬﺎ‬ ‫ﻤﺘﻔﻕ‬.
‫ﺠﻠﺘﺵ‬!‫ﻓﺈﻨﻨﺎ‬‫ﺍﻟﻤﺴﺎﻓﺔ‬ ‫ﺘﻠﻙ‬ ‫ﺘﻘﺩﻴﺭ‬ ‫ﻨﺴﺘﻁﻴﻊ‬ ‫ﻟﻥ‬
‫ﻨﺴﺘﺨﺩﻤﻪ‬ ‫ﺍﻟﺫﻱ‬ ‫ﺍﻟﻘﻴﺎﺴﺎﺕ‬ ‫ﻨﻅﺎﻡ‬ ‫ﻴﻌﺭﻑ‬ ‫ﺸﺨﺹ‬ ‫ﻫﻨﺎﻙ‬
‫ﺤﻴﺙ‬ ،‫ﺒﺎﻟﻤﺘﺭ‬ ‫ﺘﻌﺭﻑ‬‫ﺃﻥ‬‫ﻴﻌﺎﺩل‬ ‫ﺍﻟﺠﺩﺍﺭ‬ ‫ﻁﻭل‬
‫ﻨﻼﺤﻅ‬ ‫ﻭﻫﻨﺎ‬ ‫ﻜﻴﻠﻭﺠﺭﺍﻡ‬‫ﺇﻥ‬‫ﻴﻌﻨﻲ‬ ‫ﻫﺫﺍ‬ ‫ﻓﺎﻥ‬ ،‫ﺍﻟﻜﻴﻠﻭﺠﺭﺍﻡ‬ ‫ﻫﻲ‬ ‫ﺍﺴﺘﺨﺩﻤﺕ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﻜﺘﻠﺔ‬ ‫ﻭﺤﺩﺓ‬
‫ﻜﺘﻠﺔ‬1‫ﻜﻴﻠﻭﺠﺭﺍﻡ‬.‫ﻴﺠﺏ‬ ‫ﻓﺈﻨﻪ‬ ‫ﺍﻟﻤﺴﺘﺨﺩﻤﺔ‬ ‫ﺍﻟﻭﺤﺩﺍﺕ‬ ‫ﻜﺎﻨﺕ‬ ‫ﻭﻤﻬﻤﺎ‬
‫ﻗﻴﺎﺴﺎﺘﻨﺎ‬ ‫ﺘﻌﺎﺩل‬ ‫ﺒﻬﺎ‬ ‫ﻗﻴﺎﺴﺎﺘﻬﻡ‬ ‫ﻟﺘﻜﻭﻥ‬ ‫ﺍﻟﻜل‬‫ﻤﻜﺎﻨﻨﺎ‬ ‫ﺍﺨﺘﻠﻑ‬ ‫ﻤﻬﻤﺎ‬
‫ﺍﻟﻌﺎﻡ‬ ‫ﻓﻲ‬1960‫ﻓﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﻭﻜﻤﻴﺎﺕ‬ ‫ﻭﺍﻟﻜﺘﻠﺔ‬ ‫ﻟﻠﻁﻭل‬ ‫ﺍﻟﻤﺴﺘﺨﺩﻤﺔ‬ ‫ﺍﻟﻤﻌﺎﻴﻴﺭ‬ ‫ﻟﺘﺄﺴﻴﺱ‬ ‫ﺍﻟﻌﺎﻟﻤﻲ‬ ‫ﺍﻟﻤﺅﺘﻤﺭ‬ ‫ﻋﻘﺩ‬
‫ﺍﻟﻤﺘﺭﻱ‬ ‫ﺍﻟﻨﻅﺎﻡ‬ ‫ﺒﺎﺴﻡ‬ ‫ﺘﻌﺭﻑ‬ ‫ﺍﻟﻤﺅﺘﻤﺭ‬ ‫ﺫﻟﻙ‬ ‫ﻓﻲ‬ ‫ﻭﻀﻌﺕ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﻤﻌﺎﻴﻴﺭ‬

9
Systeme Internatio".‫ﻭﺤﺩﺍﺕ‬ ‫ﺍﻟﻨﻅﺎﻡ‬ ‫ﻫﺫﺍ‬ ‫ﻓﻲ‬‫ﻫﻲ‬ ‫ﻭﺍﻟﺯﻤﻥ‬ ‫ﻭﺍﻟﻜﺘﻠﺔ‬ ‫ﺍﻟﻁﻭل‬"‫ﺍﻟﻤﺘﺭ‬"
‫ﻫﻲ‬ ‫ﺃﺨﺭﻯ‬ ‫ﻭﺤﺩﺍﺕ‬ ‫ﺇﻟﻰ‬ ‫ﺒﺎﻹﻀﺎﻓﺔ‬"‫ﺍﻟﻜﻠﻔﻥ‬"‫ﻭ‬ ‫ﺍﻟﺤﺭﺍﺭﺓ‬ ‫ﺩﺭﺠﺔ‬ ‫ﻭﺤﺩﺓ‬"‫ﺍﻷﻤﺒﻴﺭ‬"‫ﺍﻟﻜﻬﺭﺒﻲ‬ ‫ﺍﻟﺘﻴﺎﺭ‬ ‫ﻭﺤﺩﺓ‬
‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﻜﻤﻴﺔ‬ ‫ﻗﻴﺎﺱ‬ ‫ﻭﺤﺩﺓ‬.‫ﺍﻟﻤﻴﻜﺎﻨﻴﻜ‬ ‫ﻟﻌﻠﻡ‬ ‫ﺩﺭﺍﺴﺘﻨﺎ‬ ‫ﻭﻓﻲ‬‫ﻋﻠﻰ‬ ‫ﻨﺭﻜﺯ‬ ‫ﺴﻭﻑ‬ ‫ﺎ‬
‫ﻭﺍﻟﺯﻤﻥ‬ ‫ﻭﺍﻟﻜﺘﻠﺔ‬ ‫ﺍﻟﻁﻭل‬ ‫ﻫﻲ‬ ‫ﻭﺍﻟﺘﻲ‬ ‫ﺍﻷﺴﺎﺴﻴﺔ‬ ‫ﺍﻟﻜﻤﻴﺎﺕ‬ ‫ﺍﻟﻭﺤﺩﺍﺕ‬.
‫ﺍﻟﻁﻭل‬ ‫ﻗﻴﺎﺱ‬ ‫ﻭﺤﺩﺓ‬ ‫ﺘﻌﺘﻤﺩ‬‫ﻭﺃﻋﻁﺎﻫﺎ‬‫ﺍﻟﻴﺎﺭﺩﺍ‬ ‫ﺍﺴﻡ‬yard‫ﻋﻠﻰ‬‫ﺃﻥ‬‫ﺍﻟﻴﺎﺭﺩﺍ‬ ‫ﻤﻘﺩﺍﺭ‬ ‫ﻴﻜﻭﻥ‬
‫ﺍﺴﺘﻘﺎﻤﺘﻬﺎ‬ ‫ﻋﻠﻰ‬ ‫ﻤﺩﻫﺎ‬ ‫ﻋﻨﺩ‬ ‫ﻴﺩﻩ‬ ‫ﻁﺭﻑ‬.‫ﺍﻥ‬ ‫ﻜﻤﺎ‬‫ﻫﻲ‬ ‫ﻟﻠﻁﻭل‬ ‫ﺃﺨﺭﻯ‬ ‫ﻭﺤﺩﺓ‬ ‫ﺃﻴﻀﺎ‬ ‫ﻫﻨﺎﻙ‬‫ﻭﺤﺩﺓ‬
‫ﻋﺸﺭ‬ ‫ﺍﻟﺭﺍﺒﻊ‬ ‫ﻟﻭﻴﺱ‬ ‫ﺍﻟﻔﺭﻨﺴﻲ‬ ‫ﺍﻟﻤﻠﻙ‬ ‫ﻗﺩﻡ‬ ‫ﻟﻁﻭل‬ ‫ﺘﻌﻭﺩ‬.‫ﺤﺘﻰ‬ ‫ﺍﺴﺘﺨﺩﺍﻤﻬﻤﺎ‬ ‫ﺍﺴﺘﻤﺭ‬ ‫ﺍﻟﻭﺤﺩﺘﻴﻥ‬ ‫ﻫﺎﺘﻴﻥ‬
‫ﻋﻠﻰ‬ ‫ﻋﺭﻓﺕ‬ ‫ﻭﺍﻟﺘﻲ‬ ‫ﺍﻟﻘﻴﺎﺴﻴﺔ‬ ‫ﺍﻟﻭﺤﺩﺓ‬ ‫ﻫﻲ‬ ‫ﺍﻟﻤﺘﺭ‬ ‫ﻭﺤﺩﺓ‬‫ﺇﻨﻬﺎ‬‫ﺨﻁ‬ ‫ﺒﻴﻥ‬ ‫ﺍﻟﻤﺴﺎﻓﺔ‬ ‫ﻤﻠﻴﻭﻥ‬ ‫ﻋﺸﺭ‬
‫ﺒﺎﺭﻴﺱ‬ ‫ﻋﺒﺭ‬ ‫ﻴﻤﺭ‬ ‫ﻁﻭل‬ ‫ﺨﻁ‬ ‫ﺍﻤﺘﺩﺍﺩ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﺸﻤﺎﻟﻲ‬.
‫ﺍﻟﻘﻴﺎﺴﺎﺕ‬ ‫ﻟﺘﻭﺤﻴﺩ‬ ‫ﺍﻟﻌﺎﻟﻤﻲ‬ ‫ﺍﻟﻤﺅﺘﻤﺭ‬ ‫ﺒﻔﻀل‬ ‫ﻭﻟﻜﻥ‬ ‫ﺍﻟﺴﻨﻭﺍﺕ‬ ‫ﻤﺩﺍﺭ‬ ‫ﻋﻠﻰ‬ ‫ﺍﺴﺘﺨﺩﺍﻤﻬﺎ‬ ‫ﺘﻡ‬ ‫ﺍﻟﻁﻭل‬ ‫ﻗﻴﺎﺱ‬‫ﺃﺼﺒﺤﺕ‬
‫ﺍﻟﻤﺘﺭ‬ ‫ﻭﻫﻲ‬ ‫ﺍﻟﻁﻭل‬ ‫ﻗﻴﺎﺱ‬ ‫ﻭﺤﺩﺓ‬ ‫ﻨﻔﺱ‬ ‫ﺘﺴﺘﺨﺩﻡ‬ ‫ﺍﻟﺩﻭل‬ ‫ﻜﺎﻓﺔ‬.‫ﺍﻟﻌﺎﻡ‬ ‫ﻭﻓﻲ‬1960‫ﺘﻡ‬‫ﺇﻋﺎﺩﺓ‬‫ﺒﻴﻥ‬ ‫ﺍﻟﻤﺴﺎﻓﺔ‬ ‫ﺍﻨﻪ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﻤﺘﺭ‬ ‫ﺘﻌﺭﻴﻑ‬
www.trgma.com
‫ﺍﻟﻔﺭﻨﺴﻲ‬ ‫ﻟﻠﻤﺼﻁﻠﺢ‬"Systeme International
‫ﻭ‬"‫ﺍﻟﻜﻴﻠﻭﺠﺭﺍﻡ‬"‫ﻭ‬"‫ﺍﻟﺜﺎﻨﻴﺔ‬."‫ﻫﻲ‬ ‫ﺃﺨﺭﻯ‬ ‫ﻭﺤﺩﺍﺕ‬ ‫ﺇﻟﻰ‬ ‫ﺒﺎﻹﻀﺎﻓﺔ‬
‫ﻭ‬"‫ﺍﻟﺸﻤﻌﺔ‬"‫ﻭ‬ ‫ﺍﻹﻀﺎﺀﺓ‬ ‫ﺸﺩﺓ‬ ‫ﻭﺤﺩﺓ‬"‫ﺍﻟﻤﻭل‬"‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﻜﻤﻴﺔ‬ ‫ﻗﻴﺎﺱ‬ ‫ﻭﺤﺩﺓ‬
‫ﻭﺍﻟﺯﻤﻥ‬ ‫ﻭﺍﻟﻜﺘﻠﺔ‬ ‫ﺍﻟﻁﻭل‬ ‫ﻫﻲ‬ ‫ﻭﺍﻟﺘﻲ‬ ‫ﺍﻷﺴﺎﺴﻴﺔ‬ ‫ﺍﻟﻜﻤﻴﺎﺕ‬ ‫ﺍﻟﻭﺤﺩﺍﺕ‬
‫ﺍﻟﻁﻭل‬Length
‫ﺍﻟﻌﺎﻡ‬ ‫ﻓﻲ‬1120‫ﺃﻤﺭ‬‫ﺒﺭﻴﻁﺎﻨﻴﺎ‬ ‫ﻤﻠﻙ‬‫ﺃﻥ‬‫ﺍﻟﻁﻭل‬ ‫ﻗﻴﺎﺱ‬ ‫ﻭﺤﺩﺓ‬ ‫ﺘﻌﺘﻤﺩ‬
‫ﺤﺘﻰ‬ ‫ﺍﻨﻔﻪ‬ ‫ﻁﺭﻑ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻁﻭل‬ ‫ﻫﻭ‬‫ﺍﺴﺘﻘﺎﻤﺘﻬﺎ‬ ‫ﻋﻠﻰ‬ ‫ﻤﺩﻫﺎ‬ ‫ﻋﻨﺩ‬ ‫ﻴﺩﻩ‬ ‫ﻁﺭﻑ‬
‫ﺍﻟﻘﺩﻡ‬foot‫ﺍﻟﻭﺤﺩﺓ‬ ‫ﻭﻫﺫﻩ‬‫ﻋﺸﺭ‬ ‫ﺍﻟﺭﺍﺒﻊ‬ ‫ﻟﻭﻴﺱ‬ ‫ﺍﻟﻔﺭﻨﺴﻲ‬ ‫ﺍﻟﻤﻠﻙ‬ ‫ﻗﺩﻡ‬ ‫ﻟﻁﻭل‬ ‫ﺘﻌﻭﺩ‬
‫ﺍﻟﻌﺎﻡ‬1799‫ﻋﻨﺩﻤﺎ‬ ،‫ﺃﺼﺒﺤﺕ‬‫ﻋﻠﻰ‬ ‫ﻋﺭﻓﺕ‬ ‫ﻭﺍﻟﺘﻲ‬ ‫ﺍﻟﻘﻴﺎﺴﻴﺔ‬ ‫ﺍﻟﻭﺤﺩﺓ‬ ‫ﻫﻲ‬ ‫ﺍﻟﻤﺘﺭ‬ ‫ﻭﺤﺩﺓ‬
‫ﺍﻟﻘﻁﺏ‬ ‫ﺇﻟﻰ‬ ‫ﺍﻻﺴﺘﻭﺍﺀ‬‫ﺒﺎﺭﻴﺱ‬ ‫ﻋﺒﺭ‬ ‫ﻴﻤﺭ‬ ‫ﻁﻭل‬ ‫ﺨﻁ‬ ‫ﺍﻤﺘﺩﺍﺩ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﺸﻤﺎﻟﻲ‬
‫ﻤﻥ‬ ‫ﺍﻟﻜﺜﻴﺭ‬‫ﺃﻨﻅﻤﺔ‬‫ﺍﻟﻘﻴﺎﺴﺎﺕ‬ ‫ﻟﺘﻭﺤﻴﺩ‬ ‫ﺍﻟﻌﺎﻟﻤﻲ‬ ‫ﺍﻟﻤﺅﺘﻤﺭ‬ ‫ﺒﻔﻀل‬ ‫ﻭﻟﻜﻥ‬ ‫ﺍﻟﺴﻨﻭﺍﺕ‬ ‫ﻤﺩﺍﺭ‬ ‫ﻋﻠﻰ‬ ‫ﺍﺴﺘﺨﺩﺍﻤﻬﺎ‬ ‫ﺘﻡ‬ ‫ﺍﻟﻁﻭل‬ ‫ﻗﻴﺎﺱ‬
‫ﺍﻟﻤﺘﺭ‬ ‫ﻭﻫﻲ‬ ‫ﺍﻟﻁﻭل‬ ‫ﻗﻴﺎﺱ‬ ‫ﻭﺤﺩﺓ‬ ‫ﻨﻔﺱ‬ ‫ﺘﺴﺘﺨﺩﻡ‬ ‫ﺍﻟﺩﻭل‬ ‫ﻜﺎﻓﺔ‬

10
‫ﺃﺒﻌﺎﺩ‬ ‫ﻤﺜل‬ ‫ﺍﻟﻤﺘﺭ‬ ‫ﻤﻥ‬ ‫ﺠﺩﺍ‬ ‫ﺼﻐﻴﺭﺓ‬ ‫ﺃﺠﺯﺍﺀ‬ ‫ﺇﻟﻰ‬ ‫ﺘﺘﺭﺍﻭﺡ‬ ‫ﺍﻟﺘﻲ‬ ‫ﻤﺨﺘﻠﻔﺔ‬ ‫ﻷﻁﻭﺍل‬ ‫ﺍﻟﻘﻴﺎﺴﺎﺕ‬ ‫ﻤﻥ‬ ‫ﻤﺠﻤﻭﻉ‬ ‫ﻴﻌﺭﺽ‬
‫ﺍﻷﻤﺘﺎﺭ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻤﻼﻴﻴﻥ‬ ‫ﺃﺨﺭﻯ‬ ‫ﻭﻗﻴﺎﺴﺎﺕ‬ ‫ﺍﻟﺫﺭﺓ‬.‫ﻭﺍﻟﺸﻤﺱ‬ ‫ﺍﻷﺭﺽ‬ ‫ﺒﻴﻥ‬ ‫ﻭﺍﻟﻤﺴﺎﻓﺔ‬ ‫ﺍﻷﺭﺽ‬ ‫ﻗﻁﺭ‬ ‫ﻋﻥ‬ ‫ﻨﺘﺤﺩﺙ‬ ‫ﻋﻨﺩﻤﺎ‬.
www.trgma.com
‫ﺠﺩﻭل‬1.1‫ﺃﺒﻌﺎﺩ‬ ‫ﻤﺜل‬ ‫ﺍﻟﻤﺘﺭ‬ ‫ﻤﻥ‬ ‫ﺠﺩﺍ‬ ‫ﺼﻐﻴﺭﺓ‬ ‫ﺃﺠﺯﺍﺀ‬ ‫ﺇﻟﻰ‬ ‫ﺘﺘﺭﺍﻭﺡ‬ ‫ﺍﻟﺘﻲ‬ ‫ﻤﺨﺘﻠﻔﺔ‬ ‫ﻷﻁﻭﺍل‬ ‫ﺍﻟﻘﻴﺎﺴﺎﺕ‬ ‫ﻤﻥ‬ ‫ﻤﺠﻤﻭﻉ‬ ‫ﻴﻌﺭﺽ‬
‫ﺍﻷﻤﺘﺎﺭ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻤﻼﻴﻴﻥ‬ ‫ﺃﺨﺭﻯ‬ ‫ﻭﻗﻴﺎﺴﺎﺕ‬ ‫ﺍﻟﺫﺭﺓ‬

11
‫ﻓﺭﻨﺴﺎ‬ ‫ﻓﻲ‬ ‫ﺒﻌﻨﺎﻴﺔ‬ ‫ﺤﻔﻅﻪ‬ ‫ﺘﻡ‬ ‫ﻭﺍﻻﺭﺍﺩﻴﻭﻡ‬ ‫ﺍﻟﺒﻼﺘﻴﻨﻴﻭﻡ‬ ‫ﻤﻥ‬ ‫ﺴﺎﻕ‬ ‫ﻋﻠﻰ‬ ‫ﺨﻁﻴﻥ‬.‫ﺩﻗﻴﻕ‬ ‫ﻏﻴﺭ‬ ‫ﻴﻌﺘﺒﺭ‬ ‫ﺍﻟﻤﻌﻴﺎﺭ‬ ‫ﻫﺫﺍ‬ ‫ﻭﻟﻜﻥ‬‫ﺒﻤﻘﺎﻴﻴﺴﻨﺎ‬‫ﺍﻟﻴﻭﻡ‬
‫ﻴﻤﻜﻥ‬ ‫ﺍﻟﺴﺎﻕ‬ ‫ﺫﻟﻙ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﺨﻁﻴﻥ‬ ‫ﺒﻴﻥ‬ ‫ﺍﻟﻤﺴﺎﻓﺔ‬‫ﺃﻥ‬‫ﺍﻟﺤﺭﺍﺭﺓ‬ ‫ﺩﺭﺠﺔ‬ ‫ﺒﺘﻐﻴﺭ‬ ‫ﺘﺘﻐﻴﺭ‬،‫ﻴﻁﺭﺃ‬ ‫ﺤﻴﺙ‬‫ﺘﻤﺩﺩ‬‫ﻟﻠﺴﺎﻕ‬ ‫ﻭﺍﻨﻜﻤﺎﺵ‬
‫ﻭﺤﺩﺓ‬‫ﺍﻟﻤﺘﺭ‬.‫ﺘﻡ‬ ‫ﻭﻟﻬﺫﺍ‬‫ﺇﻋﺎﺩﺓ‬‫ﻋﻠﻰ‬ ‫ﺍﻟﻤﺘﺭ‬ ‫ﺘﻌﺭﻴﻑ‬‫ﺃﻥ‬‫ﻋﺩﺩ‬ ‫ﻋﻥ‬ ‫ﻋﺒﺎﺭﺓ‬ ‫ﻴﻜﻭﻥ‬
‫ﻜﺭﺒﺘﻭﻥ‬ ‫ﻤﺼﺒﺎﺡ‬ ‫ﻤﻥ‬ ‫ﻤﻨﺒﻌﺙ‬ ‫ﻤﻭﺠﻲ‬-86.‫ﺍﻟﻤﺘﺭ‬ ‫ﻓﺎﻥ‬ ‫ﺤﺎل‬ ‫ﺃﻱ‬ ‫ﻭﻋﻠﻰ‬‫ﻴﺩ‬‫ﻋ‬ُ‫ﺃ‬‫ﻤﺭﺓ‬ ‫ﺘﻌﺭﻴﻔﻪ‬‫ﺃﺨﺭﻯ‬‫ﻓﻲ‬
‫ﻗﺩﺭﻩ‬ ‫ﺯﻤﻥ‬ ‫ﺨﻼل‬ ‫ﺍﻟﻔﺭﺍﻍ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻀﻭﺀ‬ ‫ﻴﻘﻁﻌﻬﺎ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﻤﺴﺎﻓﺔ‬ ‫ﻋﻥ‬ ‫ﻋﺒﺎﺭﺓ‬ ‫ﻟﻴﻜﻭﻥ‬1/299,792,458‫ﺜﺎﻨﻴﺔ‬.‫ﻭﻫﺫﺍ‬
‫ﺒﺩﻗﺔ‬ ‫ﺘﺴﺎﻭﻱ‬ ‫ﻭﺍﻟﺘﻲ‬ ‫ﺍﻟﻔﺭﺍﻍ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻀﻭﺀ‬ ‫ﺴﺭﻋﺔ‬ ‫ﺇﻟﻰ‬ ‫ﻴﻌﻭﺩ‬299,792,458‫ﻤﺘﺭ‬/‫ﺜﺎﻨﻴﺔ‬.
‫ﺍﻟﻜﻴﻠﻭﺠﺭﺍﻡ‬ ‫ﻫﻲ‬ ‫ﺍﻟﻜﺘﻠﺔ‬ ‫ﻟﻘﻴﺎﺱ‬ ‫ﺍﻟﻤﺴﺘﺨﺩﻤﺔ‬ ‫ﺍﻟﻭﺤﺩﺓ‬kilogram (kg)‫ﻤﻌﺩﻥ‬ ‫ﻤﻥ‬ ‫ﺍﺴﻁﻭﺍﻨﻴﺔ‬ ‫ﺴﺒﻴﻜﺔ‬ ‫ﻜﺘﻠﺔ‬ ‫ﺇﻨﻬﺎ‬ ‫ﻋﻠﻰ‬ ‫ﻭﺘﻌﺭﻑ‬
.‫ﺍﻟﻌﺎﻡ‬ ‫ﻓﻲ‬ ‫ﺍﻋﺘﻤﺎﺩﻫﺎ‬ ‫ﺘﻡ‬ ‫ﺍﻟﻭﺤﺩﺓ‬ ‫ﻫﺫﻩ‬1887‫ﺍﻟﻜﻴﻠﻭﺠﺭﺍﻡ‬ ‫ﺘﻌﺭﻴﻑ‬ ‫ﻋﻠﻰ‬ ‫ﻴﻁﺭﺃ‬ ‫ﻭﻟﻡ‬
‫ﻤﺴﺘﻘﺭﺓ‬ ‫ﺘﻌﺘﺒﺭ‬ ‫ﻭﺍﻻﺭﺍﺩﻴﻭﻡ‬ ‫ﺍﻟﺒﻼﺘﻴﻨﻭﻡ‬ ‫ﺴﺒﻴﻜﺔ‬ ‫ﻻﻥ‬ ‫ﺘﻐﻴﺭ‬ ‫ﺃﻱ‬.‫ﻭﻫﻲ‬ ‫ﺍﻻﺴﻁﻭﺍﻨﻴﺔ‬ ‫ﺍﻟﺴﺒﻴﻜﺔ‬ ‫ﺘﻠﻙ‬ ‫ﻤﻥ‬ ‫ﺃﺨﺭﻯ‬ ‫ﻨﺴﺨﺔ‬ ‫ﻋﻤل‬ ‫ﻭﺘﻡ‬
‫ﻗﻴﺎﺴﻬﺎ‬ ‫ﻜﺘل‬ ‫ﺘﺼﻨﻴﻊ‬ ‫ﻓﻲ‬ ‫ﻻﺴﺘﺨﺩﺍﻤﻬﺎ‬ ‫ﻭﺍﻟﺘﻜﻨﻭﻟﻭﺠﻴﺎ‬ ‫ﻟﻠﻤﻌﺎﻴﻴﺭ‬ ‫ﺍﻟﻭﻁﻨﻲ‬ ‫ﺍﻟﻤﻌﻬﺩ‬ ‫ﻓﻲ‬ ‫ﺤﻔﻭﻅﺔ‬1‫ﻭﺍﻟﺸﻜل‬ ‫ﺃﺨﺭﻯ‬ ‫ﻜﻴﻠﻭﺠﺭﺍﻡ‬1.1a
www.trgma.com
‫ﻓﺭﻨﺴﺎ‬ ‫ﻓﻲ‬ ‫ﺒﻌﻨﺎﻴﺔ‬ ‫ﺤﻔﻅﻪ‬ ‫ﺘﻡ‬ ‫ﻭﺍﻻﺭﺍﺩﻴﻭﻡ‬ ‫ﺍﻟﺒﻼﺘﻴﻨﻴﻭﻡ‬ ‫ﻤﻥ‬ ‫ﺴﺎﻕ‬ ‫ﻋﻠﻰ‬ ‫ﺨﻁﻴﻥ‬
‫ﺤﻴﺙ‬‫ﺃﻥ‬‫ﻴﻤﻜﻥ‬ ‫ﺍﻟﺴﺎﻕ‬ ‫ﺫﻟﻙ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﺨﻁﻴﻥ‬ ‫ﺒﻴﻥ‬ ‫ﺍﻟﻤﺴﺎﻓﺔ‬
‫ﺍﻟﺤﺭﺍﺭﺓ‬ ‫ﺩﺭﺠﺎﺕ‬ ‫ﺘﻐﻴﺭ‬ ‫ﻤﻊ‬‫ﺘﺘﻐﻴﺭ‬ ‫ﻭﺒﺎﻟﺘﺎﻟﻲ‬‫ﻭﺤﺩﺓ‬
1,650,763.73‫ﻁﻭل‬‫ﻜﺭﺒﺘﻭﻥ‬ ‫ﻤﺼﺒﺎﺡ‬ ‫ﻤﻥ‬ ‫ﻤﻨﺒﻌﺙ‬ ‫ﻤﻭﺠﻲ‬
‫ﺍﻟﻌﺎﻡ‬1983‫ﻗﺩﺭﻩ‬ ‫ﺯﻤﻥ‬ ‫ﺨﻼل‬ ‫ﺍﻟﻔﺭﺍﻍ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻀﻭﺀ‬ ‫ﻴﻘﻁﻌﻬﺎ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﻤﺴﺎﻓﺔ‬ ‫ﻋﻥ‬ ‫ﻋﺒﺎﺭﺓ‬ ‫ﻟﻴﻜﻭﻥ‬
‫ﺒﺩﻗﺔ‬ ‫ﺘﺴﺎﻭﻱ‬ ‫ﻭﺍﻟﺘﻲ‬ ‫ﺍﻟﻔﺭﺍﻍ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻀﻭﺀ‬ ‫ﺴﺭﻋﺔ‬ ‫ﺇﻟﻰ‬ ‫ﻴﻌﻭﺩ‬
‫ﺍﻟﻜﺘﻠﺔ‬Mass
‫ﺍﻟﻜﻴﻠﻭﺠﺭﺍﻡ‬ ‫ﻫﻲ‬ ‫ﺍﻟﻜﺘﻠﺔ‬ ‫ﻟﻘﻴﺎﺱ‬ ‫ﺍﻟﻤﺴﺘﺨﺩﻤﺔ‬ ‫ﺍﻟﻭﺤﺩﺓ‬
‫ﻓﺭﻨﺴﺎ‬ ‫ﻓﻲ‬ ‫ﻤﺤﻔﻭﻅﺔ‬ ‫ﻭﺍﻻﺭﺍﺩﻴﻭﻡ‬ ‫ﺍﻟﺒﻼﺘﻴﻨﻴﻭﻡ‬.
‫ﻤﺴﺘﻘﺭﺓ‬ ‫ﺘﻌﺘﺒﺭ‬ ‫ﻭﺍﻻﺭﺍﺩﻴﻭﻡ‬ ‫ﺍﻟﺒﻼﺘﻴﻨﻭﻡ‬ ‫ﺴﺒﻴﻜﺔ‬ ‫ﻻﻥ‬ ‫ﺘﻐﻴﺭ‬ ‫ﺃﻱ‬
‫ﻤ‬‫ﻗﻴﺎﺴﻬﺎ‬ ‫ﻜﺘل‬ ‫ﺘﺼﻨﻴﻊ‬ ‫ﻓﻲ‬ ‫ﻻﺴﺘﺨﺩﺍﻤﻬﺎ‬ ‫ﻭﺍﻟﺘﻜﻨﻭﻟﻭﺠﻴﺎ‬ ‫ﻟﻠﻤﻌﺎﻴﻴﺭ‬ ‫ﺍﻟﻭﻁﻨﻲ‬ ‫ﺍﻟﻤﻌﻬﺩ‬ ‫ﻓﻲ‬ ‫ﺤﻔﻭﻅﺔ‬
‫ﺍﻟﻜﺘﻠﺔ‬ ‫ﻟﻬﺫﻩ‬ ‫ﺼﻭﺭﺓ‬ ‫ﻴﻭﻀﺢ‬.
‫ﺠﺩﻭل‬1.2‫ﺃﺠﺴﺎﻡ‬ ‫ﻜﺘﻠﺔ‬ ‫ﻗﻴﻤﺔ‬ ‫ﻴﻭﻀﺢ‬ ‫ﺠﺩﻭل‬

12
(a)
‫ﻟﻠﻤﻌﺎﻴﻴﺭ‬ ‫ﺍﻟﻭﻁﻨﻲ‬ ‫ﺍﻟﻤﻌﻬﺩ‬ ‫ﻓﻲ‬ ‫ﻤﺯﺩﻭﺝ‬ ‫ﻭﻋﺎﺀ‬ ‫ﻓﻲ‬ ‫ﻤﺤﻔﻭﻅﺔ‬ ‫ﻭﻫﻲ‬ ‫ﺍﻟﻘﻴﺎﺴﻴﺔ‬ ‫ﺍﻟﻜﺘﻠﺔ‬ ‫ﻋﻥ‬ ‫ﻨﺴﺨﺔ‬ ‫ﻴﻭﻀﺢ‬
‫ﺩﻗﺔ‬ ‫ﻭﺘﻘﺩﺭ‬ ‫ﻭﺍﻟﺘﻜﻨﻭﻟﻭﺠﻴﺎ‬ ‫ﻟﻠﻤﻌﺎﻴﻴﺭ‬ ‫ﺍﻟﻭﻁﻨﻲ‬ ‫ﺍﻟﻤﻌﻬﺩ‬ ‫ﻤﺨﺘﺒﺭﺍﺕ‬ ‫ﺍﺤﺩ‬ ‫ﻓﻲ‬ ‫ﺍﻟﺫﺭﻴﺔ‬ ‫ﺍﻟﺴﺎﻋﺔ‬
‫ﺨﻼل‬ ‫ﺜﺎﻨﻴﺔ‬ ‫ﺘﺅﺨﺭ‬ ‫ﻭﻻ‬ ‫ﺘﻘﺩﻡ‬ ‫ﻻ‬ ‫ﺒﺄﻨﻬﺎ‬ ‫ﺍﻟﺴﺎﻋﺔ‬ ‫ﻫﺫﻩ‬20‫ﺴﻨﺔ‬ ‫ﻤﻠﻴﻭﻥ‬.
www.trgma.com
(b)
‫ﺸﻜل‬1.1)a(‫ﻟﻠﻤﻌﺎﻴﻴﺭ‬ ‫ﺍﻟﻭﻁﻨﻲ‬ ‫ﺍﻟﻤﻌﻬﺩ‬ ‫ﻓﻲ‬ ‫ﻤﺯﺩﻭﺝ‬ ‫ﻭﻋﺎﺀ‬ ‫ﻓﻲ‬ ‫ﻤﺤﻔﻭﻅﺔ‬ ‫ﻭﻫﻲ‬ ‫ﺍﻟﻘﻴﺎﺴﻴﺔ‬ ‫ﺍﻟﻜﺘﻠﺔ‬ ‫ﻋﻥ‬ ‫ﻨﺴﺨﺔ‬ ‫ﻴﻭﻀﺢ‬
‫ﻭﺍﻟﺘﻜﻨﻭﻟﻭﺠﻴﺎ‬) .b(‫ﻴﻭﻀﺢ‬‫ﺩﻗﺔ‬ ‫ﻭﺘﻘﺩﺭ‬ ‫ﻭﺍﻟﺘﻜﻨﻭﻟﻭﺠﻴﺎ‬ ‫ﻟﻠﻤﻌﺎﻴﻴﺭ‬ ‫ﺍﻟﻭﻁﻨﻲ‬ ‫ﺍﻟﻤﻌﻬﺩ‬ ‫ﻤﺨﺘﺒﺭﺍﺕ‬ ‫ﺍﺤﺩ‬ ‫ﻓﻲ‬ ‫ﺍﻟﺫﺭﻴﺔ‬ ‫ﺍﻟﺴﺎﻋﺔ‬
‫ﺨﻼل‬ ‫ﺜﺎﻨﻴﺔ‬ ‫ﺘﺅﺨﺭ‬ ‫ﻭﻻ‬ ‫ﺘﻘﺩﻡ‬ ‫ﻻ‬ ‫ﺒﺄﻨﻬﺎ‬ ‫ﺍﻟﺴﺎﻋﺔ‬ ‫ﻫﺫﻩ‬

13
‫ﺍﻟﺯﻤﻥ‬Time
‫ﺍﻟﻌﺎﻡ‬ ‫ﻗﺒل‬1960‫ﻤﺘﻭﺴﻁ‬ ‫ﻋﻠﻰ‬ ‫ﻴﻌﺘﻤﺩ‬ ‫ﺍﻟﺯﻤﻥ‬ ‫ﺘﻌﺭﻴﻑ‬ ‫ﻜﺎﻥ‬
‫ﺤﻴﺙ‬ ‫ﺍﻟﻴﻭﻡ‬ ‫ﻁﻭل‬‫ﺇﻥ‬‫ﻅﻬﻭﺭﻴﻥ‬ ‫ﺒﻴﻥ‬ ‫ﺍﻟﺯﻤﻨﻴﺔ‬ ‫ﺍﻟﻔﺘﺭﺓ‬ ‫ﻫﻭ‬ ‫ﺍﻟﻴﻭﻡ‬
‫ﻓﻲ‬ ‫ﻟﻬﺎ‬ ‫ﺍﺭﺘﻔﺎﻉ‬ ‫ﺃﻗﺼﻰ‬ ‫ﻓﻲ‬ ‫ﺘﻜﻭﻥ‬ ‫ﻋﻨﺩﻤﺎ‬ ‫ﻟﻠﺸﻤﺱ‬ ‫ﻤﺘﻌﺎﻗﺒﻴﻥ‬
‫ﺍﻟﺴﻤﺎﺀ‬.‫ﻋﻠﻰ‬ ‫ﺍﻟﺜﺎﻨﻴﺔ‬ ‫ﻋﺭﻓﺕ‬ ‫ﻋﻠﻴﻪ‬ ‫ﻭﺒﻨﺎﺀ‬‫ﺇﻨﻬﺎ‬
(1/60)(1/60)(1/24)‫ﺍﻟﻴﻭﻡ‬ ‫ﻁﻭل‬ ‫ﻤﺘﻭﺴﻁ‬ ‫ﻤﻥ‬.‫ﺒﻌﺩ‬ ‫ﻭﻟﻜﻥ‬
‫ﻭﻟﻬﺫﺍ‬ ،‫ﺍﻟﺯﻤﻥ‬ ‫ﻤﻊ‬ ‫ﻗﻠﻴﻼ‬ ‫ﻴﺘﻐﻴﺭ‬ ‫ﺍﻷﺭﺽ‬ ‫ﺩﻭﺭﺍﻥ‬ ‫ﺇﻥ‬ ‫ﻋﺭﻑ‬ ‫ﺃﻥ‬
‫ﻟﺘﻌﺭﻴﻑ‬ ‫ﺠﻴﺩ‬ ‫ﺨﻴﺎﺭ‬ ‫ﻴﻌﺘﺒﺭ‬ ‫ﻻ‬ ‫ﺍﻟﺤﺭﻜﺔ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻻﻋﺘﻤﺎﺩ‬ ‫ﻓﺎﻥ‬
‫ﺍﻟﺯﻤﻥ‬.
‫ﺍﻟﻌﺎﻡ‬ ‫ﻓﻲ‬1967‫ﺍﻟﺴﺎﻋﺔ‬ ‫ﻋﻠﻰ‬ ‫ﺒﺎﻻﻋﺘﻤﺎﺩ‬ ‫ﺍﻟﺜﺎﻨﻴﺔ‬ ‫ﺘﻌﺭﻴﻑ‬ ‫ﺃﻋﻴﺩ‬
‫ﺍﻟﺸﻜل‬ ‫ﺍﻟﺫﺭﻴﺔ‬1.1(b)‫ﺤﻴﺙ‬ ،‫ﺫﺭﺕ‬ ‫ﺘﺭﺩﺩ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻻﻋﺘﻤﺎﺩ‬ ‫ﺘﻡ‬
‫ﺍﻟﺴﻴﺯﻴﻭﻡ‬-133.‫ﻓﺄﺼﺒﺢ‬‫ﻋﺩﺩ‬ ‫ﺍﻨﻪ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﺜﺎﻨﻴﺔ‬ ‫ﺘﻌﺭﻴﻑ‬
9,192,631,770‫ﺍﻟﺴﻴﺯﻴﻭﻡ‬ ‫ﺫﺭﺓ‬ ‫ﻋﻥ‬ ‫ﺘﺼﺩﺭ‬ ‫ﺍﻫﺘﺯﺍﺯﺓ‬.
www.trgma.com
‫ﺠﺩﻭل‬1.3‫ﻤﺨﺘﻠﻔﺔ‬ ‫ﺯﻤﻨﻴﺔ‬ ‫ﻟﻔﺘﺭﺍﺕ‬ ‫ﺍﻟﻘﻴﻡ‬ ‫ﺒﻌﺽ‬

14
‫ﺍﻟﻘﻴﺎﺴﻲ‬ ‫ﺍﻟﻨﻅﺎﻡ‬SI‫ﻨﻅﺎﻡ‬ ‫ﻫﻨﺎﻙ‬ ‫ﻓﺎﻥ‬ ‫ﻋﻨﻪ‬ ‫ﺘﺤﺩﺜﻨﺎ‬ ‫ﺍﻟﺫﻱ‬‫ﺃﺨﺭ‬‫ﺍﻟﻤﺘﺤﺩﺓ‬ ‫ﺍﻟﻭﻻﻴﺎﺕ‬ ‫ﻓﻲ‬ ‫ﻴﺴﺘﺨﺩﻡ‬
‫ﻫﺫﺍ‬ ‫ﻴﻭﻤﻨﺎ‬ ‫ﺤﺘﻰ‬ ‫ﻴﺴﺘﺨﺩﻡ‬ ‫ﻻﺯﺍل‬.‫ﺍﻟﻘﺩﻡ‬ ‫ﻫﻲ‬ ‫ﻭﺍﻟﺯﻤﻥ‬ ‫ﻭﺍﻟﻜﺘﻠﺔ‬ ‫ﺍﻟﻁﻭل‬ ‫ﻭﺤﺩﺓ‬ ‫ﻓﺎﻥ‬ ‫ﺍﻟﻨﻅﺎﻡ‬ ‫ﻫﺫﺍ‬ ‫ﻭﻓﻲ‬
s.‫ﻻﻨﺘﺸﺎﺭﻫﺎ‬ ‫ﹰ‬‫ﺎ‬‫ﻋﺎﻟﻤﻴ‬ ‫ﺍﻟﻤﻌﺘﻤﺩﺓ‬ ‫ﺍﻟﻘﻴﺎﺴﻴﺔ‬ ‫ﺍﻟﻭﺤﺩﺍﺕ‬ ‫ﻋﻠﻰ‬ ‫ﻨﻌﺘﻤﺩ‬ ‫ﺴﻭﻑ‬ ‫ﻭﻟﻜﻨﻨﺎ‬
‫ﻭﺤﺩﺍﺕ‬ ‫ﻨﺠﺩ‬ ‫ﻓﻘﺩ‬ ‫ﻭﺍﻟﺯﻤﻥ‬ ‫ﻭﺍﻟﻜﺘﻠﺔ‬ ‫ﻟﻠﻁﻭل‬ ‫ﺍﻟﻤﻌﺭﻭﻓﺔ‬ ‫ﺍﻟﻭﺤﺩﺍﺕ‬ ‫ﺇﻟﻰ‬ ‫ﻭﺒﺎﻹﻀﺎﻓﺔ‬‫ﺍﻟﻤﻠﻴﻤﺘﺭ‬ ‫ﻤﺜل‬ ‫ﺃﺨﺭﻯ‬
‫ﺍﻟﺠﺩﻭل‬ ‫ﻭﻓﻲ‬ ‫ﺍﻷﺼﻠﻴﺔ‬ ‫ﺍﻟﻭﺤﺩﺓ‬ ‫ﻤﻥ‬ ‫ﺃﺠﺯﺍﺀ‬ ‫ﻋﻥ‬ ‫ﺘﻌﺒﺭ‬ ‫ﻋﻠﻴﻬﺎ‬ ‫ﻤﺘﻌﺎﺭﻑ‬ ‫ﺇﻀﺎﻓﻴﺔ‬ ‫ﻤﺴﻤﻴﺎﺕ‬ ‫ﻭﻫﻲ‬
‫ﻋﻨﻬﺎ‬ ‫ﺘﻌﺒﺭ‬ ‫ﺍﻟﺘﻲ‬ ‫ﻭﺍﻟﻘﻴﻡ‬ ‫ﻋﻠﻴﻬﺎ‬ ‫ﺍﻟﻤﺘﻌﺎﺭﻑ‬ ‫ﺒﺎﻟﻤﺴﻤﻴﺎﺕ‬ ‫ﻗﺎﺌﻤﺔ‬.‫ﺍﻟﻤﺜﺎل‬ ‫ﺴﺒﻴل‬ ‫ﻭﻋﻠﻰ‬10-3
m‫ﺃﻥ‬ ‫ﻴﻤﻜﻥ‬
103
m‫ﻋﻥ‬ ‫ﻟﻠﺘﻌﺒﻴﺭ‬1km‫ﺒﺎﻟﻨﺴﺒﺔ‬ ‫ﺍﻟﺤﺎل‬ ‫ﻭﻜﺫﻟﻙ‬‫ﻴﻌﺎﺩل‬ ‫ﻟﻠﻜﻴﻠﻭﺠﺭﺍﻡ‬103
g‫ﻭ‬
‫ﻭﻫﻜﺫﺍ‬.
www.trgma.com
‫ﺒﺎﻹﻀﺎﻓﺔ‬‫ﺇﻟﻰ‬‫ﺍﻟﻘﻴﺎﺴﻲ‬ ‫ﺍﻟﻨﻅﺎﻡ‬
‫ﺍﻷﻤﺭﻴﻜﻴﺔ‬‫ﻫﺫﺍ‬ ‫ﻴﻭﻤﻨﺎ‬ ‫ﺤﺘﻰ‬ ‫ﻴﺴﺘﺨﺩﻡ‬ ‫ﻻﺯﺍل‬
ft‫ﻭﺍﻟ‬‫ﺴﻠﺞ‬slug‫ﻭﺍﻟﺜﺎﻨﻴﺔ‬s
‫ﺍﻟﻭﺍﺴﻊ‬‫ﺍﻵﻥ‬.
‫ﻭﺤﺩﺍﺕ‬ ‫ﻨﺠﺩ‬ ‫ﻓﻘﺩ‬ ‫ﻭﺍﻟﺯﻤﻥ‬ ‫ﻭﺍﻟﻜﺘﻠﺔ‬ ‫ﻟﻠﻁﻭل‬ ‫ﺍﻟﻤﻌﺭﻭﻓﺔ‬ ‫ﺍﻟﻭﺤﺩﺍﺕ‬ ‫ﺇﻟﻰ‬ ‫ﻭﺒﺎﻹﻀﺎﻓﺔ‬
‫ﻭﺍﻟﻨﺎﻨﻭﺜﺎﻨﻴﺔ‬،‫ﺍﻟﺠﺩﻭل‬ ‫ﻭﻓﻲ‬ ‫ﺍﻷﺼﻠﻴﺔ‬ ‫ﺍﻟﻭﺤﺩﺓ‬ ‫ﻤﻥ‬ ‫ﺃﺠﺯﺍﺀ‬ ‫ﻋﻥ‬ ‫ﺘﻌﺒﺭ‬ ‫ﻋﻠﻴﻬﺎ‬ ‫ﻤﺘﻌﺎﺭﻑ‬ ‫ﺇﻀﺎﻓﻴﺔ‬ ‫ﻤﺴﻤﻴﺎﺕ‬ ‫ﻭﻫﻲ‬
1.4‫ﻋﻨﻬﺎ‬ ‫ﺘﻌﺒﺭ‬ ‫ﺍﻟﺘﻲ‬ ‫ﻭﺍﻟﻘﻴﻡ‬ ‫ﻋﻠﻴﻬﺎ‬ ‫ﺍﻟﻤﺘﻌﺎﺭﻑ‬ ‫ﺒﺎﻟﻤﺴﻤﻴﺎﺕ‬ ‫ﻗﺎﺌﻤﺔ‬
‫ﺒـ‬ ‫ﻋﻨﻬﺎ‬ ‫ﻨﻌﺒﺭ‬1mm‫ﺃﻭ‬m
1MV‫ﻴﻌﺎﺩل‬ ‫ﺃﻱ‬106
V‫ﻭﻫﻜﺫﺍ‬
‫ﺠﺩﻭل‬1.4

15
‫ﻤﺒﺎﺸﺭﺓ‬ ‫ﺒﻁﺭﻴﻘﺔ‬ ‫ﻤﺎ‬ ‫ﻅﺎﻫﺭﺓ‬ ‫ﻴﺩﺭﺴﻭﺍ‬‫ﻓﺈﻨﻬﻡ‬‫ﺍﻟﻅﺎﻫﺭﺓ‬ ‫ﻟﺘﻠﻙ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺌﻲ‬ ‫ﻟﻠﻨﻅﺎﻡ‬ ‫ﻨﻤﻭﺫﺝ‬ ‫ﺒﺒﻨﺎﺀ‬ ‫ﻴﻘﻭﻤﻭﻥ‬.
‫ﻭﻤﻜﻭﻨﺎﺘﻬﺎ‬ ‫ﺍﻟﺫﺭﺓ‬ ‫ﻨﻤﻭﺫﺝ‬ ‫ﺨﻼل‬ ‫ﻤﻥ‬ ‫ﺫﻟﻙ‬ ‫ﻋﻠﻰ‬ ‫ﻤﺜﺎﻻ‬ ‫ﻨﻀﺭﺏ‬ ‫ﺴﻭﻑ‬.‫ﺍﻟﺫﺭﺓ‬ ‫ﻤﻜﻭﻨﺎﺕ‬ ‫ﻟﻌﻼﻗﺔ‬ ‫ﺩﺭﺍﺴﺘﻨﺎ‬ ‫ﻓﻤﻥ‬
‫ﻟﻠﺫﺭﺓ‬ ‫ﻨﻤﻭﺫﺝ‬ ‫ﺒﻨﺎﺀ‬ ‫ﻴﻤﻜﻥ‬ ‫ﺍﻟﺨﺎﺭﺠﻲ‬ ‫ﺍﻟﻭﺴﻁ‬ ‫ﻭﻤﻊ‬ ‫ﺍﻟﺒﻌﺽ‬ ‫ﺒﻌﻀﻬﺎ‬ ‫ﻤﻊ‬.
‫ﺁﺨﺭ‬.‫ﻜﺘﻠﺘﻪ‬ ‫ﺍﻟﺫﻫﺏ‬ ‫ﻤﻥ‬ ‫ﻤﻜﻌﺏ‬1kg‫ﺍﻟﺠﺎﻨﺏ‬ ‫ﻓﻲ‬ ‫ﻤﻭﻀﺢ‬ ‫ﻫﻭ‬ ‫ﻜﻤﺎ‬‫ﺍﻷﻴﺴﺭ‬‫ﻤﻥ‬
‫ﺒﺩﺍﺨﻠﻪ؟‬ ‫ﻓﺭﺍﻍ‬ ‫ﻴﻭﺠﺩ‬ ‫ﻭﻻ‬ ‫ﺫﻫﺏ‬ ‫ﻜﻠﻪ‬ ‫ﺍﻟﻤﻜﻌﺏ‬ ‫ﻫﺫﺍ‬ ‫ﻫل‬ ‫ﻫﻨﺎ‬ ‫ﺍﻟﺴﺅﺍل‬‫ﺇﺫﺍ‬‫ﺒﻘﻁﻊ‬ ‫ﻗﻤﻨﺎ‬
‫ﺍﻟﻜﻴﻤﻴﺎﺌﻴﺔ‬ ‫ﺍﻟﺨﺼﺎﺌﺹ‬ ‫ﻓﻲ‬ ‫ﺘﻐﻴﺭ‬ ‫ﺩﻭﻥ‬ ‫ﺍﻟﺫﻫﺏ‬ ‫ﻤﻥ‬ ‫ﻗﺴﻤﻴﻥ‬ ‫ﺫﻟﻙ‬ ‫ﻋﻥ‬ ‫ﻭﻨﺘﺞ‬ ،‫ﻗﺴﻤﻴﻥ‬.‫ﺍﻻﺴﺘﻤﺭﺍﺭ‬ ‫ﺘﻡ‬ ‫ﻟﻭ‬ ‫ﻤﺎﺫﺍ‬ ‫ﻭﻟﻜﻥ‬
‫ﺍﻟﺴﺅﺍل‬ ‫ﻫﺫﺍ‬ ‫ﺫﻫﺏ؟‬ ‫ﺘﻌﻁﻴﻨﺎ‬ ‫ﺘﺴﺘﻤﺭ‬ ‫ﺴﻭﻑ‬ ‫ﺍﻟﻤﺘﻭﺍﻟﻴﺔ‬ ‫ﺍﻟﺼﻐﻴﺭﺓ‬ ‫ﺍﻟﻨﻭﺍﺘﺞ‬ ‫ﻓﻬل‬ ‫ﺍﻟﻘﻁﻊ؟‬ ‫ﻓﻲ‬‫ﻴﻌﻴﺩﻨﺎ‬‫ﺇﻟﻰ‬‫ﺍﻟﻴﻭﻨﺎﻨﻴﻭﻥ‬ ‫ﺍﻟﻔﻼﺴﻔﺔ‬ ‫ﻋﺼﺭ‬.
Democritus‫ﻴﻘﺒﻼ‬ ‫ﻟﻡ‬‫ﺃﺒﺩﺍ‬‫ﺒﻔﻜﺭﺓ‬‫ﺇﻥ‬‫ﻴﻤﻜﻥ‬ ‫ﺍﻟﻘﻁﻊ‬ ‫ﻋﻤﻠﻴﺔ‬‫ﺃﻥ‬‫ﺘﺴﺘﻤﺭ‬‫ﺇﻟﻰ‬‫ﻤﺎﻻ‬
‫ﺒﻌﺩﻩ‬ ‫ﻴﻤﻜﻥ‬ ‫ﻻ‬ ‫ﻤﻌﻴﻥ‬ ‫ﺤﺩ‬‫ﺃﻥ‬‫ﺘﺠﺯﺃ‬‫ﺍﻟﻤﺎﺩﺓ‬‫ﺇﻟﻰ‬‫ﻤﻨﻬﺎ‬ ‫ﺍﺼﻐﺭ‬.‫ﻴﻘﺒل‬ ‫ﻻ‬ ‫ﺠﺯﺀ‬ ‫ﺍﺼﻐﺭ‬ ‫ﻭﺴﻤﻴﺕ‬
‫ﺍﻻﻨﺠﻠﻴﺯﻴﺔ‬ ‫ﺍﻟﺘﺴﻤﻴﺔ‬ ‫ﺠﺎﺀﺕ‬ ‫ﻭﻤﻨﻬﺎ‬ ‫ﻟﻼﻨﻘﺴﺎﻡ‬ ‫ﻗﺎﺒل‬ ‫ﻏﻴﺭ‬ ‫ﺃﻱ‬atom‫ﺍﻟﺫﺭﺓ‬ ‫ﺃﻱ‬.
www.trgma.com
2.1‫ﺍﻟﻨﻤﺎﺫﺝ‬ ‫ﻭﺒﻨﺎﺀ‬ ‫ﺍﻟﻤﺎﺩﺓ‬
‫ﻴﺘﺴﻨﻰ‬ ‫ﻟﻡ‬ ‫ﺇﺫﺍ‬‫ﻟﻠﻔﻴﺯﻴﺎﺌﻴﻴﻥ‬‫ﺃﻥ‬‫ﻤﺒﺎﺸﺭﺓ‬ ‫ﺒﻁﺭﻴﻘﺔ‬ ‫ﻤﺎ‬ ‫ﻅﺎﻫﺭﺓ‬ ‫ﻴﺩﺭﺴﻭﺍ‬
‫ﻫﺫﺍ‬ ‫ﻭﻟﺘﻭﻀﻴﺢ‬‫ﺍﻷﻤﺭ‬‫ﻭﻤﻜﻭﻨﺎﺘﻬﺎ‬ ‫ﺍﻟﺫﺭﺓ‬ ‫ﻨﻤﻭﺫﺝ‬ ‫ﺨﻼل‬ ‫ﻤﻥ‬ ‫ﺫﻟﻙ‬ ‫ﻋﻠﻰ‬ ‫ﻤﺜﺎﻻ‬ ‫ﻨﻀﺭﺏ‬ ‫ﺴﻭﻑ‬
‫ﻟﻠﺫﺭﺓ‬ ‫ﻨﻤﻭﺫﺝ‬ ‫ﺒﻨﺎﺀ‬ ‫ﻴﻤﻜﻥ‬ ‫ﺍﻟﺨﺎﺭﺠﻲ‬ ‫ﺍﻟﻭﺴﻁ‬ ‫ﻭﻤﻊ‬ ‫ﺍﻟﺒﻌﺽ‬ ‫ﺒﻌﻀﻬﺎ‬ ‫ﻤﻊ‬
‫ﻭﺴﻭﻑ‬‫ﻨﺄﺨﺫ‬‫ﺘﻭﻀﻴﺤﻲ‬ ‫ﻜﻤﺜﺎل‬ ‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﺴﻠﻭﻙ‬‫ﺁﺨﺭ‬
‫ﺍﻟﺸﻜل‬1.2‫ﻀﻠ‬ ‫ﻁﻭل‬‫ﻌﻪ‬3.73cm.‫ﺒﺩﺍﺨﻠﻪ؟‬ ‫ﻓﺭﺍﻍ‬ ‫ﻴﻭﺠﺩ‬ ‫ﻭﻻ‬ ‫ﺫﻫﺏ‬ ‫ﻜﻠﻪ‬ ‫ﺍﻟﻤﻜﻌﺏ‬ ‫ﻫﺫﺍ‬ ‫ﻫل‬ ‫ﻫﻨﺎ‬ ‫ﺍﻟﺴﺅﺍل‬
‫ﺍﻟﻤﻜﻌﺏ‬‫ﺇﻟﻰ‬‫ﺍﻟﻜﻴﻤﻴﺎﺌﻴﺔ‬ ‫ﺍﻟﺨﺼﺎﺌﺹ‬ ‫ﻓﻲ‬ ‫ﺘﻐﻴﺭ‬ ‫ﺩﻭﻥ‬ ‫ﺍﻟﺫﻫﺏ‬ ‫ﻤﻥ‬ ‫ﻗﺴﻤﻴﻥ‬ ‫ﺫﻟﻙ‬ ‫ﻋﻥ‬ ‫ﻭﻨﺘﺞ‬ ،‫ﻗﺴﻤﻴﻥ‬
‫ﺍﻟﺴﺅﺍل‬ ‫ﻫﺫﺍ‬ ‫ﺫﻫﺏ؟‬ ‫ﺘﻌﻁﻴﻨﺎ‬ ‫ﺘﺴﺘﻤﺭ‬ ‫ﺴﻭﻑ‬ ‫ﺍﻟﻤﺘﻭﺍﻟﻴﺔ‬ ‫ﺍﻟﺼﻐﻴﺭﺓ‬ ‫ﺍﻟﻨﻭﺍﺘﺞ‬ ‫ﻓﻬل‬ ‫ﺍﻟﻘﻁﻊ؟‬ ‫ﻓﻲ‬
‫ﺤﻴﺙ‬‫ﺃﻥ‬‫ﺍﻟﻔﻴﻠﺴﻭﻑ‬Leucippus‫ﻭﺘﻠﻤﻴﺫﻩ‬Democritus
‫ﻨﻬﺎﻴﺔ‬.‫ﺘﻭﻗﻌﺎ‬ ‫ﻫﻤﺎ‬‫ﺃﻥ‬‫ﻴﺼﻼ‬‫ﺇﻟﻰ‬‫ﺒﻌﺩﻩ‬ ‫ﻴﻤﻜﻥ‬ ‫ﻻ‬ ‫ﻤﻌﻴﻥ‬ ‫ﺤﺩ‬
‫ﺍﻻﻨﻘﺴﺎﻡ‬atomos‫ﺍﻻﻨﺠﻠﻴﺯﻴﺔ‬ ‫ﺍﻟﺘﺴﻤﻴﺔ‬ ‫ﺠﺎﺀﺕ‬ ‫ﻭﻤﻨﻬﺎ‬ ‫ﻟﻼﻨﻘﺴﺎﻡ‬ ‫ﻗﺎﺒل‬ ‫ﻏﻴﺭ‬ ‫ﺃﻱ‬

16
‫ﺒﺭﻭﺘﻭﻨﺎﺕ‬ ‫ﻤﻥ‬ ‫ﻤﻜﻭﻨﺔ‬ ‫ﻨﻭﺍﺓ‬ ‫ﻴﻭﺠﺩ‬ ‫ﺫﺭﺓ‬ ‫ﻜل‬ ‫ﻤﺭﻜﺯ‬ ‫ﻭﻓﻲ‬ ‫ﺫﺭﺍﺕ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﺘﺘﺭﻜﺏ‬
‫ﺍﻟﻜﻭﺍﺭﻜﺎﺕ‬ ‫ﻤﻥ‬ ‫ﻤﻜﻭﻨﺔ‬ ‫ﻭﺍﻟﻨﻴﻭﺘﺭﻭﻨﺎﺕ‬ ‫ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ‬.
www.trgma.com
‫ﺸﻜل‬1.2‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﺘﺭﻜﻴﺏ‬ ‫ﻴﻭﻀﺢ‬.‫ﺒﺭﻭﺘﻭﻨﺎﺕ‬ ‫ﻤﻥ‬ ‫ﻤﻜﻭﻨﺔ‬ ‫ﻨﻭﺍﺓ‬ ‫ﻴﻭﺠﺩ‬ ‫ﺫﺭﺓ‬ ‫ﻜل‬ ‫ﻤﺭﻜﺯ‬ ‫ﻭﻓﻲ‬ ‫ﺫﺭﺍﺕ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﺘﺘﺭﻜﺏ‬
‫ﻭﻨﻴﻭﺘﺭﻭﻨﺎﺕ‬.‫ﺍﻟﻜﻭﺍﺭﻜﺎﺕ‬ ‫ﻤﻥ‬ ‫ﻤﻜﻭﻨﺔ‬ ‫ﻭﺍﻟﻨﻴﻭﺘﺭﻭﻨﺎﺕ‬ ‫ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ‬

17
‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﻟﺘﺭﻜﻴﺏ‬ ‫ﺍﻟﻨﻤﺎﺫﺝ‬ ‫ﺒﻌﺽ‬ ‫ﻨﺴﺘﻌﺭﺽ‬‫ﺯﻤﻨﻴﺎ‬ ‫ﺘﺴﻠﺴﻠﻬﺎ‬ ‫ﺤﺴﺏ‬.‫ﻫﻭ‬ ‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﻟﺘﺭﻜﻴﺏ‬ ‫ﺍﻟﻴﻭﻨﺎﻨﻲ‬ ‫ﺍﻟﻨﻤﻭﺫﺝ‬‫ﺃﻥ‬‫ﻜل‬
‫ﺍﻟﺠﺎﻨﺏ‬ ‫ﻓﻲ‬ ‫ﻤﻭﻀﺢ‬ ‫ﻫﻭ‬ ‫ﻜﻤﺎ‬ ‫ﺍﻟﺫﺭﺍﺕ‬ ‫ﻤﻥ‬ ‫ﻤﺠﻤﻭﻋﺔ‬ ‫ﻤﻥ‬ ‫ﺘﺘﻜﻭﻥ‬ ‫ﺍﻟﻤﻭﺍﺩ‬‫ﺍﻷﻴﻤﻥ‬‫ﺍﻟﺸﻜل‬ ‫ﻤﻥ‬1.2.‫ﻋﻥ‬ ‫ﺸﻲﺀ‬ ‫ﺃﻱ‬ ‫ﺫﻜﺭ‬ ‫ﺒﺩﻭﻥ‬
J.J.‫ﺍﻜﺘﺸﺎﻑ‬ ‫ﻤﻥ‬‫ﺍﻹﻟﻜﺘﺭﻭﻥ‬‫ﺍﻟﺫﺭﺓ‬ ‫ﻤﻜﻭﻨﺎﺕ‬ ‫ﺍﺤﺩ‬ ‫ﻭﺍﻨﻪ‬ ‫ﻤﺸﺤﻭﻥ‬ ‫ﻜﺠﺴﻴﻡ‬.‫ﻫﺫﺍ‬
‫ﺍﻟﺩﺍﺨﻠﻲ‬ ‫ﺘﺭﻜﻴﺒﻬﺎ‬ ‫ﻋﻥ‬ ‫ﻴﺘﺤﺩﺙ‬ ‫ﻟﻠﺫﺭﺓ‬ ‫ﻨﻤﻭﺫﺝ‬.‫ﻓﻲ‬ ‫ﺍﻟﻨﻤﻭﺫﺝ‬ ‫ﻫﺫﺍ‬ ‫ﻋﻥ‬ ‫ﺒﺎﻟﺘﻔﺼﻴل‬ ‫ﻨﺘﺤﺩﺙ‬ ‫ﻭﺴﻭﻑ‬
‫ﻤﺭﻜ‬ ‫ﺒﻨﻭﺍﺓ‬ ‫ﺘﺤﻴﻁ‬ ‫ﺍﻻﻟﻜﺘﺭﻭﻨﺎﺕ‬ ‫ﻓﻴﻪ‬ ‫ﺃﺨﺭ‬ ‫ﻨﻤﻭﺫﺠﺎ‬ ‫ﺘﻁﻭﻴﺭ‬ ‫ﺘﻡ‬‫ﺍﻟﺸﻜل‬ ‫ﻓﻲ‬ ‫ﻤﻭﻀﺢ‬ ‫ﻫﻭ‬ ‫ﻜﻤﺎ‬ ‫ﺯﻴﺔ‬1.2.‫ﻫﺫﺍ‬
‫ﺘﺭﻜﻴﺏ‬ ‫ﻟﻬﺎ‬ ‫ﺍﻟﻨﻭﺍﺓ‬ ‫ﻫل‬‫ﺃﻴﻀﺎ‬‫؟‬‫ﻤﻥ‬ ‫ﻤﺠﻤﻭﻋﺔ‬ ‫ﻤﻥ‬ ‫ﻤﻜﻭﻨﺔ‬ ‫ﺍﻟﻨﻭﺍﺓ‬ ‫ﻫل‬‫ﺍﻟﺠﺴﻴﻤﺎﺕ‬
‫ﺍﻟﻌﺎﻡ‬ ‫ﻓﻲ‬ ‫ﻭﻟﻜﻥ‬ ‫ﻫﺫﺍ‬ ‫ﻴﻭﻤﻨﺎ‬ ‫ﺤﺘﻰ‬ ‫ﻤﻌﺭﻭﻑ‬ ‫ﻏﻴﺭ‬ ‫ﻟﻠﻨﻭﺍﺓ‬ ‫ﺍﻟﻔﻌﻠﻲ‬ ‫ﺍﻟﺘﺭﻜﻴﺏ‬1930‫ﺴﻠﻭﻙ‬ ‫ﻓﻬﻡ‬ ‫ﻓﻲ‬ ‫ﺴﺎﻫﻡ‬ ‫ﺠﺩﻴﺩ‬ ‫ﻨﻤﻭﺫﺝ‬
‫ﺇﻟﻰ‬‫ﺃﻥ‬‫ﻫﻤﺎ‬ ‫ﺠﺴﻤﻴﻥ‬ ‫ﻤﻥ‬ ‫ﻤﻜﻭﻨﺔ‬ ‫ﺍﻟﻨﻭﺍﺓ‬‫ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ‬‫ﻭﺍﻟﻨﻴﻭﺘﺭﻭﻨﺎﺕ‬.‫ﺍﻟﺒﺭﻭﺘﻭﻥ‬
‫ﻋﺩﺩ‬ ‫ﻭﻴﻌﺭﻑ‬ ‫ﻟﻠﻤﺎﺩﺓ‬ ‫ﺍﻟﻜﻴﻤﻴﺎﺌﻲ‬ ‫ﺍﻟﺴﻠﻭﻙ‬ ‫ﻴﺤﺩﺩ‬ ‫ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ‬ ‫ﻭﻋﺩﺩ‬‫ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ‬‫ﺍﻟﺫﺭﻱ‬ ‫ﺒﺎﻟﻌﺩﺩ‬ ‫ﻓﻲ‬
‫ﻭﺍﺤﺩ‬ ‫ﺒﺭﻭﺘﻭﻥ‬ ‫ﻋﻠﻰ‬ ‫ﺘﺤﺘﻭﻱ‬ ‫ﺍﻟﻬﻴﺩﺭﻭﺠﻴﻥ‬ ‫ﺫﺭﺓ‬ ‫ﻨﻭﺍﺓ‬ ،‫ﺍﻟﻤﺜﺎل‬)‫ﻟﻠﻬﻴﺩﺭﻭﺠﻴﻥ‬ ‫ﺍﻟﺫﺭﻱ‬ ‫ﻭﺍﻟﻌﺩﺩ‬
‫ﻋﺩﺩ‬ ‫ﻋﻠﻰ‬ ‫ﺘﺤﺘﻭﻱ‬2‫ﺒﺭﻭﺘﻭﻥ‬)‫ﺍﻟﺫﺭﻱ‬ ‫ﻭﺍﻟﻌﺩﺩ‬‫ﻟﻠﻬﻠﻴﻭﻡ‬‫ﻫﻭ‬2(،‫ﺃﻤﺎ‬‫ﻓﻴﻭﺠﺩ‬ ‫ﺍﻟﻴﻭﺭﺍﻨﻴﻭﻡ‬ ‫ﻨﻭﺍﺓ‬ ‫ﻓﻲ‬92
www.trgma.com
‫ﺩﻋﻨﺎ‬‫ﺍﻵﻥ‬‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﻟﺘﺭﻜﻴﺏ‬ ‫ﺍﻟﻨﻤﺎﺫﺝ‬ ‫ﺒﻌﺽ‬ ‫ﻨﺴﺘﻌﺭﺽ‬
‫ﺍﻟﺠﺎﻨﺏ‬ ‫ﻓﻲ‬ ‫ﻤﻭﻀﺢ‬ ‫ﻫﻭ‬ ‫ﻜﻤﺎ‬ ‫ﺍﻟﺫﺭﺍﺕ‬ ‫ﻤﻥ‬ ‫ﻤﺠﻤﻭﻋﺔ‬ ‫ﻤﻥ‬ ‫ﺘﺘﻜﻭﻥ‬ ‫ﺍﻟﻤﻭﺍﺩ‬
‫ﺘﺘﻜﻭﻥ‬ ‫ﻭﻤﻤﺎ‬ ‫ﺍﻟﺫﺭﺍﺕ‬ ‫ﻫﺫﻩ‬ ‫ﻁﺒﻴﻌﺔ‬.
‫ﺍﻟﻌﺎﻡ‬ ‫ﻓﻲ‬1897‫ﺍﻟﻌﺎﻟﻡ‬ ‫ﺘﻤﻜﻥ‬J.J. Thomson
‫ﺍﻻﻜﺘﺸﺎﻑ‬‫ﺃﺩﻯ‬‫ﺇﻟﻰ‬‫ﻭﻀﻊ‬‫ﺃﻭ‬‫ﺍﻟﺩﺍﺨﻠﻲ‬ ‫ﺘﺭﻜﻴﺒﻬﺎ‬ ‫ﻋﻥ‬ ‫ﻴﺘﺤﺩﺙ‬ ‫ﻟﻠﺫﺭﺓ‬ ‫ﻨﻤﻭﺫﺝ‬
‫ﺍﻟﺠﺯﺀ‬42‫ﺍﻟﻜﺘﺎﺏ‬ ‫ﻫﺫﺍ‬ ‫ﻤﻥ‬.
‫ﺍﻟﻌﺎﻡ‬ ‫ﻭﻓﻲ‬1911‫ﻤﺭﻜ‬ ‫ﺒﻨﻭﺍﺓ‬ ‫ﺘﺤﻴﻁ‬ ‫ﺍﻻﻟﻜﺘﺭﻭﻨﺎﺕ‬ ‫ﻓﻴﻪ‬ ‫ﺃﺨﺭ‬ ‫ﻨﻤﻭﺫﺠﺎ‬ ‫ﺘﻁﻭﻴﺭ‬ ‫ﺘﻡ‬
‫ﻭﻫﻭ‬ ‫ﻫﺎﻡ‬ ‫ﻟﺘﺴﺎﺅل‬ ‫ﺍﻟﻤﺠﺎل‬ ‫ﻓﺘﺢ‬ ‫ﺍﻟﻨﻤﻭﺫﺝ‬‫ﺘﺭﻜﻴﺏ‬ ‫ﻟﻬﺎ‬ ‫ﺍﻟﻨﻭﺍﺓ‬ ‫ﻫل‬
‫ﺍﻟﻤﺘﻤﺎﺜﻠﺔ؟‬‫ﺍﻟﻌﺎﻡ‬ ‫ﻓﻲ‬ ‫ﻭﻟﻜﻥ‬ ‫ﻫﺫﺍ‬ ‫ﻴﻭﻤﻨﺎ‬ ‫ﺤﺘﻰ‬ ‫ﻤﻌﺭﻭﻑ‬ ‫ﻏﻴﺭ‬ ‫ﻟﻠﻨﻭﺍﺓ‬ ‫ﺍﻟﻔﻌﻠﻲ‬ ‫ﺍﻟﺘﺭﻜﻴﺏ‬
‫ﺍﻟﻨﻭﺍﺓ‬.‫ﺍﻟﻌﻠﻤﺎﺀ‬ ‫ﻤﻥ‬ ‫ﻤﺠﻤﻭﻋﺔ‬ ‫ﺘﻭﺼل‬ ‫ﺤﻴﺙ‬‫ﺇﻟﻰ‬
،‫ﻤﻭﺠﺒﺔ‬ ‫ﺸﺤﻨﺔ‬ ‫ﻴﺤﻤل‬‫ﻋﺩﺩ‬ ‫ﻭﻴﻌﺭﻑ‬ ‫ﻟﻠﻤﺎﺩﺓ‬ ‫ﺍﻟﻜﻴﻤﻴﺎﺌﻲ‬ ‫ﺍﻟﺴﻠﻭﻙ‬ ‫ﻴﺤﺩﺩ‬ ‫ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ‬ ‫ﻭﻋﺩﺩ‬
atomic number.‫ﺴﺒﻴل‬ ‫ﻓﻌﻠﻰ‬‫ﻭﺍﺤﺩ‬ ‫ﺒﺭﻭﺘﻭﻥ‬ ‫ﻋﻠﻰ‬ ‫ﺘﺤﺘﻭﻱ‬ ‫ﺍﻟﻬﻴﺩﺭﻭﺠﻴﻥ‬ ‫ﺫﺭﺓ‬ ‫ﻨﻭﺍﺓ‬ ،‫ﺍﻟﻤﺜﺎل‬
‫ﻫﻭ‬1(‫ﺫﺭﺓ‬ ‫ﻭﻨﻭﺍﺓ‬ ،‫ﺍﻟﻬﻠﻴﻭﻡ‬‫ﻋﺩﺩ‬ ‫ﻋﻠﻰ‬ ‫ﺘﺤﺘﻭﻱ‬

18
.(‫ﺒﺎﻹﻀﺎﻓﺔ‬‫ﺇﻟﻰ‬‫ﺍﻟﻜﺘﻠﻲ‬ ‫ﺍﻟﻌﺩﺩ‬ ‫ﻫﻨﺎﻙ‬ ‫ﺍﻟﺫﺭﻱ‬ ‫ﺍﻟﻌﺩﺩ‬mass number‫ﻴﺤﺩﺩ‬ ‫ﻭﺍﻟﺫﻱ‬
.
‫ﺃﻥ‬‫ﺜﺎﺒﺘﺔ‬ ‫ﺍﻟﻭﺍﺤﺩ‬ ‫ﺍﻟﻌﻨﺼﺭ‬ ‫ﺫﺭﺍﺕ‬ ‫ﺠﻤﻴﻊ‬ ‫ﻓﻲ‬ ‫ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ‬ ‫ﻋﺩﺩ‬(‫ﺍﻟﻜﺘﻠﻲ‬ ‫ﺍﻟﻌﺩﺩ‬ ‫ﺒﻴﻨﻤﺎ‬
‫ﺍﻟﻌ‬ ‫ﻟﻨﻔﺱ‬ ‫ﻴﺨﺘﻠﻑ‬‫ﻨﺼﺭ‬.(
‫ﺍﻟﻌﺎﻡ‬ ‫ﻓﻲ‬ ‫ﻋﻤﻠﻴﺎ‬ ‫ﺍﻟﻨﻴﻭﺘﺭﻭﻨﺎﺕ‬ ‫ﻭﺠﻭﺩ‬ ‫ﻤﻥ‬ ‫ﺍﻟﺘﺤﻘﻕ‬ ‫ﺘﻡ‬1932.‫ﺍﻟﺒﺭﻭﺘﻭﻥ‬ ‫ﻜﺘﻠﺔ‬ ‫ﺘﻌﺎﺩل‬ ‫ﻭﻜﺘﻠﺘﻬﺎ‬ ‫ﺸﺤﻨﺔ‬ ‫ﻟﻬﺎ‬ ‫ﻟﻴﺱ‬ ‫ﺍﻟﻨﻴﻭﺘﺭﻭﻨﺎﺕ‬
‫ﺍﻟﺼﻤﻎ‬ ‫ﻤﺜل‬ ‫ﺍﻟﻨﻭﺍﺓ‬ ‫ﺘﻤﺎﺴﻙ‬ ‫ﻓﻲ‬ ‫ﻤﻬﻤﺎ‬ ‫ﺩﻭﺭﺍ‬ ‫ﺍﻟﻨﻴﻭﺘﺭﻭﻨﺎﺕ‬ ‫ﻭﺘﻠﻌﺏ‬.‫ﻓﺈﺫﺍ‬‫ﺍﻟﻘﻭﺓ‬ ‫ﻓﺎﻥ‬ ‫ﺍﻟﻨﻭﺍﺓ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻨﻴﻭﺘﺭﻭﻨﺎﺕ‬ ‫ﺘﻭﺠﺩ‬ ‫ﻟﻡ‬
‫ﻭﺘﻘﺴﻤﻬﺎ‬ ‫ﺍﻟﻨﻭﺍﺓ‬ ‫ﺘﻔﺘﺕ‬.
‫ﺃﻗﺼﻰ‬‫ﺍﻟﻤﺎﺩﺓ؟‬ ‫ﻟﻪ‬ ‫ﺘﻘﺴﻡ‬ ‫ﺍﻥ‬ ‫ﻴﻤﻜﻥ‬ ‫ﻤﺎ‬‫ﺍﻹﺠﺎﺒﺔ‬‫ﻭﺍﻟﻨﻴﻭﺘﺭﻭﻨﺎﺕ‬ ‫ﻓﺎﻟﺒﺭﻭﺘﻭﻨﺎﺕ‬ ‫ﻻ‬
‫ﺍﻟﻜﻭﺍﺭﻜﺎﺕ‬ ‫ﺒﺎﺴﻡ‬ ‫ﺘﻌﺭﻑ‬ ‫ﺍﺼﻐﺭ‬quarks،‫ﻟﻬﺎ‬ ‫ﻭﺍﻟﺘﻲ‬‫ﺃﺴﻤﺎﺀ‬‫ﻭﺘﺤﺕ‬ ‫ﺃﻋﻠﻰ‬ ‫ﻫﻲ‬ ‫ﻤﺤﺩﺩﺓ‬
‫ﺘﻌﺎﺩل‬ ‫ﻤﻭﺠﺒﺔ‬ ‫ﺸﺤﻨﺔ‬ ‫ﻟﻬﺎ‬ ‫ﻭﻓﻭﻕ‬ ‫ﻭﺠﺫﺍﺏ‬ ‫ﺃﻋﻠﻰ‬ ‫ﻭﺍﻟﻜﻭﺍﺭﻜﺎﺕ‬2/3،‫ﺍﻟﺒﺭﻭﺘﻭﻥ‬ ‫ﺸﺤﻨﺔ‬ ‫ﻤﻥ‬
‫ﺘﺴﺎﻭﻱ‬ ‫ﺴﺎﻟﺒﺔ‬ ‫ﺸﺤﻨﺔ‬ ‫ﻟﻬﺎ‬-1/3‫ﺍﻟﺒﺭﻭﺘﻭﻥ‬ ‫ﺸﺤﻨﺔ‬.‫ﺍﻟﺒﺭﻭﺘﻭﻥ‬‫ﻋﺩﺩ‬ ‫ﻤﻥ‬ ‫ﻴﺘﻜﻭﻥ‬2‫ﻜﻭﺍﺭﻙ‬
‫ﺍﻋﻠﻲ‬‫ﺍﻟﺸﻜل‬1.2.‫ﺍﻟﺴﻬل‬ ‫ﻭﻤﻥ‬‫ﺇﺜﺒﺎﺕ‬‫ﺇﻥ‬‫ﺍﻟﺒﺭﻭﺘﻭﻥ‬ ‫ﺸﺤﻨﺔ‬ ‫ﻴﻌﻁﻲ‬ ‫ﺍﻟﺘﺭﺘﻴﺏ‬ ‫ﻫﺫﺍ‬.
‫ﻭﻜﻭﺍﺭﻙ‬ ‫ﺃﺴﻔل‬ ‫ﻜﻭﺍﺭﻙ‬‫ﺍﻋﻠﻲ‬‫ﺼﻔﺭ‬ ‫ﺘﺴﺎﻭﻱ‬ ‫ﺍﻟﺸﺤﻨﺔ‬ ‫ﻴﺠﻌل‬ ‫ﻭﻫﺫﺍ‬.
www.trgma.com
‫ﺒﺭﻭﺘﻭﻥ‬)‫ﻫﻭ‬ ‫ﻟﻠﻴﻭﺭﺍﻨﻴﻭﻡ‬ ‫ﺍﻟﺫﺭﻱ‬ ‫ﻭﺍﻟﻌﺩﺩ‬92.(
‫ﻋﺩﺩ‬‫ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ‬‫ﻭﺍﻟﻨﻴﻭﺘﺭﻭﻨﺎﺕ‬‫ﺍﻟﻨﻭﺍﺓ‬ ‫ﺩﺍﺨل‬.
‫ﻴﺘﻐﻴﺭ‬ ‫ﻻ‬ ‫ﻋﻨﺼﺭ‬ ‫ﻷﻱ‬ ‫ﺍﻟﺫﺭﻱ‬ ‫ﺍﻟﻌﺩﺩ‬‫ﺃﺒﺩﺍ‬)‫ﺃﻱ‬‫ﺃﻥ‬
‫ﻴﺘﻐﻴﺭ‬)‫ﺃﻱ‬‫ﺃﻥ‬‫ﻴﻤﻜﻥ‬ ‫ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ‬ ‫ﻋﺩﺩ‬‫ﺃﻥ‬‫ﺍﻟﻌ‬ ‫ﻟﻨﻔﺱ‬ ‫ﻴﺨﺘﻠﻑ‬
‫ﺍﻟﻌﺎﻡ‬ ‫ﻓﻲ‬ ‫ﻋﻤﻠﻴﺎ‬ ‫ﺍﻟﻨﻴﻭﺘﺭﻭﻨﺎﺕ‬ ‫ﻭﺠﻭﺩ‬ ‫ﻤﻥ‬ ‫ﺍﻟﺘﺤﻘﻕ‬ ‫ﺘﻡ‬
‫ﹰ‬‫ﺎ‬‫ﺘﻘﺭﻴﺒ‬.‫ﺍﻟﺼﻤﻎ‬ ‫ﻤﺜل‬ ‫ﺍﻟﻨﻭﺍﺓ‬ ‫ﺘﻤﺎﺴﻙ‬ ‫ﻓﻲ‬ ‫ﻤﻬﻤﺎ‬ ‫ﺩﻭﺭﺍ‬ ‫ﺍﻟﻨﻴﻭﺘﺭﻭﻨﺎﺕ‬ ‫ﻭﺘﻠﻌﺏ‬
‫ﺍﻟﻤﻭﺠﺒﺔ‬ ‫ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ‬ ‫ﺒﻴﻥ‬ ‫ﺍﻟﺘﻨﺎﻓﺭﻴﺔ‬‫ﺴﻭﻑ‬‫ﻭﺘﻘﺴﻤﻬﺎ‬ ‫ﺍﻟﻨﻭﺍﺓ‬ ‫ﺘﻔﺘﺕ‬
‫ﻭﻟﻜﻥ‬‫ﻫﻲ‬ ‫ﻭﺍﻟﻨﻴﻭﺘﺭﻭﻨﺎﺕ‬ ‫ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ‬ ‫ﻫل‬‫ﺃﻗﺼﻰ‬
‫ﻭﺠﺩﺕ‬‫ﺃﻨﻬﺎ‬‫ﻤﻥ‬ ‫ﺘﺘﻜﻭﻥ‬6‫ﺠﺴﻴﻤﺎﺕ‬‫ﺍﻟﻜﻭﺍﺭﻜﺎﺕ‬ ‫ﺒﺎﺴﻡ‬ ‫ﺘﻌﺭﻑ‬ ‫ﺍﺼﻐﺭ‬
‫ﻭﻓﻭﻕ‬ ‫ﻭﺘﺤﺕ‬ ‫ﻭﺠﺫﺍﺏ‬ ‫ﻭﻏﺭﻴﺏ‬.‫ﺘﻌﺎﺩل‬ ‫ﻤﻭﺠﺒﺔ‬ ‫ﺸﺤﻨﺔ‬ ‫ﻟﻬﺎ‬ ‫ﻭﻓﻭﻕ‬ ‫ﻭﺠﺫﺍﺏ‬ ‫ﺃﻋﻠﻰ‬ ‫ﻭﺍﻟﻜﻭﺍﺭﻜﺎﺕ‬
‫ﻭﻏﺭﻴﺏ‬ ‫ﺘﺤﺕ‬ ‫ﻭﺍﻟﻜﻭﺍﺭﻜﺎﺕ‬‫ﻭﺃﺴﻔل‬‫ﺘﺴﺎﻭﻱ‬ ‫ﺴﺎﻟﺒﺔ‬ ‫ﺸﺤﻨﺔ‬ ‫ﻟﻬﺎ‬
‫ﺍﻋﻠﻲ‬‫ﻭﻜﻭﺍﺭﻙ‬‫ﺃﺴﻔل‬‫ﻓﻲ‬ ‫ﻤﻭﻀﺢ‬ ‫ﻫﻭ‬ ‫ﻜﻤﺎ‬ ،‫ﺍﻋﻠﻲ‬
‫ﺇﻤﺎ‬‫ﻋﺩﺩ‬ ‫ﻤﻥ‬ ‫ﻴﺘﻜﻭﻥ‬ ‫ﺍﻟﻨﻴﻭﺘﺭﻭﻥ‬2‫ﻭﻜﻭﺍﺭﻙ‬ ‫ﺃﺴﻔل‬ ‫ﻜﻭﺍﺭﻙ‬

19
‫ﺍﻟﺘﻌﻤﻕ‬ ‫ﻤﻊ‬‫ﺃﻜﺜﺭ‬‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬ ‫ﺩﺭﺍﺴﺔ‬ ‫ﻓﻲ‬.‫ﻭﻤﻥ‬‫ﺃﻫﻡ‬‫ﻨﻤﻭﺫﺝ‬ ‫ﻟﺒﻨﺎﺀ‬ ‫ﺍﻟﻤﺘﺒﻌﺔ‬ ‫ﺍﻟﻁﺭﻕ‬
‫ﺒﻌﻀﻬﺎ‬ ‫ﻤﻊ‬ ‫ﻭﺘﻔﺎﻋﻠﻬﺎ‬ ‫ﺍﻟﻤﻜﻭﻨﺎﺕ‬ ‫ﻫﺫﻩ‬ ‫ﻟﺴﻠﻭﻙ‬ ‫ﺘﻭﻗﻊ‬ ‫ﻭﻋﻤل‬ ‫ﺍﻟﻤﺸﻜﻠﺔ‬ ‫ﻭﻋﻨﺎﺼﺭ‬ ‫ﻤﻜﻭﻨﺎﺕ‬ ‫ﺘﺤﺩﻴﺩ‬‫ﻭﺘﻔﺎﻋﻠﻬﺎ‬ ‫ﺍﻟﺒﻌﺽ‬
‫ﺍﻟﺫﺭﺓ‬ ‫ﻭﻜﺘﻠﺔ‬ ‫ﺍﻟﻜﺜﺎﻓﺔ‬
‫ﺍﻟﻤﻴﻜﺎﻨﻴﻜﺎ‬ ‫ﻋﻠﻡ‬ ‫ﻓﻲ‬ ‫ﺃﺴﺎﺴﻴﺔ‬ ‫ﻓﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﻜﻤﻴﺎﺕ‬ ‫ﺜﻼﺙ‬ ‫ﺒﺘﻌﺭﻴﻑ‬ ‫ﻗﻤﻨﺎ‬.‫ﻭﺍﻵﻥ‬‫ﺴﻭﻑ‬
‫ﺍﻟﻜﺜﺎﻓﺔ‬ ‫ﻭﻫﻲ‬ ‫ﻤﺸﺘﻘﺔ‬ ‫ﻓﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﻜﻤﻴﺔ‬density.‫ﺍﻟﻴﻭﻨﺎﻨﻲ‬ ‫ﺒﺎﻟﺭﻤﺯ‬ ‫ﻟﻬﺎ‬ ‫ﻴﺭﻤﺯ‬ ‫ﺍﻟﻜﺜﺎﻓﺔ‬
(‫ﻋﻠﻰ‬ ‫ﻭﺘﻌﺭﻑ‬‫ﺇﻨﻬﺎ‬‫ﺤﺠﻭﻡ‬ ‫ﻭﺤﺩﺓ‬ ‫ﻟﻜل‬ ‫ﺍﻟﻜﺘﻠﺔ‬:
≡ (1.1)
،‫ﺍﻟﻤﺜﺎل‬ ‫ﺴﺒﻴل‬ ‫ﻓﻌﻠﻰ‬‫ﺍﻷﻟﻭﻤﻨﻴﻭﻡ‬‫ﺘﺴﺎﻭﻱ‬ ‫ﻜﺜﺎﻓﺔ‬ ‫ﻟﻪ‬2.70g/cm3
‫ﺘﺴﺎﻭﻱ‬ ‫ﻜﺜﺎﻓﺔ‬ ‫ﻟﻪ‬ ‫ﻭﺍﻟﺭﺼﺎﺹ‬ ،
.‫ﻤﻥ‬ ‫ﻗﻁﻌﺔ‬ ‫ﻓﺎﻥ‬ ‫ﻭﻟﻬﺫﺍ‬‫ﺍﻷﻟﻭﻤﻨﻴﻭﻡ‬‫ﺤﺠﻤﻬﺎ‬10cm3
‫ﺘﺴﺎﻭﻱ‬ ‫ﻜﺘﻠﺔ‬ ‫ﻟﻬﺎ‬27g،
‫ﺃﺨﺭﻯ‬‫ﻜﺘﻠﺘﻬﺎ‬ ‫ﺘﻜﻭﻥ‬ ‫ﺍﻟﺤﺠﻡ‬ ‫ﻨﻔﺱ‬ ‫ﻟﻬﺎ‬ ‫ﺍﻟﺭﺼﺎﺹ‬ ‫ﻤﻥ‬113g.‫ﻭﺍﻟﺠﺩﻭل‬1.5
‫ﺍﻟﻤﻭﺍﺩ‬ ‫ﺒﻌﺽ‬ ‫ﻜﺜﺎﻓﺔ‬ ‫ﻴﻭﻀﺢ‬.
www.trgma.com
‫ﻤﻌﻙ‬ ‫ﺘﺘﻁﻭﺭ‬ ‫ﺴﻭﻑ‬ ‫ﺍﻟﻨﻤﺎﺫﺝ‬ ‫ﺒﻨﺎﺀ‬ ‫ﻋﻤﻠﻴﺔ‬‫ﺃﻜﺜﺭ‬
‫ﻤﺎ‬ ‫ﻟﻤﺸﻜﻠﺔ‬‫ﻫﻭ‬‫ﺒﻌﻀﻬﺎ‬ ‫ﻤﻊ‬ ‫ﻭﺘﻔﺎﻋﻠﻬﺎ‬ ‫ﺍﻟﻤﻜﻭﻨﺎﺕ‬ ‫ﻫﺫﻩ‬ ‫ﻟﺴﻠﻭﻙ‬ ‫ﺘﻭﻗﻊ‬ ‫ﻭﻋﻤل‬ ‫ﺍﻟﻤﺸﻜﻠﺔ‬ ‫ﻭﻋﻨﺎﺼﺭ‬ ‫ﻤﻜﻭﻨﺎﺕ‬ ‫ﺘﺤﺩﻴﺩ‬
‫ﺍﻟﻤﺤﻴﻁ‬ ‫ﺍﻟﻭﺴﻁ‬ ‫ﻤﻊ‬.
3.1‫ﺍﻟﺫﺭﺓ‬ ‫ﻭﻜﺘﻠﺔ‬ ‫ﺍﻟﻜﺜﺎﻓﺔ‬
‫ﺍﻟﺠﺯﺀ‬ ‫ﻓﻲ‬1.1
‫ﺒﺸﺭﺡ‬ ‫ﻨﻘﻭﻡ‬‫ﺍﻟﻜﺜﺎﻓﺔ‬ ‫ﻭﻫﻲ‬ ‫ﻤﺸﺘﻘﺔ‬ ‫ﻓﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﻜﻤﻴﺔ‬
ρ‫ﻭ‬‫ﺘ‬‫ﻠﻔﻅ‬)‫ﺭﻭ‬(
،‫ﺍﻟﻤﺜﺎل‬ ‫ﺴﺒﻴل‬ ‫ﻓﻌﻠﻰ‬
11.3g/cm3
.
‫ﻟﻘﻁﻌﺔ‬ ‫ﻭﻟﻜﻥ‬‫ﺃﺨﺭﻯ‬
‫ﺍﻟﻤﻭﺍﺩ‬ ‫ﺒﻌﺽ‬ ‫ﻜﺜﺎﻓﺔ‬ ‫ﻴﻭﻀﺢ‬
‫ﺠﺩﻭل‬1.5‫ﺍﻟﻤﺨﺘﻠﻔﺔ‬ ‫ﺍﻟﻤﻭﺍﺩ‬ ‫ﺒﻌﺽ‬ ‫ﻜﺜﺎﻓﺔ‬

20
‫ﺍﻟﻜﺘﻠﻲ‬ ‫ﺒﺎﻟﻌﺩﺩ‬ ‫ﻤﺭﺘﺒﻁ‬ ‫ﻤﺎ‬ ‫ﻋﻨﺼﺭ‬ ‫ﺫﺭﺓ‬ ‫ﻨﻭﺍﺓ‬ ‫ﻓﻲ‬ ‫ﻭﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ‬ ‫ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ‬ ‫ﻋﺩﺩ‬atomic mass‫ﺘﻘﺩﺭ‬ ‫ﻭﺍﻟﺘﻲ‬ ،‫ﺍﻟﻌﻨﺼﺭ‬ ‫ﻟﻬﺫﺍ‬
atomic mass units (u)‫ﺒﺎﻥ‬ ‫ﻋﻠﻤﺎ‬
u = 1.660,538,7x10-27
kg.
‫ﺘﺴﺎﻭﻱ‬ ‫ﻟﻭﻤﻨﻴﻭﻡ‬27u.،‫ﺍﻟﺫﺭﻴﺔ‬ ‫ﻜﺘﻠﻬﻡ‬ ‫ﺒﻴﻥ‬ ‫ﺍﻟﻨﺴﺒﺔ‬ ‫ﻭﻟﻜﻥ‬207u/27u=6.67،
(11.3x103kg.m3)/(2.72x103kg.m3)=4.19.‫ﺍﻻﺨﺘﻼﻑ‬ ‫ﻋﻥ‬ ‫ﻨﺘﺞ‬ ‫ﺍﻟﺘﻌﺎﺭﺽ‬ ‫ﻭﻫﺫﺍ‬
‫ﻟﻠﻌﻨﺼﺭﻴﻥ‬ ‫ﺍﻟﺒﻠﻭﺭﻱ‬ ‫ﺍﻟﺘﺭﻜﻴﺏ‬ ‫ﻓﻲ‬ ‫ﺍﻟﺫﺭﺍﺕ‬ ‫ﺘﺭﺘﻴﺏ‬ ‫ﻓﻲ‬.
‫ﺍﻷﻟﻭﻤﻨﻴﻭﻡ‬‫ﻭﺍﻷﺨﺭﻯ‬‫ﺍﻟﺤﺩﻴﺩ‬ ‫ﻤﻥ‬.‫ﺍﻟﻜﺘﻠﺔ‬ ‫ﻨﻔﺱ‬ ‫ﻟﻬﻤﺎ‬ ‫ﺍﻟﻌﻠﺒﺘﻴﻥ‬ ‫ﻤﻥ‬ ‫ﻜﻼ‬.‫ﺍﻟﻌﻠﺒﺘﻴﻥ‬ ‫ﻤﻥ‬ ‫ﺃﻱ‬
)‫ﺠـ‬(‫ﺍﻟﺤﺠﻡ‬ ‫ﻨﻔﺱ‬ ‫ﻟﻬﻤﺎ‬ ‫ﺍﻟﻌﻠﺒﺘﻴﻥ‬.
www.trgma.com
‫ﺍﻟﻜﺘﻠﻲ‬ ‫ﺒﺎﻟﻌﺩﺩ‬ ‫ﻤﺭﺘﺒﻁ‬ ‫ﻤﺎ‬ ‫ﻋﻨﺼﺭ‬ ‫ﺫﺭﺓ‬ ‫ﻨﻭﺍﺓ‬ ‫ﻓﻲ‬ ‫ﻭﺍﻟﻨﻴﺘﺭﻭﻨﺎﺕ‬ ‫ﺍﻟﺒﺭﻭﺘﻭﻨﺎﺕ‬ ‫ﻋﺩﺩ‬
‫ﺍﻟﺫﺭﻴﺔ‬ ‫ﺍﻟﻜﺘﻠﺔ‬ ‫ﺒﻭﺤﺩﺓ‬atomic mass units (u)
kg
‫ﺘﺴﺎﻭﻱ‬ ‫ﻟﻠﺭﺼﺎﺹ‬ ‫ﺍﻟﺫﺭﻴﺔ‬ ‫ﺍﻟﻜﺘﻠﺔ‬207u‫ﻭﻟﻸ‬‫ﺘﺴﺎﻭﻱ‬ ‫ﻟﻭﻤﻨﻴﻭﻡ‬
،‫ﻜﺜﺎﻓﺘﻬﻤﺎ‬ ‫ﺒﻴﻥ‬ ‫ﺍﻟﻨﺴﺒﺔ‬ ‫ﺘﻌﺎﺩل‬ ‫ﻻ‬11.3x103kg.m3)/(2.72x103kg.m3)=4.19
‫ﻟﻠﻌﻨﺼﺭﻴﻥ‬ ‫ﺍﻟﺒﻠﻭﺭﻱ‬ ‫ﺍﻟﺘﺭﻜﻴﺏ‬ ‫ﻓﻲ‬ ‫ﺍﻟﺫﺭﺍﺕ‬ ‫ﺘﺭﺘﻴﺏ‬ ‫ﻓﻲ‬
‫ﻟﻠﺘﻔﻜﻴﺭ‬ ‫ﺴﺅﺍل‬1.1
‫ﻤﺼﻨﻊ‬ ‫ﻗﺎﻡ‬‫ﺒﺈﻨﺘﺎﺝ‬‫ﻤﻥ‬ ‫ﻭﺍﺤﺩﺓ‬ ‫ﻋﻠﺒﺘﻴﻥ‬‫ﺍﻷﻟﻭﻤﻨﻴﻭﻡ‬
‫ﺍﻜﺒﺭ؟‬)‫ﺃ‬(‫ﻋﻠﺒﺔ‬‫ﺍﻷﻟﻭﻤﻨﻴﻭﻡ‬)‫ﺏ‬(‫ﺍﻟﺤﺩﻴﺩ‬ ‫ﻋﻠﺒﺔ‬)

21
.‫ﺍﻟﻤﻌﺭﻭﻑ‬ ‫ﻤﻥ‬‫ﺇﻥ‬27g‫ﻤﻥ‬‫ﺍﻷﻟﻭﻤﻨﻴﻭﻡ‬‫ﻋﻠﻰ‬ ‫ﻴﺤﺘﻭﻱ‬6.02x1023
‫ﺫﺭﺓ‬.‫ﻜﻡ‬
‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﺘﺤﺘﻭﻴﻬﺎ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﺫﺭﺍﺕ‬ ‫ﻋﺩﺩ‬ ‫ﻤﻊ‬ ‫ﺘﺘﻨﺎﺴﺏ‬ ‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﻜﺘﻠﺔ‬ ‫ﺒﻴﻥ‬ ‫ﺍﻟﻨﺴﺒﺔ‬.‫ﺍﻨﻪ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﺘﻨﺎﺴﺏ‬ ‫ﻫﺫﺍ‬ ‫ﻋﻥ‬ ‫ﻨﻌﺒﺭ‬ ‫ﺩﻋﻨﺎ‬
‫ﺍﻟﺘﻨﺎ‬ ‫ﺜﺎﺒﺕ‬ ‫ﻫﻭ‬‫ﻤﺠﻬﻭل‬ ‫ﻭﻫﻭ‬ ‫ﺴﺏ‬.‫ﻴﻤﻜﻨﻨﺎ‬‫ﺃﻥ‬‫ﺍﻷﻭﻟﻰ‬ ‫ﺍﻟﻤﺭﺓ‬ ،‫ﻤﺭﺘﻴﻥ‬ ‫ﺍﻟﻌﻼﻗﺔ‬ ‫ﻫﺫﻩ‬ ‫ﻨﻜﺘﺏ‬
‫ﺍﻟﺘﺎﻟﻲ‬ ‫ﺍﻟﻨﺤﻭ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﻨﺎﺘﺠﺘﻴﻥ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺘﻴﻥ‬ ‫ﺒﻘﺴﻤﺔ‬ ‫ﻨﻘﻭﻡ‬ ‫ﺜﻡ‬ ‫ﻭﻤﻥ‬ ،:
www.trgma.com
‫ﻤﺜﺎل‬1.1‫ﺍﻟﻤﻜﻌﺏ؟‬ ‫ﻓﻲ‬ ‫ﺍﻟﺫﺭﺍﺕ‬ ‫ﻋﺩﺩ‬ ‫ﻜﻡ‬
‫ﻤﻥ‬ ‫ﻤﻜﻌﺏ‬‫ﺍﻷﻟﻭﻤﻨﻴﻭﻡ‬)‫ﺍﻷ‬ ‫ﻜﺜﺎﻓﺔ‬‫ﻟﻭﻤﻨﻴﻭﻡ‬2.g/cm3
(‫ﺤﺠﻤﻪ‬0.2cm3
.‫ﺍﻟﻤﻌﺭﻭﻑ‬ ‫ﻤﻥ‬
‫ﺫﺭﺓ‬‫ﺃ‬‫ﺍﻟﻤﻜﻌﺏ؟‬ ‫ﻫﺫﺍ‬ ‫ﻓﻲ‬ ‫ﻟﻭﻤﻨﻴﻭﻡ‬
‫ﺍﻟﺤل‬:‫ﻫﻲ‬ ‫ﺍﻟﻤﻜﻌﺏ‬ ‫ﻜﺘﻠﺔ‬ ‫ﻓﺎﻥ‬ ،‫ﺤﺠﻡ‬ ‫ﻭﺤﺩﺓ‬ ‫ﻟﻜل‬ ‫ﺍﻟﻜﺘﻠﺔ‬ ‫ﺘﺴﺎﻭﻱ‬ ‫ﺍﻟﻜﺜﺎﻓﺔ‬ ‫ﻻﻥ‬
‫ﻨﻔﺘﺭﺽ‬ ‫ﺴﻭﻑ‬ ،‫ﺍﻟﺴﺅﺍل‬ ‫ﻫﺫﺍ‬ ‫ﻭﻟﺤل‬‫ﺇﻥ‬‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﺘﺤﺘﻭﻴﻬﺎ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﺫﺭﺍﺕ‬ ‫ﻋﺩﺩ‬ ‫ﻤﻊ‬ ‫ﺘﺘﻨﺎﺴﺏ‬ ‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﻜﺘﻠﺔ‬ ‫ﺒﻴﻥ‬ ‫ﺍﻟﻨﺴﺒﺔ‬
m=kN‫ﺤﻴﺙ‬ ،m‫ﻭ‬ ،‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﻜﺘﻠﺔ‬N‫ﻭ‬ ،‫ﺍﻟﻤﺎﺩﺓ‬ ‫ﻓﻲ‬ ‫ﺍﻟﺫﺭﺍﺕ‬ ‫ﻋﺩﺩ‬k‫ﺍﻟﺘﻨﺎ‬ ‫ﺜﺎﺒﺕ‬ ‫ﻫﻭ‬
‫ﻟﻤﻜﻌﺏ‬‫ﺍﻷﻟﻭﻤﻨﻴﻭﻡ‬‫ﺫﺍﺕ‬ ‫ﻟﻠﻜﺘﻠﺔ‬ ‫ﻭﺍﻟﺜﺎﻨﻴﺔ‬27g‫ﺍﻟﺘﺎﻟﻲ‬ ‫ﺍﻟﻨﺤﻭ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﻨﺎﺘﺠﺘﻴﻥ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺘﻴﻥ‬ ‫ﺒﻘﺴﻤﺔ‬ ‫ﻨﻘﻭﻡ‬ ‫ﺜﻡ‬ ‫ﻭﻤﻥ‬ ،

22
‫ﻗﻴﻤﺘﻪ‬ ‫ﻤﻌﺭﻓﺔ‬ ‫ﻨﺤﺘﺎﺝ‬ ‫ﻻ‬.‫ﻭﺍﻵﻥ‬‫ﺍﻟﻘﻴﻡ‬ ‫ﻋﻥ‬ ‫ﻨﻌﻭﺽ‬ ‫ﺴﻭﻑ‬:
Dimensional Analysis
‫ﻟﻬﺎ‬‫ﻤﺨﺘﻠﻑ‬ ‫ﻤﻌﻨﻲ‬.‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﺍﻟﻜﻤﻴﺔ‬ ‫ﻁﺒﻴﻌﺔ‬ ‫ﺇﻟﻰ‬ ‫ﺘﺸﻴﺭ‬ ‫ﻓﻬﻲ‬.‫ﺍﻟﻤﺴﺎﻓﺔ‬ ‫ﻨﻘﻴﺱ‬ ‫ﻋﻨﺩﻤﺎ‬
‫ﺃﺨﺭﻯ‬‫ﻭﻟﻬﺫﺍ‬ ،‫ﻓﺈﻨﻨﺎ‬‫ﻨﻘﻭل‬‫ﺇﻥ‬‫ﺍﻟﻔﻴﺯ‬ ‫ﺍﻟﻜﻤﻴﺔ‬ ‫ﻟﻬﺫﻩ‬‫ﻴﺎ‬‫ﺒﻌﺩ‬ ‫ﺌﻴﺔ‬‫ﻁﻭل‬.
‫ﻋﻥ‬ ‫ﻟﻠﺘﻌﺒﻴﺭ‬ ‫ﺍﻟﻜﺘﺎﺏ‬ ‫ﻫﺫﺍ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻤﺴﺘﺨﺩﻤﺔ‬ ‫ﺍﻟﺭﻤﻭﺯ‬‫ﺃﺒﻌﺎﺩ‬‫ﻫﻲ‬ ‫ﻭﺍﻟﺯﻤﻥ‬ ‫ﻭﺍﻟﻜﺘﻠﺔ‬ ‫ﺍﻟﻁﻭل‬L, M, T‫ﺍﻟﺘﻭﺍﻟﻲ‬ ‫ﻋﻠﻰ‬.‫ﻭﺴﻭﻑ‬
‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﺒﺎﻟﻜﻤﻴﺔ‬ ‫ﺍﻟﺨﺎﺹ‬ ‫ﺍﻟﺒﻌﺩ‬ ‫ﻋﻠﻰ‬ ‫ﻟﻠﺩﻻﻟﺔ‬.‫ﺍﻟﺭﻤﺯ‬ ‫ﻨﺴﺘﺨﺩﻡ‬ ‫ﺍﻟﻤﺜﺎل‬ ‫ﺴﺒﻴل‬ ‫ﻋﻠﻰ‬v‫ﻟﻠﺩﻻﻟﺔ‬
www.trgma.com
‫ﻻﺤﻅ‬‫ﺇﻥ‬‫ﺍﻟﻤﺠﻬﻭل‬ ‫ﺍﻟﺘﻨﺎﺴﺏ‬ ‫ﺜﺎﺒﺕ‬k‫ﻭﺒﻬﺫﺍ‬ ‫ﺒﺎﻟﻘﺴﻤﺔ‬ ‫ﻴﺨﺘﺼﺭ‬‫ﻓﺈﻨﻨﺎ‬‫ﻗﻴﻤﺘﻪ‬ ‫ﻤﻌﺭﻓﺔ‬ ‫ﻨﺤﺘﺎﺝ‬ ‫ﻻ‬
4.1‫ﺍﻷﺒﻌﺎﺩ‬ ‫ﺘﺤﻠﻴل‬Dimensional Analysis
‫ﻜﻠﻤﺔ‬‫ﺍﻷﺒﻌﺎﺩ‬dimensions‫ﺍﻟﻔﻴﺯﻴﺎﺀ‬ ‫ﻓﻲ‬‫ﻟﻬﺎ‬
‫ﺍﻟﻤﺘﺭ‬ ‫ﻭﺤﺩﺓ‬ ‫ﻨﺴﺘﺨﺩﻡ‬‫ﺃﻭ‬‫ﻁﻭل‬ ‫ﻭﺤﺩﺓ‬ ‫ﺃﻱ‬‫ﺃﺨﺭﻯ‬
‫ﻋﻥ‬ ‫ﻟﻠﺘﻌﺒﻴﺭ‬ ‫ﺍﻟﻜﺘﺎﺏ‬ ‫ﻫﺫﺍ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻤﺴﺘﺨﺩﻤﺔ‬ ‫ﺍﻟﺭﻤﻭﺯ‬
‫ﻨﺴﺘﺨﺩﻡ‬‫ﺍﻷﻗﻭﺍﺱ‬‫ﺍﻟﻤﺭﺒﻌﺔ‬[ ]‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﺒﺎﻟﻜﻤﻴﺔ‬ ‫ﺍﻟﺨﺎﺹ‬ ‫ﺍﻟﺒﻌﺩ‬ ‫ﻋﻠﻰ‬ ‫ﻟﻠﺩﻻﻟﺔ‬

23
‫ﻨﻜﺘﺏ‬ ‫ﺍﻟﺴﺭﻋﺔ‬[v] = L/T.‫ﻭﻜﻤﺜﺎل‬‫ﺃﺨﺭ‬،‫ﺃﺒﻌﺎﺩ‬‫ﺍﻟﻤﺴﺎﺤﺔ‬A‫ﺘﻜﺘﺏ‬[A] = L2
.‫ﺃﺒﻌﺎﺩ‬
‫ﺍﻟﺠﺩﻭل‬ ‫ﻓﻲ‬ ‫ﻤﻭﻀﺤﺔ‬ ‫ﻭﺍﻟﻌﺠﻠﺔ‬ ‫ﻭﺍﻟﺴﺭﻋﺔ‬ ‫ﻭﺍﻟﺤﺠﻡ‬ ‫ﺍﻟﻤﺴﺎﺤﺔ‬ ‫ﻭﻭﺤﺩﺍﺕ‬1.6.‫ﺃﺒﻌﺎﺩ‬‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﺍﻟﻜﻤﻴﺎﺕ‬‫ﺍﻷﺨﺭﻯ‬‫ﺍﻟﻘﻭﺓ‬ ‫ﻤﺜل‬
‫ﺍﻟﻤﻭﻀﻭﻉ‬ ‫ﻓﻲ‬ ‫ﻨﺘﻘﺩﻡ‬ ‫ﻋﻨﺩﻤﺎ‬ ‫ﻨﻭﺼﻔﻬﺎ‬ ‫ﺴﻭﻑ‬ ‫ﻭﺍﻟﻁﺎﻗﺔ‬.
‫ﺠﺩﻭل‬1.6‫ﻟﻠﻤﺴﺎﺤﺔ‬ ‫ﺍﻟﻤﺴﺘﺨﺩﻤﺔ‬ ‫ﺍﻟﻭﺤﺩﺍﺕ‬Area‫ﻭﺍﻟﺤﺠﻡ‬
Volume‫ﻭﺍﻟﺴﺭﻋﺔ‬Speed‫ﻭﺍﻟﻌﺠﻠﺔ‬Acceleration.
‫ﻤﻌﺎﺩﻟﺔ‬ ‫ﺸﺘﻕ‬‫ﺃﻭ‬‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻫﺫﻩ‬ ‫ﺼﺤﺔ‬ ‫ﻤﻥ‬ ‫ﻭﻟﻠﺘﺤﻘﻕ‬ ‫ﻓﻴﺯﻴﺎﺌﻲ‬ ‫ﻗﺎﻨﻭﻥ‬‫ﻓﺈﻨﻨﺎ‬‫ﻨﺴﺘﺨﺩﻡ‬
‫ﺘﻌﺩ‬ ‫ﻭﺍﻟﺘﻲ‬‫ﻭﺍﻟﺘﺄﻜﺩ‬ ‫ﻟﻠﺘﺤﻘﻕ‬ ‫ﻤﻔﻴﺩﺓ‬ ‫ﻁﺭﻴﻘﺔ‬‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﺼﺤﺔ‬ ‫ﻤﻥ‬.‫ﺘﺤﻠﻴل‬ ‫ﻁﺭﻴﻘﺔ‬ ‫ﺘﻌﺘﻤﺩ‬
‫ﻋﻠﻰ‬ ‫ﻤﻌﻬﺎ‬ ‫ﺍﻟﺘﻌﺎﻤل‬ ‫ﻴﻤﻜﻥ‬‫ﺇﻨﻬﺎ‬‫ﺠﺒﺭﻴﺔ‬ ‫ﻤﻘﺎﺩﻴﺭ‬.‫ﺍﻟﻜﻤﻴﺎﺕ‬ ،‫ﺍﻟﻤﺜﺎل‬ ‫ﺴﺒﻴل‬ ‫ﻋﻠﻰ‬
‫ﺍﻟﺒﻌﺩ‬ ‫ﻨﻔﺱ‬ ‫ﻟﻬﺎ‬ ‫ﻜﺎﻨﺕ‬)‫ﺍﻟﻭﺤﺩﺓ‬.(‫ﺇﻀﺎﻓﺔ‬‫ﺇﻟﻰ‬‫ﺫﻟﻙ‬‫ﺇﻥ‬‫ﺍﻟﻜﻤﻴﺎﺕ‬‫ﻋﻠﻰ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬
‫ﺍﻟﺒﻌﺩ‬ ‫ﻨﻔﺱ‬ ‫ﻟﻬﺎ‬ ‫ﺘﻜﻭﻥ‬‫ﺃﻴﻀﺎ‬.‫ﻭ‬‫ﺘﺤﻠﻴل‬ ‫ﺍﺴﺘﺨﺩﺍﻡ‬ ‫ﻴﻤﻜﻥ‬ ،‫ﺍﻟﺒﺴﻴﻁﺔ‬ ‫ﺍﻟﻘﻭﺍﻋﺩ‬ ‫ﻫﺫﻩ‬ ‫ﺒﺎﺴﺘﺨﺩﺍﻡ‬‫ﺍﻷﺒﻌﺎﺩ‬
.‫ﺍﻟﻁﺭﻑ‬ ‫ﻭﺤﺩﺓ‬ ‫ﺒﺠﻌل‬ ‫ﻭﺘﺼﺤﻴﺤﻬﺎ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻫﺫﻩ‬ ‫ﺘﻌﺩﻴل‬ ‫ﻭﻴﻤﻜﻥ‬‫ﺍﻷﻴﻤﻥ‬‫ﻟﻠﻤﻌﺎﺩﻟﺔ‬
www.trgma.com
‫ﻋﻥ‬ ‫ﻭﻟﻠﺘﻌﺒﻴﺭ‬ ‫ﺍﻟﺴﺭﻋﺔ‬ ‫ﻋﻠﻰ‬‫ﺃﺒﻌﺎﺩ‬‫ﻨﻜﺘﺏ‬ ‫ﺍﻟﺴﺭﻋﺔ‬
‫ﺍﻟﺠﺩﻭل‬ ‫ﻓﻲ‬ ‫ﻤﻭﻀﺤﺔ‬ ‫ﻭﺍﻟﻌﺠﻠﺔ‬ ‫ﻭﺍﻟﺴﺭﻋﺔ‬ ‫ﻭﺍﻟﺤﺠﻡ‬ ‫ﺍﻟﻤﺴﺎﺤﺔ‬ ‫ﻭﻭﺤﺩﺍﺕ‬
‫ﺍﻟﻤﻭﻀﻭﻉ‬ ‫ﻓﻲ‬ ‫ﻨﺘﻘﺩﻡ‬ ‫ﻋﻨﺩﻤﺎ‬ ‫ﻨﻭﺼﻔﻬﺎ‬ ‫ﺴﻭﻑ‬ ‫ﻭﺍﻟﻁﺎﻗﺔ‬
‫ﻤﻥ‬ ‫ﺍﻟﻜﺜﻴﺭ‬ ‫ﻓﻲ‬‫ﺍﻷﺤﻴﺎﻥ‬،‫ﻨ‬‫ﺤﺘﺎﺝ‬‫ﺇﻟﻰ‬‫ﺃﻥ‬‫ﻨ‬‫ﻤﻌﺎﺩﻟﺔ‬ ‫ﺸﺘﻕ‬
‫ﺘﺤﻠﻴل‬‫ﺍﻷﺒﻌﺎﺩ‬dimensional analyse،‫ﺘﻌﺩ‬ ‫ﻭﺍﻟﺘﻲ‬
‫ﺍﻷﺒﻌﺎﺩ‬‫ﻭﻫﻲ‬ ‫ﻤﻬﻤﺔ‬ ‫ﺤﻘﻴﻘﺔ‬ ‫ﻋﻠﻰ‬‫ﺇﻥ‬‫ﺍﻷﺒﻌﺎﺩ‬‫ﻋﻠﻰ‬ ‫ﻤﻌﻬﺎ‬ ‫ﺍﻟﺘﻌﺎﻤل‬ ‫ﻴﻤﻜﻥ‬
‫ﻤﻤﻜﻥ‬ ‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬‫ﺃﻥ‬‫ﻓﻘﻁ‬ ‫ﻭﺘﻁﺭﺡ‬ ‫ﺘﺠﻤﻊ‬‫ﺇﺫﺍ‬‫ﺍﻟﺒﻌﺩ‬ ‫ﻨﻔﺱ‬ ‫ﻟﻬﺎ‬ ‫ﻜﺎﻨﺕ‬
‫ﻴﺠﺏ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻁﺭﻓﻲ‬‫ﺃﻥ‬‫ﺍﻟﺒﻌﺩ‬ ‫ﻨﻔﺱ‬ ‫ﻟﻬﺎ‬ ‫ﺘﻜﻭﻥ‬
‫ﻟﺘﺤﺩﻴﺩ‬‫ﺇﺫﺍ‬‫ﺼﺤﻴﺤﺔ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻜﺎﻨﺕ‬ ‫ﻤﺎ‬‫ﺃﻡ‬‫ﻻ‬.
‫ﺘﺴﺎﻭﻱ‬‫ﺍﻟﻁﺭﻑ‬ ‫ﻭﺤﺩﺓ‬‫ﺍﻷﻴﺴﺭ‬‫ﻟﻠﻤﻌﺎﺩﻟﺔ‬.

24
‫ﺴﻴﺎﺭﺓ‬ ‫ﻤﻜﺎﻥ‬ ‫ﻟﺘﺤﺩﻴﺩ‬ ‫ﻤﻌﺎﺩﻟﺔ‬ ‫ﺍﺸﺘﻘﺎﻕ‬ ‫ﻨﺭﻴﺩ‬x‫ﺯﻤﻥ‬ ‫ﻋﻨﺩ‬t‫ﺇﺫﺍ‬‫ﺍﻟﺴﻴﺎﺭﺓ‬ ‫ﻜﺎﻨﺕ‬‫ﺘﺒﺩﺃ‬
.‫ﻫﻲ‬ ‫ﺍﻟﺤﺎﻟﺔ‬ ‫ﻫﺫﻩ‬ ‫ﺘﺼﻑ‬ ‫ﺍﻟﺘﻲ‬ ‫ﻭﺍﻟﻤﻌﺎﺩﻟﺔ‬x=1/2at2
.‫ﺩﻋﻨﺎ‬‫ﺍﻵﻥ‬‫ﺘﺤﻠﻴل‬ ‫ﻨﺴﺘﺨﺩﻡ‬
‫ﻁﻭل‬ ‫ﺒﻌﺩ‬ ‫ﻟﻪ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻴﺴﺎﺭ‬.‫ﺍﻟﻁﺭﻑ‬ ‫ﻓﺎﻥ‬ ‫ﺼﺤﻴﺤﺔ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﺘﻠﻙ‬ ‫ﺘﻜﻭﻥ‬ ‫ﻭﻟﻜﻲ‬‫ﺍﻷﻴﻤﻥ‬‫ﻤﻥ‬
.‫ﺇﺫﺍ‬‫ﺍﻟﻁﺭﻑ‬ ‫ﺒﻔﺤﺹ‬ ‫ﻨﻘﻭﻡ‬ ‫ﺍﻥ‬ ‫ﻋﻠﻴﻨﺎ‬‫ﺍﻷﻴﻤﻥ‬‫ﺍﻟﻜﻤﻴﺎﺕ‬ ‫ﻋﻥ‬ ‫ﺍﻟﺘﻌﻭﻴﺽ‬ ‫ﻁﺭﻴﻕ‬ ‫ﻋﻥ‬
‫ﺒﻌﺩ‬ ‫ﻟﻬﺎ‬ ‫ﺍﻟﻌﺠﻠﺔ‬L/T2
)‫ﺠﺩﻭل‬ ‫ﺍﻨﻅﺭ‬1.6(‫ﺒﻌﺩ‬ ‫ﻟﻪ‬ ‫ﻭﺍﻟﺯﻤﻥ‬T‫ﺇﺫﺍ‬‫ﻓﻲ‬ ‫ﺒﺎﻟﺘﻌﻭﻴﺽ‬
x=1/2at2
‫ﻟﻠﻁﺭﻑ‬‫ﺍﻷﻴﻤﻥ‬‫ﺍﻟﻁﺭﻑ‬ ‫ﺒﻌﺩ‬ ‫ﻨﻔﺱ‬‫ﺍﻷﻴﺴﺭ‬‫ﺼﺤﻴﺤﺔ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﺍﺫﺍ‬.
www.trgma.com
‫ﺍﻟﻤﻭﻀﻭﻉ‬ ‫ﻫﺫﺍ‬ ‫ﻟﺘﻭﻀﻴﺢ‬‫ﺃﻜﺜﺭ‬‫ﺍﻓﺘﺭﺽ‬ ،‫ﺇﻨﻨﺎ‬‫ﺴﻴﺎﺭﺓ‬ ‫ﻤﻜﺎﻥ‬ ‫ﻟﺘﺤﺩﻴﺩ‬ ‫ﻤﻌﺎﺩﻟﺔ‬ ‫ﺍﺸﺘﻘﺎﻕ‬ ‫ﻨﺭﻴﺩ‬
‫ﺜﺎﺒﺘﺔ‬ ‫ﺒﻌﺠﻠﺔ‬ ‫ﻭﺘﺴﻴﺭ‬ ‫ﺍﻟﺴﻜﻭﻥ‬ ‫ﻤﻥ‬ ‫ﺤﺭﻜﺘﻬﺎ‬a.
‫ﺍﻷﺒﻌﺎﺩ‬‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻫﺫﻩ‬ ‫ﺼﺤﺔ‬ ‫ﻤﻥ‬ ‫ﻟﻠﺘﺤﻘﻕ‬.
‫ﺇﻥ‬‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﺍﻟﻜﻤﻴﺔ‬x‫ﻋﻠﻰ‬‫ﻁﻭل‬ ‫ﺒﻌﺩ‬ ‫ﻟﻪ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻴﺴﺎﺭ‬
‫ﻁﻭل‬ ‫ﺒﻌﺩ‬ ‫ﻟﻪ‬ ‫ﻴﻜﻭﻥ‬ ‫ﺍﻥ‬ ‫ﻴﺠﺏ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬‫ﺃﻴﻀﺎ‬.
‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬‫ﺒﺎﻷﺒﻌﺎﺩ‬‫ﻭﺤﻴﺙ‬ ،‫ﺒﻬﺎ‬ ‫ﺍﻟﺨﺎﺼﺔ‬‫ﺇﻥ‬‫ﺒﻌﺩ‬ ‫ﻟﻬﺎ‬ ‫ﺍﻟﻌﺠﻠﺔ‬
‫ﺍﻟﻁﺭﻑ‬‫ﺍﻷﻴﻤﻥ‬‫ﻟﻠﻤﻌﺎﺩﻟﺔ‬
‫ﻋﻠﻰ‬ ‫ﻨﺤﺼل‬
‫ﻻﺤﻅ‬‫ﺇﻥ‬‫ﺍﺨﺘﺼﺎﺭﻩ‬ ‫ﺘﻡ‬ ‫ﺍﻟﺯﻤﻥ‬ ‫ﺒﻌﺩ‬‫ﻭﺃﺼﺒﺢ‬‫ﻟﻠﻁﺭﻑ‬

25
‫ﺍﻟﻤﺘﻐﻴﺭﺍﺕ‬ ‫ﻤﻥ‬ ‫ﻤﺠﻤﻭﻋﺔ‬ ‫ﺒﻴﻥ‬ ‫ﻋﻼﻗﺔ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﺤﺼﻭل‬ ‫ﻫﻭ‬،‫ﻓﻤﺜﻼ‬‫ﺇﺫﺍ‬‫ﺍﻟﻌﻼﻗﺔ‬ ‫ﻫﺫﻩ‬ ‫ﻜﺎﻨﺕ‬
x α an
tm
‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﺍﻟﻜﻤﻴﺔ‬ ‫ﻟﻪ‬ ‫ﺍﻟﻤﺭﻓﻭﻉ‬a‫ﻭ‬t‫ﻭ‬ ‫ﺍﻟﺘﻭﺍﻟﻲ‬ ‫ﻋﻠﻰ‬α‫ﺍﻟﺘﻨﺎﺴﺏ‬ ‫ﺜﺎﺒﺕ‬.‫ﺘﻜﻭﻥ‬ ‫ﺍﻟﻌﻼﻗﺔ‬ ‫ﻫﺫﻩ‬
‫ﻤﺘﺴﺎﻭﻱ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻁﺭﻓﻲ‬ ‫ﻋﻠﻰ‬.‫ﺍﻟﻁﺭﻑ‬ ‫ﺒﻌﺩ‬ ‫ﻭﻻﻥ‬‫ﺍﻷﻴﺴﺭ‬‫ﻁﻭل‬ ‫ﺒﻌﺩ‬ ‫ﻫﻭ‬L‫ﺍﻟﻁﺭﻑ‬ ‫ﻓﺎﻥ‬
.‫ﻴﻜﻭﻥ‬ ‫ﻭﻟﻬﺫﺍ‬
[an
tm
] = L = L1
T0
T‫ﻟﺩﻴﻨﺎ‬ ‫ﻴﻜﻭﻥ‬
(L/T2
)n
Tm
= L1
T0
(L n
Tm-2n
) = L1
T0
www.trgma.com
‫ﻁﺭﻴﻘﺔ‬‫ﺃﺨﺭﻯ‬‫ﺘﺤﻠﻴل‬ ‫ﻻﺴﺘﺨﺩﺍﻡ‬‫ﺍﻷﺒﻌﺎﺩ‬‫ﺍﻟﻤﺘﻐﻴﺭﺍﺕ‬ ‫ﻤﻥ‬ ‫ﻤﺠﻤﻭﻋﺔ‬ ‫ﺒﻴﻥ‬ ‫ﻋﻼﻗﺔ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﺤﺼﻭل‬ ‫ﻫﻭ‬
‫ﺍﻟﺘﺎﻟﻲ‬ ‫ﺍﻟﻨﺤﻭ‬ ‫ﻋﻠﻰ‬:
‫ﺤﻴﺙ‬n‫ﻭ‬m‫ﻫﻲ‬‫ﺍﻷﺱ‬‫ﺍﻟﻔﻴﺯﻴﺎﺌﻴﺔ‬ ‫ﺍﻟﻜﻤﻴﺔ‬ ‫ﻟﻪ‬ ‫ﺍﻟﻤﺭﻓﻭﻉ‬
‫ﺼﺤﻴﺤﺔ‬‫ﻓﻘﻁ‬‫ﺇﺫﺍ‬‫ﻜﺎﻨﺕ‬‫ﺍﻷﺒﻌﺎﺩ‬‫ﻤﺘﺴﺎﻭﻱ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻁﺭﻓﻲ‬ ‫ﻋﻠﻰ‬
‫ﺍﻷﻴﻤﻥ‬‫ﻴﺠﺏ‬‫ﺃﻥ‬‫ﻁﻭل‬ ‫ﺒﻌﺩ‬ ‫ﻟﻪ‬ ‫ﻴﻜﻭﻥ‬‫ﺃﻴﻀﺎ‬L.
‫ﺍﻟﻌﺠﻠﺔ‬ ‫ﺒﻌﺩ‬ ‫ﻻﻥ‬‫ﻫﻭ‬L/T2
‫ﻫﻭ‬ ‫ﺍﻟﺯﻤﻥ‬ ‫ﻭﺒﻌﺩ‬T

26
‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻁﺭﻓﻲ‬ ‫ﻋﻠﻰ‬ ‫ﻤﺘﺴﺎﻭﻴﻴﻥ‬ ‫ﻴﻜﻭﻨﺎ‬.‫ﻨﺴﺘﻁﻴﻊ‬ ‫ﻭﻟﻬﺫﺍ‬‫ﺃﻥ‬‫ﻨﺴﺘﻨﺘﺞ‬‫ﺇﻥ‬n = 1.‫ﻭﻤﻥ‬
‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻓﻲ‬ ‫ﺒﺎﻟﺘﻌﻭﻴﺽ‬ ‫ﺘﻨﺘﺞ‬ ‫ﻭﺍﻟﺘﻲ‬m – 2n = 0‫ﻗﻴﻤﺔ‬ ‫ﻋﻥ‬ ‫ﺍﻟﺘﻌﻭﻴﺽ‬ ‫ﻭﺒﻤﺠﺭﺩ‬
‫ﻨﺴﺘﻨﺘﺞ‬ ،‫ﺃﻥ‬‫ﺘﻜﻭﻥ‬ ‫ﺴﻭﻑ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬x α a t2
.
‫ﻴﻤﻜﻥ‬‫ﺃﻥ‬‫ﺍﻟﺠﺒﺭﻴﺔ‬ ‫ﺍﻟﻌﻼﻗﺎﺕ‬ ‫ﻓﻲ‬ ‫ﻴﻅﻬﺭ‬ ‫ﺍﻟﺫﻱ‬ ‫ﺍﻟﺘﻨﺎﺴﺏ‬ ‫ﻟﺜﺎﺒﺕ‬ ‫ﻋﺩﺩﻴﺔ‬ ‫ﺒﻘﻴﻤﺔ‬ ‫ﻴﺯﻭﺩﻨﺎ‬.
www.trgma.com
‫ﺍﻥ‬ ‫ﻻﺤﻅ‬‫ﺍﻷﺱ‬‫ﻟـ‬L‫ﻭ‬T‫ﻴﺠﺏ‬‫ﺃﻥ‬‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻁﺭﻓﻲ‬ ‫ﻋﻠﻰ‬ ‫ﻤﺘﺴﺎﻭﻴﻴﻥ‬ ‫ﻴﻜﻭﻨﺎ‬
‫ﻨﺴﺘﻁﻴﻊ‬ ‫ﺍﻟﻤﻌﻠﻭﻤﺔ‬ ‫ﻫﺫﻩ‬‫ﺃﻥ‬‫ﻨﺤﺴﺏ‬‫ﻗﻴﻤﺔ‬m‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻓﻲ‬ ‫ﺒﺎﻟﺘﻌﻭﻴﺽ‬ ‫ﺘﻨﺘﺞ‬ ‫ﻭﺍﻟﺘﻲ‬
n = 1‫ﻋﻠﻰ‬ ‫ﻨﺤﺼل‬m = 2.
‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﺇﻟﻰ‬ ‫ﺒﺎﻟﻌﻭﺩﺓ‬‫ﺍﻷﺴﺎﺴﻴﺔ‬x α an
tm
‫ﻨﺴﺘﻨﺘﺞ‬ ،
‫ﺴﺅﺍل‬1.2‫ﺼﺢ‬‫ﺃﻡ‬‫ﺨﻁﺄ‬:‫ﺘﺤﻴل‬‫ﺍﻷﺒﻌﺎﺩ‬‫ﻴﻤﻜﻥ‬

27
‫ﻭ‬ ‫ﺍﻟﻌﺠﻠﺔ‬ ‫ﻋﻥ‬ ‫ﺘﻌﺒﺭ‬t‫ﺍﻟﺯﻤﻥ‬ ‫ﻋﻥ‬ ‫ﺘﻌﺒﺭ‬.
‫ﺍﻟﺘﺎﻟﻲ‬ ‫ﺍﻟﻨﺤﻭ‬ ‫ﻋﻠﻰ‬ ‫ﺴﺭﻋﺔ‬ ‫ﺒﻌﺩ‬ ‫ﻟﻪ‬ ‫ﻴﻜﻭﻥ‬ ‫ﻭﺍﻟﺫﻱ‬ ‫ﺍﻟﺴﺭﻋﺔ‬ ‫ﻋﻥ‬ ‫ﻴﻌﺒﺭ‬ ‫ﻟﻠﻤﻌﺎﺩﻟﺔ‬:
‫ﻋﻥ‬ ‫ﻭﺒﺎﻟﺘﻌﻭﻴﺽ‬ ،‫ﺍﻟﺯﻤﻥ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻌﺠﻠﺔ‬ ‫ﻀﺭﺏ‬ ‫ﺤﺎﺼل‬ ‫ﻋﻥ‬ ‫ﻋﺒﺎﺭﺓ‬‫ﺃﺒﻌﺎﺩﻫﻤﺎ‬‫ﻋﻠﻰ‬ ‫ﻨﺤﺼل‬:
‫ﺼﺤﻴﺤﺔ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻓﺎﻥ‬ ‫ﻭﺒﺎﻟﺘﺎﻟﻲ‬ ‫ﻟﻠﻤﻌﺎﺩﻟﺔ‬.
‫ﺼﺤﻴﺤﺔ‬ ‫ﺘﻜﻭﻥ‬ ‫ﻫﻲ‬‫ﺃﻡ‬‫ﺨﻁﺄ‬.‫ﺒﻨﻔﺴﻙ‬ ‫ﺫﻟﻙ‬ ‫ﻤﻥ‬ ‫ﺘﺘﺤﻘﻕ‬ ‫ﺍﻥ‬ ‫ﺤﺎﻭل‬!
www.trgma.com
‫ﻤﺜﺎل‬1.2‫ﺘﺤﻠﻴل‬‫ﺃﺒﻌﺎﺩ‬‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬
‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﺍﻥ‬ ‫ﺍﺜﺒﺕ‬v = at‫ﺍﻥ‬ ‫ﺤﻴﺙ‬ ،‫ﺼﺤﻴﺤﺔ‬v‫ﻭ‬ ،‫ﺍﻟﺴﺭﻋﺔ‬ ‫ﻋﻥ‬ ‫ﺘﻌﺒﺭ‬a‫ﻭ‬ ‫ﺍﻟﻌﺠﻠﺔ‬ ‫ﻋﻥ‬ ‫ﺘﻌﺒﺭ‬
‫ﺍﻟﺤل‬:‫ﺍﻟﻁﺭﻑ‬‫ﺍﻷﻴﺴﺭ‬‫ﺍﻟﺘﺎﻟﻲ‬ ‫ﺍﻟﻨﺤﻭ‬ ‫ﻋﻠﻰ‬ ‫ﺴﺭﻋﺔ‬ ‫ﺒﻌﺩ‬ ‫ﻟﻪ‬ ‫ﻴﻜﻭﻥ‬ ‫ﻭﺍﻟﺫﻱ‬ ‫ﺍﻟﺴﺭﻋﺔ‬ ‫ﻋﻥ‬ ‫ﻴﻌﺒﺭ‬ ‫ﻟﻠﻤﻌﺎﺩﻟﺔ‬
‫ﻭﺍﻟﻁﺭﻑ‬‫ﺍﻷﻴﻤﻥ‬‫ﻋﻥ‬ ‫ﻭﺒﺎﻟﺘﻌﻭﻴﺽ‬ ،‫ﺍﻟﺯﻤﻥ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻌﺠﻠﺔ‬ ‫ﻀﺭﺏ‬ ‫ﺤﺎﺼل‬ ‫ﻋﻥ‬ ‫ﻋﺒﺎﺭﺓ‬
‫ﻭﺒﻬﺫﺍ‬‫ﺍﻥ‬ ‫ﻨﺠﺩ‬‫ﺃﺒﻌﺎﺩ‬‫ﺍﻟﻁﺭﻑ‬‫ﺍﻷﻴﺴﺭ‬‫ﺘﺴﺎﻭﻱ‬‫ﺃﺒﻌﺎﺩ‬‫ﺍﻟﻁﺭﻑ‬‫ﺍﻷﻴﻤﻥ‬‫ﺼﺤﻴﺤﺔ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻓﺎﻥ‬ ‫ﻭﺒﺎﻟﺘﺎﻟﻲ‬ ‫ﻟﻠﻤﻌﺎﺩﻟﺔ‬
‫ﻫﻲ‬ ‫ﻤﻨﻬﺎ‬ ‫ﺍﻟﺘﺤﻘﻕ‬ ‫ﺍﻟﻤﻁﻠﻭﺏ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﻜﺎﻨﺕ‬ ‫ﻟﻭ‬ ‫ﻤﺎﺫﺍ‬v = at2
‫ﺼﺤﻴﺤﺔ‬ ‫ﺘﻜﻭﻥ‬ ‫ﻫﻲ‬

28
‫ﻤﻨﺘﻅﻤﺔ‬ ‫ﺒﺴﺭﻋﺔ‬ ‫ﻴﺘﺤﺭﻙ‬ ‫ﺠﺴﻡ‬ ‫ﻋﺠﻠﺔ‬v‫ﻗﻁﺭﻩ‬ ‫ﻨﺼﻑ‬ ‫ﺩﺍﺌﺭﻱ‬ ‫ﻤﺴﺎﺭ‬ ‫ﻓﻲ‬r‫ﻤﻊ‬ ‫ﻴﺘﻨﺎﺴﺏ‬rn
‫ﺍﻟﺴﺭﻋﺔ‬ ‫ﻭﻤﻊ‬vm
،
A = k rn
‫ﺍﻟﻔﻴﺯ‬ ‫ﺍﻟﻜﻤﻴﺎﺕ‬‫ﻴﺎ‬‫ﺌﻴﺔ‬a‫ﻭ‬r‫ﻭ‬v‫ﻋﻠﻰ‬ ‫ﻨﺤﺼل‬:
‫ﺍﻟﺘﺎﻟﻴﻴﻥ‬ ‫ﺍﻟﺸﺭﻁﻴﻥ‬ ‫ﺘﺤﻘﻕ‬
N + m = 1 & m = 2
‫ﺍﻟﺘﺎﻟﻲ‬ ‫ﺍﻟﻨﺤﻭ‬ ‫ﻋﻠﻰ‬ ‫ﻤﻨﺘﻅﻤﺔ‬ ‫ﺒﺴﺭﻋﺔ‬ ‫ﺩﺍﺌﺭﺓ‬ ‫ﺤﺭﻜﺔ‬ ‫ﻴﺘﺤﺭﻙ‬ ‫ﻟﺠﺴﻡ‬ ‫ﺍﻟﻌﺠﻠﺔ‬ ‫ﻤﻌﺎﺩﻟﺔ‬ ‫ﺘﻜﻭﻥ‬ ‫ﻭﺒﺎﻟﺘﺎﻟﻲ‬:
www.trgma.com
‫ﻤﺜﺎل‬1.3‫ﺘﺤﻠﻴل‬‫ﺍﻷﺒﻌﺎﺩ‬‫ﻹﻴﺠﺎﺩ‬‫ﻗﻴﻤﺔ‬‫ﺍﻷﺱ‬
‫ﻟﻙ‬ ‫ﺘﺒﻴﻥ‬ ‫ﻗﺩ‬ ‫ﺒﺎﻟﺘﺠﺭﺒﺔ‬ ‫ﺍﻨﻪ‬ ‫ﻟﻨﻔﺘﺭﺽ‬‫ﺇﻥ‬‫ﻤﻨﺘﻅﻤﺔ‬ ‫ﺒﺴﺭﻋﺔ‬ ‫ﻴﺘﺤﺭﻙ‬ ‫ﺠﺴﻡ‬ ‫ﻋﺠﻠﺔ‬
‫ﺘﺤﻠﻴل‬ ‫ﺍﺴﺘﺨﺩﻡ‬‫ﺍﻷﺒﻌﺎﺩ‬‫ﻗﻴﻤﺔ‬ ‫ﻟﻤﻌﺭﻓﺔ‬n‫ﻭ‬m.
‫ﺍﻟﺤل‬:‫ﺍﻟﻌﺠﻠﺔ‬ ‫ﻨﻜﺘﺏ‬ ‫ﺍﻥ‬ ‫ﺍﻟﻤﺜﺎل‬ ‫ﻤﻌﻁﻴﺎﺕ‬ ‫ﻤﻥ‬ ‫ﻨﺴﺘﻁﻴﻊ‬a‫ﺍﻟﻨﺤﻭ‬ ‫ﻋﻠﻰ‬vm
‫ﺤﻴﺙ‬k‫ﻭﺤﺩﺓ‬ ‫ﻟﻪ‬ ‫ﻟﻴﺱ‬ ‫ﻭﻫﻭ‬ ‫ﺍﻟﺘﻨﺎﺴﺏ‬ ‫ﺜﺎﺒﺕ‬‫ﻋﻥ‬ ‫ﻭﺒﺎﻟﺘﻌﻭﻴﺽ‬‫ﺃﺒﻌﺎﺩ‬‫ﺍﻟﻔﻴﺯ‬ ‫ﺍﻟﻜﻤﻴﺎﺕ‬
‫ﺇﺫﺍ‬‫ﻨﺎﺤﻴﺔ‬ ‫ﻤﻥ‬ ‫ﻤﺘﺯﻨﺔ‬ ‫ﺍﻟﻤﻌﺎﺩﻟﺔ‬ ‫ﺘﻜﻭﻥ‬‫ﺃﺒﻌﺎﺩ‬‫ﺍﻟﻁﺭﻑ‬‫ﺍﻷﻴﻤﻥ‬‫ﻭﺍﻷﻴﺴﺭ‬‫ﺇﺫﺍ‬‫ﺍﻟﺘﺎﻟﻴﻴﻥ‬ ‫ﺍﻟﺸﺭﻁﻴﻥ‬ ‫ﺘﺤﻘﻕ‬
N + m = 1 & m = 2
‫ﻓﺎﻥ‬ ‫ﻭﻟﻬﺫﺍ‬n = -1‫ﺍﻟﺘﺎﻟﻲ‬ ‫ﺍﻟﻨﺤﻭ‬ ‫ﻋﻠﻰ‬ ‫ﻤﻨﺘﻅﻤﺔ‬ ‫ﺒﺴﺭﻋﺔ‬ ‫ﺩﺍﺌﺭﺓ‬ ‫ﺤﺭﻜﺔ‬ ‫ﻴﺘﺤﺭﻙ‬ ‫ﻟﺠﺴﻡ‬ ‫ﺍﻟﻌﺠﻠﺔ‬ ‫ﻤﻌﺎﺩﻟﺔ‬ ‫ﺘﻜﻭﻥ‬ ‫ﻭﺒﺎﻟﺘﺎﻟﻲ‬

29
‫ﺍﻟﻀﺭﻭﺭﻱ‬ ‫ﻤﻥ‬ ‫ﻴﻜﻭﻥ‬ ‫ﺍﻷﺤﻴﺎﻥ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻜﺜﻴﺭ‬ ‫ﻓﻲ‬‫ﺃﻥ‬‫ﻨﻅﺎﻡ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻘﻴﺎﺱ‬ ‫ﻭﺤﺩﺍﺕ‬ ‫ﻨﺤﻭل‬‫ﻷﺨﺭ‬،‫ﺃﻭ‬‫ﺴﺒﻴل‬ ‫ﻋﻠﻰ‬ ،‫ﺍﻟﻨﻅﺎﻡ‬ ‫ﻨﻔﺱ‬ ‫ﻓﻲ‬
‫ﻭﺍﻟﻨﻅﺎﻡ‬ ‫ﺍﻟﻌﺎﻟﻤﻲ‬ ‫ﺍﻟﻨﻅﺎﻡ‬ ‫ﻭﺤﺩﺍﺕ‬ ‫ﺒﻴﻥ‬ ‫ﻭﺍﻟﻤﺴﺎﻭﺍﺓ‬‫ﺍﻷﻤﺭﻴﻜﻲ‬‫ﻟﻸﻁﻭﺍل‬‫ﺍﻟﺘﺎﻟﻲ‬ ‫ﺍﻟﻨﺤﻭ‬ ‫ﻋﻠﻰ‬ ‫ﻫﻭ‬:
1 mile = 1,609 m = 1.609 km 1 ft = 0.304,8 m =
1 m = 39.37 in = 3.218 ft 1 in = 0.025,4 m = 2.45 cm
.
‫ﺍﻟﺒﻌﺽ‬ ‫ﺒﻌﻀﻬﺎ‬ ‫ﺘﻠﻐﻲ‬ ‫ﺠﺒﺭﻴﺔ‬ ‫ﻜﻤﻴﺎﺕ‬ ‫ﺇﻨﻬﺎ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﻭﺤﺩﺍﺕ‬ ‫ﻤﻊ‬ ‫ﺍﻟﺘﻌﺎﻤل‬ ‫ﻴﺘﻡ‬.‫ﻓﻲ‬ ‫ﺘﺭﻏﺏ‬ ‫ﺍﻨﻙ‬ ‫ﺍﻓﺘﺭﺽ‬ ،‫ﺍﻟﻤﺜﺎل‬ ‫ﺴﺒﻴل‬ ‫ﻋﻠﻰ‬
‫ﻴﻌﺎﺩل‬2.54cm‫ﺍﻥ‬ ‫ﻨﺠﺩ‬
‫ﻻﺤﻅ‬‫ﺇﻨﻨﺎ‬‫ﺍﻟﻭﺤﺩﺓ‬ ‫ﻨﻀﻊ‬ ‫ﺍﺨﺘﺭﻨﺎ‬)‫ﺍﻨﺵ‬in(‫ﺍﻻﻨﺵ‬ ‫ﻭﺤﺩﺓ‬ ‫ﻤﻊ‬ ‫ﻟﺘﺨﺘﺼﺭ‬ ‫ﺍﻟﻤﻘﺎﻡ‬ ‫ﻓﻲ‬
cm‫ﻜﻨﺘﻴﺠﺔ‬ ‫ﺍﻟﻤﻁﻠﻭﺏ‬ ‫ﻫﻭ‬ ‫ﻭﻫﺫﺍ‬.
www.trgma.com
5.1‫ﺍﻟﻭﺤﺩﺍﺕ‬ ‫ﺘﺤﻭﻴل‬
‫ﺍﻟﻀﺭﻭﺭﻱ‬ ‫ﻤﻥ‬ ‫ﻴﻜﻭﻥ‬ ‫ﺍﻷﺤﻴﺎﻥ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻜﺜﻴﺭ‬ ‫ﻓﻲ‬
‫ﻤﺘﺭ‬ ‫ﺇﻟﻰ‬ ‫ﻜﻴﻠﻭﻤﺘﺭ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻤﺜﺎل‬.‫ﻭﺍﻟﻨﻅﺎﻡ‬ ‫ﺍﻟﻌﺎﻟﻤﻲ‬ ‫ﺍﻟﻨﻅﺎﻡ‬ ‫ﻭﺤﺩﺍﺕ‬ ‫ﺒﻴﻥ‬ ‫ﻭﺍﻟﻤﺴﺎﻭﺍﺓ‬
1 ft = 0.304,8 m = 30.48 cm
1 in = 0.025,4 m = 2.45 cm
‫ﺍﻨﻅﺭ‬ ‫ﺍﻟﺘﺤﻭﻴﻼﺕ‬ ‫ﻤﻥ‬ ‫ﻭﻟﻠﻤﺯﻴﺩ‬‫ﺇﻟﻰ‬‫ﺍﻟﻤﻠﺤﻕ‬A.
‫ﺍﻟﺒﻌﺽ‬ ‫ﺒﻌﻀﻬﺎ‬ ‫ﺘﻠﻐﻲ‬ ‫ﺠﺒﺭﻴﺔ‬ ‫ﻜﻤﻴﺎﺕ‬ ‫ﺇﻨﻬﺎ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﻭﺤﺩﺍﺕ‬ ‫ﻤﻊ‬ ‫ﺍﻟﺘﻌﺎﻤل‬ ‫ﻴﺘﻡ‬
‫ﺘﺤﻭﻴل‬15in‫ﺇﻟﻰ‬cm.‫ﺇﻥ‬ ‫ﺤﻴﺙ‬1in‫ﻴﻌﺎﺩل‬
‫ﺒﻴﻥ‬ ‫ﺍﻟﻨﺴﺒﺔ‬ ‫ﺍﻥ‬ ‫ﺤﻴﺙ‬‫ﺍﻷﻗﻭﺍﺱ‬‫ﺘﺴﺎﻭﻱ‬1.‫ﻻﺤﻅ‬
‫ﺍﻟﻘﻴﻤﺔ‬ ‫ﻓﻲ‬‫ﺍﻷﺼﻠﻴﺔ‬.‫ﺴﺘﻜﻭﻥ‬ ‫ﺍﻟﻤﺘﺒﻘﻴﺔ‬ ‫ﺍﻟﻭﺤﺩﺓ‬cm

30
100 mi.‫ﺴﺘﻜﻭﻥ‬ ‫ﺍﻟﻤﺩﻴﻨﺘﻴﻥ‬ ‫ﺒﻴﻥ‬ ‫ﺒﺎﻟﻜﻴﻠﻭﻤﺘﺭ‬ ‫ﺍﻟﻤﺴﺎﻓﺔ‬ ‫ﻫل‬)‫ﺃ‬(‫ﻤﻥ‬ ‫ﺍﻗل‬100‫ﺃﻭ‬)‫ﺏ‬(
‫ﺒﺴﺭﻋﺔ‬ ‫ﺘﻨﻁﻠﻕ‬ ‫ﺴﻴﺎﺭﺓ‬ ‫ﻜﺎﻨﺕ‬ ،‫ﺍﻟﻤﺩﻥ‬38m/s.‫ﺍﻟﺴﻴﺎﺭﺓ‬ ‫ﻫل‬
75mi/h‫؟‬
‫ﺷﻛل‬1.3
www.trgma.com
‫ﺴﺅﺍل‬1.3‫ﻫﻲ‬ ‫ﻤﺩﻴﻨﺘﻴﻥ‬ ‫ﺒﻴﻥ‬ ‫ﺍﻟﻤﺴﺎﻓﺔ‬100 mi
‫ﻤﻥ‬ ‫ﺍﻜﺒﺭ‬100‫ﺃﻭ‬)‫ﺠـ‬(‫ﺘﺴﺎﻭﻱ‬100.
‫ﻤﺜﺎل‬1.4‫ﺍﻟﺴﺭﻋﺔ؟‬ ‫ﺤﺩ‬ ‫ﺘﺠﺎﻭﺯ‬ ‫ﻫل‬
‫ﻓﻲ‬ ‫ﺍﻟﺴﺭﻴﻊ‬ ‫ﺍﻟﻁﺭﻴﻕ‬ ‫ﺘﻘﺎﻁﻌﺎﺕ‬ ‫ﺍﺤﺩ‬ ‫ﻓﻲ‬‫ﺇﺤﺩﻯ‬‫ﺒﺴﺭﻋﺔ‬ ‫ﺘﻨﻁﻠﻕ‬ ‫ﺴﻴﺎﺭﺓ‬ ‫ﻜﺎﻨﺕ‬ ،‫ﺍﻟﻤﺩﻥ‬
‫ﺍﻟﺤﺩ‬ ‫ﺘﺠﺎﻭﺯﺕ‬‫ﺍﻷﻗﺼﻰ‬‫ﻫﻭ‬ ‫ﻭﺍﻟﺫﻱ‬ ‫ﺍﻟﺸﺎﺭﻉ‬ ‫ﺫﻟﻙ‬ ‫ﻓﻲ‬ ‫ﻟﻠﺴﺭﻋﺔ‬ ‫ﺒﻪ‬ ‫ﺍﻟﻤﺴﻤﻭﺡ‬75mi/h
‫ﺍﻟﺤل‬:‫ﻤﻴل‬ ‫ﺇﻟﻰ‬ ‫ﺍﻟﻤﺘﺭ‬ ‫ﺒﺘﺤﻭﻴل‬ ‫ﻨﻘﻭﻡ‬ ‫ﺴﻭﻑ‬
‫ﺴﺎﻋﺎﺕ‬ ‫ﺇﻟﻰ‬ ‫ﺍﻟﺜﻭﺍﻨﻲ‬ ‫ﻨﺤﻭل‬ ‫ﺴﻭﻑ‬ ‫ﻭﺍﻵﻥ‬

31
‫ﺒﻭﺤﺩﺓ‬ ‫ﺍﻟﺴﺭﻋﺔ‬ ‫ﻤﻘﺩﺍﺭ‬km/h‫؟‬
‫ﺒﻭﺤﺩﺓ‬ ‫ﺘﺩﺭﻴﺠﻴﻥ‬ ‫ﻫﻨﺎﻙ‬ ‫ﻴﻜﻭﻥ‬ ‫ﻤﺎ‬ ‫ﻭﻏﺎﻟﺒﺎ‬ ‫ﺴﻴﺎﺭﺓ‬ ‫ﻓﻲ‬ ‫ﺍﻟﺴﺭﻋﺔ‬ ‫ﻤﻘﻴﺎﺱ‬ ‫ﻴﻭﻀﺢ‬km/h‫ﻭﺒﻭﺤﺩﺓ‬mi/h.
www.trgma.com
‫ﺒﻪ‬ ‫ﺍﻟﻤﺴﻤﻭﺡ‬ ‫ﺍﻟﺴﺭﻋﺔ‬ ‫ﺤﺩ‬ ‫ﺘﺘﺠﺎﻭﺯ‬ ‫ﺍﻟﺴﻴﺎﺭﺓ‬ ‫ﻓﺎﻥ‬ ‫ﻭﺒﻬﺫﺍ‬.
‫ﻤﺎﺫﺍ‬ ‫ﻟﻭ؟‬ ‫ﻤﺎﺫﺍ‬‫ﺇﺫﺍ‬‫ﻜﺎﻥ‬‫ﻭﺤﺩﺓ‬ ‫ﻤﻊ‬ ‫ﺍﻟﺘﻌﺎﻤل‬ ‫ﻴﺠﻴﺩ‬ ‫ﻻ‬mi/h‫ﻓﻲ‬ ‫ﻭﻴﺭﻏﺏ‬‫ﺇﻴﺠﺎﺩ‬‫ﺒﻭﺤﺩﺓ‬ ‫ﺍﻟﺴﺭﻋﺔ‬ ‫ﻤﻘﺩﺍﺭ‬
‫ﺍﻟﺤل‬:‫ﺍﻟﺘﺎﻟﻲ‬ ‫ﺍﻟﻨﺤﻭ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻷﺨﻴﺭﺓ‬ ‫ﺍﻹﺠﺎﺒﺔ‬ ‫ﻨﺤﻭل‬ ‫ﺍﻥ‬ ‫ﻴﻤﻜﻨﻨﺎ‬:
‫ﺍﻟﺸﻜل‬1.3‫ﺒﻭﺤﺩﺓ‬ ‫ﺘﺩﺭﻴﺠﻴﻥ‬ ‫ﻫﻨﺎﻙ‬ ‫ﻴﻜﻭﻥ‬ ‫ﻤﺎ‬ ‫ﻭﻏﺎﻟﺒﺎ‬ ‫ﺴﻴﺎﺭﺓ‬ ‫ﻓﻲ‬ ‫ﺍﻟﺴﺭﻋﺔ‬ ‫ﻤﻘﻴﺎﺱ‬ ‫ﻴﻭﻀﺢ‬

32
‫ﻨﻀﻊ‬‫ﺇﺠﺎﺒﺘﻨﺎ‬‫ﻤﻘﺭﺏ‬ ‫ﻋﺩﺩﻱ‬ ‫ﺭﻗﻡ‬ ‫ﺒﺸﻜل‬.‫ﻫﺫﻩ‬‫ﺍﻹﺠﺎﺒﺔ‬‫ﻗﻴﻡ‬ ‫ﺘﻌﻴﻴﻥ‬ ‫ﻓﻲ‬ ‫ﺘﺴﺘﺨﺩﻡ‬‫ﺃﺨﺭﻯ‬.
‫ﻴﺠﺏ‬ ‫ﻭﺍﻟﺘﻲ‬ ،‫ﻤﺤﺩﺩﺓ‬ ‫ﻓﺭﻀﻴﺎﺕ‬ ‫ﻋﻠﻰ‬ ‫ﻤﺒﻨﻴﺔ‬ ‫ﺘﻜﻭﻥ‬ ‫ﻋﺎﺩﺓ‬ ‫ﺍﻟﺤﺴﺎﺒﺎﺕ‬ ‫ﻫﺫﻩ‬ ‫ﻤﺜل‬‫ﺃﻥ‬‫ﺍﻟﻤﻁﻠﻭﺒﺔ‬ ‫ﺍﻟﺩﻗﺔ‬ ‫ﺩﺭﺠﺔ‬ ‫ﺤﺴﺏ‬ ‫ﺘﻌﺩل‬.‫ﺍﻨﻪ‬ ‫ﻜﻤﺎ‬
‫ﺼﻭﺭﺓ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻌﺩﺩ‬ ‫ﺭﺘﺒﺔ‬ ‫ﻨﻀﻊ‬10n
‫ﺤﻴﺙ‬n‫ﺼﺤﻴﺢ‬ ‫ﻋﺩﺩ‬ ‫ﻫﻲ‬.‫ﻓﻌﻨﺩﻤﺎ‬‫ﻨﻘﻭﻡ‬‫ﺒﺈﺠﺭﺍﺀ‬‫ﻤﻌﻴﻨﺔ‬ ‫ﺤﺴﺎﺒﺎﺕ‬
‫ﺒﻤﻌﺎﻤل‬ ‫ﺍﻟﻘﻴﻤﺔ‬ ‫ﻋﻥ‬ ‫ﻨﻌﺒﺭ‬10‫ﺍﻟﺭﻗﻡ‬ ‫ﻓﻤﺜﻼ‬ ،1000‫ﻴﻜﺘﺏ‬103
.‫ﻭﻜﺫﻟﻙ‬
0.008,6 ~ 10-2
0.002,1 ~ 10-3
‫ﺍﻟﻌﺩﺩﻴﺔ‬ ‫ﻟﻠﻘﻴﻤﺔ‬ ‫ﺍﻟﺘﻘﺭﻴﺏ‬ ‫ﺍﺴﺘﺨﺩﺍﻡ‬.
‫ﺘﺨﻤﻴﻥ‬ ‫ﺒﻌﻤﻠﻴﺔ‬ ‫ﻨﻘﻭﻡ‬ ‫ﻋﻨﺩﻤﺎ‬ ‫ﻜﺜﻴﺭﺍ‬ ‫ﺍﻟﻁﺭﻴﻘﺔ‬ ‫ﻫﺫﻩ‬ ‫ﺘﺴﺘﺨﺩﻡ‬‫ﻟﻤﺴﺄﻟﺔ‬‫ﻗﺒل‬ ‫ﺤﺴﺎﺒﻴﺔ‬‫ﺃﻥ‬‫ﻨﻘﻭﻡ‬‫ﺒﺈﺠﺭﺍﺀ‬‫ﺍﻟﺘﻭﻗﻊ‬ ‫ﻤﻥ‬ ‫ﻜﻨﻭﻉ‬ ‫ﺒﺩﻗﺔ‬ ‫ﺍﻟﺤﺴﺎﺒﺎﺕ‬
www.trgma.com
6.1‫ﻭﺍﻷﺭﻗﺎﻡ‬ ‫ﺍﻟﺘﻘﺩﻴﺭﺍﺕ‬
‫ﻓﻲ‬‫ﺍﻷﺤﻴﺎﻥ‬ ‫ﻤﻥ‬ ‫ﺍﻟﻜﺜﻴﺭ‬‫ﻴﻜﻭﻥ‬‫ﻤﻔﻴﺩﺍ‬‫ﺃﻥ‬‫ﻨﻀﻊ‬
‫ﻴﺠﺏ‬ ‫ﻭﺍﻟﺘﻲ‬ ،‫ﻤﺤﺩﺩﺓ‬ ‫ﻓﺭﻀﻴﺎﺕ‬ ‫ﻋﻠﻰ‬ ‫ﻤﺒﻨﻴﺔ‬ ‫ﺘﻜﻭﻥ‬ ‫ﻋﺎﺩﺓ‬ ‫ﺍﻟﺤﺴﺎﺒﺎﺕ‬ ‫ﻫﺫﻩ‬ ‫ﻤﺜل‬
‫ﻤﻥ‬ ‫ﺍﻟﻜﺜﻴﺭ‬ ‫ﻓﻲ‬‫ﺍﻷﺤﻴﺎﻥ‬‫ﺼﻭﺭﺓ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻌﺩﺩ‬ ‫ﺭﺘﺒﺔ‬ ‫ﻨﻀﻊ‬
‫ﺍﻟﻤﻨﺎﺴﺏ‬ ‫ﻤﻥ‬ ‫ﻴﻜﻭﻥ‬‫ﺃﻥ‬‫ﺒﻤﻌﺎﻤل‬ ‫ﺍﻟﻘﻴﻤﺔ‬ ‫ﻋﻥ‬ ‫ﻨﻌﺒﺭ‬
720 ~ 103
‫ﻭﺍﻟﺭﻤﺯ‬~‫ﻴﺸﻴﺭ‬‫ﺇﻟﻰ‬‫ﺍﻟﻌﺩﺩﻴﺔ‬ ‫ﻟﻠﻘﻴﻤﺔ‬ ‫ﺍﻟﺘﻘﺭﻴﺏ‬ ‫ﺍﺴﺘﺨﺩﺍﻡ‬
‫ﺘﺨﻤﻴﻥ‬ ‫ﺒﻌﻤﻠﻴﺔ‬ ‫ﻨﻘﻭﻡ‬ ‫ﻋﻨﺩﻤﺎ‬ ‫ﻜﺜﻴﺭﺍ‬ ‫ﺍﻟﻁﺭﻴﻘﺔ‬ ‫ﻫﺫﻩ‬ ‫ﺘﺴﺘﺨﺩﻡ‬
‫ﺍﻟﺤل‬ ‫ﻗﺒل‬ ‫ﺍﻟﻨﺎﺘﺠﺔ‬ ‫ﻟﻠﻘﻴﻤﺔ‬.

Ch1 physics and measurements

Recommended

Recommended

More Related Content

Featured

Featured (20)

Ch1 physics and measurements