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--:22/03/2013:1 ––:، ،.: ********************************************************************************** 1−‫و‬ ‫א‬ ‫א‬‫א‬ ‫ط‬ ‫א‬ ‫و‬: -، ‫ا‬ ‫د‬ ‫ا‬ ‫ط‬ ‫ا‬ ‫و‬ ‫ا‬ ‫أ‬ ‫ا‬ ‫ت‬ ‫إذا‬ ، ‫أ‬ ‫ل‬ ‫ـ‬ ‫آ‬ ‫ة‬ ‫ﺥ‬ ‫ا‬ ‫ه‬ ‫ا‬ ‫و‬EP‫ل‬ ‫ا‬ ‫و‬ ‫و‬)J. ( -‫ه‬ ‫راﺱ‬ ‫ا‬ ‫ل‬ ‫ن‬ ‫ﺱ‬ ‫ا‬ ‫و‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫أه‬: ●‫ا‬)+‫ض‬ ‫أر‬: ( -‫ا‬)+‫أرض‬(‫ا‬ ‫إذا‬‫رض‬ ‫ا‬ ‫و‬ ‫ا‬. -‫ا‬)+‫أرض‬(‫ـ‬ ‫آ‬EPP. ●‫ا‬)+( - : 04 ‫ﺍﻟﻄﺎﻗﺔ‬ ‫ﻭ‬ ‫ﺍﻟﻤﻴﻜﺎﻧﻴﻚ‬‫ﺍﻟﻄﺎﻗﺔ‬ ‫ﻭ‬ ‫ﺍﻟﻤﻴﻜﺎﻧﻴﻚ‬‫ﺍﻟﻄﺎﻗﺔ‬ ‫ﻭ‬ ‫ﺍﻟﻤﻴﻜﺎﻧﻴﻚ‬‫ﺍﻟﻄﺎﻗﺔ‬ ‫ﻭ‬ ‫ﺍﻟﻤﻴﻜﺎﻧﻴﻚ‬ ‫ا‬:‫م‬ ‫ر‬ ، ‫ت‬ ‫ر‬ ‫ا‬-1: h1 h2 h1 ≠≠≠≠ h2←←←←‫ا‬)‫ﺝ‬+‫أرض‬(‫ه‬. ‫ا‬-2: ℓ1 ℓ2 = ℓ1 + ∆ℓ ℓ1 ≠ ℓ2←←←←‫ا‬)‫ﺝ‬+‫ﺏ‬ ‫ﻥ‬(‫ه‬ www.sites.google.com/site/faresfergani ‫ر‬:22/03/2013
--:22/03/2013:2 ––:، ،.: -‫ا‬)+(‫ا‬ ‫ل‬)‫ط‬ ‫ا‬ ‫أو‬ ‫اﺱ‬. ( -‫ا‬)+(‫ـ‬ ‫و‬ ‫آ‬EPe. ●‫ا‬)+‫ﺱ‬( -‫ا‬)+‫ﺱ‬(‫او‬ ‫ا‬θ. -‫ا‬)+‫ﺱ‬(‫آ‬θ‫ـ‬EPe. ‫ﻡ‬: -‫ا‬ ‫ا‬ ‫ا‬‫س‬ ، ‫ي‬ ‫ار‬ ‫آ‬ ، ‫ار‬ ‫ه‬ ‫د‬ ‫و‬ ‫ا‬ ‫ا‬.‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫أن‬. -‫ازن‬ ‫ا‬ ‫وﺽ‬ ‫دة‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫و‬ ‫و‬ ‫ا‬ ‫ا‬‫ا‬ ‫ا‬ ‫ب‬ ‫و‬ ‫ا‬)x = 0(‫ا‬ ‫ا‬ ‫ا‬ ‫و‬)θ = 0. ( 2–‫א‬ ‫א‬ ‫ط‬ ‫א‬: ‫ط‬ ‫ﻥ‬-1: -)S(‫آ‬m‫ا‬)‫ا‬ ‫ا‬ ‫ﺱ‬ ‫ون‬(‫ﺽ‬ ‫اءا‬ ‫ا‬A‫ﺽ‬B‫ﺽ‬ ‫ورا‬ ‫آ‬M)‫ا‬ ‫اء‬ ‫ا‬ ‫ات‬. ( -‫ﺽ‬ ‫ا‬ ‫ر‬ ‫ا‬ ‫ا‬ ‫ي‬ ‫ا‬B‫ا‬ ‫ه‬ ‫و‬ ، ‫ا‬ ‫ا‬ ‫ا‬ ‫ب‬zA‫ه‬ ‫ﺽ‬ ‫ا‬A، ‫ا‬ ‫ي‬ ‫ا‬zM‫ا‬ ‫ﺽ‬ ‫ا‬M‫ا‬ ‫ي‬ ‫ا‬)‫ا‬-4. ( ‫ا‬-3: B(θ2) A(θ1) ‫ازن‬ ‫ا‬ ‫و‬θ = 0 θ2≠≠≠≠θ1←←←←‫ا‬)‫ﺝ‬+‫ﺱ‬(‫ه‬. ‫ا‬-4:z A B Az Mz h 0=E,0=z PP M
--:22/03/2013:3 ––:، ،.: 1-‫ا‬ ‫ر‬ ‫و‬ ‫ا‬ ‫ظ‬ ‫ا‬ ‫أ‬)+‫أرض‬(‫ﺽ‬ ‫ا‬ ‫أو‬M‫رة‬‫آ‬ ‫ا‬ ‫ا‬ECM EPPA‫ﺽ‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬A‫و‬EPPM‫ا‬ ‫ا‬ ‫ا‬‫ﺽ‬ ‫ا‬M. 2-‫ا‬ ‫ا‬ ‫ظ‬ ‫ا‬ ‫أ‬)(‫ﺽ‬ ‫ا‬ ‫أو‬M‫رة‬‫آ‬ ‫ا‬ ‫ا‬ECzA ‫ا‬ ‫ع‬ ‫ار‬‫ﺽ‬A‫و‬ ‫ا‬ ‫ي‬ ‫ا‬zM‫ﺽ‬ ‫ا‬ ‫ع‬ ‫ار‬M‫ا‬ ‫ي‬ ‫ا‬. 3-‫ﺽ‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫رة‬ ‫اﺱ‬ ‫ا‬ ‫ر‬ ‫ا‬ ‫دا‬ ‫ا‬A‫ﺽ‬ ‫ا‬ ‫و‬‫ا‬M. ‫ط‬ ‫ا‬: 1-‫رة‬‫آ‬ ‫ا‬ ‫ا‬MCEPPAE،PPME: -‫روﺱ‬ ‫ا‬ ‫ا‬) :+‫أرض‬( -‫راﺱ‬ ‫ا‬:‫أرﺽ‬ ‫ﺱ‬. -‫ر‬ ‫ﺥ‬ ‫ى‬. -‫ﺽ‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ظ‬ ‫ا‬ ‫أ‬A‫و‬M: EA + E - E = EM ECA + EppA = ECM + EppM ▪ ECA = 0 (vA = 0 ) ‫و‬: EppA = ECM + EppM ECM = EppA - EppM .............................................. (1) 1-‫رة‬‫آ‬ ‫ا‬ ‫ا‬MCEAz،Mz: -‫روﺱ‬ ‫ا‬ ‫ا‬) :S( -‫راﺱ‬ ‫ا‬:‫أرﺽ‬ ‫ﺱ‬. -‫ر‬ ‫ا‬ ‫ى‬ ‫ا‬‫ة‬ ‫ا‬:‫ا‬P. -‫ﺽ‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ظ‬ ‫ا‬ ‫أ‬A‫و‬M: EA + E - E = EM ▪ ECA = 0 (vA = 0 ) ▪ m.g.z-m.g.z=)z-(zm.g=m.g.h=)P(W MAMAM-A ‫ا‬-5:z A B Az Mz h 0=E,0=z PP M P
--:22/03/2013:4 ––:، ،.: ‫و‬: E=m.g.z-m.g.z+0 CMMA m.g.z-m.g.z=E MACM .................................................. (2) 3-‫ﺽ‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫رة‬A‫ﺽ‬ ‫ا‬ ‫و‬‫ا‬M: ‫ﺱ‬: ECM = EppA - EppM ............................................................. (1) m.g.z-m.g.z=E MACM .................................................. (2) : EppA = m.g.zA EppM = m.g.zB ‫ﻥ‬: ‫ن‬)S(‫ع‬ ‫ار‬z‫ا‬ ‫ن‬ ‫ي‬)S+‫أرض‬(‫آ‬ : Epp = m.g.z ‫ط‬−2:)‫ا‬ ‫ا‬ ‫ا‬ ‫ه‬‫؟‬ ‫ي‬ ‫أم‬ -‫ك‬‫ء‬ ،AB‫ا‬)‫ا‬-6(. -‫وا‬ ‫ا‬ ‫ا‬ ‫ت‬ ‫ا‬ ‫دراﺱ‬‫د‬ ‫ﺹ‬ ‫ل‬ ‫ﺥ‬ ‫وذ‬ ‫ا‬ ‫م‬‫ا‬‫ا‬‫ل‬AB ‫ا‬. 1-‫ء‬ ‫أ‬ ‫ا‬ ‫ا‬ ‫ى‬ ‫ا‬‫ا‬ ‫ا‬ ، ‫د‬ ‫ﺹ‬)‫ا‬(‫ﺽ‬ ‫آ‬ ‫ﺽ‬ ‫و‬ ‫ا‬ ‫ا‬‫ا‬ ‫ظ‬ ‫إ‬ ‫د‬ ‫أآ‬ ‫و‬. 2-‫ا‬ ‫ّم‬ ‫أو‬ ‫ا‬ ‫ه‬ ، ‫رأ‬‫ء‬ ‫أ‬ ،‫ء‬ ‫ا‬AB‫ا‬‫؟‬ -‫ا‬ ‫ه‬ ّ ‫ا‬ ‫م‬ ‫ا‬ ‫ه‬ ، ‫ا‬)‫و‬/‫أو‬(‫ت‬ ‫أﺥ‬ ‫ا‬ ‫م‬ ‫ا‬ ‫ه‬‫ا‬‫؟‬ -‫ذا؟‬ ، ‫ا‬ ‫ر‬ ‫ا‬)‫ا‬ ( ‫ا‬-6:
--:22/03/2013:5 ––:، ،.: 3-‫؟‬ ‫ط‬ ‫ا‬ ‫أن‬ ‫وا‬ ‫ا‬ ‫ف‬ ّ ، ‫رأ‬ ‫ه‬ 4-‫ا‬ ‫ف‬ ‫ﺽ‬ ، ‫رأ‬ ‫ه‬‫؟‬ ‫أن‬ ‫وا‬ ‫ت‬ ‫ا‬‫ث‬:‫ا‬ ‫ا‬ ، ‫ا‬ ‫ا‬)‫اﺱ‬ ‫ا‬(‫ا‬ ‫ا‬ ،) ‫اﺱ‬. ( ‫ط‬ ‫ا‬: 1-‫ى‬ ‫ا‬: ‫ا‬ ‫ا‬)(: -‫ا‬ ‫ة‬ ‫ا‬ ‫ر‬ ‫ا‬ ‫ى‬ ‫ا‬: ▪‫ا‬ ‫ة‬T←‫آ‬ ‫ا‬←0>)T(W B‫ـ‬A.‫أي‬. ▪‫ا‬ ‫ة‬P←‫آ‬ ‫ا‬ ‫آ‬←0<)P(W B‫ـ‬A.‫أي‬. ▪‫ك‬ ‫ا‬ ‫ة‬f←‫آ‬ ‫ا‬ ‫آ‬←0<)f(W B‫ـ‬A.‫أي‬. -‫ا‬ ‫ل‬ ‫أﺵ‬:‫ل‬ ‫ا‬ ‫ء‬ ‫أ‬ ‫آ‬A‫إ‬B‫ل‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ء‬ ‫أ‬ ‫ا‬ ‫ﺱ‬ ‫ن‬. ‫ا‬ ‫ا‬ ‫ن‬ ‫و‬)(‫آ‬: ‫ا‬ ‫ظ‬ ‫إ‬ ‫د‬: ‫ا‬‫ﺡ‬ )P(W r )f(W r )T(W r ‫ا‬-7: B A P f R T
--:22/03/2013:6 ––:، ،.: ‫ا‬ ‫ا‬ ‫ظ‬ ‫ا‬ ‫أ‬)(‫ﺽ‬ ‫ا‬A‫و‬B‫ن‬: EA + E - E = EB E=)f(W+)P(W(-)T(W+E CBB-AB-AB-ACA ‫ل‬ ‫ا‬ ‫ء‬ ‫أ‬ ‫آ‬ ‫ا‬ ‫ا‬ ‫أن‬ ‫ن‬ ‫آ‬ ‫و‬A‫إ‬B‫أي‬ECA = ECB: 0=)f(W-)P(W-)T(W B-AB-AB-A 2-‫ء‬ ‫أ‬‫ا‬AB‫ا‬ ‫ة‬ ‫و‬ ‫ا‬)T(W r ُ ،‫ك‬‫ك‬ ‫ا‬ ‫ءا‬‫ا‬ ‫ه‬‫ك‬ ‫ا‬ ‫ة‬ ‫وي‬ ‫ا‬)f(W r ‫ا‬ ‫ء‬ ‫ا‬ ‫أ‬ ،‫ا‬ ‫ة‬ ‫وي‬ ‫ا‬)P(W r ُ‫ف‬ ‫ّن‬‫ا‬‫ن‬‫رض‬ ‫ا‬ ‫دل‬. 3-‫ط‬ ‫ا‬ ‫أن‬ ‫وا‬ ‫ا‬ ‫ف‬ ّ‫ه‬ ‫ا‬ ‫ه‬ ،‫ز‬ ‫ا‬ ‫ا‬ ‫ا‬A‫إ‬B‫ا‬ ‫ة‬ ‫و‬ ‫ن‬ ‫ا‬ ‫و‬)T(W B-A‫ا‬ ‫ه‬ ‫ع‬ ‫اﺱ‬ ، ‫ه‬‫و‬ ‫ا‬ ‫ه‬ ‫و‬ ‫ا‬ ‫و‬ ‫رض‬ ‫ا‬ ‫دل‬ ‫ﺵ‬ ‫ا‬ ‫ط‬ ‫ا‬ ‫ة‬)P(W B‫ـ‬A r . 4-‫ا‬ ‫ف‬ ‫ﺽ‬‫أن‬ ‫وا‬‫ا‬ ‫ه‬‫ا‬‫ك‬ ‫ا‬ ‫و‬‫ك‬ ‫ا‬ ‫ة‬)f(W r ‫ا‬ ‫و‬‫ه‬‫وا‬ ‫اﺥ‬ ‫ا‬ ‫ا‬ ‫ﺵ‬. 3–‫و‬ ‫א‬ ‫א‬ ‫ط‬ ‫א‬: ‫ط‬ ‫ﻥ‬: ‫آ‬M‫و‬ ‫ن‬ ‫أ‬ ‫إ‬K = 50 N/m‫ﺽ‬ ‫ا‬ ‫آ‬ ، A‫ا‬ ‫ا‬ ‫ﺱ‬ ‫ون‬‫ﺽ‬ ‫ا‬ ‫ا‬B‫ا‬ ‫و‬ ‫ا‬ ‫ﺱ‬ ‫م‬ ‫أ‬ ‫ار‬x)‫ا‬-8. ( ‫ا‬-8:
--:22/03/2013:7 ––:، ،.: 1-‫ا‬ ‫ا‬ ‫ظ‬ ‫ا‬ ‫أ‬)+‫أرض‬+(‫ﺽ‬ ‫ا‬A‫و‬B‫ي‬ ‫ا‬ ‫ر‬ ‫و‬ ‫ﺽ‬ ‫ا‬ ‫ر‬ ‫ا‬ ‫ا‬B‫ا‬ ‫ب‬‫و‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫أن‬ ‫أ‬ ، ‫ا‬ ‫ا‬ )++‫أرض‬(‫ﺽ‬ ‫ا‬B‫ار‬ ‫ا‬ ‫ن‬ ‫أ‬x: Epe = m.g.x. 2-‫أ‬ ‫ا‬ ‫ر‬ ‫آ‬M‫و‬‫ﺱ‬ ‫ا‬ ‫س‬ ‫ة‬ ‫آ‬x‫ا‬ ‫ا‬ ‫ول‬ ‫ا‬ ‫و‬ ‫ا‬: x2 (m2 )Epe = Mgx (J)x(m)M(kg) 0.040.100 0.060.150 0.080.200 0.100.250 ‫أ‬-‫ول‬ ‫ا‬ ‫أآ‬.g = 10 m/s2 . ‫ب‬-‫ن‬ ‫ا‬ ‫أرﺱ‬EPe = f(x2 )‫ا‬ ‫ه‬ ‫د‬ ‫أن‬ ،‫ا‬ ‫ن‬ ‫ا‬EPe = Ke x2 Ke‫ن‬ ‫ا‬ ‫ه‬ . 3-‫ا‬Ke‫آ‬ ‫اﺱ‬ ‫س‬ ‫و‬ ‫م‬ ‫أ‬ ‫ذ‬ ‫و‬ ‫ا‬ ‫ا‬ ‫ة‬ ‫ا‬ ‫و‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ن‬ ‫ة‬. ‫ا‬ ‫ول‬ ‫ا‬‫ا‬ ‫ا‬: T = M.g (N)x(m)M(kg) 0.020.100 0.030.150 0.040.200 0.050.250 ‫ا‬-9:
--:22/03/2013:8 ––:، ،.: ‫ب‬-‫ا‬ ‫أن‬ ‫أ‬ ‫ازن‬ ‫ا‬ ‫ط‬ ‫ﺵ‬ ‫د‬ ‫ا‬:T = M.g‫أآ‬ ‫ا‬ ‫ه‬ ‫دا‬ ‫ا‬ ‫و‬ ‫ا‬ ‫ول‬ ‫ا‬. ‫ب‬-‫ن‬ ‫ا‬ ‫أرﺱ‬T = f(x)،‫ا‬ ‫د‬ ‫أ‬T = Ke' xKe'‫ن‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ه‬. 3-‫رن‬Ke،Ka'K‫ا‬ ‫و‬. 5-‫ر‬ ‫ا‬ ‫ى‬ ‫أﺥ‬ ‫ا‬ ‫ل‬ ‫ﺱ‬ ‫ا‬ ‫ر‬ ‫آ‬.‫ا‬ ‫ة‬ ‫رة‬ ‫إذن‬ ‫اﺱ‬ ‫و‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫رة‬ ‫و‬. ‫ط‬ ‫ا‬: 1-‫إ‬‫أن‬ ‫ت‬x.g.m=peE: -‫روﺱ‬ ‫ا‬ ‫ا‬) :+‫أرض‬+( -‫راﺱ‬ ‫ا‬:‫أرﺽ‬ ‫ﺱ‬. -‫ا‬ ‫ة‬ ‫ر‬ ‫ﺥ‬ ‫ى‬. -‫ﺽ‬ ‫ا‬ ‫ا‬ ‫ظ‬ ‫ا‬ ‫أ‬A‫و‬B: EA + E - E = EB ECA + EppA + EpeA = ECB + EppB + EpeB ▪ ECA = 0 (vA = 0 ) ▪ EppA = m.g.zA = m.g.x ▪ EpeA = 0 (x = 0) ▪ ECB = 0 (vB = 0 ) ▪ EppB = 0 ( ‫ا‬ ‫ي‬ ‫ا‬) : EpeB = m.g.x 2-‫أ‬-‫ول‬ ‫ا‬ ‫ل‬ ‫إآ‬: x2 (m2 )Epe = Mgx (J)x(m)M(kg) 1.6 . 10-3 0.040.040.100 3.6 . 10-3 0.090.060.150 6.4 . 10-3 0.160.080.200 10-2 0.250.100.250 ‫ا‬-10: A B P T x
--:22/03/2013:9 ––:، ،.: ‫ب‬-‫ن‬ ‫ا‬)2 x(f=peE: -‫ن‬ ‫ا‬Epe = f(x2 )‫ا‬ ‫د‬ ‫رة‬Epe = Ke x2 Ke‫ن‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ه‬. -‫ن‬ ‫ا‬: 25= 0.002.3 0.05.3 =Ke 3-‫ا‬ ‫أن‬ ‫ت‬ ‫إ‬g.M=T‫ازن‬ ‫ا‬: -‫روﺱ‬ ‫ا‬ ‫ا‬:)S. ( -‫راﺱ‬ ‫ا‬:‫أرﺽ‬ ‫ﺱ‬. -‫ا‬ ‫ة‬ ‫ا‬ ‫ر‬ ‫ا‬ ‫ى‬ ‫ا‬:‫ا‬P،‫ا‬T. -‫ا‬ ‫ازن‬ ‫ط‬ ‫ﺵ‬: 0=F∑ ext 0=T+P ‫ر‬ ‫ا‬ ‫و‬ ‫ا‬ ‫ا‬ox‫ﺱ‬ ‫ا‬ ‫ا‬: P - T = 0 M.g - T = 0 → T = M.g 0 0,05 0,1 0,15 0,2 0,25 0,3 0 0,002 0,004 0,006 0,008 0,01 0,012 x 2 (m 2 ) E pe(J) ‫ا‬-10: P T x
--:22/03/2013:10 ––:، ،.: -‫ول‬ ‫ا‬ ‫ل‬ ‫إآ‬: T = M.g (N)x(m)M(kg) 1.00.020.100 1.50.030.150 2.00.040.200 2.50.050.250 ‫ب‬-‫ن‬ ‫ا‬)x(f=T: ‫ن‬ ‫ا‬T = f(x)‫ا‬ ‫د‬ ‫أ‬ ‫ا‬ ‫رة‬T = Ke' xKe'‫ن‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ه‬. -‫ن‬ ‫ا‬: 50= 0.01.3 0.5.3 ='Ke 3-‫ر‬eK،'aKK: K = 50 Ke = 25 → 2 K =Ke Ke' = 50 → Ke' = K 4-‫ا‬ ‫ة‬ ‫ة‬ ‫ﺵ‬ ‫رة‬T‫و‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫و‬peE: ‫ﺱ‬: xK=E 2 ePe T = Ke’ x ‫أن‬ ‫و‬: 2 K =Ke،K='Ke‫ن‬: 0 0,5 1 1,5 2 2,5 3 0 0,01 0,02 0,03 0,04 0,05 0,06 x (m) T(N)
--:22/03/2013:11 ––:، ،.: K x 2 1 =E 2 Pe T = K x ‫ﻥ‬: -‫و‬ ‫ن‬K‫ار‬ ‫أو‬x‫ة‬ ‫ا‬ ‫ا‬ ،T‫ﺵ‬ : T = K x -‫ار‬ ‫أو‬ ‫ا‬x‫ا‬ ‫ن‬)+(‫و‬ ‫آ‬ : 2 pe K x 2 1 =E -‫ا‬ ‫و‬ ‫ر‬k‫ـ‬N/m ‫ﻡ‬: ‫ا‬ ‫رج‬ ‫ﺥ‬ ‫ا‬ ‫ن‬ ‫و‬ ‫ا‬ ‫ن‬ ‫ا‬ ‫داﺥ‬ ‫ن‬ ‫ا‬ ‫ة‬ ‫ا‬ ‫ا‬ ‫ر‬ ‫ن‬ ‫أ‬ ، ‫ن‬)‫ا‬. ( 3–‫א‬ ‫א‬ ‫ط‬ ‫א‬: ‫ط‬ ‫ﻥ‬: -‫و‬‫ﺏ‬ ‫ﻥ‬)1(C = 0.125 N.m/rad‫اﺥ‬ ‫ا‬ ‫ا‬O‫و‬ ،‫ل‬ ‫ﺱ‬)2(‫و‬K = 12.5 N/m‫ا‬ ‫ا‬ ‫ف‬ ‫ا‬)1( ‫د‬ ‫ة‬AO‫ة‬ ‫ا‬ ‫دوران‬ ‫زاو‬ ‫س‬ ‫ر‬)‫ا‬. ( ‫ا‬-12: T T ‫ازن‬ ‫ا‬ ‫اﺱ‬ ‫ا‬ ‫ط‬ ‫ا‬ ‫ا‬
--:22/03/2013:12 ––:، ،.: 1-‫ﺱ‬ ‫ا‬ ‫ة‬ ‫آ‬ ‫و‬ ‫ا‬ ‫ة‬ ‫ا‬ ‫ة‬ ‫ا‬x)2(‫وران‬ ‫ا‬ ‫زاو‬ ‫و‬θ‫ا‬)1( ‫ﺥ‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ول‬ ‫ا‬R = 10 cm: R.F=)F(M=M o/F (N)θ (rd)x(cm) 0.50.44 1.00.88 1.51.212 ‫أ‬-‫ول‬ ‫ا‬ ‫أآ‬. ‫ب‬-‫ن‬ ‫ا‬ ‫أرﺱ‬M = f(θ)‫ة‬ ‫ا‬ ‫م‬ ‫وي‬ ‫ا‬ ‫و‬ ‫ا‬ ‫دو‬ ‫م‬ ‫ات‬ ‫ي‬ ‫ا‬ ،F‫د‬ ‫أن‬ ، ‫ا‬M = Ce θCe‫ا‬ ‫ا‬ ‫ه‬ ‫ه‬‫ن‬. 2-‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ب‬)‫ط‬ ‫ا‬-1(‫ا‬ ‫ا‬ ‫ا‬ ‫أن‬)1( ‫ا‬ ‫ا‬ ‫ا‬ ‫وﺽ‬ ‫آ‬ ‫وي‬)2. (‫ول‬ ‫ا‬ ‫أ‬ ‫ا‬ ‫ول‬ ‫ا‬ ‫و‬ ‫ا‬ ‫ا‬ ‫ل‬ ‫ﺱ‬ ‫ا‬: θ 2 (rd)2‫ا‬ ‫ا‬‫ا‬)1( EPe = 1/2Kx2 (J) θ (rd)x(cm) 0.44 0.88 1.212 ‫أ‬-‫ا‬ ‫ات‬ ‫أرﺱ‬Epe‫ا‬ ‫ا‬)1(‫او‬ ‫ا‬θ2 ‫ا‬ ‫د‬ ‫أن‬ Epe = Ce ' θ2 Kc'‫ن‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ه‬. ‫ب‬-‫رن‬Ce،Ce ' ‫و‬C‫ا‬. 3-‫رن‬Ce‫ا‬C.‫؟‬ ‫ذا‬ 4-‫ا‬ ‫ا‬ ‫و‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫رة‬ ‫أن‬ ‫اﺱ‬:2 pe θC 2 1 =E. 5-‫ى‬ ‫أﺥ‬ ‫ا‬ ‫ل‬ ‫ﺱ‬ ‫ا‬ ‫ر‬ ‫آ‬‫ر‬ ‫ا‬.‫دو‬ ‫م‬ ‫رة‬ ‫إذن‬ ‫اﺱ‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫رة‬ ‫و‬ ‫ا‬. ‫ا‬-6:
--:22/03/2013:13 ––:، ،.: ‫ط‬ ‫ا‬: 1-‫أ‬-‫ول‬ ‫ا‬ ‫ل‬ ‫إآ‬: ‫ب‬-‫ن‬ ‫ا‬)θ(f=M: ‫ن‬ ‫ا‬M = f(θ)‫د‬ ‫أ‬ ‫ا‬ ‫رة‬M = Ce θ‫د‬ ‫أ‬ ‫ا‬ ‫رة‬ M = Ce θCe‫ن‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ه‬. -‫ن‬ ‫ا‬: 0.125= 0.5.1.6 0.02.5 =Ce 2-‫أ‬-‫ول‬ ‫ا‬ ‫ل‬ ‫إآ‬:
--:22/03/2013:14 ––:، ،.: ‫ب‬-‫ن‬ ‫ا‬)2 θ(f=peE: ‫ن‬ ‫ا‬Epe = f(θ)‫ا‬ ‫د‬ ‫أ‬ ‫ا‬ ‫رة‬Epe = Ce' θ2 Ce'‫ن‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ه‬. 0.0625= 0.5.1.6 0.01.5 =Ce ‫ـ‬-‫ر‬ ‫ا‬eC‫و‬'eCC: C = 0.125 Ce = 0.125 → Ce = C Ce = 0.125 → Ce = 2 C 4-‫ا‬ ‫ة‬ ‫ة‬ ‫ﺵ‬ ‫رة‬T‫و‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫و‬peE: ‫ﺱ‬: M = Ceθ EPe = Ce' θ2 ‫أن‬ ‫و‬:Ce = C، 2 C 'Ce‫ن‬: M = Cθ EPe = 2 1 C θ2 ‫ﻥ‬: -‫اس‬C‫دو‬ ‫ا‬ ‫ا‬ ، ‫ار‬M : M = C θ
--:22/03/2013:15 ––:، ،.: -‫ار‬ ‫اس‬θ‫ا‬ ‫ن‬)+‫ﺱ‬(‫آ‬: θC 2 1 =E 2 pe ‫ـ‬ ‫ا‬ ‫ر‬N.m/rad. ‫و‬ ‫ا‬ ‫ه‬.‫ا‬ ‫ان‬ ‫ا‬ ‫ذو‬ ‫ذ‬ ‫ﺱ‬ ‫ا‬ ‫أدﺥ‬: www.sites.google.com/site/faresfergani **‫ذ‬ ‫ﺱ‬ ‫ا‬:‫رس‬** ‫ﺱ‬ ‫ﺱ‬ ‫د‬ ‫وب‬ ‫ا‬- Fares_Fergani@yahoo.Fr Tel : 0771998109 ‫و‬ ‫ر‬ ‫ا‬ ‫أو‬ ‫روس‬ ‫ا‬ ‫ﺥ‬ ‫ي‬ ‫و‬ ‫ا‬ ‫ا‬ ‫إ‬. ‫ا‬ ‫وﺵ‬

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Physics unit4-lesson

  • 1.
    --:22/03/2013:1 ––:، ،.: ********************************************************************************** 1−‫و‬ ‫א‬‫א‬‫א‬ ‫ط‬ ‫א‬ ‫و‬: -، ‫ا‬ ‫د‬ ‫ا‬ ‫ط‬ ‫ا‬ ‫و‬ ‫ا‬ ‫أ‬ ‫ا‬ ‫ت‬ ‫إذا‬ ، ‫أ‬ ‫ل‬ ‫ـ‬ ‫آ‬ ‫ة‬ ‫ﺥ‬ ‫ا‬ ‫ه‬ ‫ا‬ ‫و‬EP‫ل‬ ‫ا‬ ‫و‬ ‫و‬)J. ( -‫ه‬ ‫راﺱ‬ ‫ا‬ ‫ل‬ ‫ن‬ ‫ﺱ‬ ‫ا‬ ‫و‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫أه‬: ●‫ا‬)+‫ض‬ ‫أر‬: ( -‫ا‬)+‫أرض‬(‫ا‬ ‫إذا‬‫رض‬ ‫ا‬ ‫و‬ ‫ا‬. -‫ا‬)+‫أرض‬(‫ـ‬ ‫آ‬EPP. ●‫ا‬)+( - : 04 ‫ﺍﻟﻄﺎﻗﺔ‬ ‫ﻭ‬ ‫ﺍﻟﻤﻴﻜﺎﻧﻴﻚ‬‫ﺍﻟﻄﺎﻗﺔ‬ ‫ﻭ‬ ‫ﺍﻟﻤﻴﻜﺎﻧﻴﻚ‬‫ﺍﻟﻄﺎﻗﺔ‬ ‫ﻭ‬ ‫ﺍﻟﻤﻴﻜﺎﻧﻴﻚ‬‫ﺍﻟﻄﺎﻗﺔ‬ ‫ﻭ‬ ‫ﺍﻟﻤﻴﻜﺎﻧﻴﻚ‬ ‫ا‬:‫م‬ ‫ر‬ ، ‫ت‬ ‫ر‬ ‫ا‬-1: h1 h2 h1 ≠≠≠≠ h2←←←←‫ا‬)‫ﺝ‬+‫أرض‬(‫ه‬. ‫ا‬-2: ℓ1 ℓ2 = ℓ1 + ∆ℓ ℓ1 ≠ ℓ2←←←←‫ا‬)‫ﺝ‬+‫ﺏ‬ ‫ﻥ‬(‫ه‬ www.sites.google.com/site/faresfergani ‫ر‬:22/03/2013
  • 2.
    --:22/03/2013:2 ––:، ،.: -‫ا‬)+(‫ا‬ ‫ل‬)‫ط‬‫ا‬ ‫أو‬ ‫اﺱ‬. ( -‫ا‬)+(‫ـ‬ ‫و‬ ‫آ‬EPe. ●‫ا‬)+‫ﺱ‬( -‫ا‬)+‫ﺱ‬(‫او‬ ‫ا‬θ. -‫ا‬)+‫ﺱ‬(‫آ‬θ‫ـ‬EPe. ‫ﻡ‬: -‫ا‬ ‫ا‬ ‫ا‬‫س‬ ، ‫ي‬ ‫ار‬ ‫آ‬ ، ‫ار‬ ‫ه‬ ‫د‬ ‫و‬ ‫ا‬ ‫ا‬.‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫أن‬. -‫ازن‬ ‫ا‬ ‫وﺽ‬ ‫دة‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫و‬ ‫و‬ ‫ا‬ ‫ا‬‫ا‬ ‫ا‬ ‫ب‬ ‫و‬ ‫ا‬)x = 0(‫ا‬ ‫ا‬ ‫ا‬ ‫و‬)θ = 0. ( 2–‫א‬ ‫א‬ ‫ط‬ ‫א‬: ‫ط‬ ‫ﻥ‬-1: -)S(‫آ‬m‫ا‬)‫ا‬ ‫ا‬ ‫ﺱ‬ ‫ون‬(‫ﺽ‬ ‫اءا‬ ‫ا‬A‫ﺽ‬B‫ﺽ‬ ‫ورا‬ ‫آ‬M)‫ا‬ ‫اء‬ ‫ا‬ ‫ات‬. ( -‫ﺽ‬ ‫ا‬ ‫ر‬ ‫ا‬ ‫ا‬ ‫ي‬ ‫ا‬B‫ا‬ ‫ه‬ ‫و‬ ، ‫ا‬ ‫ا‬ ‫ا‬ ‫ب‬zA‫ه‬ ‫ﺽ‬ ‫ا‬A، ‫ا‬ ‫ي‬ ‫ا‬zM‫ا‬ ‫ﺽ‬ ‫ا‬M‫ا‬ ‫ي‬ ‫ا‬)‫ا‬-4. ( ‫ا‬-3: B(θ2) A(θ1) ‫ازن‬ ‫ا‬ ‫و‬θ = 0 θ2≠≠≠≠θ1←←←←‫ا‬)‫ﺝ‬+‫ﺱ‬(‫ه‬. ‫ا‬-4:z A B Az Mz h 0=E,0=z PP M
  • 3.
    --:22/03/2013:3 ––:، ،.: 1-‫ا‬ ‫ر‬‫و‬ ‫ا‬ ‫ظ‬ ‫ا‬ ‫أ‬)+‫أرض‬(‫ﺽ‬ ‫ا‬ ‫أو‬M‫رة‬‫آ‬ ‫ا‬ ‫ا‬ECM EPPA‫ﺽ‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬A‫و‬EPPM‫ا‬ ‫ا‬ ‫ا‬‫ﺽ‬ ‫ا‬M. 2-‫ا‬ ‫ا‬ ‫ظ‬ ‫ا‬ ‫أ‬)(‫ﺽ‬ ‫ا‬ ‫أو‬M‫رة‬‫آ‬ ‫ا‬ ‫ا‬ECzA ‫ا‬ ‫ع‬ ‫ار‬‫ﺽ‬A‫و‬ ‫ا‬ ‫ي‬ ‫ا‬zM‫ﺽ‬ ‫ا‬ ‫ع‬ ‫ار‬M‫ا‬ ‫ي‬ ‫ا‬. 3-‫ﺽ‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫رة‬ ‫اﺱ‬ ‫ا‬ ‫ر‬ ‫ا‬ ‫دا‬ ‫ا‬A‫ﺽ‬ ‫ا‬ ‫و‬‫ا‬M. ‫ط‬ ‫ا‬: 1-‫رة‬‫آ‬ ‫ا‬ ‫ا‬MCEPPAE،PPME: -‫روﺱ‬ ‫ا‬ ‫ا‬) :+‫أرض‬( -‫راﺱ‬ ‫ا‬:‫أرﺽ‬ ‫ﺱ‬. -‫ر‬ ‫ﺥ‬ ‫ى‬. -‫ﺽ‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ظ‬ ‫ا‬ ‫أ‬A‫و‬M: EA + E - E = EM ECA + EppA = ECM + EppM ▪ ECA = 0 (vA = 0 ) ‫و‬: EppA = ECM + EppM ECM = EppA - EppM .............................................. (1) 1-‫رة‬‫آ‬ ‫ا‬ ‫ا‬MCEAz،Mz: -‫روﺱ‬ ‫ا‬ ‫ا‬) :S( -‫راﺱ‬ ‫ا‬:‫أرﺽ‬ ‫ﺱ‬. -‫ر‬ ‫ا‬ ‫ى‬ ‫ا‬‫ة‬ ‫ا‬:‫ا‬P. -‫ﺽ‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ظ‬ ‫ا‬ ‫أ‬A‫و‬M: EA + E - E = EM ▪ ECA = 0 (vA = 0 ) ▪ m.g.z-m.g.z=)z-(zm.g=m.g.h=)P(W MAMAM-A ‫ا‬-5:z A B Az Mz h 0=E,0=z PP M P
  • 4.
    --:22/03/2013:4 ––:، ،.: ‫و‬: E=m.g.z-m.g.z+0 CMMA m.g.z-m.g.z=EMACM .................................................. (2) 3-‫ﺽ‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫رة‬A‫ﺽ‬ ‫ا‬ ‫و‬‫ا‬M: ‫ﺱ‬: ECM = EppA - EppM ............................................................. (1) m.g.z-m.g.z=E MACM .................................................. (2) : EppA = m.g.zA EppM = m.g.zB ‫ﻥ‬: ‫ن‬)S(‫ع‬ ‫ار‬z‫ا‬ ‫ن‬ ‫ي‬)S+‫أرض‬(‫آ‬ : Epp = m.g.z ‫ط‬−2:)‫ا‬ ‫ا‬ ‫ا‬ ‫ه‬‫؟‬ ‫ي‬ ‫أم‬ -‫ك‬‫ء‬ ،AB‫ا‬)‫ا‬-6(. -‫وا‬ ‫ا‬ ‫ا‬ ‫ت‬ ‫ا‬ ‫دراﺱ‬‫د‬ ‫ﺹ‬ ‫ل‬ ‫ﺥ‬ ‫وذ‬ ‫ا‬ ‫م‬‫ا‬‫ا‬‫ل‬AB ‫ا‬. 1-‫ء‬ ‫أ‬ ‫ا‬ ‫ا‬ ‫ى‬ ‫ا‬‫ا‬ ‫ا‬ ، ‫د‬ ‫ﺹ‬)‫ا‬(‫ﺽ‬ ‫آ‬ ‫ﺽ‬ ‫و‬ ‫ا‬ ‫ا‬‫ا‬ ‫ظ‬ ‫إ‬ ‫د‬ ‫أآ‬ ‫و‬. 2-‫ا‬ ‫ّم‬ ‫أو‬ ‫ا‬ ‫ه‬ ، ‫رأ‬‫ء‬ ‫أ‬ ،‫ء‬ ‫ا‬AB‫ا‬‫؟‬ -‫ا‬ ‫ه‬ ّ ‫ا‬ ‫م‬ ‫ا‬ ‫ه‬ ، ‫ا‬)‫و‬/‫أو‬(‫ت‬ ‫أﺥ‬ ‫ا‬ ‫م‬ ‫ا‬ ‫ه‬‫ا‬‫؟‬ -‫ذا؟‬ ، ‫ا‬ ‫ر‬ ‫ا‬)‫ا‬ ( ‫ا‬-6:
  • 5.
    --:22/03/2013:5 ––:، ،.: 3-‫؟‬ ‫ط‬‫ا‬ ‫أن‬ ‫وا‬ ‫ا‬ ‫ف‬ ّ ، ‫رأ‬ ‫ه‬ 4-‫ا‬ ‫ف‬ ‫ﺽ‬ ، ‫رأ‬ ‫ه‬‫؟‬ ‫أن‬ ‫وا‬ ‫ت‬ ‫ا‬‫ث‬:‫ا‬ ‫ا‬ ، ‫ا‬ ‫ا‬)‫اﺱ‬ ‫ا‬(‫ا‬ ‫ا‬ ،) ‫اﺱ‬. ( ‫ط‬ ‫ا‬: 1-‫ى‬ ‫ا‬: ‫ا‬ ‫ا‬)(: -‫ا‬ ‫ة‬ ‫ا‬ ‫ر‬ ‫ا‬ ‫ى‬ ‫ا‬: ▪‫ا‬ ‫ة‬T←‫آ‬ ‫ا‬←0>)T(W B‫ـ‬A.‫أي‬. ▪‫ا‬ ‫ة‬P←‫آ‬ ‫ا‬ ‫آ‬←0<)P(W B‫ـ‬A.‫أي‬. ▪‫ك‬ ‫ا‬ ‫ة‬f←‫آ‬ ‫ا‬ ‫آ‬←0<)f(W B‫ـ‬A.‫أي‬. -‫ا‬ ‫ل‬ ‫أﺵ‬:‫ل‬ ‫ا‬ ‫ء‬ ‫أ‬ ‫آ‬A‫إ‬B‫ل‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ء‬ ‫أ‬ ‫ا‬ ‫ﺱ‬ ‫ن‬. ‫ا‬ ‫ا‬ ‫ن‬ ‫و‬)(‫آ‬: ‫ا‬ ‫ظ‬ ‫إ‬ ‫د‬: ‫ا‬‫ﺡ‬ )P(W r )f(W r )T(W r ‫ا‬-7: B A P f R T
  • 6.
    --:22/03/2013:6 ––:، ،.: ‫ا‬ ‫ا‬‫ظ‬ ‫ا‬ ‫أ‬)(‫ﺽ‬ ‫ا‬A‫و‬B‫ن‬: EA + E - E = EB E=)f(W+)P(W(-)T(W+E CBB-AB-AB-ACA ‫ل‬ ‫ا‬ ‫ء‬ ‫أ‬ ‫آ‬ ‫ا‬ ‫ا‬ ‫أن‬ ‫ن‬ ‫آ‬ ‫و‬A‫إ‬B‫أي‬ECA = ECB: 0=)f(W-)P(W-)T(W B-AB-AB-A 2-‫ء‬ ‫أ‬‫ا‬AB‫ا‬ ‫ة‬ ‫و‬ ‫ا‬)T(W r ُ ،‫ك‬‫ك‬ ‫ا‬ ‫ءا‬‫ا‬ ‫ه‬‫ك‬ ‫ا‬ ‫ة‬ ‫وي‬ ‫ا‬)f(W r ‫ا‬ ‫ء‬ ‫ا‬ ‫أ‬ ،‫ا‬ ‫ة‬ ‫وي‬ ‫ا‬)P(W r ُ‫ف‬ ‫ّن‬‫ا‬‫ن‬‫رض‬ ‫ا‬ ‫دل‬. 3-‫ط‬ ‫ا‬ ‫أن‬ ‫وا‬ ‫ا‬ ‫ف‬ ّ‫ه‬ ‫ا‬ ‫ه‬ ،‫ز‬ ‫ا‬ ‫ا‬ ‫ا‬A‫إ‬B‫ا‬ ‫ة‬ ‫و‬ ‫ن‬ ‫ا‬ ‫و‬)T(W B-A‫ا‬ ‫ه‬ ‫ع‬ ‫اﺱ‬ ، ‫ه‬‫و‬ ‫ا‬ ‫ه‬ ‫و‬ ‫ا‬ ‫و‬ ‫رض‬ ‫ا‬ ‫دل‬ ‫ﺵ‬ ‫ا‬ ‫ط‬ ‫ا‬ ‫ة‬)P(W B‫ـ‬A r . 4-‫ا‬ ‫ف‬ ‫ﺽ‬‫أن‬ ‫وا‬‫ا‬ ‫ه‬‫ا‬‫ك‬ ‫ا‬ ‫و‬‫ك‬ ‫ا‬ ‫ة‬)f(W r ‫ا‬ ‫و‬‫ه‬‫وا‬ ‫اﺥ‬ ‫ا‬ ‫ا‬ ‫ﺵ‬. 3–‫و‬ ‫א‬ ‫א‬ ‫ط‬ ‫א‬: ‫ط‬ ‫ﻥ‬: ‫آ‬M‫و‬ ‫ن‬ ‫أ‬ ‫إ‬K = 50 N/m‫ﺽ‬ ‫ا‬ ‫آ‬ ، A‫ا‬ ‫ا‬ ‫ﺱ‬ ‫ون‬‫ﺽ‬ ‫ا‬ ‫ا‬B‫ا‬ ‫و‬ ‫ا‬ ‫ﺱ‬ ‫م‬ ‫أ‬ ‫ار‬x)‫ا‬-8. ( ‫ا‬-8:
  • 7.
    --:22/03/2013:7 ––:، ،.: 1-‫ا‬ ‫ا‬‫ظ‬ ‫ا‬ ‫أ‬)+‫أرض‬+(‫ﺽ‬ ‫ا‬A‫و‬B‫ي‬ ‫ا‬ ‫ر‬ ‫و‬ ‫ﺽ‬ ‫ا‬ ‫ر‬ ‫ا‬ ‫ا‬B‫ا‬ ‫ب‬‫و‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫أن‬ ‫أ‬ ، ‫ا‬ ‫ا‬ )++‫أرض‬(‫ﺽ‬ ‫ا‬B‫ار‬ ‫ا‬ ‫ن‬ ‫أ‬x: Epe = m.g.x. 2-‫أ‬ ‫ا‬ ‫ر‬ ‫آ‬M‫و‬‫ﺱ‬ ‫ا‬ ‫س‬ ‫ة‬ ‫آ‬x‫ا‬ ‫ا‬ ‫ول‬ ‫ا‬ ‫و‬ ‫ا‬: x2 (m2 )Epe = Mgx (J)x(m)M(kg) 0.040.100 0.060.150 0.080.200 0.100.250 ‫أ‬-‫ول‬ ‫ا‬ ‫أآ‬.g = 10 m/s2 . ‫ب‬-‫ن‬ ‫ا‬ ‫أرﺱ‬EPe = f(x2 )‫ا‬ ‫ه‬ ‫د‬ ‫أن‬ ،‫ا‬ ‫ن‬ ‫ا‬EPe = Ke x2 Ke‫ن‬ ‫ا‬ ‫ه‬ . 3-‫ا‬Ke‫آ‬ ‫اﺱ‬ ‫س‬ ‫و‬ ‫م‬ ‫أ‬ ‫ذ‬ ‫و‬ ‫ا‬ ‫ا‬ ‫ة‬ ‫ا‬ ‫و‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ن‬ ‫ة‬. ‫ا‬ ‫ول‬ ‫ا‬‫ا‬ ‫ا‬: T = M.g (N)x(m)M(kg) 0.020.100 0.030.150 0.040.200 0.050.250 ‫ا‬-9:
  • 8.
    --:22/03/2013:8 ––:، ،.: ‫ب‬-‫ا‬ ‫أن‬‫أ‬ ‫ازن‬ ‫ا‬ ‫ط‬ ‫ﺵ‬ ‫د‬ ‫ا‬:T = M.g‫أآ‬ ‫ا‬ ‫ه‬ ‫دا‬ ‫ا‬ ‫و‬ ‫ا‬ ‫ول‬ ‫ا‬. ‫ب‬-‫ن‬ ‫ا‬ ‫أرﺱ‬T = f(x)،‫ا‬ ‫د‬ ‫أ‬T = Ke' xKe'‫ن‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ه‬. 3-‫رن‬Ke،Ka'K‫ا‬ ‫و‬. 5-‫ر‬ ‫ا‬ ‫ى‬ ‫أﺥ‬ ‫ا‬ ‫ل‬ ‫ﺱ‬ ‫ا‬ ‫ر‬ ‫آ‬.‫ا‬ ‫ة‬ ‫رة‬ ‫إذن‬ ‫اﺱ‬ ‫و‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫رة‬ ‫و‬. ‫ط‬ ‫ا‬: 1-‫إ‬‫أن‬ ‫ت‬x.g.m=peE: -‫روﺱ‬ ‫ا‬ ‫ا‬) :+‫أرض‬+( -‫راﺱ‬ ‫ا‬:‫أرﺽ‬ ‫ﺱ‬. -‫ا‬ ‫ة‬ ‫ر‬ ‫ﺥ‬ ‫ى‬. -‫ﺽ‬ ‫ا‬ ‫ا‬ ‫ظ‬ ‫ا‬ ‫أ‬A‫و‬B: EA + E - E = EB ECA + EppA + EpeA = ECB + EppB + EpeB ▪ ECA = 0 (vA = 0 ) ▪ EppA = m.g.zA = m.g.x ▪ EpeA = 0 (x = 0) ▪ ECB = 0 (vB = 0 ) ▪ EppB = 0 ( ‫ا‬ ‫ي‬ ‫ا‬) : EpeB = m.g.x 2-‫أ‬-‫ول‬ ‫ا‬ ‫ل‬ ‫إآ‬: x2 (m2 )Epe = Mgx (J)x(m)M(kg) 1.6 . 10-3 0.040.040.100 3.6 . 10-3 0.090.060.150 6.4 . 10-3 0.160.080.200 10-2 0.250.100.250 ‫ا‬-10: A B P T x
  • 9.
    --:22/03/2013:9 ––:، ،.: ‫ب‬-‫ن‬ ‫ا‬)2 x(f=peE: -‫ن‬‫ا‬Epe = f(x2 )‫ا‬ ‫د‬ ‫رة‬Epe = Ke x2 Ke‫ن‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ه‬. -‫ن‬ ‫ا‬: 25= 0.002.3 0.05.3 =Ke 3-‫ا‬ ‫أن‬ ‫ت‬ ‫إ‬g.M=T‫ازن‬ ‫ا‬: -‫روﺱ‬ ‫ا‬ ‫ا‬:)S. ( -‫راﺱ‬ ‫ا‬:‫أرﺽ‬ ‫ﺱ‬. -‫ا‬ ‫ة‬ ‫ا‬ ‫ر‬ ‫ا‬ ‫ى‬ ‫ا‬:‫ا‬P،‫ا‬T. -‫ا‬ ‫ازن‬ ‫ط‬ ‫ﺵ‬: 0=F∑ ext 0=T+P ‫ر‬ ‫ا‬ ‫و‬ ‫ا‬ ‫ا‬ox‫ﺱ‬ ‫ا‬ ‫ا‬: P - T = 0 M.g - T = 0 → T = M.g 0 0,05 0,1 0,15 0,2 0,25 0,3 0 0,002 0,004 0,006 0,008 0,01 0,012 x 2 (m 2 ) E pe(J) ‫ا‬-10: P T x
  • 10.
    --:22/03/2013:10 ––:، ،.: -‫ول‬ ‫ا‬‫ل‬ ‫إآ‬: T = M.g (N)x(m)M(kg) 1.00.020.100 1.50.030.150 2.00.040.200 2.50.050.250 ‫ب‬-‫ن‬ ‫ا‬)x(f=T: ‫ن‬ ‫ا‬T = f(x)‫ا‬ ‫د‬ ‫أ‬ ‫ا‬ ‫رة‬T = Ke' xKe'‫ن‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ه‬. -‫ن‬ ‫ا‬: 50= 0.01.3 0.5.3 ='Ke 3-‫ر‬eK،'aKK: K = 50 Ke = 25 → 2 K =Ke Ke' = 50 → Ke' = K 4-‫ا‬ ‫ة‬ ‫ة‬ ‫ﺵ‬ ‫رة‬T‫و‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫و‬peE: ‫ﺱ‬: xK=E 2 ePe T = Ke’ x ‫أن‬ ‫و‬: 2 K =Ke،K='Ke‫ن‬: 0 0,5 1 1,5 2 2,5 3 0 0,01 0,02 0,03 0,04 0,05 0,06 x (m) T(N)
  • 11.
    --:22/03/2013:11 ––:، ،.: K x 2 1 =E2 Pe T = K x ‫ﻥ‬: -‫و‬ ‫ن‬K‫ار‬ ‫أو‬x‫ة‬ ‫ا‬ ‫ا‬ ،T‫ﺵ‬ : T = K x -‫ار‬ ‫أو‬ ‫ا‬x‫ا‬ ‫ن‬)+(‫و‬ ‫آ‬ : 2 pe K x 2 1 =E -‫ا‬ ‫و‬ ‫ر‬k‫ـ‬N/m ‫ﻡ‬: ‫ا‬ ‫رج‬ ‫ﺥ‬ ‫ا‬ ‫ن‬ ‫و‬ ‫ا‬ ‫ن‬ ‫ا‬ ‫داﺥ‬ ‫ن‬ ‫ا‬ ‫ة‬ ‫ا‬ ‫ا‬ ‫ر‬ ‫ن‬ ‫أ‬ ، ‫ن‬)‫ا‬. ( 3–‫א‬ ‫א‬ ‫ط‬ ‫א‬: ‫ط‬ ‫ﻥ‬: -‫و‬‫ﺏ‬ ‫ﻥ‬)1(C = 0.125 N.m/rad‫اﺥ‬ ‫ا‬ ‫ا‬O‫و‬ ،‫ل‬ ‫ﺱ‬)2(‫و‬K = 12.5 N/m‫ا‬ ‫ا‬ ‫ف‬ ‫ا‬)1( ‫د‬ ‫ة‬AO‫ة‬ ‫ا‬ ‫دوران‬ ‫زاو‬ ‫س‬ ‫ر‬)‫ا‬. ( ‫ا‬-12: T T ‫ازن‬ ‫ا‬ ‫اﺱ‬ ‫ا‬ ‫ط‬ ‫ا‬ ‫ا‬
  • 12.
    --:22/03/2013:12 ––:، ،.: 1-‫ﺱ‬ ‫ا‬‫ة‬ ‫آ‬ ‫و‬ ‫ا‬ ‫ة‬ ‫ا‬ ‫ة‬ ‫ا‬x)2(‫وران‬ ‫ا‬ ‫زاو‬ ‫و‬θ‫ا‬)1( ‫ﺥ‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ول‬ ‫ا‬R = 10 cm: R.F=)F(M=M o/F (N)θ (rd)x(cm) 0.50.44 1.00.88 1.51.212 ‫أ‬-‫ول‬ ‫ا‬ ‫أآ‬. ‫ب‬-‫ن‬ ‫ا‬ ‫أرﺱ‬M = f(θ)‫ة‬ ‫ا‬ ‫م‬ ‫وي‬ ‫ا‬ ‫و‬ ‫ا‬ ‫دو‬ ‫م‬ ‫ات‬ ‫ي‬ ‫ا‬ ،F‫د‬ ‫أن‬ ، ‫ا‬M = Ce θCe‫ا‬ ‫ا‬ ‫ه‬ ‫ه‬‫ن‬. 2-‫ا‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫ب‬)‫ط‬ ‫ا‬-1(‫ا‬ ‫ا‬ ‫ا‬ ‫أن‬)1( ‫ا‬ ‫ا‬ ‫ا‬ ‫وﺽ‬ ‫آ‬ ‫وي‬)2. (‫ول‬ ‫ا‬ ‫أ‬ ‫ا‬ ‫ول‬ ‫ا‬ ‫و‬ ‫ا‬ ‫ا‬ ‫ل‬ ‫ﺱ‬ ‫ا‬: θ 2 (rd)2‫ا‬ ‫ا‬‫ا‬)1( EPe = 1/2Kx2 (J) θ (rd)x(cm) 0.44 0.88 1.212 ‫أ‬-‫ا‬ ‫ات‬ ‫أرﺱ‬Epe‫ا‬ ‫ا‬)1(‫او‬ ‫ا‬θ2 ‫ا‬ ‫د‬ ‫أن‬ Epe = Ce ' θ2 Kc'‫ن‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ه‬. ‫ب‬-‫رن‬Ce،Ce ' ‫و‬C‫ا‬. 3-‫رن‬Ce‫ا‬C.‫؟‬ ‫ذا‬ 4-‫ا‬ ‫ا‬ ‫و‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫رة‬ ‫أن‬ ‫اﺱ‬:2 pe θC 2 1 =E. 5-‫ى‬ ‫أﺥ‬ ‫ا‬ ‫ل‬ ‫ﺱ‬ ‫ا‬ ‫ر‬ ‫آ‬‫ر‬ ‫ا‬.‫دو‬ ‫م‬ ‫رة‬ ‫إذن‬ ‫اﺱ‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫رة‬ ‫و‬ ‫ا‬. ‫ا‬-6:
  • 13.
    --:22/03/2013:13 ––:، ،.: ‫ط‬ ‫ا‬: 1-‫أ‬-‫ول‬‫ا‬ ‫ل‬ ‫إآ‬: ‫ب‬-‫ن‬ ‫ا‬)θ(f=M: ‫ن‬ ‫ا‬M = f(θ)‫د‬ ‫أ‬ ‫ا‬ ‫رة‬M = Ce θ‫د‬ ‫أ‬ ‫ا‬ ‫رة‬ M = Ce θCe‫ن‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ه‬. -‫ن‬ ‫ا‬: 0.125= 0.5.1.6 0.02.5 =Ce 2-‫أ‬-‫ول‬ ‫ا‬ ‫ل‬ ‫إآ‬:
  • 14.
    --:22/03/2013:14 ––:، ،.: ‫ب‬-‫ن‬ ‫ا‬)2 θ(f=peE: ‫ن‬‫ا‬Epe = f(θ)‫ا‬ ‫د‬ ‫أ‬ ‫ا‬ ‫رة‬Epe = Ce' θ2 Ce'‫ن‬ ‫ا‬ ‫ا‬ ‫ه‬ ‫ه‬. 0.0625= 0.5.1.6 0.01.5 =Ce ‫ـ‬-‫ر‬ ‫ا‬eC‫و‬'eCC: C = 0.125 Ce = 0.125 → Ce = C Ce = 0.125 → Ce = 2 C 4-‫ا‬ ‫ة‬ ‫ة‬ ‫ﺵ‬ ‫رة‬T‫و‬ ‫ا‬ ‫ا‬ ‫ا‬ ‫و‬peE: ‫ﺱ‬: M = Ceθ EPe = Ce' θ2 ‫أن‬ ‫و‬:Ce = C، 2 C 'Ce‫ن‬: M = Cθ EPe = 2 1 C θ2 ‫ﻥ‬: -‫اس‬C‫دو‬ ‫ا‬ ‫ا‬ ، ‫ار‬M : M = C θ
  • 15.
    --:22/03/2013:15 ––:، ،.: -‫ار‬ ‫اس‬θ‫ا‬‫ن‬)+‫ﺱ‬(‫آ‬: θC 2 1 =E 2 pe ‫ـ‬ ‫ا‬ ‫ر‬N.m/rad. ‫و‬ ‫ا‬ ‫ه‬.‫ا‬ ‫ان‬ ‫ا‬ ‫ذو‬ ‫ذ‬ ‫ﺱ‬ ‫ا‬ ‫أدﺥ‬: www.sites.google.com/site/faresfergani **‫ذ‬ ‫ﺱ‬ ‫ا‬:‫رس‬** ‫ﺱ‬ ‫ﺱ‬ ‫د‬ ‫وب‬ ‫ا‬- Fares_Fergani@yahoo.Fr Tel : 0771998109 ‫و‬ ‫ر‬ ‫ا‬ ‫أو‬ ‫روس‬ ‫ا‬ ‫ﺥ‬ ‫ي‬ ‫و‬ ‫ا‬ ‫ا‬ ‫إ‬. ‫ا‬ ‫وﺵ‬