Diese Präsentation wurde erfolgreich gemeldet.
Wir verwenden Ihre LinkedIn Profilangaben und Informationen zu Ihren Aktivitäten, um Anzeigen zu personalisieren und Ihnen relevantere Inhalte anzuzeigen. Sie können Ihre Anzeigeneinstellungen jederzeit ändern.

มวลแรงกฏการเคลื่อนที่

40.096 Aufrufe

Veröffentlicht am

Veröffentlicht in: Sport, Automobil
  • Loggen Sie sich ein, um Kommentare anzuzeigen.

มวลแรงกฏการเคลื่อนที่

  1. 1.    SchoolDD.com3 www.schoolDD.com
  2. 2. 3 F ˈ F F F F ˈ ˈ F F F FF ˈ F F F F3.1 , F ʽ F F F F F F F F ˈ F F 45 F F F 45 450 F ʽ F (Force) F F F F F F F F F ˈ F ˈ F F ˈ (N) F ˈ u=0 v v1 v2 F F ˈ F v1 ˈ v2 (Mass) m F ˈ F F ˈ (kg) F F F F F F F – F ˆ F www.schoolDD.com 1
  3. 3. (Weight) w F F m F F g F g F F F F F ˈ (N) “ F ” m W = mg F - ˈ (= ) - F FF F F F F F F g F - ˈ F F F F F F F 2 F F x-y ˈ F y F F sinθ F F x F cos θ 2 1 F F y F sin θ θ x F cosθ F θ x F x F F F F 1 x F F cosθ F y F 2 F F sinθ FF F FF cosθ F F FF sinθ .... F F α y F F α F F F F F .F . F F θ = 30°, α = 60° ( F F cos30° =F sin 60° F sin 30° = F cos60° ?) ʿ F F ! F - ˈ F F F F ˈ F ( ) F F F - F F F ˈ F FF F – F ˆ F www.schoolDD.com 2
  4. 4. F sin , cos , tan F F sin , cos , tan F F F 30°, 60°, 37°, 53° 45° F sin , cos , tan F F F F F F F FF F F F ˆ F F F F F F F ˈ F F F ˈ θ 2 c F sinθ F F 1՜2 F F 1 a F sinθ = a/c θ 4 c F cosθ F F 3՜4 F F θ F cosθ = b/c b 3 a F tanθ F F 5՜6 F F 5 F tanθ = a/b θ b 6 F F sin , cos , tan F F F F F F ʿ ʿ F FF F F ˈ F F F F F F ˈ 30°, 60°, 37°,53° 45° 60 53 45 2 5 √2 1 3 1 30 37 45 √3 4 1 F F F sin , cos , tan 30°, 60°, 37°,53° 45° F F F F F – F ˆ F www.schoolDD.com 3
  5. 5. F 1 F1 = 3 N F2 = 4 N m F . F2 F1 m ˈ + F F = F 1 - F2 = 3-4 = -1 ( F F F F ) ∴ F 1N F Ans . F2 60° F1 m F2 ˈ x y F F1 F y y F2 sin60 F2 F F ΣFy 60° x α x F1 F2 cos60 ΣFX x ΣFx = F1 + F2 cos60 = 3 + 4 (½ ) =5N y ΣFy = F2 sin60 ଷ = 4 ሺ√ ሻ ଶ = 2√3 N F F = ඥΣFxଶ ൅ Fyଶ ଶ = ට5ଶ ൅ ሺ2ඥ3ሻ = 6.08 N – F ˆ F www.schoolDD.com 4
  6. 6. ∴ F 6.08 N Ans Σ ୊౯ ଶ√ଷ F F tan α = Σ ୊౮ = ହ = 0.7 ∴ α = tan-1 0.7 Ans . F1 F2 m F F= F1 + F2 =3+4 =7N ∴ F 7N Ans3.2 F (Sir Issac Newton) ʽ F F F F ˈ F F F F 3 F F 1 F F F F F ˈ F F F 2 F F F ˈ F F F F F F F F 3 Action = Reaction F F F F 3 F V=0 ,a=0 V ,a=0 ∑F =0 m m F F 1 F F F F – F ˆ F www.schoolDD.com 5
  7. 7. F F ˈ F F F a ∑F = ma ∑F m F F ˈ F F 2 F F F ˈ F F F F F F F F F ∑‫ܨ‬ F F F a F ∑ ‫ = ܨ‬ma F21 F12 F12 = F21 F 3 Action = Reaction F F F F F12 F F21 F F F- F F 3 F F F F F F ˂ F ˈ F- 3 F ˈ F F F F F F 3 F F F F ( F F ..?) F F F F F F F F F F F F F F F F F F F ? F FF F ˈ F ? F F ? FF F F a F g – F ˆ F www.schoolDD.com 6
  8. 8. F 2 F 20 kg F F F 24 m/s 8 .F . F F F F F FF F F F F ˈ F ” F u=0( F ) v = 24 m/s t=8 s F=? m m = 20 kg m F F F F F 2 ∑F = ma F ∑F F F F F ∑F =F F = ma --- (1)F F Fm F Fa ∴ F a F F a F v = u + at ( ) 24 = 0 + a (8) a = 3 m/s2 F a=3 (1) F F = 20 (3) ∴ F = 60 N Ans F- F F F 2 F F F ˆ F F ˈ F ʽ F F F F F F F F F F F F F F F F F ʽ F FF – F ˆ F www.schoolDD.com 7
  9. 9. F 3 5 kg ˂ 100 m F F m = 5 kg F=? a =g 100 m 80 F = ma ∑F F F = m(g) F = 5(10) ∴ F = 50 N Ans F - F F 4 200 N F F F 10 m/s2 F F 100 N F F F a1 = 10 m/s2 a2 = ? F1 = 200 N F2 = 100 N m m F F = ma ∑F F F1 = ma1 ୊ ଶ଴଴ ∴ m = ୟభ = 10 = 20 kg భ F a2 F F = ma ∑F F F2 = ma2 ୊భ ଵ଴଴ ∴ a2 = ୫ = 20 = 5 m/s2 Ans – F ˆ F www.schoolDD.com 8
  10. 10. F F ˈ ∑F = ma F = ma m F F F‫ן‬a ୊మ ୟ ୊ = ୟమ భ భ ଵ଴଴ ୟమ F F = ଵ଴ ଶ଴଴ ∴ a2 = 5 m/s2 Ans F 5 m1 F F 20 m/s2 m2 F F 5 m/s2 F m1/m2 F a1 = 20 m/s2 a2 = 5 m/s2 ୫భ ୫మ =? F F m1 m2F = ma ∑F F F = m1a1 --- (1) F = m2a2 --- (2) (1) = (2) , m1a1 = m2a2 ୫ ୟ ହ ଵ ∴ ୫భ = ୟమ = ଶ଴ = ସ Ans మ భ F F ˈ ∑F = ma F = ma ଵ F F F m‫ן‬ୟ ୫భ ୟ ୫ = ୟమ మ భ ୫భ ହ F F ୫మ = ଶ଴ ୫భ ଵ ∴୫ = ସ Ans మ F - F F F F F ˈ F F F F ʿ F F F ˈ ( ) ʿ F F F – F ˆ F www.schoolDD.com 9
  11. 11. F 6 20 N F F F 10 F50 m F F u=0 ‫׶‬ m=? F = 20 t = 10 F F m m F ” s = 50 = ma ∑F F F = ma --- (1) m FF F Fa ‫ ׵‬a F a F s = ut + ½ at2 ( ) 50 = 0 + ½ a (102) a = 1 m/s2 F a = 1 (1) F = ma 20 = m(1) ‫ ׵‬m = 20 kg Ans F 7 5 kg 6N 8N F 6N 5 kg 8N = ma --- (1) ∑F a F m F F ∑F ‫∑ ׵‬F F F ∑F 6N 8N F F ∑F = √6ଶ ൅ 8ଶ = √100 = 10 N 10 N 8N F ߙ ଼ ସ 6N tanߙ = ଺ = ଷ ߙ = 53° – F ˆ F www.schoolDD.com 10
  12. 12. F ∑F = 10 (1) ∑୊ ଵ଴ F a= ୫ = ହ = 2 m/s2 F 53° 6 N Ans3.3 (Frictional force) f F F F F F F F F F F F F F F F ˈ F ... .. .. F mg f = ࣆN f ߤ N f F F ߤ N F ˈ 2 1. (Static friction) fs ˈ F F F F F F F F ˈ F F ( F ) 2. F (Kinetic friction) fk ˈ F ˈ .F . .. F F F FF 0... fs (= ߤsN) fs F F fk (= ߤkN) F F F F F ˈ F ? F - ߤs > F ߤk (F F F F .) - F ˈ F F F - (ߤsN) > F(ߤkN) - N - W = mg F F – F ˆ F www.schoolDD.com 11
  13. 13. F ?F 8 F 10 kg F F F 70 N F F F 40 N. F F. F F F F F F F v=0 F v F = 70 N m = 10 kg F = 40 N mg mg fs = ? ߤs =? fk = ? ߤ k = ? N N. fs = ? , ߤs = ? fs max ∑ Fx = F fs = max 70 fs = 10(0) ( F ‫ ׵‬ax = 0) ‫ ׵‬fs = 70 N Ans ߤs fs = ߤsN --- (1) ∑ Fy = may N mg = may N 10(10) = 10(0) ( F ‫ ׵‬ay = 0) N = 100 N F N = 100 (1) fs = ߤsN 70 = ߤs(100) ‫ߤ ׵‬s = 0.7 Ans – F ˆ F www.schoolDD.com 12
  14. 14. . fk = ? , ߤk = ? F F fk = max ∑ Fx F fk = max 40 fk = 10(0) ( F v ‫ ׵‬ax = 0) ‫ ׵‬fk = 40 N Ans F ߤk fk = ߤkN --- (1) ∑ Fy = may N mg = may N 10(10) = 10(0) ( F ‫ ׵‬ay = 0) N = 100 N F N = 100 (1) fk = ߤkN 40 = ߤs(100) ‫ߤ ׵‬k = 0.4 (< ߤs ) Ans F - F mg N F mg mg mg FF N N N F FF ˈ mg F FF F N F F F F F F F mg N F F ( F ) F- F ߤs F – F ˆ F www.schoolDD.com 13
  15. 15. F 9 120 kg F F F F 20 m/s F F 50 m F F u = 20 v=0 ‫׶‬ F t = 10 F Fm = 120 m f=? m F ” s = 50 F F u F u = 20 m/s F F( F ) F F F 2 F F F F F FF F F 20 m/s F 1 = ma ∑F F f = ma --- (1) f Fm F Fa ‫ ׵‬a F a v2 = u2 + 2as ( ) 0 = 202 + 2a (50) a = -4 m/s2 (a ˈ F F u) F a = -4 (1) f = ma f = 120 (-4) f = -480 N ( F F ) ‫׵‬ F 480 N Ans F 10 500 N 37° 40 kg F 0.4 F F 500 N 37° N F F ” – F ˆ F www.schoolDD.com 14
  16. 16. y F F . 500 sin37 500 a=? F ˈ . F F F F m = 40 37° mg 500 cos37 x F F F f ߤ= 0.4 F F ˈ . N FF 500 N F F (x-y)F F a ∑ Fx = max F 500 cos37 - f = ma --- (1) a Fm F Ff ‫ ׵‬f F f = ߤN F ߤ F F N N = may ∑ Fy F N + 500 sin37 - mg = may N + 500(3/5) 40(10) = 0 ( F ‫ ׵‬ay = 0) N = 100 N F F f = ߤN = 0.4(100) = 40 N F f = 40 (1) 500 cos37 - f = ma 500(4/5) - 40 = 40a ‫ ׵‬a = 9 m/s2 Ans F - F ∑F = ma F 2 ∑F ( F) F F m F F a F FF F ∑F F F F F F a N = ma ∑F T F F F F = ma m F T f = ma mg f – F ˆ F www.schoolDD.com 15
  17. 17. F 11 F F ˈ F F ߤ s = 1.0 ߤk = 0.80 F θ F F F F F F F F F F F F ˆ F FF ˈ F F ʽ F “ ˈ F F F F F F F ˂ 3 w = mg , f , N ˈ 2 mg sinθ mg cosθ ”‫׶‬ 90-θ ‫׵‬ θ N F 180 F f mg sinθ θ mg cosθ θ W = mg θ F F F ˈ F F = ma ∑F F F F = ma F mg sinθ - fs = ma F a = 0 ( F ) ‫ ׵‬mg sinθ = fs --- (1) fs fs = µs N F µs F F N N = ma ∑F F N - mg cosθ = ma N - mg cosθ = 0 ( F ‫ ׵‬a = 0) N = mg cosθ – F ˆ F www.schoolDD.com 16
  18. 18. F N F fs = µs N = 1.0 mg cosθ = mg cosθ F fs (1) mg sinθ = mg cosθ ୱ୧୬θ ୡ୭ୱθ = 1.0 tanθ = 1.0 ‫ ׵‬θ = 45° Ans F F F F ˈ F F = ma ∑F F F F = ma F mg sinθ fk = ma mg sinθ - µk N = mamg sinθ - µk (mg cos θ) = ma (N = mg cos ߠ) ଵ ଵ10 (√ଶ) - 0.80 (10)(√ଶ) = a ( F m F ) ‫ ׵‬a = √2 = 1.414 m/s2 Ans F - F F F ˈ F F m F F F F F F F F F F F FF F F F F F F F 12 90 N 10 kg F F 20 kg F a=? . F . F 90 N 20 kg . F 90 N F 20 kg F 10 kg F ˈ F F . F a=? ∑F = ma – F ˆ F www.schoolDD.com 17
  19. 19. F F F = ma m = 10 + 20 = 30 kg ( F ˈ F ) F 90 = 30 (a) ‫ ׵‬a = 3 m/s2 Ans. F R F F F 10 kg a = 3 m/s2 F R ˈ F - F F F 90 N R 10kg F F 3 ” = ma ∑F F F F = ma 90 - R = 10 (3) ‫ ׵‬R = 60 N Ans 20 kg a = 3 m/s2 R 20 kg ∑F = ma F F F = ma R = 20 (3) ‫ ׵‬R = 60 N Ans ( F 10 kg) F F F F F F. a=? 20 kg 90 N 10 kg F a=? – F ˆ F www.schoolDD.com 18
  20. 20. ∑F = ma F F F = ma m = 10 + 20 = 30 kg F 90 = 30 (a) ‫ ׵‬a = 3 m/s2 Ans ( F F FF F ) 20 kg a = 3 m/s2 R 90 N 20 kg = ma ∑F F F F = ma 90 - R = 20 (3) ‫ ׵‬R = 30 N Ans ( F F F F .) 10 kg a = 3 m/s2 R 10kg ∑F = ma F F F = ma R = 10 (3) ‫ ׵‬R = 30 N AnsF - ˈ F mg N F F F F F F F ˈ F F F F F F F F – F ˆ F www.schoolDD.com 19
  21. 21. F 13 F 120 N 5 kg 10 kg 15 kg F F F T1 T2 F µ = 0.10 15 kg T1 10 kg T2 F 5 kg F a F ” a=? N1 N2 N3 m1 T1 T2 F m2 m3 f1 µ = 0.10 f2 f3 m1g m2g m3g = ma ∑F F F F = ma F F - f1 - f2 - f3 = ma F - µN1 - µN2 - µN3 = (m1+ m2 + m3)a 120 - µ(N1 + N2 + N3 ) = (15 + 10 + 5)a120 - 0.1(15(10) + 10(10) + 5(10)) = 30 a ( F N = mg) ‫ ׵‬a = 3 m/s2 Ans F T1 15 kg T1 F F F 10 kg 15 kg 15 kg F m1 a = 3 m/s2 N1 T1 = ? m1 f1 m1g ∑F = ma – F ˆ F www.schoolDD.com 20
  22. 22. F F F = ma F T1 - f1 = m1a T1 - µN1 = m1a T1 - µ m1g = m1a T1 = m1(a + µg) T1 = 15(3 + 0.1(10)) ‫ ׵‬T1 = 60 N Ans F T2 5 kg N3 a = 3 m/s2 T2 = ? F = 120 N m3 m3g f3 = ma ∑F F F F = ma F F T2 f3 = m3a F T2 µN3 = m3a F T2 µ(m3g) = m3a120 T2 0.1(5x10) = 5(3) ‫ ׵‬T2 = 100 N Ans F - F F F F F F F F F F F F F F F F F F F F F F T F m1 m2 T T T m m T T F m1 m2 mg mg – F ˆ F www.schoolDD.com 21
  23. 23. F 14 80 N 2 kg 3 kg F F F F F F = 80 N 2 kg T a 3 kg F a F ˈ F T F ˈ F F = 80 N m1 m1g a=? m2 m2g = ma ∑F F F F = ma F F m1g m2g = (m1 + m2)a80 2(10) 3(10) = (2 + 3)a ‫ ׵‬a = 6 m/s2 Ans F T 3 kg T=? m2 a = 6 m/s2 m2g – F ˆ F www.schoolDD.com 22
  24. 24. ∑F = ma F F F = ma F T m2g = m2a T 3(10) = 3(6) ‫ ׵‬T = 48 N Ans F 15 2 kg 3 kg F F F F F F F T T 2 3 F a 3 kg F F 2 kg F F a F F F F ”a=? m1 m2 a=? m1g m2g = ma ∑F F F F = ma F m2g m1g = (m1 + m2)a 3(10) 2(10) = (2 + 3)a ‫ ׵‬a = 2 m/s2 Ans – F ˆ F www.schoolDD.com 23
  25. 25. F 2 kg T=? 2 a = 2 m/s m1 m1g = ma ∑F F F F = ma F T m1g = m1a T 2(10) = 2(2) ‫ ׵‬T = 24 N Ans F 16 F F F F F F T1 T1 1010 kg kg 25 kg T2 37° T2 15 kg F a a N F F 102kg m m1 a F a m2g sin37 F F F F 37° m2g m2g cos37 m1ga m3 F m3g F m1 ∑F = ma – F ˆ F www.schoolDD.com 24
  26. 26. F F F = ma F m1g m2g sin37 m3g = (m1 + m2 + m3)a 25(10) 10 (10)(3/5) 15(10) = (25 + 10 + 15)a ‫ ׵‬a = 0.8 m/s2 Ans F a ˈ F F a ˈ F F T1 m1 T1 = ? m1 a = 0.8 m/s2 m1g = ma ∑F F F F = ma F m1g T1 = m1a 25(10) T1 = 25(0.8) ‫ ׵‬T1 = 230 N Ans F T2 m3T2 = ? m3 a = 0.8 m/s2 m3g = ma ∑F F F F = ma F T2 m3g = m3a T2 15(10) = 15(0.8) ‫ ׵‬T2 = 162 N Ans – F ˆ F www.schoolDD.com 25
  27. 27. F - F F F F F F T2 = 2T1 T2 = T1/2 T2 = T1/2 T1 T1 m1 T1 1 m2 m1 1 13.4 F F F F F F mg T T m m T T T N m1 m2 m m1g m2g mg mg 1 2 3 1 2 F F F F T 3 F F F F F N F F F F F F ? F F F F ? F 17 F 1 kg F F F F F F F . F . F . F . F F 0.5 m/s2 . F F 0.5 m/s2 m = 1 kg m – F ˆ F www.schoolDD.com 26
  28. 28. F F F F. F F F T m a=0 mg = ma ∑F F F F = ma F T mg = ma T 1(10) = 1(0) ‫ ׵‬T = 10 N ( F ) Ans. F F F T m v ,a=0 mg = ma ∑F F F F = ma F T mg = ma T 1(10) = 1(0) ‫ ׵‬T = 10 N ( F ) Ans. F F F T m v ,a=0 mg – F ˆ F www.schoolDD.com 27
  29. 29. ∑F = ma F F F = ma F mg T = ma 1(10) T = 1(0) ‫ ׵‬T = 10 N ( F ) Ans. F F 0.5 m/s2 F F T m a = 0.5 m/s2 mg ∑F = ma F F F = ma F T mg = ma T 1(10) = 1(0.5) ‫ ׵‬T = 10.5 N ( F ) Ans. F F 0.5 m/s2 F F T m a = 0.5 m/s2 mg ∑F = ma F F F = ma F mg T = ma 1(10) T = 1(0.5) ‫ ׵‬T = 9.5 N ( F F ) Ans – F ˆ F www.schoolDD.com 28
  30. 30. F 18 5 kg 15 kg F F F F 15 5 F F F F F F F F a F T T T T a m1 m2 a m1g m2g mg F 15 kg F 5 kg F a = ma ∑F F F F = ma F m1g m2g = (m1 + m2) a 15(10) 5(10) = (15 + 5)a ‫ ׵‬a = 5 m/s2 T m2 T=? m2 a = 5 m/s2 m2g = ma ∑F F F F = ma F T m2g = m2a T 5(10) = 5(5) ‫ ׵‬T = 75 N Ans – F ˆ F www.schoolDD.com 29
  31. 31. F 19 F 100 kg F F F F F F F F F F F F F F F 5 m/s2 FF F F F F F F F F F F F FF F F F a = 5 m/s2 N F mg F F F 3 ” N F F a = 5 m/s2 F ( ) ∑ F = ma F F F = ma F mg N = ma 100(10) N = 100(5) N = 500 N ‫׵‬ F F = 50 ˈ F Ans F F F !!” F 20 F F 20 F F F F ˈ F F . F F . F F F 1 m/s2 . F F F 1 m/s2 . F F 1 m/s . F F F 1 m/s2 . F F F 1 m/s2 . F F 1 m/s . F – F ˆ F www.schoolDD.com 30
  32. 32. . F F a=0 F ” ∑ F = ma N - mg = 0 a=0 mg N = mg N = 100 (10) = 1000 NN ‫׵‬ F F = 100 Ans . F F F a = 1 m/s2 = ma ∑F N - mg = ma F F F ˈ F 2 a = 1 m/s F N = m (a + g) mg F 2 F ” N = 100 (1 + 10)N N = 1100 N ‫׵‬ F F = 110 Ans . F F F a = -1 m/s2 = ma ∑F N - mg = ma F F F a ˈ - F a = -1 m/s2 F mg N = m (a + g) F F ” N = 100 (-1 + 10)N N = 900 N ‫׵‬ F F = 90 Ans . F F v = 1 m/s ‫ ׵‬a = 0 = ma ∑F v mg a=0 N - mg = 0 F F ‫׵‬ F ˈ N = mg F F ”N N = 100 (10) N = 1000 N ‫׵‬ F F = 100 Ans . F F F a = 1 m/s2 ∑ F = ma 2 a = 1 m/s mg - N = ma mg N = m (g - a) N = 100 (10 - 1)N – F ˆ F www.schoolDD.com 31
  33. 33. N = 900 N ‫׵‬ F F = 90 Ans . F F F a = -1 m/s2 ∑ F = ma 2 a = -1 m/s mg - N = ma mg N = m (g - a) N = 100 (10 - (-1))N N = 1100 N ‫׵‬ F F = 110 Ans . F F v = 1 m/s ‫ ׵‬a = 0 ∑F = ma mg - N = 0 v mg a=0 N = mg N = 100 (10)N N = 1000 N ‫׵‬ F F = 100 Ans . a=g F F !! ! F F F ∑ F = ma F F a=g mg mg - N = mg F F a = g” N = 0 NN ‫׵‬ F F= 0 AnsF 21 50 kg F F F F 0.5 m/s2 F F F F 40 kg F – F ˆ F www.schoolDD.com 32
  34. 34. ( ) F T=? a = 0.5 mg N = 400 N = ma ∑F F F F = ma F mg N T = ma 50(10) 400 T = 50(0.5) ‫ ׵‬T = 75 N Ans F 22 F 40 kg F 30 F F ˈ 30° ( F ) F a mg ax = a cos30 ay mgmg sin30 30° N N=? a ay = a sin30 30° FF F F F N F FF F F F F N – F ˆ F www.schoolDD.com 33
  35. 35. F mg sin30 mg ∑F = ma F F F = ma F mg sin30 = ma a = g sin30 = 10(1/2) a = 5 m/s2 ‫ ׵‬ay = a sin30 = (5x1/2) = 2.5 m/s2 = ma ∑F F F F = ma F mg N = may 40(10) N = 40(2.5) N = 300 N‫׵‬ F F = 30 AnsF 23 70 kg F F . F F 1 m/s2 . F F 1 m/s2 F ( ) F T mg” . F F a = 1 m/s2 T a = 1 m/s2 mg ∑F = ma – F ˆ F www.schoolDD.com 34

×