63 3 Section 3.1 g 3.1 3.1: :
64 3 g=9.85 m/s 2 g=9.791 m/s 2 36, km ( ) 1 () 2 () 3 9.8 m/s 2 3.2 3.2: : a) b) 5 15 4 1 1. 1 3 14. 1 3 kg/m 3 2 3.3 1 3 5.8 1 3 kg/m 3 3 2.65 1 3 kg/m 3 4 6 m
3.1. 65 5 5 1 15 1 1-5 -5 1 5 5-5 1-5 5 5 1-5 5-5 -1-15 15 1 3.3: 1 5 m/s 2 5 6 7 3.3 5 1 6 2 7 3
66 3 l u B S 3.4 l S l l S l d C 2 C G 2 S 2 A 3.4 Section 3.2 3.4 S S A A 8 8 3.5.4
3.2. 67 S (S ) l S (l S ) l (= l S + l S ) T d (T u ) g α (2π) 2 g = [ Td 2 + T u 2 + T d 2 T 2 ]( u 1 1 2l 2(l S l S ) 8 α2 + O(α 4 ) ) (3.1) (l S ) (3.1) l S l S g = (2π)2 l T 2 ( 1 + 1 8 α2) (T = T d = T u ) (3.2) T l l 3.2.1 3.4 A, B, C-C l l θ(θ =.19 deg 1 ) T R ( C) l l = l (1 + (T R 15)θ) (3.3) 3.2.2
68 3 3.2.3 9 9. 9 9 9 9 3.5 3.2.4 ( 3.6) I I II 1 1 µsec ( 1 ) 99.9999 sec ( 3.5) 1 1 1/1 1 µsec 1/1 3.6 Section 3.3 T d = T u 1 2
3.3. 69 3. cm(±1 mm ) TA C C 77 cm 79 cm 81 cm 83 cm 85 cm
7 3 1 T d = T u A T d = T u C C 1. T d C C 77 cm 85 cm 2. T u C C 77 cm 85 cm 3. C C T d T u T d T u T d = T u T A 3.7 4. A 2 T d = T u B A C C 79 cm, 81 cm, 83 cm T d T u T d = T u 1. C C 79 cm, 81 cm, 83 cm 2. C C 79 cm, 81 cm, 83 cm 3. TA 4. T d, T u B 5. B
3.3. 71 d= (down) u= (up) C-C (cm) (sec) 1 d77. 1 2.468 2 2.471 C-C (cm) (sec) 3 2.469 1 u85. 1 2.976 4 2.47 2 2.971 5 2.467 3 2.974 2.469 : : : 2 d79. 1 2.56 2.974 2 2.545 2 u83. 1 1.52235 3 2.552 2 2.721 : : : 3 1.972 2.552 4 1.9722 3 d81. 1 1.79956 : : : 2 2.65 2.721 3 2.654 3 u81. 1 2.444 4 2.652 : : : : : : : 2.652 : : : l TA 2 cm =.1 sec 2.5 2.4 2.3 2.2 2.1 77. 79. 81. 83. 85. C-C cm 3.7
72 3 3 B B C C T d = T u A 1. C C 2. C C T d T u 3. T d T u T = T d T u 3 B T d T u AC C T d T u T 4, p. 1 1 2
3.3. 73 1. 1 2 3 2. 1 2 C C 77 79 81 83 85 cm T d T u 3. 2 B TA 4. A B Section 3.4 1 2 3 1 3
74 3 Section 3.4 3.4.1 1 1. T d = T u A B T d = T u CT d = T u T 5 2. C A B C A B B C C 77, 79, 81, 83, 85 cm T d T u 3. C 3.2 C T g( m/s 2 ) g 4 π = 3.1415 A.2 p. 271 4. l l g( ) g(+) A.3 A.4 p. 272 274 Section 3.5 g = 9.83 ±.2 m/s 2 (3.4) 9.81 m/s 2 9.85 m/s 2 5. C A B T A B - - A.4 p. 274
3.4. 75 3.4.2 2 m 38 15 37 Section 3.5 (g N ) 9.816 m/s 2 m Section 3.5 3 g 1. h = 67.8 m g 1 m 3.86 1 6 m/s 2 g f : g f = 3.86 1 6 h m g B = 2πGρh ρ = 2.65 1 3 kg/m 3 G = 6.672 1 11 m 3 kg 1 s 2 2. g N g f g B g = (g + g f g B ) g N (3.5) 3.4.3 3 1. 2-2 1-4 2-2 1-4 3.4 2. ρ = 2.65 1 3 kg/m 3 g ρ
76 3 Section 3.5 3.5.1 2 m m 3.5.2 (g N ) 1984 g N = 9.783267714( 1 +.193185138639 sin2 λ ) (3.6) 1.66943799913 sin 2 λ (λ 3.5.3 h g(= g g f ) g R g R 2 = g (R + h) 2 ( mg = G mm R, mg = G mm 2 (R + h) ) (3.7) 2 (m: M: G: g g g =g+3.86 1 6 h g f = 3.86 1 6 h
3.5. 77 ρ h ρ g B g B = 2πGρh (3.8) g g N g g = (g + 3.86 1 6 h 2πGρh) g N (3.9) g > g < 3.5.4 S S A A M I l S θ d 2 dt θ(t) = 2 ω2 sin θ(t) (3.1) ω 2 = Mgl S I + Ml 2 S (3.11) θ d 2 dt θ(t) = ( 1 2 ω2 θ(t) 6 θ(t)3 + O(θ 5 ) ) (3.12) α α 4 θ(t) = α ( sin ωt 1 192 α2 sin 3ωt + O(α 4 ) ) (3.13) ω = ω ( 1 1 16 α2 + O(α 4 ) ) (3.14) I + Ml 2 ( S 1 T d = 2π 1 + Mgl S 16 α2 O(α 4 ) ) (3.15)
78 3 I T d T u T u I + Ml 2 ( S 1 T u = 2π 1 + Mgl S 16 α2 O(α 4 ) ) (3.16) (3.15) (3.16) I (3.1) 3.5.5 (3.2) g = (2π)2 l T 2 ( 1 + 1 8 α2) (3.2) l T α g T α l 1-4 l α l l δl l + δl (3.2) g l δl l = 999.14 ±.2 mm.2 mm (3.3) 1 C 15 C 22 C +.19 (22 15) = 1.133 999.14 mm 999.27 mm ±.2 mm.2 1.133 m m
3.5. 79 3.5.6 h r 99.93 mm 1.7 mm 1 mm.7 mm 1 mm δh δr(> ) h h δh h + δh V π V = πr 2 h (3.17) V + V + = π(r + δr) 2 (h + δh) = π(r 2 h + 2rhδr + hδr 2 + r2 δh + 2rδrδh + δr2 δh ) (3.18) 2 V + = π(r 2 h + 2rhδr + r 2 δh) (3.19) π(2rhδr + r 2 δh) V V = π(r 2 h 2rhδr r 2 δh) (3.2) V V + V δv ±π(2rhδr + r 2 δh) δv 1 2πrhδr V r r δr 2 V h δh δv δv = V r V δr + δh (3.21) h X Y Z R(X, Y, Z, ) δx δy δz R δr δr = R X δx + R Y R δy + δz + (3.22) Z δr δr = R X δx + R Y δy + R Z δz + (3.23)
8 3 3.5.7 (3.2) 3 ± g A.3 A.4 68.3% 1/3