: : ( CIP ) ( ) /. - :,003.1 ( ) ISBN CIP (003) : : ( ) : / 3 :14.65 : :
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- 非 石
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1 ( )
2 : : ( CIP ) ( ) /. - :,003.1 ( ) ISBN CIP (003) : : ( ) : / 3 :14.65 : : ISBN / G066 :4.00
3 , () () ()( ) : 1.,.,, :,,, ;,,, ; ; ; ( ) 3., (),,,, 4., 5.,,,,,, 005 3
4 ( 1) ( ) ( 3) ( 4) ( 4) (10) (6) (6) (9) (31) (39) (41) (41) (46) (60) (60) (63) (65) (74) (75) (75) (79) (84) (84) 1
5 (88) (88) (93) (95) (95) ( 100) ( 109) ( 109) ( 114) ( 116) ( 1) ( 14) ( 14) ( 131) ( 148) ( 148) ( 15) ( 154) ( 174) ( 176) ( 176) ( 18) ( 195) ( 195) ( 199) ( 01) ( 16) ( 18) ( 18) ( ) ( 38)
6 ( 38) ( 41) ( 43) ( 60) ( 6) ( 6) ( 65) ( 75) ( 75) ( 78) ( 79) ( 90) ( 9) ( 9) ( 96) ( 303) ( 303) ( 305) ( 307) ( 313) ( 315) ( 315) ( 316) ( 317) ( 317) ( 318) ( 318) ( 30) ( 30) ( 36) ( 337) 3
7 ( 337) ( 343) ( 346) ( 356) ( 358) ( 358) ( 36) ( 367) ( 367) ( 368) ( 370) ( 377) ( 378) ( 378) ( 381) ( 386) ( 386) ( 390) ( 390) ( 393) ( 394) ( 394) ( 395) ( 395) ( 395) ( 396) ( 397) ( 398) ( 398) ( 400) ( 401) 4
8 ( 40) ( 403) ( 403) ( 404) ( 404) ( 406) ( 406) ( 406) ( 407) ( 408) ( 408) ( 408) ( 409) ( 410) ( 410) ( 410) ( 411) ( 41) ( 41) ( 41) ( 419) ( 419) ( 40) ( 41) () ( 4) () ( 43) () ( 436) () ( 443) 5
9 005 () (040) ( 446) ( ) (040) ( 455) 6
10 , ( ),,, (),,,, ()?,,,, 1.,,,,,,,.,,,,,, 3.,,,, 4.,, 1
11 5.,, 6.,,,,,,, (),,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ( ),
12 ,,,,,,,,,, 60%,?,,,,,,, 3
13 1. (1) :,,.,. () :. (3) :,.. (1) :,,. r = xi + yj + zk,. () :. r ( t) = x ( t) i + y ( t) j + z( t) k (3) : t t + t, r( r + t) r( t) r = r ( t + t) - r( t),, ;,,, 4
14 , r s 3. (1) :,.. : t r t v = r t = r( t + t) - r ( t) t ( ) :. v = d r d t = d x d t i + d y d t j + d z d t k.,,,.,. () :. a = v t (). a = d v d t = d r d t 4. (1) = d v x d t i + d v y d t j + d v z d t k = d x i + d y j + d z d t d t d t x = x 0 + vt v = k 5
15 a = 0 x = x 0 + v 0 t + 1 at v = v 0 + at a = :,, ;,,.. () ( y ) r = v 0 cos ti + v 0 sin t - v = v 0 cos i + ( v 0 sin- gt) j a = - gj 1 gt j,,. (3) () ( t) = ( t + t) - ( t) = d d t a = d d t = d d t s = r v = r a= ra a = a n + a an = v r = r. 6
16 a = d v d t 5. r = r 0 + r v = v 0 + v a = a 0 + a 11..,, ( S ), ( S ),. : S S, v0 =, a0 = 0, a = a,. : (1), ; (), ; (3), ; (4),. 1. ( ) (1) :, 7
17 . () :.,.. :. (1) :, a F, m ;. () F = ma F x = ma x F y = ma y F z = ma z F = ma x = m d v d t F n = ma n = m v r ( ).,,, (1) : A F B, B, FA. : () : F = - F F F,,. F F,,. 8
18 :,,,. ( v c),. 1. :. F = G m 1 m r 3 r 0 G = Nm kg -,.. :. P = mg 3.:,,,.., 1 : F = - kx k: (1) f = N,. () : 9
19 ,,. f max = 0 N 0, N. f 0 f max, : 0 f fmax f,,. 1.x, : x = t - t : x? x?x - tv - t a - t. : v = d x d t = - t(m s) a = d v d t = - (m s ) t = 1s, v = - t = 0, 0 < t < 1s, x ; t > 1s, x. x - t v - ta - t 13 : 10,,
20 : x( t) v( t) a( t),... r = ( t - 3 t ) i + ( - 4 t m, t s, : : (1) t = s, t = 0 t = s ; () ; (3) t = s. + t 3 ) j, r :, v = d r d t = ( - 6 t) i + ( - 8 t + 3 t ) j a = d v d t = - 6 i + ( t) j (1) t = s : r = - 8 i - 8 j t = 0, r 0 = 0 t = 0 t = s r = r - r 0 = - 8 i - 8 j () v = r t = 0 t = s t v = r t = r - r 0 t = - 8 i - 8 j = - 4 i - 4 j a = v t, v = v - v 0, v 0 = i, v = - 10 i - 4 j, t = 0 t = s a = v t = v - v 0 t = - 1 i - 4 j = - 6 i - j (3) t = s v( t)a( t) v a = - 10 i - 4 j = - 6 i + 4 j 11
21 3. x, a = 6 t( SI ), t = 0, x 0 = 10m, v 0 = 0,. : a = d v d t = 6 t d v = 6 td t v 0 d v = t 0 6 td t v = 3 t ( SI ) v = d x d t = 3 t, d x = 3 t d t x 10 d x = t 0 3 t d t x = t ( SI ),., m, = + 4 t 3. t,.(1 ) t = s.( ),.(3) t,. : ( 1) = + 4 t 3 = d = 1 t d t a = d d t = 4 t a= d v d t = R d = 4 Rt d t a n = v R = 144 Rt4 t = s a = = 4.8 (m s ) a n = = 30( m s ) 1
22 () a = 1 a 4 Rt = 1 (4 Rt) + ( 144 Rt 4 ) t = 0.66s = + 4 t 3 = + 4 (0.66) 3 = 3.15(rad) (3) a n = a, 4 Rt = 144 Rt 4 t = 0.55s,, a n a. 5.30m s, 5s. : 14, r = v 0 ti + 1 gt j x = v 0 t y = 1 gt v v x = d x d t = v 0 13
23 v y t, v v = v x + v y v x a n a a n = v 0 = arctan v y v x = d y d t = gt + g t = arctan gt v 0 = v R ( R ) a = d v d t a = d v d t = g t g t + v 0 g, g = a n a n a, a n v 0 a n = g - a = = 30m s t = 5s a n a = a n = v 0 gv 0 + g t a = 8.36( m s ) = 5.1(m s ) a 6. 1.m s,.44m s,,.74m, : (1) ; (). :., Oy, 14
24 , 15. (1), v 0 ; v 0.: 1 at 1 y 1 = H + v 0 t - a 1 gt y = v0 t + 1 at t 1, y 1 ( t 1 ) = y ( t 1 ) H + v 0 t 1 - t 1 = 1 gt 1 = v 0 t 1 + H a + g = = 0.71 ( s) () h h = H - y 1 ( t 1 ) = H - ( H + v 0 t 1 - = 1 gt 1 - v 0 t 1 = 0.74m 1 gt 1 ) :,.,. 7. x, x = 3 t - t 3. : (1) 4s ; () x. : ( 1) x = 3 t v = 0,6 t - 3 t t = 0 : x 0 = 0 - t 3, v = d x d t = 6 t - 3 t = 0, t = s t = s : x = 3-3 = 4( m) t = 4s : x 4 = = - 16( m) 15
25 4s 16 4s r = x 4 - x 0 = = - 16( m), 4s s = x + x 4 = = 4 (m). () t = s v = 0, x, x x = 4m.a = d v d t = 6-6 t, a = 0, t = 1s, a = 0 v, x : v max = = 3( m s ) 8. 36km h,, 30. : (1)?? ()?? : ( 1), = 10( m s ), () : v = v + v v = 100m s, v, v 30, 17 v = v cot30= 17.3m s. v = v sin30 = 0m s (a), h, v 0,. 16. s
26 : 18( b), O, t r( t), v 0 ; v 0 > 0, t t + d t d r < 0, r = s + h, - v0 = d d t - v 0 = d r d t s + h = s d s s + h d t d s Os t t + d t, d s < 0, 18( b), tt + d t d r, d r = - d s., v = s + h s v = d r d t v 0 = - d s d t, v 0. l, s = l - h, v = d s d t = d d t l - h = s + h s d l d t d l d t, v 0, v 0 v = s + h s v 0,, 17
27 . v 0, v = s s + h v 0., v 0 cos=,,,. 10. A 10m s. 60. B.. : 19 S, Oxy, S, O x y, Su = 10m s O x S., S A, v xyv x v y. tan60= v y vx v S, xy v x v y, v = u + v v x = u + v x v y = v y SB, v x = 0, v x = - u = - 10m s. S Sy, v y = v y = v x tan60 = 10tan60= 17.3m s 18
28 y = v y g = = 15.3( m) 11. m, x = Acost y = Asint A,. : x + y = A A, F = ma,, a F. (1) F x = ma x = m d x d t F y = ma y = m d y d t a = d x i + d y j d t d t F = F x i + F y j = - m Acos t = - m Asin t F = F x i + F y j = - m A( cos ti + sin tj) () v = v x v x v y + v y = d x d t = - A sint = d y d t = Acost a = d v v + d t r n F = F + F n n v = ( - A sint) v, + ( Acos t) = A 19
29 F = ma n F = m d v d t = 0 F n = m v r = m ( A) A = ma,,. 1. 1kg F = (1 t + 4)N,.t = 0, x 0 = 3m, v 0 = 8m s.. : (1 t + 4) d t = d v v 8 F = m d v d t 1 t + 4 = d v d t d v = t 0 (1 t + 4) d t v = 6 t + 4 t + 8 v = d x d t 6 t + 4 t + 8 = d x d t d x = ( 6 t + 4 t + 8) d t x 3 d x = t 0 (6 t + 4 t + 8) d t x = t 3 + t + 8 t M, = 0.6,, h = 1.5m, l? 0 : 110(a), sin= hl 110 (b), Fcos- Ff = 0 Fsin+ N - Mg = 0 F f = N
30 F = Mg cos+ sin d F Mg( - sin+ cos = - ) = 0 d (cos+ sin ) tan= = 0.6 d l = F > 0 d = h sin=.9m, (a),,,? :,, 111 (b) : P N. 111( c), : P N N 1,,.,? N, 1
31 ,,, N. 15. R, m.,? 11(a). : 11( b), m r, a n P N, P + N =., Nsin= = r = R sin, F mr sin (1) Ncos- P = 0 ( ) (1) N = mr () cos= cos= P N = mg = mr R - h R g = R - h R R h = R - g g R 16.a., m 1 m, m 1 > m, (1 ) m 1 m (3 )
32 ; ( ). :, m 1 m T 1 T, T 1 = T = T. m 1 m a a1 a, 113, at m 1 m, a 1 = a t - a a = a t + a m 1 m m 1 g - T = m 1 a 1 = m 1 ( a 1 - a) T - m g = m a = m ( a t + a) (1) m 1 m () a t = m 1 - m m 1 + m ( g + a) T = m 1 m m 1 + m ( g + a) 17. m 1 m = 4kg A, = kg B, 0 = :, A F?. : 114 A B, 3
33 A: F - f 0 = m 1 f 0 = 0 N N = m g a B: f 0 = m a N = m g f 0 = f 0 a = 0 g = = 5.39(m s ) f 0 F max = ( m 1 + m ) 0 g = (4 + ) = 3.3 (N) F, A B = 0 N, F A B. 18., 115, l, m, O,. v o,,. : 115, P, v, P mg T, :, T + P = ma T - mgcos= ma n = m v l - mgsin= ma = m d v d t v = () vd v = - lgsin d (1) () l= l d d t 4
34 v v 0 vd v = 0 - lgsind (1) v = v 0 + lg( cos- 1) T = m v 0 l - g + 3 gcos v, 0, v,,, v.., T, T, T. 19.M,. m. 116(a)., M m. : a 1, a, 116( b). 5
35 : N sin= m( a cos- a 1 ) N cos- mg = - ma sin - Nsin= - Ma1 N 1 - Mg - Ncos= 0 a 1 = msincos g M + msin ; a = ( M + m) sing M + msin , A C, ( ). A.4 R ; R B.4R ; 4 R C.4 R ;R D.4 R; R. 1 r 1, v 1. t, r v. t ( ). A. v - v 1 B. v - v 1 t C. r - r 1 t D. r - r 1 3., r, s, a t 6
36 . ( ). A. d v d t = a C. d s d t = v B.d r d t = v D. d v d t = a t 4., v = m s, a = - m s, 1 ( ). A. C. m s B. - m s D. 5. R ( v ) ( ). A. d v d t C. d v d t + v R B. v R D. 6., ( ). d v d t A., B., C., D., + v 4 R 4 7.,, a 1,,,? 118 ( ). A.a 1 + g B.( a 1 + g) C. a 1 D. a 1 + g 8. A O. W,, A,, 119 ( ). 1 7
37 A.arctan C.arccos B.arcsin D.arccot 9., m 1 m 1 ( m 1 < m ).., : ( ). A.m 1 g B.m g C. m 1 m g ( m 1 + m ) D.m 1 m g ( m 1 + m ) 10., ( ). A., B., C., D., 11. ( ). A., B. C. D. 1. ( ). A., B., C., D. 13. ( ). A. B. C., D. E., ,., 8
38 ( ). A. B. O C. A D. B , F A., F, ( ). A.A B.A C.A D.A 16.( ). A. B. C. D. 17. R., ( ) A.R B.R C.R D.R 18. R, m,, 1, PQ d, ( ). A. d R mg B. R d mg C. d R + d mg D. R + d d mg (, 9
39 ,, ) 1.v R,,, ;,..x = 3 t, y = 4 t + 1( SI ).,,.. 3.m = 1kg ; F 1 = i(n), F = j(n), x a x =, y a y =. 4.A,,, f 0, F,. 5. R, = t ( SI), t a = ; a n = ; a = kg,, 0 = 0.3, = 0.16, F = t ( SI), 4 v =. 7. 5kg ( ), r = 6 i - 3 t hj( SI), i, j X, Y, f ;. 8.PQ,, x P = 16 t, x Q = 4 t., 0, Q P. 9. v 0,, t,. 10. XOY, x = 5 t, y = 13-30
40 4 t ( t, xy ).3 s,. 1., 13, x = t - t ( SI ).(1).() t = 4s? : (1) v = d x d t = 4 - t, v = 0, t = s, x 4 - = 9(m),s = x 4 - x 0 = 9-5 = 4( m). x = () 0 4s : 0 s: s 1 = 4m,s 4s: s = x 4 - = 5-9 = 4(m), 0 4s s = = 8 (m).0 4s r = 0..R S = 1 v 0 t + bt 1.5, v 0 b. (1) t. ()? : ( 1) v = S = 1 v bt 0.5, a n = v R a = v = 0.75 bt a = a n ^n + a ^= v R ^n bt ^ 31
41 () a = ( a n + a ) 1 = [ v4 + (0.75 bt ) ] 1 R 3., m s., 10m s.,? : x = 1 at = t (m), v = t x = x, t x = vt = 10 t( m) v = 10m s = 10 t t = 10s.x = 100m,, v = 0m s. 4.x, v = 10 + t m s, t = 0 ( + x )0m.(1) t = s ; ( ). : v = d x d t = 10 +, x t d x 0 = t 0 (10 + t ) d t, x = 3 t t + 0 (m), t = s, x = 45.3m, a = d v d t = 4 t(m s ), t = s, a = 8m s. 5.R = 400m. 10m s, a = 0.m s,,. : a n = v R = = 0.5(m s ) a = a n + a = = 0.3( m s ) 6. 5m s, 0m,., (1) 0.5s s ; ( ),?? : 14,, 3
42 x = t - v = d x d t = t 1 gt = t t (1) t = 0.5s, x = 1.3m, v = 0.1m s, ; t = s x = 10.4m, v = m s,. () x = 0, t t = 0 t =.59s, v = - 0.4m s,. 7.x x = t - t ( SI ), (1) 3.() 1 3.( 3) 1 3.( 4) 1 3. : ( 1) v = d x d t = 4 - t, a = d v d t = - m s, t = 3s, v3 = 4-3 = - ( m s) a 3 = - m s d x d t ()x = x 3 - x 1 = 0m ( 3) v = x t = 0 = 0m s (4) ; = 4 - t = 0, t = s, v = 0,. s = x - x 1 + x 3 - x = m 33
43 8. 15,, h, l 0 ; v 0, : (1) ( ). () (). : l = l 0 - v 0 t, x = l - h (1) v = d x d t = d ( l0 - v0 t) - h d t () a = d v d t = - h v 0 [ ( l 0 - v 0 t) - h ] 3 16 : 9., l,,, 17, v,. :, = l0 - v0 t ( l 0 - v 0 t) - h v0 T P. a n = v R, R = lsin, 34
44 a = d v d t = 0, a = a n = v lsin. 10.,, ,. :,, = 0 - t( rad s ), t = 1s, = 0.9 0, = rad s.= t, t = s, = = ( rad s) 11. v1 = 5kmh, v = 40kmh, :? : 18 v 1 = v - v 1 v 1 = - v 1 + v = = 47.( kmh) :, 1. 1.m = 5kg,, 19. F = 10N = 30, a. = 0.1. : 130 : 35
45 N - mg - Fsin30= 0 Fcos30- f = ma f = N a = Fcos30- N m = 0.436m s 13.A B, 10kg0kg,.15N F B( 131).. : T, A B F - T= T = ma a T= T m B a a = F 1 + m B m A = 5N 14., 50kg.,? 4.9m s,? :, F = 0, N = mg = 500N( 50kg) ; N - mg = ma, N = mg + ma = 735N( 75kg), mg - N = ma, N = mg - ma = 45N, ( 5kg) : 13, v 0,, x F = - Mm, : x F = - G mm = m d v x d t G 36
46 d x : x - GM d x R x v = v 0 = v vd v v 0 + GM 1 x - 1 R,, x =, v 0 v = 0, v 0, v 0 = = m s. GM R 16., AB ( 133), m A = 0.30kg, m B = 0.0kg, = 30,.(1)?( )? : ( 1) a = m B g - m A gsin30= ( m A + m B ) a mb g - ma gsin30 = 0.98m s m A + m B () m B g - T = m B a, T = m B g - m B a = 1.76N kg, 80m. 134,, v = 30kmh.(1 )?( ),? : ( 1) mg - N = m v R, N = mg - m v R = N () N = mg = = N 18.m, l, A B, 37
47 m A m B. B F,, y T( y). 135 : ( 1) AB F - mg - m A g - m B g = ( m + m A a = F - mg - ma g - mb g m A + m B + m + m B ) a () y A T( y ) - m A + my L g = m A + my L T( y ) = m A + my L ( g + a) = F( m A + myl) m + m A + m B a M MD.,,. AB CD?? : mgcos= ma, a = gcos MC = Rcos= s, R. s = 1 at 38
48 t = s a = 4 Rcos gcos = 4 R g t,. 0. A B C( 1-37 ), B m B = 500, C = m C = 100, B C, F = B, BC, B C f. : : a = F m B + m C = = 0.98( ms ) m C, f = mc a = = 0.098() 1.C.C 3.C 4.D 5.D 6.B 7.D 8.A 9.C 10.ABD 11.CD 1.D 13.CD 14.B 15.A 16.C 17.A 18.B 39
49 1.v; 0;0; v R..y = 4 3 x + 1;5m s; 0; 3.m s ;1m s 4.f Rm s ;64 Rt m s ; 8rad s m s N, Y 8.;4 9. gt ( gt) + v 0 g; v 0 ( gt) + v ms ; x g 40
50 1. (1) : m v mv.. p = mv () :. I = t Fd t t 1 t 1 t F., F F.F,. I = Ft (1) : ( ). I = t Fd t = p - p 1 = p = mv - mv 1 t 1 I x I y = t F x d t = mv x - mv 1 x t 1 = t F y d t = mv y - mv 1 y t 1 41
51 I z = t F z d t = mv z - mv 1 z t 1., () :. I = t t 1 F d t = p - p 1 = m i v i - m i v i1.,,. 3. ( ),,. F = 0 m i v i =,.,,.. 4. (1) ( ). (),. (3),. (4). 1. : O L = r p = r mv r O.. : M L. 4
52 M = d L d t M = r F 3. :,.. M = 0, L = r mv =, 1. :, ( ),..: M, I. M = I : M I. I,.,,. 3. (1) ( ) L = I () ( ) :,. t Md t = L = L - L0 t 0 M. I (3) :, I. 43
53 M = 0, L = I=., I,. I, I.,,. 1. (1) F d r, d W F d r. () d W = Fd r = Fd rcos F d r., W = B Fd r A,.:,.... :. (1), () N = W t v. N = Fv 1. : 1 mv. 44
54 E k = 1 mv,.:. W = E k - E k0 E k, E k0. 3. :. W + W = E k i - E k oi E k i, E k oi. 1.:,,... :.E P. :.,... W = E P = - ( E P - E P0 ) 3.. W+ W = E - E0 E = E k + E p ( ), E 0 = E k0 + E p0 ( ) 45
55 ,,. W = 0, W = 0 E = E p + E k = : 1..,,..,,,. 3.. : 1.,..,,,. 3.,. 4., m,, t,, v,? :, mg N( N ), : N - mg = ( mg - N)t = 0 - mv N = mg + mv t 46 mv t ( N > mg)
56 ..50kg, 5m, 1s,,?( g 10m s ) :,.. 5m v 0, v 0 = gh = 10 5 = 10( m s) ( ) F. ( F - mg)t = 0 - ( - mv 0 ) = mv 0 F = mg + mv 0 t = = 1000( N).,.., : ( F - mg)t = 0 - mv 0 F = mg -,,.,,,,. 3., mv 0 t = 0 47
57 , 1.. (1) m 1 = m, v 1 = v ; () m 1 m, v 1 = v ; (3) m 1 = m, v 1 v. :,,. v, m,, m 1 v 1 + mv - m v = 0 v = m v - m 1 v 1 m (1) m 1 = m, v 1 = v, v = 0,. () m 1 m, v 1 = v : m 1 > m, v < 0,. m 1 < m, v > 0,. (3) m 1 = m, v 1 v : v1 > v, v < 0,. v 1 < v, v > 0,. 4.m MA B. B, H h. A B B.A B. A B, B. : 3, A B.A B v, B v. 48
58 , Mv+ m( v- vcos) = 0 (1), W = 0, W = 0. mg( H - h) = 1 Mv + 1 m[ v sin + ( v- vcos ) ] () (1) () B Mv= Mm : + x. g( H - h) ( M + m) [ M + ( M + m)tan ] 5. 4, A B, m A = kg, m B = 3kg, m = 100g v0 = 800m s A, 0.01s B, B.A N, : (1) A, B A ; ( ) B A B. : A B, A B. a = B A N = F = ( m A + m B ) a F = m A + m B + 3 = 600(m s ) mb a = = (N) A t, A A v A = at = = 6 (m s).b,b A v A. 49
59 A B, B B v B, x mv 0 = m A v A + ( m + m B ) v B v B = mv 0 - m A v A m + m B., = = ( m s) 6.F = 4 x - 3 x x1 = 6m.. : W = x Fd x x 1 = x (4 x - 3) d x x 1 = x - 3 x x x 1 = 63J. = 3m 7. 10m, 10kg,, 1m, 0.kg.,. : 5.,, F P. P = P 0-0. gy = y = ( y)n F = P = ( y)n W = 10 Fd y 0 = 10 ( y) dy 0 = 88J 50
60 8.MR,,, m, T( I = 1 MR ). : 6,, :.6. mg - T = ma (1) : N T, T. T R = I= 1 MR ( ) T = T ( 3) = Ra (4 ) (1) () (3) (4) :. a = T = mg m + M Mmg m + M mm g, a Ta T,. 51
61 ,,, m, 60, 7,. 1 3 ml, m l, : (1) ; (). = I : ( 1) 60, M M = 1 mglsin30= 1 4 ml, I = 1 3 ml = M I = 3 g 4 l = = 9.19( rad s ) (), M = 1 mgl, = M I = 3 g l = = 18.38(rad s ) 10. M, R 0..m (1)?(), r,?. : ( 1),,. I = 5
62 1 MR, I = mr, = I 0 = ( I + I ) = 1 MR 0 1 MR + mr M M + m 0 (),.r I = mr, ( I + I )= ( I + I ) = = 1 MR + mr M 1 MR + mr M + m 0 MR MR + mr 0 11., 50kg, 3m,. 3m, 3m, ()., (1) ; () 1m,? : ( 1),, 1 mlv + 1 mlv = 1 4 ml ml 0 m = 50kg, l = 3m. 0 = v l = 6.67rad s O 6.67rad s. (),, 53
63 , 1 4 ml ml 0 = l= 1m, = ml ml l 0 = 9 0 l 1. 8, kg 1.5m,. F = 100N, t = 0.01s, (1 ),?( ). : ( 1) F. :, L = Mt = Flt = = 1.5 (Nms ) (),. c. 1 I, mgh, 1 I = mgh L = I- I 0 = I- 0 = I= 1.5Nms, I = 1 3 ml, h = 54
64 1 (1 - cos ),, cos= 1 - = 1 - = L m gl 3 = arccos = ,, M l0, O. k,. m, v 0,, A B. OB = l, ( ) B. : v 1.,, mv 0 = ( m + M) v 1 (1),,, 1 ( m + M) v 1 = 1 ( M + m) v + 1 k( l - l 0 ) (), mv 0 l = ( m + M) vlsin (3) 55
65 (1) v 1 = v 1 () v = v ( 3) m m + M v 0 1 m + M m v 0 - k( m + M) ( l - l 0 ) = arcsin mv 0 l 0 l mv 0 - k ( m + M) ( l - l 0 ) :, 1 mv 0 = 1 ( m + M) v + 1 k( l - l 0 ).,,, , m 1 A m B, m 1 = 5kg, m = 3kg., A B, A?( k = Nm) : A, ( ), y, l 1 = m 1 g k B, l = m g k B, A,, : (1) () 1 k( l 1 + l ) = 1 m 1 v max + 1 kl 1 + m 1 gl (3) ( A B ). (1) () (3) : 56 v max = m g m 1 k = = 438 (m s)
66 15. 11, m 1 A m B. A, A B. : B, B,.,, A., O, x.a O x, B, N = 0, kx - m g = 0 F, A x 1 ( x 1 A, k x 1 - F - m 1 g = 0 < 0). F F A x 1 x, A.O, ( x > 0, x1 < 0) 1 kx + m 1 gx = 1 kx 1 + m 1 gx 1 F = ( m 1 + m ) g,., B ; 57
67 ,. 16.m = 50g h = 0m v 0 = 18m s, v = 0m s,. 1 : : F f. P, mgh, W f, 1 mv 0 1 mv. W f + mgh = 1 mv - 1 mv 0 W f = 1 mv - 1 mv 0 - mgh = (0 ) - = - 7.9( J) (18) , ;,,. 1 mv 0 + mgh; 1 mv., W f = 1 mv - = - 7.9( J) 1 mv 0 - mgh 58
68 ,, R, m, h ( 13 ). : N = 0., mgcos, mgcos= m v R v m. cos= R - h R, ( N v, N ),.., ; m, 1 mv - mgh., 0 = 1 mv - mgh, h = 1 3 R, : (1) ; (), ; (3) W = 0 W = 0, ; ( 4), ; (5) ; ( 6). 59
69 1.,,,,,, ( ). A. B. C. D..,, ( ) ( ). A. C. B. D. 3.0g x 500m s, 50m s x, ( ). A. - 9Ns C.9Ns B. - 10Ns D.10Ns 4., ( ). A. B. C. D. 5.( ). A. C. B. D. 6., ( ). 60 A.
70 B. C., D., R B 7. R A. L A L B, ( ). A.L B > L A B.L B < L A C.L A = L B D , m h,. k,, ( ). A.mgh B.mgh - C. mgh + m g k m g k D.mgh + m g k 9. 15,,,,, R,, ( ). A., B., C., D., 10.m v 1 v, ( ). A. 1 m( v - v 1 ) B.m( v 1 - v ) 61
71 C. 1 m( v - v 1 ) D. 1 m( v 1 - v ) 11., AB,, m A B ( ). A.11 C.1 = m B,, A B.1 D l,, 16. A, B, ( ). A. B., C., D. 13. ( ). A. B. C. D. 14.( ). A., B., C., D. E., 15.m,, v,, ( ). 6
72 A. mvsin C. mvsin B. mvcos D.mvcos m.0.03 m,?( ). A.= C.> B.< D. 17.,, I0, 0 ;, I 0 3, : ( ). A. 3 0 B. 3 0 C. 3 0 D , F = 3 x, F x x 1 = 1 m x = m, ( ). A.3 J C.1 J B.7 J D.4 J ,,,, 1 a 1 a ( ). A.a 1 = g, a = g B.a 1 = 0, a = g C.a 1 = g, a = 0 D.a 1 = g, a = 0 (,,, ) 1.: F 1 = kn, F = 8 kn, 1s, y p y =. 63
73 . 18 l = 0.5m, O. O I = 5kgm., m = 0.01kg, v = 400m s, =. 3.F = ( + 4 x) i(si ) x, x = 0 x = 10m, F , m = kg, 1 4 A B, B v = 6m s, R = 4m, A B W =. 5.: ( ). 6.? ( ) kg, X, X = t - 1( SI), t 1 = 1 s t = 3 s, ;. 9. 0, R, R,, R C, :. 64
74 10., 10m, 10kg,, 1m 0.kg,,. 1.m = kg, h = 1.5m,. : (1)t = 0.1s, ()t = 0.01s,. : v = gh = = (5. 4)m s, Ft = p, (1)t = 0.1s, F = ()t = 0.01 s, F = mv t mv t = = = (N) = (N). 300, 9.6g, 80m s,? : 1.t = 1min = 60s, M = =.88( kg), Ft = Mv - Mv 0, F = Mv t = = 39.4(N) 3., m 1 = kg, m = kg,,, m 3 = 100kg., v = m s,. v 0 v 10? = 1.m s,, :.,, m 1 v 10 - m v 0 = ( m 1 - m 3 ) v 1 v 10 = ( m 1 - m 3 ) v 1 - m v 0 m 1 = ( )
75 =.(m s ) 4. 1, m 1 m, I, r.. m, T 1 T. :, m 1 m, T - m g= m m 1 g - T 1 = m 1 T 1 r - T r = I = r a = ( m 1 - m ) g m 1 + m + Ir T 1 = m 1 ( m + m + Ir ) m1 + m + Ir g T = m ( m 1 + m 1 + Ir ) m 1 + m + Ir g 5.m 1 m. R r, I 1 I,,,. ( m 1 > m ). 66 :
76 m 1 g - T 1 = m 1 a 1 T - m g = m a T 1 R - T r = ( I 1 + I ) a 1 a a 1 = a = = R = r ( m 1 R - m r) Rg I 1 + I + m 1 R + m r ( m1 R - m r) rg I 1 + I + m 1 R + m r T 1 = I 1 + I + m r + m rr I 1 + I + m 1 R + m r m 1 g T = I 1 + I + m 1 R + m 1 rr I 1 + I + m 1 R + m r m g 6.60kg m s 80kg, 1m s.: ( 1)? (),? :.,. (1) m v + m v = ( m + m ) v v= m v + m v m + m = () m v - m v = ( m + m ) v v= m v - m v m + m -. = = 1.43 (m s) = (m s) 7., 70kg, 4m s 1.5m.,, 1.5m,.(1 ) ; (). 67
77 : (1) p = mv - mv = 0. L = I= mrv = = 40 (kgm s) ()= v r = = 5.33 (rad s ) 8. 3, AB, l, M.B O,, m, v A, A 1 v,,. O I = 1 3 Ml. :, mvl = I+ mv l v= 1 v = 3 mv Ml I = 1 3 Ml 9. M, R,,. mv,, :, mvr = = 1 MR + mr mv ( m + M) R
78 10. m = 0kg F = 0 tv( SI ), x, 4s. : W = Fd r = Fd x = 0 tvd t F = ma = m d v d t, v 0 d v = t td t 0 v = 1 t W = 4 0 t 1 0 t d t = 5 t4 4 0 = 640J 11. x = kt, k, t.,, x = 0 x = l,. : x = kt F f W f v = d x d t = kt = v = k t, = F f d r = - l F f d x = 0 - l 0 kxd x = kl3 1..h = 1. 0m, l = 4.0m, m = 300kg. F = 860N,??( = 0.03)? : 5 : W = Fcos l = = (J ) 4 69
79 W = - mgh = = ( J) W = - F f l = - ( mgcos+ Fsin ) l = = ( J) , q m = 50kg s, v = 1.5m s,.. :, : F = Ft = mv - 0 mv t = q mtv t = q m v P = Fv = Fv = q m v = 50 ( 1.5) = 11.5W. 14. F = 0N m l = 0.5m, F 30, Ff. = 0.N. :. W + W = E E = Fcos30 l - Ff l = = 8.56 ( J). 15.k = 100Nm,, m = 0.1kg A. A x 1 = 0. 70
80 0m, 6., A x = 0.035m.. :, : mgx = 1 k( x - x 1 ) - = k( x1 - x ) mg = 100 ( ) kx 1 = = 0.0, = 45. v 0 = 10m s, ( 7 ),.,, v. : ( 1), - fl = mgh - 1 mv 0 - mgcos45 h sin45 = mgh - 1 mv 0, h = v 0 g(1 + cot45 ) = 4.5m; () - fl = 1 mv - mgh v = gh(1 - cot45 ) = 66.59, v = 8.16m s. 17. m v ( 8). M,. h. : mv = ( m + M) v, 1 ( M + m) v = ( M + m) gh, : 71
81 h = v g m m + M 18.m 1 = kg, v 10 =.0m s, v 0 = 1.0m s, m = kg.,. :, m 1 v 10 + m v 0 = ( m 1 + m ) v v= m 1 v 10 + m v 0 m 1 + m = ( ) 10 3 = 1.17(m s) E k = 1 m 1 v m v J. 1 ( m 1 + m ) v = m = 1kg A l = 1m, O. 9 M = 5kg B, B k = 000Nm.. : A : mgl = 1 mv A B : mv 1 = mv + Mv 7
82 1 mv 1 = 1 mv = 1 Mv ( B ) : :x = Mv = 1 k (x) Mgl k = m. 0.m v 0,,, k( k > 0)..,. :, f = - m d v d t = - kv d v v = - k m d t v v 0 d v v ln v v 0 = - v = v 0 e k m t = t - k 0 m d t k m t 1. m, R, O. M L., 30. F,,. : ( 1) ; kv, ( ) ( O 73
83 I = 1 mr ) : (1) F f,, F - f = Ma Rf = I I = 1 mr R= a f = mf m + M () ( F - f) L = 1 Mv v = 4 FL m + M 1.A.C 3.C 4.B 5.C 6.B 7.C 8.D 9.D 10.C 11.C 1.C 13.BD 14.AD 15.A 16.B 17.C 18.B 19.D rad s 3.0J J W = - E p 8.64J 8 kg ms 9. 5 g J 74
84 1. (1),. (). (3)... (1) V:.,. m 3 ( ). L( ),1L = 10-3 m 3. () p:,., Pa( ) :1Pa = 1Nm ( ). mmhg( ) atm(). 1mmHg = 133.3Pa 1atm = 760mmHg = Pa () T:.. (t, ) ( T, K ), 3. TK = t 75
85 (1) :,.. pv T. () :,. 4. (1) :,,.,,,.,,. () :, pvt., pv = M M mol R, RT R = 8.314J ( molk) R = 0.08atmL(molK) 1. p = 1 3 nmv n, m, v. p v... T = 3 kt = 1 mv T, k = JK 76
86 . k = R, N N A A.,.,.,. 1. (1) :,, 1 kt.. i, = i kt : i = 3, i = 5, i = 6. () :. 1 : Mkg : E 0 = N A = i N AkT = i RT E = M M mol i RT T,.. (1) : v v + d v, d N N = f( v)d v, 77
87 . d N v v + d v, N, f( v). (), : f( v) = 4 m kt 3 e - mv kt v. 31, :, v 0 v, f( v) 0,,,. f( v),, v p., 31. d S = f( v) d v = d N N v v + d v. 3, M mol, v p T. 1,,,,,. (3) 78
88 v = v p =. : v = 3 kt m = 3 RT M mol kt m = RT M mol = kt m = 8 RT M mol RT M mol = RT M mol T M mol, v > v > v p K, Pa,. : pv = N A m, n = N V, k = R N A T = 300K,,p = Pa n 1 = p 1 kt, n = p kt, n = n - n 1 = p kt n = M M mol RTM = Nm, M mol = = (m - 3 ) p =,. nkt 79
89 .V, p, T, m, k, R, A.pVm C.pVmT B.pVRT D.pVkT : N = nv n. p = nkt, n = p kt, N = D. N = pv kt 3.,,,?? nv : t = 3 kt,, T t,,. p = 1 3 nmv = 3 n: n, = nm, 1, m 1 m, n n, p. 4. M, v., (1)?( )? : ( 1) v,. 1 Mv.,,,,. T 1 80
90 T, E = 1 Mv = M Mmol i R( T - T 1 ) T = T - T 1 = M mol v pv = (), V, M M mol RT (p) V = M Mmol ir RT p = MR T = Mv VM mol Vi = v i = M V : ( 1). ( ),. ( 3). 5., J.(1).(). : ( 1) O H T,, to = th, th = J t = 1 m v, M = M mol N A v = t m = t N A = M mol = 483(m s) () t = 3 kt T O = t 3 k = = 300(K)
91 6. 33,? : v P = 1.41 RT M mol : T, vp Mmol.MmolH < M molh e, v ph > v ph e, v ph e = 1000m s. v phe = 1.41 RT M mo lhe = 1000m s, :1.41 RT = M mo lhe 1000 = = 000 : v phe = 1.41 RT = 000 M m olh = 1000(m s ). : 7. f( v), (1) f( v) d v () v p f( v)d v 0 (3) v Nf( v )d v v 1 (4) vf( v) d v 0 : ( 1) f( v )d v = d N Nd v d v = d N N,, v v + d v. 8
92 () v p f( v)d v 0 = v p d N 0 Nd v d v = v p d N 0 N 0 - v p (3) v v 1 v p = d N 0 N. Nf( v )d v = v v 1 Nd v d v = v N d N v 1 d N = N, v1 v. = N N, (4) vf( v) d v 0 = v d N 0 Nd v d v = vd N,, 0 N,., f( v) = d N Nd v..,. 8. (1) 1 kt, ( ) 3 kt, (3 ) i kt, (4 ) i RT, (5) M M mol i RT. : ( 1) 1 kt. () 3 kt. (3) (4) (5) i i M M mol kt i. RT i 1. i RT M. 9.10, m s, v = : v = v i N, = 8.( m s) 83
93 v = v i v = N 1, = 9.19 (m s), v = RT M mol v = 1.73 RT, v = 1.73 M mol 1.60 v = 8.87m s. v = 1.60 RT M mol v = 1.73 RT m mol,. 10,, v v : M mol = 3g = 0.03kg, T = = 300(K), v = 1.73 RT M mol = = 48.87( m s) vp = 1.41 RT M mol = = ( m s) v = 1.60 RT M mol = = ( m s) ( ). 1.,, 84
94 A., B., C., D.,.v, v p, v., ( ). A. v = v = v p B.v = v p < v C.v p < v < v D.v p > v > v 3., ( ). A. B., 4 C. 4, D ,, ( ). A.4% B.0.5 C.1% D.9% 5. ( ). pv A. MRT C. RT p B. MkT pv D. kt p 6.( ),, ( ). A. B. C. D. 85
95 7.,, ( ). A. B. C. D. 8., ( ). A. B., C. D. 9. ( ). A.41 B.14 C..831 D V 1 E 1, V E, V 1 V = 1, E 1 E ( ). A.56 B.53 C.1 D. 11. ( ) 34, ( ). A. B. 86
96 C. D A B, ( ). A. C , A B, ( ). A.v 0 B.v 0 C.v 0 D.v 0 B. D. 14.N, T, m,, f( v) ( ). ( ) A.m, T B.N C.N, m D.N, m, T 15., ( ). A. B., C. D., 16.1mol, T, A. 3 RT C. 3 kt B. 5 RT D.5 kt ( R, k ) 87
97 (,,, ) 1.3atm7 1atm, 7, atm g cm 3,. 3., 1cm 3. 4., 1mol J. 5.T. 6.,,.. 7.1mol i. 8. T 1 T, T T 1 =. 9. f( v), n, v p, nf( v) d v. ; v p f( v) d v 0 10., ;,,,. 1.( 1) 56.6L,, : 137atm, 300K,?( ), () 1atm, 33K, 88
98 ? : ( 1) pv = M = M M mol RT, M = = 10.1 (kg). () pv = M M mol V = MRT pm mol = RT pvmmol RT = 8.35m 3.,. 768mmHg, 748mm, 80mm. : 743mm,?(, ). : p 1, V 1 ; p, V, S, : p1 = ( ) = 0mmHg, V1 = 0.08 S V = [ ( ) ] S,, p 1 V 1 = p V, p = V 1 V p 1 = p = = 75(mmHg) = 18.8(mmHg), ( ) m 3, J.(1) ; ( ) 5.410,? : ( 1) N, E = i ktn p = nkt = N kt V : p = E iv = = ( Pa) () t = 3 kt E = N 5 kt : t = 3 E 5 N = = ( J), t = 3 kt, T 89
99 = t 3 k = = 36(K) atm,, 7 1m 3? : p = nkt = N kt V N = pv kt = = () 5., p = 1.0atm, T = 300K, (1) ; ( ) ; (3) ; (4)? : ( 1) p = n = nkt, p kt = () pv = M M mol RT : = ( m 3 ). = M V = PM mol RT = (3) = M V = Nm V = nm = pm kt : m = kt p = 1.3( kgm 3 ) = = (kg) (4) t = 3 kt = = ( J) K, (1 )1mol?() kg,?( ). : (1) E H e = 3 RT = = ( Jmol).E H = 5 RT = = ( Jmol), E O = 5 RT = ( Jmol). 90 () E He = M M mol i RT = = ( J)
100 E H = = ( J). E O = = ( J) , J, ( ). T = : E = N A E N A k i = i kt, = 300(K) 7( ) m s, : (1) ; ( ). : v p = 1.41 = 63.4.(1) v p H = 1.41 RT Mmol 1.41 RT = M mol v p = 89.4, RT RT M mol = () v = (m s), v = = 10 3 (m s) 10-3 RT = 1.73 M mol 1.41 v p = = RT = 1.60 M mol 1.41 v p = 567 (m s). 9., m s, (1) ; ( ),. : v = (1)= M V = = 0.18( kgm 3 ). pm mol RT = p RT M mol = () M mol = RT = RT = M mol M mol = ( kgmol), 91
101 . 10.,,,,? :, p 1 p = T 1 T, T = p p 1 T 1 = 73 = 546(K). v = 1.73 RT M mol = = 65(m s ). v = = 603( m s) Pa, g1.54l (). : pv = M M mol RT t = 3 kt : t = 3 RT N A = 3 pvm mol N A M = = ( J) 1.., 7 177,. : ( 1)?()? (3). : ( 1) T 1 = = 300K, T = = 450K, p 1 V 1 T 1 = p V T, V = 1 V 1, p = p 1 V 1 T V T 1 = 3 p 1. () t = 3 kt, t = 3 kt = ( ) 9
102 = ( J) (3) v = 1.73 RT M mol, M mol, v T, v v 1 = T T 1 = = m s, Pa,. : p = 1 3 nm v = 1 3 v, 3 pv = = 1.90 (kgm ). 1.A.C 3.D 4.A 5.C 6.D 7.B 8.C 9.A 10.A 11.D 1.A 13.D 14.A 15.ABC 16.B p 1 V 1 T 1 = p V T V V 1 = p 1 p T T 1 = = kg p = 1 3 nm v = 1 3 v = 1 3 M mol 3 RT M mol = RT M mol = RT P = = 0.08 (kg)
103 4.63.5J 5. 3 kt 6.1 pv = M RT, E = M i RT = i pv = i nk TV = i NkT, i, N, T, E. 7. i RT , v v + d v ; 0 v p 10. ; ; ; ; ; ;. 94
104 1.,, ( ),.,,,.,., ( pvt)..,.,,,,. p - V, p - V.. 3.., E = E( TV)., E = E( T).M, i, E( T) = M M mol i RT 95
105 4..,,.,..,,. (1), W = V pd V V 1. p - V,, W = V pd V = p( V - V1 ) V 1, () W = V pd V = M RTln V V 1 M mol V 1. Q = M M mol C( T - T 1 ) C, 1 1. C v 1. C P 1 C v = i R Cp = i + R
106 C p C v = C p = i + C v i 5. C p = C v + R a b,, b a, a,,, a b a, a,, a b.., , W Q, E - E 1 W+ Q = E - E 1. W, W = - W Q = W + E - E 1 Q W : Q > 0, Q < 0 ; W > 0 ; W < 0. 97
107 ,.SI, QW E,,1 ( cal) = 4.18 ( J).. (1) :,,. :. :.,.,. (). :,. :.,. ( 4.1 ) 4.1 Q V = M M mol C v ( T - T 1 ) E W M M mol C v ( T - T 1 ) 0 C v = i R p = M M mol C p ( T - T 1 ) M M mol C v ( T - T 1 ) P( V - V 1 ) M M mol R( T - T 1 ) C p = i + i R T = M M mol RTln V V 1 0 M M mol RTln V V 1 V V 1 = P 1 P pv = 0 M M C M v ( T - T 1 ) - C mol M v (T - T 1 ) mol 98
108 ,.,, E = 0, p - V,.. 1. ( p - V, ), := W Q1 = 1 - Q Q1, Q 1 : ; Q : ; W:... ( p - V, ), : = Q W = Q Q 1 - Q, Q 1 : ; Q : ; W : S = kln, k,.,., :S > 0 S,. 99
109 . 1.,E TWQ? (1) ; () ; (3). : ( 1) W = 0, Q v = E = M M mol p < 0, Q v < 0,E < 0,T < 0 () i RT = i Vp, W = pv,v < 0, W < 0. pv = M Mmol RT T < 0,E = M Mmol Q p = E + W p, Q p < 0 (3) i RT, E < 0. T = 0,V > 0, E > 0, W > 0. Q T > 0. : QWE,.. 41, a acb b, 334, 16. : (1) adb, 4,? () b ba a, 84,?? 100
110 (3) E d - E a = 40, ad, db? : ( 1), a b, adb acb, : E abc = E ab = E adb = Q acb - W acb = = 08( J), adb Qadb = Eadb + Wadb = = 50( J ) () b ba a, E ba = - E ab = 08J, Q ba = E ba + W ba = = - 9( J) Qba < 0,. (3) adb,, W adb = W ad = 4( J) ad, Q = E + W Q ad = E ad + W ad = = 8 ( J) Q ad > 0,. db Q db = Q adb - Q ad = 50-8 = 168( J ) : (1). () WQ, 101
111 Q W 3.1mol,,. 1.0L, 1atm.,,,,,. (1) p - V ; (). : ( 1) p - V 4. (),,, E = E d - E a = 0,.,, : a b : W = Wab + Wbc + Wcd W ab = p a ( V b - V a ) = p a ( V a - V a ) = p a V a = 1atmL b c : W bc = 0 c d : W cd = - = Pa 10-3 m 3 = J = - = - M M mol i R( T d - T c ) 3 R( T a - T c ) 3 ( pa Va - pcvc ) = - 3 ( pa Va - pa Va ) = 3 3 P a V a = = ( J) W = ( ) J = J, E = E d - E a = 0, 10
112 , W = Q. Q = Qab + Qbc + Qcd a b : Q ab = M M mol C p ( T b - T a ) = 5 ( T b - T a ) b a : = 5 ( p b V b - p a V a ) Q bc = M M mol C v ( T c - T b ) = 3 R( T c - T b ) = 3 ( p c V c - p b V b ) c d : Q cd = 0 Q = 5 ( p b V b - p a V a ) + 3 ( p c V c - p b V b ) + 0 = 5 p a ( V a - V a ) + 3 V a (4 p a - p a ) + 0 = 11 p a V a = W = Q = ( J) : (1). = ( J) () E = 0,,. 4. ( T 1 T ). :. 43, T1 T Q. : pv =. 43, p Q V Q = M M mol RT 1 p Q V Q 103
113 = M M mol RT, T 1 = T, T 1 T,,,. 5.1mol 1 ( p 1 V 1 ) 44 ( p V ), : (1) ; () ; (3). : pv = RT : T - T 1 = 1 R ( p V - p 1 V 1 ), E = E - E 1 = M M mol i R( T - T 1 ) = 5 R 1 R ( p V - p 1 V 1 ) = 5 ( p V - p 1 V 1 ) () 1 W = 1 ( p + p 1 ) ( V - V 1 ) = 1 ( p V - p 1 V 1 ) 104
114 (3) Q = E + W, Q = 5 ( p V - p 1 V 1 ) + 1 ( p V - p 1 V 1 ) = 3 ( p V - p 1 V 1 ) :,, E, W = S = V pd V, V 1 Q. 6.1mol 45, p = p 1, V 4 = V 1, : 1 p 1 V 1 T 1.: : p = p 1 V = V 1 T = p p 1 T 1 = T 1 3 : p 3 = p = p 1 V 3 = V 4 = V 1 T 3 = V 3 V T = 4T 1 4 : p 4 = p 1 V 4 = V 1 T 4 = V 4 V 1 T 1 = T 1 i = 3, C v = 3 R, C p = 5 R. 1 : Q1 = E - E1 = 3 R( T - T1 ) = 3 R( T1 - T1 ) = 3 RT1 Q 1 > 0, 3 : Q 3 Q 3 = M M mol C p ( T 3 - T ) = 5 R(4 T 1 - T 1 ) = 5 RT : > 0, Q 34 = E 4 - E 3 = 3 R( T 4 - T 3 ) = - 3 RT 1 105
115 Q : Q 41 < 0, Q 41 = M M mol C p ( T 1 - T 4 ) = 5 R( T 1 - T 1 ) = - < 0,, Q = Q 1 + Q 3 = 3 RT RT 1 = 13 RT 1, Q = Q 34 + Q 41 = 3 RT RT 1 = 11 RT 1 W = Q = Q - Q = RT1 - RT1 = RT1 W = S = ( p - p 1 ) ( V 4 - V 1 ) = p 1 V 1 = RT 1 5 RT 1 = W Q = 1 - Q Q = RT1 13 RT 1 = 15% 7. 46, 1mol, A B, C A,, : (1),. 106
116 () (C v = 5 R) : ( 1) ABC, A B C A, W. W = 1 ( p B - p C ) ( V C - V A ) = = ( J) () A B Q AB = E B - E A + W AB T B > T A, E B - E A > 0, W AB > 0, Q A B > 0,. B C Q BC = E C - E B T C < T B, E C - E B < 0, Q BC < 0,. C A Q CA = E A - E C + W CA W CA < 0, T A < T C, E A - E C < 0,, Q CA < 0,. Q = Q AB = W + Q Q = Q BC + Q CA = C v ( T B - T C ) + C P ( T C - T A ) = 3 R p BV B R - p C V C R + 5 R p C V C R - p A V A R = 6 p A V A + 5 p A V A = 17 p A V A = = (J ) Q = = ( J) 107
117 = 1 - Q = W Q Q = = 11% 8.E 1 E, ( ),??? :, E 1 E,,., Q = E + W,,., E p = E v, W p 0, W v = o, W p W v, Q p = Ep + Wp, Qv = Ev, Qp Qv.: E 1 E,,,. 9.,,, ( ),. 5,,,? : : V1 = V p1 = p T1 = T ( 1 ). pv = W : M 1 M 1mol = M M mol M M mol RT :, Q = E + M 1 5 M 1mol 108 Q v = E = M M mol RT = 5( J ) i RT
118 M 1 M 1mol RT = ( J) : Q v = E = M M mol 3 RT M M mol RT = M 1 M 1mol RT = ( J ) Q v = 3 = 3 ( J) 3. : (1),. () ( ). 10.? :.,,,. 1.( ). A. B. 109
119 C.,, D.1. He O CO,,, ( ). A.He B.O C.CO D. 3., ( ). A. C. B. D E p ( ). A. C. B. D , V 1 V ; A B, A C ; A D. ( ). A.A B C.A D B.A C D. 6. H He,, ( ). 110 A.H He B.He H C.H He D.He H
120 7., ( ). A. B., C., D. 8.( ). A., B., C. D. 9., ( ). A. B. C. D. 10., ( ). A. B. C. D , acd 00J, acbda, ( ). 111
121 A J B J C J D.1000J 1.( ). A.,, B.,, C.,, D.,, 13.,,.,, ( ). A., B., C., D., 14.,,,,, ( ). A., B., C., ( ) D. 15.A B, 410,, ( ). A. B. C. D. 16.ABCD, 4-11, ( ). 11
122 A.A C.C B.B D.D 17.,,., ( ). A. C. B. D. 18.Cp Cv, ( ). A. C. B. D. 19.,,, ( ). ( ). A. C. B. D. 0., ( ). A. C. B. D. 1., A. C. B. D..v f( v) : ( ). A.v B. v C.v D.v 3.T 1 1 mol T 1 mol, 113
123 , ( ). A. 1 ( T1 + T ) B. 1 3 ( T1 + T ) C. 1 8 (5 T T ) D., 4. ( p0, V0 ), ( p 1, V 0 ), A 1, ( p 0, V 0 ) ( p, V 0 ), A, ( ). A.A1 > A B.A1 < A C.A 1 = A D. 5.N, ( ). A m C m B m D m (,,, ) 1.p - V (1) ; () ; (3).. :. ; 3., A (p 1, V 1 ) 41 B (p 1,V 1 ), AB W = ; 114
124 E =. 4., ( i), Q, W, E, : W Q ; E Q 5., V 1 V 1 : (1) ; ( ) ; ( 3). ; ;. 6., ( ) Pa, m 3,,.( N A = mol - 1 ) Jmol - 1 K - 1, 10.0 K, J L 10 g v = 600 ms - 1, T = K, p = Pa mol ( ), 1 m 3, v = 10 ms - 1,, 80%, T = p = Pa. K, 11., V 1,, V, V v 1 v =. = V1, 1.p V p = p 0 - V ( p 0, ), v = 1 T 1, T V T =, T m ax =. 115
125 13., p - T 413. a b c d,., 14., P,, ( P). 1.10mol,, 09J, 1,. : i = 3, 1,T = 1 K, E = M M mol = 10mol, W = - 09J,t = M M mol Q = E + W = = - 84( J) i RT = = 15( J),.8g 0,?16g 0, 08J,?. E = E= : M = 8g, M mol = 3gmol, i = 5,t = 0,t = 0K, M C M v ( T - T 1 ) = 8 mol = 104( J). M= 16g, t = 0, T = = 93K,E= 08J. M i ( T - T 1 ) = 08( J) M mol T 1 = T - M mol E = 93 - i R 08 = 73(K) t 1 = T 1-73 = = 0 () 3., J, 116
126 ? E = :, i = 3, W = M 3 M mol R( T - T 1 ) = 3 W M M mol R( T - T1 ), Q = E + W = 3 W + W = 5 W = ( J) W = = 6000( J),E = 3 W = = 9000( J) 4.1mol 7 6L, Pa, 1L,. : i = 3, T 1 E = = = 300(K) M C M v ( T - T 1 ) = 0, W = M RT mol M 1 ln V mol V 1 = ln 1 6 = 173( J) Q = E + W = = 173( J) , 1mol.( 1) a b, () a c, c b. EQ W.( ) : Tb = T a = T b = 546K, T c = p c V c R (1)E = 0, W = = 3145( J) M Mmol pb Vb R = RT a ln V b Va Q = E + W = J = 3145( J ) ()E = 0, W = p c ( V b = = 73 (K) = ln = 546 (K), V c ) = 1atm.4L =.4atmL = = 69( J ) Q = E + W = = 69( J) 117
127 6.1mol, 300K, 10-3 m 3, : ( 1) 10 - m 3 ; () 10 - m 3 ; ( 3) p - V,. : M M mol = 1mol, i = 5, C v = 5 R, C p = 7 R,= C p C v = 7 5 = 1.4, T 1 = 300K, V 1 = 10-3 m 3, V 10 - m 3 (1) 1 V T 1 = V - 1 T, T = T 1 V 1 V Q = 0, W = - E = - M Mmol - 1 i R( T - T 1 ) = = = 119(K). = ( ) = ( J) () 1 3,3 W = W 13 + W 3 = M M mol RT 1 ln V V = ln = 5740 ( J) (3) p - V
128 , p - V,. 7.1mol, 416 abca, a b, b c, c a. : ( 1) ; () ; (3). : a b, W ab = 0, Q ab = E = T a ), T b > T a,. b c,e = 0, Q bc = W bc = M M mol M M mol RT b ln V c V b i R( T b - V c > C b,.c a, W c a = P a ( V a - V c ) < 0,E c a = M M mol i R( T a - T c ) T a < T c, E c a < 0, Q ca = E ca + W c a < T a = p a V a R = = 546(K), T b = T c = 546(K). = 73(K), T c = p c V c R = (1) W = W ab + W bc + W ca = 0 + M M mol RT b ln v c V b + p a ( V a - V c ) = ln ( )
129 = = 876( J) () E = 0, Q = W = 876J (3)= W Q R( T b - T a ) + RT b ln V c V b = 9.9% 8.417, a b, c d ; b c, d a. = 1 - Td T c - Ta - T b = C p C v. : a b : Qab = 0.b c : Qbc = Ebc = M M mol C v ( T c - T b ), T c > T b.c d : Q cd = 0.d a : Q da = M M mol C p ( T a - T d ), T a < T d,, Q da = M M mol C p ( T d - T a ) = 1 - Q Q = 1 - Q da Q bc = 1 - := 1 - T d T c - T a - T b M Cp ( Td M mol - Ta ) M Cv ( Tc M mol - Tb ) 9.1mol, 300K 350K. (1) ; ().:??? : ( 1), W = 0, Q = E = M 3 M mol RT = ( ) = 63( J).(),E = 63( J), W = p( V - V 1 ) = M M mol RT = 8.31( ) = 416( J), Q = E + W = = 1039( J). 10
130 a b c d ; b cd a.a b cd J,. : W = P V = = J Q = Q + W = J = W Q = = 4% 11.1 mol, ( P 0 V 0 T 0 ) : ( A) ; ( B),. (1) p - V 419 ; (). : ( 1) a b a c () a b: W = P V = P 0 V 0 E = 5 R T = 5 P V = 5 P 0 V 0 Q = E + W = 7 P 0 V 0 a c: W = V 0 Pdv = RTln = p0 v0 ln V 0 E = 0 Q = W = p 0 v 0 ln ( kg) 11
131 500 ms m, ( ). 40. : : ( mv) = m v 0 cos45= m 0 v 0 : p = N m 0 v 0 p = F t p = F S = Nm 0 v 0 St Pa = = 1.C.A 3.A 4.A 5.A 6.C 7.AB 8.D 9.B 10.ABD 11.B 1.D 13.B 14.C 15.A 16.C 17.C 18.C 19.C 0.A 1.B.D 3.C 4.A 5.D 1.; ;.., ; p 1 V 1 ; 0. 1
132 4. i + ; i i + 5. ; ; J ; ( 1 ) ( P 0 - v ) V P 0-3 P P ; P 0 - T ; 5%. 14. P. 13
133 ,,,.. 1. F q 1 q, r,., F = 1 q1 q r = 4 0 r r, q1 q 0 r r r, C N - 1 m -.. (1),, (). q 1 q, F ; q 1 q, F 1., q 0 F q 0,,, E, r E = F q 0 14
134 ,,.,,. NC Vm..,, E = E i = 1 4 q i 3 0 r i E i i q i.,. E =, d q = r 0 d q r d V, dv d S, d S d l, d l,,, ( ). E = d E d S ds, d E d S.. r i 15
135 E =Ed S S =Ecosd S S d S, E d S., E =Ed S S =Ecos d S S., S.,,,. 3., 0, Ed S = S : 1 0 q i (1) E Ed S S. E,.Ed S, S. (),.,,.,. 1. Ed L = 0 L,., 16
136 ,., q 0. a W a = q 0 a Ed l,,.,,.,,, a U a = W a q0 = Ed l a, P, U p = 0, a U a = p Ed l a,.. 3., 4. U ab = U a - U b = b Ed l a,, U a = U i = U a = n r 0 d q 0 i = 1 1. ( x,, q i r i 17
137 R, q) E = R) 1 qx i U = 4 0 ( x + R ) 3. 1 q 4 0 ( x + R ) 1 ( x,, E = E = 1 q r 4 0 r x i U = ( x + R - x) ( x + R ) 1 0 ( r R) 0 ( r < R) R, r. 4. E = 1 4 q 0 r 1 qr 4 0 R 3 r r ( r R) ( r R) 5. E = 0 r r U = U = U = ln r a 0 r 1 q 4 0 r 1 q 4 0 r 1 q 4 0 R ( r > R) ( r R) ( r R) q( 3 R - r ) ( r R) 8 0 R 3 r, r = r a. E = 6. 0 r r ( r R) r r ( r < R) 0 R U = ln r a 0 r ( r R) ( r - r ) (0 r < R) 4 0 R, R, r, r = ra 7. E = 18 r 0 U = - Er.
138 , r, :,,., 1. E = 0 Dd S = S q i S, S.. D = 0 r E : (1) ; (), r, E = E 0 r, r. 1. q U,,,, C = q U 19
139 .,, ( F ).. C = 4 0 R.., q U. C = q U qu. (1), C qu,. (). C 0 (3) r C = r C (1) C = 0 r S d S, d. () ( RB > RA ) C = 4 0 r R B RA RB (3) ( R B > R A ) R A L C = 0 r ln R B R A
140 1.. W e e = 1 DE = 1 E = 1 1 = e d V V = V E d V. 3. D, W e = q C = 1 qu = 1 CU 1. R, q, x P. : O, x,, 51, x P, ( x,0, 0). d l, d q = P, r = x + R d q P d E = = d q 4 0 r q R d l 4 0 ( x + R ) q d l R P, 51 x P. 131
141 E y = d E y = 0, E z = d E z = 0 P P x, E = E x = d E x = d Ecos= = d E x = R 0 qx 4 0 ( x + R ) 3, E = qd l 8 0 R( x + R ) qdl 8 0 R( x + R ) 3 qx 4 0 ( x + R ) 3 i x x + R i x., q > 0,, x > 0, E i ;, x < 0, E i.q < 0,. (1) x R, ( x E = + R ) 3 x 3, q i 4 0 x,. () x = 0, E = 0,. 13
142 .R,,. : O, x,, 5, x P, x,, r, d r, d S = rd r, d q = d S = rd r.1, P d E = = xd q 4 0 ( x + r ) 3 x rd r 4 0 ( x + r ) 3 d E x, d E y = 0, d E z = 0, d E = d E x P x, P, E = d E x = R 0 E x. x rd r = 1-0 ( x + r ) 3 0 x x + R (1) R,, i x. E = i 0 () x R, x x + R 1 - E =. q 4 0 x (3), +, R, O x P, OP = x.p E 1 R x 133
143 E = R xrd r i = 4 0 ( r + x ) 3 x 0 R + x i, P + - R, E = i x R + x i =. x 0 R + x i (1), d q () d q d E (3),, Ex Ey Ez, E. (4),,,., , R,,. : Oxy,, d S = R sind O O ( OO= d E = 1 yd q 4 0 ( y + a ) 3 d q = d S = R sin d y = Rcos, a = Rsin 134 E = d E = Rcos R sind ( R cos + R sin = 0 sin cosd= y) ) 3
144 y. 4.,, 54.. : ( 1) ( EA EB ) E = E A + E B = + = E, A B. () ( EA EB ) E = 0 5. d,,.. 55, Oxyz.,,,., x > 0. (1) P x < d, P P E 1 = x d - dx = x + d 0 0 P P d E x dx = 0 0 d - x 135
145 P E = E1 - E = x 0 () P x d E = d - d d x = d d = d 0 P P, P P,,, x,, S, 55. Ed S S =Ed S + Ed S = ES (1) P x < d q i = xs ES = xs 0 E = x 0 () P x > d q i E. = Sd ES = Sd 0 E = d 0 136
146 6.E R n, 56. S, S ES. : S,., ES + E R cos= 0 ES = - R cos 7., R,,. : ( 1),, 137
147 ,, 57. () P, P, l, r, ( ), 57(a). (3) Ed S s =Ed S + Ed S =Ecos0 d S = E rl P r > R, q i = Rl E rl = Rl 0 E = R 0 r = R, E = E. 0 r,. P r < R E = 0. q i = 0 8., R,, :., r 138
148 E = 1 lr 0 q i (1) r < R, q i = r l E = r 0 () r > R, q i = R l E = R r ,.,,,., ( ) ( ) ( ),,,,..,,,, ,,. a,. : () ( - ).,, 139
149 . 8 :, E1 = r1 0,, E = - r 0, E = E 1 + E = ( r 1 - r ) 0 58, r 1 - r = ai E = ai 0,, x.. ( a = 0), 10., q, R. :.., ( 140
150 59). P, E = 1 q E = 4 0 r 4 r E = 1 4 q 0 r q 0 r P, E = q= 4 r E = q 0 q r3 = qr3 R 3 3 R3 qr E = 4 0 R 3 1 qr ABCD, a = , b = , q 1 = q = , A B, 510. (1) q 0 = DC,?? () q 0 AB E DC F, : ( 1) q 0 q 0 D C,, DC,, DC., R 3 U D = q b + q 4 0 b + a = (V) 141
151 U C = q b + a () q1 = - q, q 4 0 b = (V) A = q 0 ( U D - U C ) = ( J) U E = 0, U F = 0 A = q 0 ( U E - U F ) = 0 1.R,,. : 511, r, d r, P d U = = d q = 4 0 r + x rd r 0 r + x P U = R 0 0 rd r 4 0 r + x r r + x d r = ( R + x - x ) 0 13.R, q, U R. 14
152 51 (a),, UR = Ed l = R q 4 R. 0 1 d r = r q 4 0 R 51 (b),, d q = Rsin Rd Rsin, Rd. r = R + x - Rxcos U p = d q rd r = Rxsind r = Rxsind d r 4 0 r = R sind 4 0 R x sind d r = R 0 x d r P, x > R, ( x - R) ( x + R), x = R. U x + R p x - R R 0 x d r = R 0 x = q R 4R 0 x = q 4 0 x U R = q 4 0 R 14.R, q, : 513,, 143
153 E = E = qr ( r < R) 4 0 R 3 q ( r > R) 4 0 r,. P UP = p R = Ed l = R r qd r 4 0 r qr 8 0 R 3 R r Ed r + + Q P U P = P 1 r Ed l = r Ed r R = R r R = E d r = r qrd r R 3 q (3 R - r ) 8 0 R 3 qd r = 4 0 r q 4 0 r :,.. 15.,,. : P r, E r. E = 0 r,., ra., P U = a Ed l p = r a r 0 r d r = ln r 0 r a r a = ln r a 0 r 1m, r 144
154 U = - ln r AB, R A R B ( R A < R B ), : AB q,,. E = 1 4 q 0 r AB U = B Ed l A = R B d r = 4 r R A 1 0 q q R B - R A 4 0 R A R B R B C = q U = 4 R B - R A 0 RA RB, (1) ; C = 4 0 R (), ; (3),.,, , R a + q. P r. P : P q P E 1, E. E = E 1 + E = 0 145
155 E = E 1 = P q. q 4 0 ( a + r - arcos ) , d, S, U, t, r,.. (1) E D; () q; (3) E 0 ; (4). : ( 1) U = Et + E 0 ( d - t) = Et + r E( d - t) U E = r d + (1 - r ) t, D = 0 r U 0 r E = r d + (1 - r ) t (), S, 516. Dd S = q D S = S q = S = DS = (3) 146 E 0 = r E = D = 0 r SU r d + ( 1 - r ) t r U r d(1 - r ) t
156 (4) C = q U = 0 r S r d + (1 - r ) t 19. R 1. R, r, l, , -,, (1) ; (). : (1) r, d r, l, d V = rld r : e = 1 0 r E = 1 0 r 0 r r dw e = e dv = W e rldr = 8 0 r r = R R 1 () ldr 4 0 r r = W e = 1 C = q W e = 1 = 8 0 r r ldr 4 0 r r l ln R 4 0 r R 1 q C l l ln R = 4 0 r R 1 0 r l ln R R 1 0.R,,. 147
157 : r < R, E = r 3 0 r > R, E = R3 3 0 r r, d r, dv = 4r d r r < R, W e = 1 0 E = 1 r r > R, We W e = 1 0 E = 1 R r = r 18 0 = rr r 4 We =d v V = R r 4r d r R = r5 = 4 R R R r R 6 18 R 0 r 4 4r d r , Q S q, q S, ( ). A. S, 148
158 B. S, C. S, D. S,.( ). A., B., C. E = Fq, q, q, F D., 3., ( ). A. E, B., E C. E, D., 4.0.3m abc, a 10-8 C, b 10-8 C, c E U ( ). A.E = 0, U = 0 C.E = 1000Vm, U = 0 B.E = 1000Vm, U = 600V D.E = 000Vm, U = 600V , S q, P S, S A q, qb, ( ). 149
159 A.S, P B.S, P C.S P D.S P 6. E U ( ). A.E, U B.U, E C.E, U D., E 7.N q, :,, O z P, 50, ( ). A., B., C. E z D. E z,, 8.F U ( ). A.F U B.F 1U C.F 1U D.F U 9., q, r a A r b r c B, A B, A (U = 0) ( ). q A.0 B. 4 0 r a 1 C. - 4 r b 0 q q q r D. c 4 0 r c 10., ( ). 150 A., U a = Ed l a
160 B. C., D. 11.( ). A. B. C., D. 1.,,,,, : ( ). A. C. B. D. 13.,, p 1 p : ( ). A.p1 p B.p 1 p p C. d r p 1 E D.p 1 p 14.R E r ( ). 15. q, d,, ( ). A.q B. - q 151
161 C. - q d D. - q 16.a Q, ( ). A. C. 1 Q B. 4 0 a 1 4 Q 4 D. 0 a 1 Q 4 0 a 1 Q , ;,,, ( ). A. B. C. D C, vm,, ( ). A m C m a B m D m (,,, ) 1. ;..qr B B R A A, , a, O a, q,. 15
162 4. e =, 0. 5.R, q( q < 0 ). S( ), ( 5), S E =,. 6.,.. 7., (< 0), E 0, E 0, 53,,. 8., = Ccm -,, U = V,. 9., C ( ) 0.1 m, J,. 10., Jm - 3.,,.., 153
163 11. 54, A B, 1 ( 1 > 0, > 0 ) X :, E 1 =,, E 11 = , Q( Q > 0) R 3 4 abc.q( q > 0 ) a c, ; q c. 13.AB,,, A, B.. A B r A r B A : B =. 14., 1,,, b, a, r < b ; , d,, 1 > 0, < 0,, ( ) q. a. q, q AB r.q q AB.q AB, 154
164 ? q q ( 56). : q F = AB. F d r d qq 4 0 ( a + r ) r a + r = qq r 0 ( a + r ) 3 d F d r = 0 ( a + r ) - 3 r = 0, r = < 0, r = a. a., q q, qa B q.q q, qab, AB.r a,..57,,.,., E,.r = cm, E = NC, kgm 3,. :, 4 3 r3 g + qe = 0, 155
165 q = E r3 g = ( ) = ( C) 3., m,. 79, ( ), + e = C, kg m ( ),. : N, m s 4. ( ).,,, m. m n = kg, m e = kg, e = C, G = Nm kg.(1 ) ; ()?( 3) ( 58). : ( 1) F = 1 q 1 q = ( ) 4 0 r ( ) = (N) () F= G m 1 m r = ( ) = (N) F F = = (3) F, F = 156
166 mv R v = FR m = = (m s ) ,.( 59 )? : E y, q, v0 x = v0 y = v 0 x,, tcos tsin+ Eqt m t, y =.. v 0 xtan+ Eq mv 0 cos x E ( ), m,,, m, + e = C,,., 3 kt( k =
167 JK, T ),? : E k = qu = q 4 0 r = ( ) = ( J) = ( ev) E k = 3 kt T = E k 3 k = = (K) 7. p = ql, + q A. A r. r l, A - q,? q : 4 r r + q 4 0 r - l l l - - r - r + l r l, ql, E = 0 r 3 1 r + l l = p 0 r 3 ; q lr 4 0 r l - 8., a, + -,. : F = 4 0 a 9. R = 5.0cm, q = C..P, P x.x = 0 x R,?? ( 530)? : ( 1), P E = 158 d Ecos= 1 4 d q x 0 r r = R 0 x q ( x + R ) 3 R d l
168 = qx 4 0 ( x + R ) 3 x = 0, E = 0 x R, ( x + R ) 3 x 3, E = q 4 0 x, () d E d x = d d t qx 4 0 ( x + R ) 3 = 0 x = R R E max E max = q R : x = 3.54cm, = 0.69Vm 10., 0.50m,.0cm, C, ( 531). := tan E = E x = tan = 1.45 = R sind 159
169 . = 0.7Vm 11., 53,, R, O. : O : (1) : d E = d q = d 4 0 R 4 0 R E 1 = E 1 x = 0 d E 1 x = () O E = E x = - d E x = - 0 R O E = 0 R 0 = - 0 sind= 0 R Rd x 4 0 ( R + x ) 3 0 R - 0 R = : E =, P E. > 0, 0 r E ; < 0, E , b, 160
170 ., c P. :,.,, E = P E = E y 0 r,. d E = d E y = d x 0 r cos= cd x 0 ( x + c ) = b d E = cd x - 0 ( c + x ) = tan - 1 b 0 c b , m = g, q = C,, 30,. : mg + T + F = 0, F = Eq = q, 0 Tsin30= q, Tcos30= mg, tan30= q 0 0 mg, = 0 mg q tan30= = ( Cm). 15.q 1 q q 3 q tan C, 161
171 , O 5cm.? (1) O ; () q 0 = 10-9 C O, (3)? : ( 1)0, V; () J; (3) J. 16., + 4 q - q, l,,? 4 q : 4 0 ( l - x) E = 4 q 4 l q l 5 = + q 4 0 x = 0, 4 l - x = 1 x = 0, x = l 5 q l = 15 q 16 0 l q, l 17. R, = 0 sin, 0, R x, 535, O. :, O d E = d q = d l = 0 Rsind d q = 0 sind 4 0 R 4 0 R xy d Ex d E y = - d Esin, E x E y 16 = d E x = - = d E y = R R 0 = - d Ecos sincosd= 0 sin d= R
172 E = E y i + E y j = R j ,. u 1, R 1, u, R, r ( R 1. E = : P r( R 1 0 r, P R U 1 - U = R 1 U 1 - U P = r R 1 U P = U 1 - ( U 1 - U ) < r < R ) < r < R ), 0 r d r = ln R 1 0 R 0 r d r = ln r 0 R1 ln( rr 1 ) ln( R R 1 ) 19.Q A, R, q, u a, P : u p =? ( 537 ). : P U P = P R Ed l = r q 4 0 r + u a E 1 d l = P E d l 163
173 = R r q d r + U 4 0 r 0 =,. q 4 0 r - q 4 0 R + U a 0.R,, AB, A O x 1, B O x. m, q A, A B ( 538)? : U = d U = R 0 = R 0 R + x d l 4 0 R + x q A B, q( U A - U B ) = 1 mv B v = q( UA - UB ) m = qr m( x 1 + R ) ( x + R ) cm A, C. 0cm B A. 15cm 5cm?AB,. : ( 1) : 164
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(CIP) /,,. :,2005 ( ) ISBN 7 81010 879 4................R72 CIP (2005) 076544 ( ht tp: / / www. tcmonline. com. cn) ( 1200 201203) 850 mm 1168 mm 1/ 3
(CIP) /,,. :,2005 ( ) ISBN 7 81010 879 4................R72 CIP (2005) 076544 ( ht tp: / / www. tcmonline. com. cn) ( 1200 201203) 850 mm 1168 mm 1/ 32 14 339 1 4 160 2005 11 1 2005 11 1 ISBN 7 81010 879
WL100079ZW.PDF
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: (),,, (CIP) /. :, 2002.11 21 ISBN 7-5045 - 3715-2... - - - : - - - : -. TU767 CIP (2002)090133 ( 1 : 100029) : * 787 1092 16 23.5 583 2003 2 1 2003
: (),,, (CIP) /. :, 2002.11 21 ISBN 7-5045 - 3715-2... - - - : - - - : -. TU767 CIP (2002)090133 ( 1 : 100029) : * 787 1092 16 23.5 583 2003 2 1 2003 2 1 : : 38.00 : 64929211 : 64911190 : http : / / www.
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