: 2016 4 1 1 2 1.1......................................... 2 1.2................................... 2 2 2 2.1........................................ 2 2.2......................................... 3 2.3......................................... 4 2.4.................................. 5 2.5 Free-Body Diagras........................... 5 3 6 3.1................................ 6 3.2...................................... 7 3.3........................................ 7 4 8 4.1.......................... 8 4.2..................................... 9 4.3................................ 11 4.4................................. 11 5 12 6 13 6.1.......................................... 13 6.2.......................................... 14 7 14 A 16 B 16 1
1 1.1 [ 1] velocity [/s] 8 4 (1) MKS? (2) MKS? 1.2 [ 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 ( 1 (1a) (v(0)+v(1)+v(2)+ +v(8)+v(9)) t = (0 + 2 + 4 + 6 + 8 5 + 4)[/s] 1[s] = 56 [] (1b) 1 (4 + 10) [s] 8 [/s] = 56 [s] (1c) x = 2 4 0 2tdt + 8 4 8dt + 10 8 ( 4t + 40)dt = 56 O 2 4 6 8 10 tie [s] (1) 10 a 1 v(t) (t = 0, 1, 2,..., 9 [s]) t = 1 s v(t) t 10 b t c v t [ 4] 3 ( 2 (1) 0 (2) (3) 10 2 2.1 [ 1] MKS [ 2] 3 4 kg ( 3 ( 2 (1) 4 8 (2) 8 10 ( 3 (3) 4 8 (4) 0 4 (5) 8 2
(1) (2) (3) (4) [ 3] 2 kg 10 ( 4 x O x (1) (2) t (3) (t = 0 ) 0 v 0 ( 0) (4) velocity [/s] 4 2 O -2-4 2 4 6 8 10 tie [s] [ 5] F t = 0 x (1) 10 O F x (3) (4) (5) (6) [ 4] 10 (6) 1 N (8 10 s ) ( 4 (1) 12 (3) 4 6 (4) 2 4 (5) 2 3, 6 10 (6) 8 N (2 4 s ) (1) (2) (3) t (4) t (5) 2.2 [ 6] ( ) ( 6.7 ) 3
( HBF-362 ) (1) g = 9.8 /s 2 60 kgw 1/6 kgw (2) 9.789 9.792 /s 2, 9.803 9.807 /s 2 60 kgw gw (3)? [ 7] 200 600 k, 600 k, 6400 k [ 8] 1/4 ( 5 (1) g, R, M, G g G, M, R (2) (3) g g 2.3 [ 9] 100 g 90 k/h 360 k/h 1 kg ( 6 [ 10] (a) 0 T (b) v 0, T ( 5 (1) g = G M R 2 (2) r, ( 6 V = 4 3 πr3 = 4 3 π( R 4 )3 V = 4 3 πr3 ( 1 4 )3 ( 1 4 )3 (3) g = G r 2 = G ( 1 4 )3 M ( R 4 )2 = g 4 1/6 g 9.8 /s 2 g 10 /s 2 90 k/hr 31. 360 k/hr 500. 4
(c) v 0 T 2.4 [ 11] θ g θ (2) F (3) 30 F [ 13] B A A, B A, B B () N B, A B N A g A B (1) (2) 2.5 Free-Body Diagras [ 12] F ( 7 g F θ (1) A, B Free-Body Diagras (2) ( 8 (3) N A, N B ( 9 [ 14] θ M F F ( 10 F M θ (1) x y { ( ẍ = g sin θ F 7 (a) (b) F = g sin θ ÿ = N g cos θ (c) F = 1 2 g { ( A : A 8 ÿ A = N A A g (2) B : B ÿ B = N B N A B g ( 9 (3) ÿ A = ÿ B = 0 N A = A g, N B = ( A + B )g F = (M + )g tan θ (: ( 10 5
3 3.1 [ 1] A, B, C A F ( ) A, B, C g ( 11 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 ( 12 F P (1) P Free-Body Diagras (2) P y P y P, y (3) T (4) F? [ 3] P A, P B P A A P B B B T P A A F A, P B T F A ẍ A = F F 1 ( 11 (2) B ẍ B = F 1 F 2 C ẍ C = F 2 (3) ẍ = F/3, F 1 = 2 3 F, F 2 = 1 3 F { ( 0 yp 12 = 2F T (2) ÿ = T g (3) T = 2F (4) F = g 2 6
g ( 13 ( 14 P B P A O x k B 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 ( ) (1) (2) (3) (4) A t = 0 t 3.3 [ 5] MKS [ 6] MKS [ 7] F θ µ 0 ( 15 y F x θ ( 13 (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 (3) 2ÿ A + ÿ B = 0 (4) A = 2 B, T = B g ( 14 (2) ẍ = g kx (3) x = g/k (4) x = k A cos t + g k, ẋ = A k sin k t { ( ẍ = F cos θ Fv 15 (2) ÿ = F sin θ + N g µ 0 g (3) F = cos θ + µ 0 sin θ 7
(1) F v Free- Body Diagras (2) xy xy. (3) F [ 8] 2 A B A B B A B µ. B F. A B N 1 B N 2 ( 16 y O A B (1) A, B Free-Body Diagras (2) A, B (x A, y A ), (x B, y B ) xy { A ( 16 x A = µn 1 (2) A y A = N 1 A g { B x B = F µn 1 B y B = N 2 N 1 B g { N1 = A g (3) N 2 = A g + B g (4)A x µ A g B x F x. (3) N 1, N 2. (4) A B. 4 4.1 [ 1] ( 60 g) 180 k/h 5 s ( 17 [ 2] 2 70 k ( )50 kg 2 72 k ( 18 (1) (2) 72 k [ 3] ( 17 ( 18, v, F, t F t = (v 0) F = v/ t = 0.06[kg] 180 (1000[]/3600[s])/0.005[s] = 600[N] (1) 500 N (2) 20 8
( ) () ( 19 (1) ( ) (2) (3) ( ) [ 4] 2 v 0 ( 20 (1) 2 L ( ) a b c d (2) 2 T ( ) 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] 100 g 5 ( ) g 9.8 /s 2 ( 21 ( 19 ( 20 ) (1a) L (1b) (1c) (1d) (2a) (2b) T (2c) (2d) (1) (2) 50c ( 21 (1) 10 /s (2) 10 N (3) 20 N 9
(3) 0.05 [ 8] 40 g 9.8 [/s 2 ] ( 22 (1) ( )50 kg 40 (2) 40 ( )50 kg? (3) (4) 40 [s] [ 9] h 2 g ( 23 ( 22 (1) 19600 J (2) 19600 J (3) 28 /s = 100.8 ( 23 k/hr ( ) (4) 2.9 s ( OK) (1) v (a)(b) gh = 1 2 v2 v = 2gh (2) (b) h 2 L h h h/2 h/2 L (a) L (b) (1) h (2) L? [ 10] r v 0 x g ( 24 ( 24 (1) 1 2 v2 0 = g 2r + 1 2 v2. v = v0 2 4gr (2) v, v 0 2 gr 10
x r O v (1) v (2) v 0 4.3 [ 11] θ µ g ( 25 (i) (ii) (2) l. a b (i) µ (ii) µ c µ l L 4.4 [ 12] ( k) O. k θ L l (1) a Free-Body Diagras b c L x O x (1) (2) [ 13] k L ( 26 ( 25 (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 ( 26 (1) 1 2 kl2 (2) v 1 2 kl2 = 1 2 v2. k v = L 11
k (1) L (2) [ 14] ( k) M g k (1) (2) (3) t 5 [ 1] (1) (2) [ 2] 3 A, B, C B v A 1 C 1 A,B,C A, B, C ( 27 (1) A A,B,C (2) 3 [ 3] M h g ( 28 h M (1) v 1 (2) ( V v 2 ) A v A v A + B + C ( 27 (1) (2) A + B + C ( 28 (1) gh = 1 2 v2 1 v 1 = 2gh (2) { gh = 1 2 v2 2 + 1 2 MV v 2 V 0 = v 2 MV (3) v 2 M (1) 12
(3) v 2 v 1 [ 4] l M A, M B,, M v 0, θ g l (1) (2) v θ (3) [ 5] M k ( ) v 0 M k (1) l v 0 l (2) 6 6.1 [ 1] ( 29 (1) 360 (2) 1 30 60 90 180 (3) 2 1 rad (4) r θ [rad] [ 2] ( 30 (1) (x, y) (r, θ) a (1, 0) b ( 1, 1) c ( 1, 3) (2) (r, θ) ( 29 (1) 2π rad (2) 60 (3) 2 (4) rθ [rad] ( 30 (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) vo 13
a (2, π 3 ) b (4, π 4 ) c (0, 3) [ 3] [rad] ( 31 [ 4] (r, θ) (x, y) ( 32 6.2 [ 5] 2 l = 50 c g 9.8 /s 2 ( 33 l (a) h l (b) (1) (2) (a) (3) (b) ( 31 [rad/s], [rad/s 2 ] ( 32 (x, y) = (r cos θ, r sin θ) h 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 θ ( 33 (1) 3.5 /s (2) h = 5 l = 62.5 c 4 14
(1) + (2) (3) I θ (x,y) (b) (a) [ 5] 1 2 x 1, 2 x 1, x 2 g x2 2 O θ x1 1 (1) (2) (3) τ [ 6] l ( (a)) θ g (c) (1) (x, y) (x, y) θ (2) ( (b)) (3) ( (c)) θ [ 7] A ( 60 kgw) g 15
A (1) (2) Free-Body Diagras (3) Free-Body Diagras (4) (5) (6) (7) (8) (9) (10) (iv) (v) b (i) (ii) (iii) (iv) (3) a b c d B (1) : (2) a (i) Free-Body Diagras (ii) (iii) ( : ) 16