: 2014 4 10 1 2 2 3 2.1...................................... 3 2.2....................................... 4 2.3....................................... 4 2.4................................ 5 2.5 Free-Body Diagras......................... 5 3 7 3.1.............................. 7 3.2.................................... 8 3.3...................................... 9 4 10 4.1........................ 10 4.2................................... 11 4.3.............................. 13 4.4............................... 13 5 15 6 17 6.1........................................ 17 6.2........................................ 17 7 19 A 21 B 21 1
1 [ 1] (1) MKS? (2) MKS? [ 2] (1) (42.195k) 2006 2 4 55 40k 2 (2) 100 2006 9 77 100 10 (3) 2006 162.4k/hr 18.440 [ 3] t = 0 10 ( 1 velocity [/s] 8 4 O 2 4 6 8 10 tie [s] (1) 0 (2) (3) 10 a 1 v(t) (t = 0, 1, 2,..., 9 [s]) t = 1 s v(t) t 10 b t c v t ( 1 (1) 4 8 (2) 8 10 (3a) (v(0) + v(1) + v(2) + + v(8) + v(9)) t = (0 + 2 + 4 + 6 + 8 5 + 4)[/s] 1[s] = 56 [] (3b) 1 2 (4 + 10) [s] 8 [/s] = 56 [s] (3c) x = 4 0 2tdt + 8 4 8dt + 10 8 ( 4t + 40)dt = 56 2
2 2.1 [ 1] MKS [ 2] 2kg 10 ( 2 (1) 10 velocity [/s] 4 2 O -2-4 2 4 6 8 10 tie [s] (3) (4) (5) (6) [ 3] x (1) (2) t x O (3) (t = 0 ) 0 v 0 ( 0) (4) [ 4] F t = 0 x (1) O F x (2) (3) t (4) t (5) ( 2 (1) 12 (3) 4 6 (4) 2 4 (5) 2 3, 6 10 (6) 8 N (2 4 s ) 3
2.2 [ 5] ( ) ( 7.4 ) ( HBF-362 ) (1) g = 9.8/s 2 60kgw 1/6 kgw (2) 9.789 9.792/s 2, 9.803 9.807/s 2 60kgw gw (3)? [ 6] 200 600k,, 600k, 6400k 2.3 [ 7] 100g 90 k/h 360 k/h 1kg ( 3 [ 8] (a) 0 T (b) v 0, T (c) v 0 T ( 3 g 9.8/s 2 g 10/s 2 90k/hr 31. 360k/hr 500. 4
2.4 [ 9] θ g θ (1) (2) 2.5 Free-Body Diagras [ 10] F ( 4 g F θ (1) x y (2) F (3) 30 F [ 11] B A A, B A, B B ( ) N B, A B N A g A B { ( ẍ = g sin θ F 4 (a) ÿ = N g cos θ (b) F = g sin θ (c) F = 1 2 g 5
(1) A, B Free-Body Diagras (2) ( 5 (3) N A, N B ( 6 [ 12] θ M F F F M θ ( 7 { ( A : 5 A ÿ A = N A A g (2) B : B ÿ B = N B N A B g ( 6 (3) ÿ A = ÿ B = 0 N A = A g, N B = ( A + B )g ( 7 F = (M + )g tan θ ( : 6
3 3.1 [ 1] A, B, C A F ( ) A, B, C g ( 8 C B A F O xc xb xa x (1) A B B C F 1, F 2 Free-Body Diagras (2) x x A, x B, x C x (3) ẍ A = ẍ B = ẍ C ẍ ( A = B = C ) ẍ, F 1, F 2 [ 2] F P P P T, g ( 9 F (1) P Free-Body Diagras (2) P y P y P, y (3) T (4) F? P A ẍ A = F F 1 ( 8 2 (2) B ẍ B = F 1 F 2 (3) ẍ = F/3, F 1 = 3 F, F 2 = 1 3 F C ẍ C = F 2 { ( 0 9 yp = 2F T (2) ÿ = T g (3) T = 2F (4) F = g 2 7
[ 3] P A, P B P A A P B B B T P A A F A, P B T F g ( 10 B P B P A A (1) P A, P B A B Free-Body Diagras (2) P A, P B A B y P A, P B A B y PA, y PB y A, y B (3) B ÿ A ÿ B (4) 0 A B T B 3.2 [ 4] k x ( ) ( 11 (1) (2) (3) k O x (4) A t = 0 t ( 10 (2) P A, P B A B 0 ÿ PA = 2T F A 0 ÿ PB = T F 2T A ÿ A = F A A g B ÿ B = T B g ( 11 (3) 2ÿ A + ÿ B = 0 (4) A = 2 B, T = B g k (2) ẍ = g kx (3) x = g/k (4) x = A cos t + g k, ẋ = A k sin 8 k t
3.3 [ 5] MKS [ 6] MKS [ 7] F θ y x F θ µ 0 ( 12 (1) F v Free-Body Diagras (2) xy xy. (3) F [ 8] 2 A B A B B A B µ. B F y A B O F x. A B N 1 B N 2 ( 13 (1) A, B Free-Body Diagras (2) A, B (x A, y A ), (x B, y B ) xy. (3) N 1, N 2. (4) A B. ( 12 (2) { ẍ = F cos θ Fv ÿ = F sin θ + N g (3) F = µ 0 g { ( 13 A x A = µn 1 (2) A = N 1 A g cos θ + µ 0 sin θ { B x B = F µn 1 { N1 = A g y B = N 2 N 1 B g (3) y A B N 2 = A g + B g (4)A x µ A g B x 9
4 4.1 [ 1] ( 60g) 180 k/h 5s ( 14 [ 2] 2 70k ( )50kg 2 72k ( 15 (1) (2) 72k [ 3] ( ) ( ) ( 16 (1) ( ) (2) (3) ( ) [ 4] 2 v 0 ( 17 (1) 2 L ( ) a b c d (2) 2 T ( 14, v, F, t F t = (v 0) F = v/ t = 0.06[kg] 180 (1000[]/3600[s])/0.005[s] = 600[N] ( 15 (1) 500 N (2) 20 ( 16 ) ( 17 (1a) L (1b) (1c) (1d) (2a) (2b) T (2c) (2d) 10
( ) a b c d [ 5] MKS (1) (2) (3) ( ) (4) 4.2 [ 6] t = 0 v(0) t v(t) (1) (2) (3) t x [ 7] 100g 5 ( ) g 9.8 /s 2 ( 18 (1) (2) 50c (3) 0.05 ( 18 (1) 10 /s (2) 10 N (3) 20 N 11
[ 8] 40 g 9.8 [/s 2 ] ( 19 (1) ( )50kg 40 (2) 40 ( )50kg? (3) (4) 40 [s] [ 9] h 2 g ( 20 h h h/2 h/2 L (a) L (b) (1) h (2) L? [ 10] r v 0 x x r O v ( 19 ( 20 (1) 19600 J (2) 19600 J (3) 28 /s = 100.8 k/hr ( ) (4) 2.9 s ( OK) (1) v (a)(b) gh = 1 2 v2 v = 2gh (2) (b) h L 2 12
g ( 21 (1) v (2) v 0 4.3 [ 11] θ µ g ( 22 θ L l (1) a Free-Body Diagras b c L (i) (ii) (2) l. a b (i) µ (ii) µ c µ l L 4.4 [ 12] ( k) O. k O x x (1) (2) ( 21 (1) 1 2 v2 0 = g 2r + 1 2 v2. v = v0 2 4gr (2) v, v 0 2 gr ( 22 (1b) x ẍ = g sin θ (1c) v = 2gL tan θ (2 b i) µgl (2 b ii) gl tan θ (2c) µ = L l tan θ 13
[ 13] k L ( 23 k (1) L (2) [ 14] ( k) M g (1) (2) (3) t k ( 23 (1) 1 2 kl2 (2) v 1 2 kl2 = 1 2 v2 k. v = L 14
5 [ 1] (1) (2) [ 2] 3 A, B, C B v A 1 C 1 A,B,C A, B, C ( 24 (1) A A,B,C (2) 3 [ 3] M h g ( 25 h M (1) v 1 (2) ( V v 2 ) (3) v 2 v 1 [ 4] l M A, M B,, M v 0, l ( 24 (1) A v A + B + C (2) A v A + B + C ( 25 (1) gh = 1 2 v2 1 v 1 = 2gh (2) { gh = 1 2 v2 2 + 1 2 MV 0 = v 2 MV v 2 M (1) v 2 V (3) 15
θ g (1) (2) v θ (3) [ 5] M k ( ) M k v 0 (1) l v 0 l (2) vo 16
6 6.1 [ 1] ( 26 (1) 360 (2) 1 30 60 90 180 (3) 2 1 rad (4) r θ [rad] [ 2] ( 27 (1) (x, y) (r, θ) a (1, 0) b ( 1, 1) c ( 1, 3) (2) (r, θ) a (2, π 3 ) b (4, π 4 ) c (0, 3) [ 3] [rad] ( 28 [ 4] (r, θ) (x, y) ( 29 6.2 [ 5] 2 l = 50 c g 9.8 /s 2 ( 30 ( 26 (1) 2π rad (2) 60 (3) 2 (4) rθ [rad] ( 27 (1)(a) (1, 0) (b) ( 2, 5 4 π) (c) ( 2, 2 3 π) (2)(a) (1, 3) (b) (2 2, 2 2) (c) (0, 0) ( 28 [rad/s], [rad/s 2 ] ( 29 (x, y) = (r cos θ, r sin θ) ( 30 (1) 3.5 /s (2) h = 5 l = 62.5 c 4 17
l h l (a) (b) (1) (2) (a) (3) (b) h 18
7 [ 1] l I c I t I M I t = I M + I c [ 2] l M (1) (2) (3) [ 3] r [ 4] l µ g (1) (2) (3) I θ [ 5] 1 2 x 1, 2 x 1, x 2 g x2 O x1 2 θ 1 (1) (2) (3) τ 19
[ 6] l ( (a)) θ g + θ (x,y) (b) (a) (c) (1) (x, y) (x, y) θ (2) ( (b)) (3) ( (c)) θ [ 7] A ( 60kgw) g 20
A (1) (2) Free-Body Diagras (3) Free-Body Diagras (4) (5) (6) (7) (8) (9) (10) B (1) : (2) a (i) Free-Body Diagras (ii) (iii) ( : ) (iv) (v) b (i) (ii) (iii) (iv) (3) a b c d 21