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( )
( ) 158 <br />
<br />
( ) ( <br />
, 1999 ) , <br />
<br />
: ( ) <br />
:<br />
:<br />
:<br />
:<br />
:<br />
:<br />
:<br />
:<br />
<br />
( , 100084)<br />
ht tp: / / www. t up. tsinghua. edu. cn<br />
<br />
8501168 1/ 32: 15625: 391 <br />
2000 7 1 2001 12 4 <br />
ISBN 7302038104/ O228<br />
30014000<br />
30. 00 <br />
( )
1 ( 1)<br />
1 ( 1)<br />
2 ( 19)<br />
3 ( 42)<br />
4 ( 61)<br />
5 ( 89)<br />
6 ( 111)<br />
2 ( 129)<br />
1 ( 129)<br />
2 ( 138)<br />
3 ( 158)<br />
4 ( 181)<br />
3 ( 195)<br />
1 ( 195)<br />
2 ( 215)<br />
3 ( 218)<br />
4 ( 240)<br />
5 ( 250)<br />
6 ( 269)<br />
7 ( 277)<br />
8 ( 294)<br />
9 ( 321)<br />
10 ( 329)
11 ( 345)<br />
4 ( 355)<br />
1 ( 355)<br />
2 ( 383)<br />
3 ( 402)<br />
4 ( 417)<br />
5 ( 430)<br />
5 ( 439)<br />
1 ( 439)<br />
2 ( 453)<br />
3 ( 459)<br />
4 ( 477)<br />
5 ( 483)
1 <br />
11( 118) <br />
1920 021 / a ( [ ] , a )<br />
, 180 <br />
, ? ( <br />
1054 <br />
)<br />
<br />
1054 <br />
1920- 180/ 021= 1060 <br />
12: <br />
27410 9 l. y.<br />
( l. y. , 1l. y. = 94610 1 5 m ) , 39310 7 m/ s <br />
, <br />
? ( , <br />
)<br />
<br />
94610 1 5 27410 9<br />
39310 7 = 65910 17 s= 20910 1 0 a<br />
20910 1 0 <br />
1
13 1 <br />
200km, ? <br />
1 180m / s 2 , 1 <br />
v = 2gh = 218020010 3 = 849 m/ s<br />
14, 180s <br />
1600km/ h , <br />
25 g ? 180s ?<br />
<br />
a =<br />
v t<br />
=<br />
25 g <br />
160010 3<br />
3600180 = 247102 m/ s 2 25 g<br />
180s <br />
s = v 2 t = 1600103<br />
23600 180 =<br />
400 m<br />
15, 90k m/ h <br />
, 80m <br />
65k m/ h , <br />
070s( ) , <br />
75m/ s 2 , ? <br />
, ?<br />
v1 0 = 90km/ h= 25m/ s, v 20 = 65k m/ h = 18m / s, s0 =<br />
80m , t = 070s, a = 75m/ s 2<br />
, <br />
s0 = s0 - ( v10 + v2 0) t = 80 - ( 25 + 18)070<br />
= 50 m<br />
<br />
2<br />
s1 = v2 1 0<br />
2a = 25 2<br />
275 =<br />
417 m
s2 = v2 2 0<br />
2a = 18 2<br />
275 =<br />
217 m<br />
s1 + s2 > s0 , <br />
t , <br />
s0 = v 10t -<br />
, <br />
<br />
1<br />
2 at 2 + v2 0t -<br />
50 = ( 25 + 18) t - 75t 2<br />
t =<br />
<br />
1<br />
2 a t 2 = ( v1 0 + v2 0) t - a t 2<br />
162 s, 411 s( )<br />
v 1 = v 10 - a t = 25 - 75162 = 129m / s = 46 km/ h<br />
16 1200m , <br />
, 200km/ h<br />
50m , <br />
18km / h <br />
g / 2 , ?<br />
h 0 = 1200m, v1 = 200k m/ h = 556m/ s, v2 =<br />
18k m/ h = 5m / s, h2 = 50m<br />
<br />
t 1 =<br />
<br />
v 1<br />
h 1 =<br />
v1<br />
g / 2 =<br />
v 2 1<br />
2g / 2 = v 2 1<br />
g =<br />
<br />
t 1 = h 0 - h 1 - h 2<br />
v1<br />
=<br />
2556<br />
98<br />
= 113 s<br />
5562<br />
98 = 315 m<br />
1200 - 315 - 50<br />
556<br />
= 150 s<br />
3
v 2 <br />
t 2 = h 2<br />
v 2<br />
<br />
= 50<br />
5 = 10 s<br />
t = t1 + t 1 + t2 = 113 + 150 + 10 = 363 s<br />
17q= 280L/ min,<br />
v0= 26m/ s, <br />
? ?<br />
<br />
h = v 0 2<br />
2g = 26 2<br />
298 =<br />
<br />
t = 2v 0<br />
g = 226<br />
98<br />
345 m<br />
= 531 s<br />
t <br />
<br />
V = qt = 280531/ 60 = 247 L<br />
18v0<br />
= 150m/ s ,<br />
( 1) t1 = 10s , h =<br />
110m , ;<br />
( 2) t2 = 13s , h =<br />
110m , <br />
( 1) t , <br />
<br />
, <br />
4<br />
h = v 0t -<br />
11 = 15t -<br />
1<br />
2 g t2<br />
1<br />
2 98t 2
t 1 = 184 s, t 1 = 122 s<br />
<br />
t u = v 10/ g = 15/ 98 = 153 s<br />
t 1 > t u, ; <br />
t 1 < t u, <br />
v 20 v20t 1 t1<br />
, <br />
<br />
h = v 20( t 1 - t 1) -<br />
1<br />
2 g ( t 1 - t 1) 2<br />
v2 0=<br />
,<br />
h + 1 2 g ( t 1 - t 1) 2<br />
= 172 m/ s<br />
t1 - t 1<br />
=<br />
11 + 1 2<br />
98( 184 - 1)<br />
2<br />
184 - 1<br />
h +<br />
v2 0 =<br />
= 511 m/ s<br />
1<br />
2 g ( t 1 - t 1) 2<br />
t1 - t 1<br />
=<br />
11 + 1 2<br />
98( 122 - 1)<br />
2<br />
122 - 1<br />
( 2) t 2 = 13s > t 1 , <br />
t 1 , <br />
h + 1 2 g ( t 1 - t 2) 2<br />
v2 0 =<br />
t1 - t 2<br />
= 230 m/ s<br />
=<br />
11 + 1 2<br />
98( 184 - 13)<br />
2<br />
184 - 13<br />
19 , <br />
1<br />
, x = ut + u - t ln ( 1 - bt) , <br />
b<br />
u , , b <br />
<br />
5
( 1) ;<br />
( 2) ;<br />
( 3) u = 3010 3 m/ s, b = 7510 - 3 / s, 120s<br />
, t = 0s t = 120s ;<br />
( 4) t = 0s t = 120s <br />
( 1) v =<br />
dx = - uln ( 1 - bt)<br />
dt<br />
( 2) a = dv<br />
dt = ub<br />
1 - bt<br />
( 3) t = 0s , v = 0;<br />
t = 120s , v = - 310 3 ln( 1 - 7510 - 3 120)<br />
= 69110 3 m / s<br />
( 4) t = 0s , a = 3103 7510 - 3<br />
t = 120s , a = 3103 7510 - 3<br />
1 - 7510 - 3 120<br />
1<br />
= 225 m/ s 2<br />
= 225 m/ s<br />
2<br />
110 x y , <br />
x = 2t, y = 4t 2 - 8( SI) <br />
;<br />
( 1) <br />
( 2) t1 = 1s t 2 = 2s , <br />
<br />
( 1) t, <br />
<br />
y = x 2 - 8<br />
11 <br />
( 2) r = 2ti + ( 4t 2 - 8) j<br />
v =<br />
dr<br />
dt =<br />
2i + 8tj<br />
11 110<br />
<br />
6
a =<br />
du<br />
dt = 8j<br />
t = 1s ,<br />
r 1 = 2i - 4j , v 1 = 2i + 8j , a1 = 8j ;<br />
t = 2s <br />
r 2 = 4i + 8j , v 2 = 2i + 16j , a 2 = 8j<br />
111 12 , h , <br />
, v0, s <br />
<br />
12 111 <br />
<br />
l , v 0 = -<br />
dl/ dt12<br />
<br />
s = l 2 - h 2<br />
v =<br />
ds<br />
dt =<br />
<br />
<br />
a =<br />
dv<br />
dt = -<br />
l dl<br />
l 2 - h 2 dt = - s 2 + h 2<br />
s<br />
d<br />
dl<br />
l<br />
l 2 - h 2 v 0<br />
v 0<br />
dl<br />
dt = - h 2 v0<br />
a , <br />
s 3<br />
2<br />
7
112 v 0 =<br />
110km/ h, <br />
=<br />
45 ( 13) <br />
( 1) <br />
L ?( <br />
)<br />
( 2) , <br />
L = 165m, <br />
?<br />
13 112 <br />
( 1) 13 , <br />
x =<br />
Lcos45 = v 0t, y = Lsin45 = 1 2 g t 2<br />
, <br />
<br />
t =<br />
2v0<br />
g<br />
2<br />
v 0t<br />
L =<br />
cos45<br />
= 2 v0<br />
g cos45<br />
= 22 11010 3 2<br />
= 269 m<br />
98 2 3600<br />
( 2) L , <br />
<br />
113 <br />
v0 = 25m/ s, <br />
L =<br />
50m , h = 13m <br />
?<br />
?<br />
14 , <br />
<br />
8<br />
14 113
y = x tan -<br />
cos 2 = ( 1 + tan 2 ) - 1 <br />
gx 2<br />
2 tan 2 - x tan+<br />
2 v0<br />
1<br />
2<br />
g x 2<br />
v 0 2 cos 2 <br />
g x 2<br />
2 v 0 2 + y = 0<br />
, <br />
2<br />
tan = v0 g L 1 1 -<br />
, <br />
1 -<br />
2g<br />
v 0<br />
2 h + g L 2<br />
2g<br />
2 v0 2<br />
v0 2 h + g L 2<br />
2 = - 0022 < 0<br />
2 v 0<br />
, , <br />
<br />
<br />
1 -<br />
, , <br />
L =<br />
h v 0 2<br />
2g - g L 2<br />
2 v 0 2 =<br />
123m <br />
2g<br />
h + g L 2<br />
0<br />
v0 2 2 v0 2<br />
25 2<br />
298 - 9850 2<br />
225 2 = 123 m<br />
50m , <br />
= arct an v 0 2<br />
g L = arct an 25 2<br />
9850 =<br />
519<br />
114 , 1997 6 1 <br />
( 121) 265m, <br />
, 150km / h, 5, <br />
57m, <br />
?<br />
( 1) , <br />
9
( 2) ?<br />
( 3) 100m, <br />
?<br />
( 4) ?<br />
15 114 <br />
15 , s = 265m, v0 = 150km/ h, = 5 ,<br />
L = 57m, h 1 = 10m<br />
( 1) <br />
<br />
a = v 2<br />
0<br />
2s = 1<br />
2265<br />
t1 = 2s<br />
v 0<br />
( 2) <br />
t 2 =<br />
L<br />
v 0cos =<br />
15010 3<br />
3600<br />
( 3) <br />
2<br />
= 328 m / s 2<br />
= 22653600<br />
15010 3 = 127 s<br />
573600<br />
15010 3 cos5<br />
= 137 s<br />
2<br />
H = h 1 + v0 sin 2 <br />
= 10 + ( 15010 3 ) 2 sin 2 5<br />
2g<br />
3600 2 298 = 1067 m<br />
( 4) <br />
h 2 - h 1= v 0sin t 2 -<br />
10<br />
1<br />
2 gt 2 2<br />
= 15010 3<br />
sin5137 -<br />
3600<br />
1<br />
2 981372
= - 422 m<br />
422m<br />
115<br />
610 4 r/ min , 10cm<br />
?<br />
<br />
<br />
2 r<br />
g = 4<br />
2 2 r<br />
g<br />
= 4<br />
2 ( 610 4 ) 2 01<br />
= 410 5<br />
60 2 98<br />
116 399 <br />
<br />
<br />
v =<br />
<br />
a =<br />
2 RE<br />
T<br />
cos = 2<br />
2<br />
2<br />
R Ecos=<br />
T<br />
= 25910 - 2 m/ s 2<br />
6378103<br />
86400<br />
cos399 = 356m / s<br />
2<br />
2<br />
637810 3 cos399<br />
86400<br />
117 , <br />
?<br />
<br />
<br />
a =<br />
v= 2<br />
T R S E = 2<br />
31610 7 1510 11<br />
= 29810 4 m/ s = 29. 8 k m/ s<br />
2<br />
2<br />
R S E =<br />
T<br />
= 59310 - 3 m/ s 2<br />
2<br />
2<br />
1510 11<br />
31610 7<br />
118( ) <br />
2910 4<br />
l. y. ?<br />
11
a =<br />
v= 2<br />
T R G S =<br />
229104<br />
94610 15<br />
2510 8 31510 7<br />
= 2210 5 m / s = 220 km / s<br />
2<br />
2<br />
T<br />
RG S =<br />
= 1810 - 1 0 m/ s 2<br />
( 2 ) 2 2910 4 94610 15<br />
( 2510 8 31510 7 ) 2<br />
119, , <br />
2210 6 m/ s, 053<br />
10 - 1 0 m<br />
<br />
=<br />
<br />
a =<br />
v<br />
2 r = 2210 6<br />
= 6610 1 5 H z<br />
205310 - 10<br />
v2<br />
r<br />
= ( 22106 ) 2<br />
05310 - 10 = 9110 22 m/ s 2<br />
120240m, <br />
<br />
?<br />
<br />
v 2<br />
Rg =<br />
121 R =<br />
( 3108 ) 2 2<br />
= 2410 14<br />
24098<br />
400m <br />
, v = 10m/ s, a t =<br />
02m/ s 2 ?<br />
16 , <br />
12<br />
a n = v2<br />
R = 10 2<br />
400<br />
= 025 m/ s<br />
2
16 121 <br />
a = a 2 n + a 2 t = 025 2 + 02 2 = 032 m/ s 2<br />
<br />
<br />
180 - = 180 - arctan a n<br />
a t<br />
= 180 - arctan 025<br />
020 =<br />
122 R = 10m , <br />
<br />
, A ( 17) <br />
, A , t =<br />
20s h = 04m<br />
t = 3s , <br />
<br />
A <br />
a =<br />
2h = 204 = 02 m / s 2<br />
t 2 2 2<br />
t = 3s <br />
, <br />
a t = 02 m/ s 2<br />
t = 3s <br />
128 40<br />
17 <br />
122 <br />
13
an = v<br />
2<br />
R =<br />
( a t ) 2<br />
R = ( 023) 2<br />
10<br />
= 036 m/ s 2<br />
<br />
123( CD) R 1 = 22cm,<br />
R 2 = 56cm ( <br />
18) , N = 650<br />
/ mm CD , <br />
, <br />
, <br />
v = 13m/ s <br />
( 1) ?<br />
18123 <br />
( 2) r = 50cm , <br />
?<br />
( 1) r ,<br />
dr 2 r N dr <br />
dt = 2 r N dr/ v<br />
T = dt = <br />
R 2<br />
R 1<br />
( 2) <br />
<br />
=<br />
d<br />
dt = -<br />
= -<br />
2 rN dr<br />
v<br />
= N v ( R2 - R 2 1)<br />
= 65010 3 ( 0056 2 - 0022 2 )<br />
13<br />
= 41610 3 s = 694 min<br />
v<br />
r 2<br />
=<br />
dr<br />
dt = -<br />
v r<br />
v<br />
r 2<br />
= 13<br />
005 =<br />
26 rad/ s<br />
v<br />
2 rN = - v 2<br />
2 N r 3<br />
13 2<br />
= - 33110 - 3 rad/ s 2<br />
265010 3 005 3<br />
124 12m/ s 2<br />
14<br />
,
05s 15m <br />
<br />
a = 12m/ s 2 , t 0 = 05s, h 0 = 15m<br />
19 , , , <br />
<br />
v 0 = at 0 = 1205 = 06 m/ s<br />
t , <br />
, <br />
h = v0t + 1 2 g t 2<br />
<br />
<br />
h = v0t + 1 2 a t 2<br />
19 <br />
124 <br />
h 0 = h - h = 1 2 ( g - a ) t2<br />
<br />
t =<br />
<br />
2h 0<br />
g - a = 215<br />
98 - 12 = 059 s<br />
h= v 0t + 1 2 g t2<br />
= 06059 + 1 2 980592<br />
= 206 m<br />
125 30m / s , , <br />
? <br />
344m/ s<br />
v1 = 30 m/ s, v 2 = 344 m/ s<br />
15
v E = v1 + v2 = 30 + 344 = 374 m / s<br />
<br />
vW = v2 - v1 = 344 - 30 = 314 m/ s<br />
<br />
2<br />
2<br />
vN = v 2 - v 1<br />
= 344 2 - 30 2 = 343 m / s<br />
126 18km/ h , <br />
36k m/ h , <br />
120 , <br />
v m 1 = 18km/ h, v m 2 = 36km/ h, = 90 , = 120v rm 1<br />
v rm 2 , v r <br />
110 <br />
<br />
110 126 <br />
vrm 1 + v m1 = vr = vrm 2 + v m 2<br />
<br />
<br />
16<br />
vr = vm 2 = 36 km / h<br />
= 90 - 60 = 30
30<br />
127 A v A = 1000km/ h<br />
( ) , <br />
B v B = 800km/ h <br />
( ) 30 <br />
A B B <br />
A <br />
<br />
111 = 60<br />
A B <br />
v A B = v 2 A + v 2 B - 2v AvBcos<br />
111 127 <br />
= 1000 2 + 800 2 - 21000800cos60<br />
= 917 m/ s<br />
<br />
=<br />
arccos<br />
40 56<br />
vB cos30<br />
= arccos 8000866<br />
vA B<br />
917<br />
B A v BA = - v A B , <br />
vB A =<br />
40 56<br />
917 m / s<br />
= 40 56<br />
<br />
128 150k m/ h , <br />
, 750km/ h <br />
950km/ h <br />
<br />
vW = 150km/ h , v 1W = 750km/ h , v 21 = 950km / h, = 45<br />
v 1 v2 , <br />
112 <br />
17
112 128 <br />
v 1 = v 2 W + v 2 1W = 150 2 + 750 2 = 765 km/ h<br />
1 = arctan vW<br />
v1W<br />
= arct an 150<br />
750 = 113<br />
2 = 45 - 1 = 45 - 113 = 337<br />
v2= v 2 1 + v 2 2 1 - 2v 1v2 1cos 2<br />
= arct an<br />
= 765 2 + 950 2 - 2765950cos337<br />
= 527 km / h<br />
v 1W - v2 1sin<br />
= arctan<br />
v 21cos - v W<br />
750 - 950sin 45<br />
950cos45 - 150 = 8 32<br />
527km/ h 8 32<br />
18
2 <br />
21F M ( 21) <br />
F , <br />
k s<br />
( 1) , F ? , F<br />
?<br />
( 2) , F <br />
?<br />
( 1) , <br />
, ,<br />
<br />
x : F mi ncos - f m a x= 0<br />
y : N - F m insin - Mg = 0<br />
f m a x= sN<br />
2121 <br />
F <br />
F mi n=<br />
sMg<br />
cos - ssin <br />
, F <br />
F =<br />
kMg<br />
cos - ksin<br />
( 2) F m in , cos - ssin0, F m in <br />
, , <br />
<br />
<br />
cos - ssin 0<br />
19
= arct an 1 s<br />
22m= 050kg = 30 <br />
( 22) <br />
( 1) a = 20m/ s 2 ,<br />
?<br />
( 2) , ?<br />
2222 <br />
( 1) , <br />
x : T cos - N sin = ma<br />
y : T sin + N cos - mg = 0<br />
, <br />
T = m( a cos + g sin ) = 05( 2cos30 + 98sin 30 ) = 332 N<br />
N = m( g cos - a sin ) = 05( 98cos30 - 2sin 30 ) = 375 N<br />
, <br />
N = N = 375 N<br />
( 2) N = 0, <br />
<br />
T cos = ma , T sin = mg<br />
a = g / t an = 98/ t an30 = 170 m/ s 2<br />
2323 A , B , 3 <br />
: m 1= 200g, m 2= 100g, m 3= 50g<br />
( 1) <br />
20
( 2) T 1 T 2 <br />
<br />
( 1) , <br />
a1 a2 a3, <br />
23 a m 2<br />
B , <br />
a2= a - a1, a3= a + a1<br />
<br />
m1, m 2 m 3 <br />
:<br />
m 1g - T 1= m 1a 1<br />
m 2g - T 2= m 2a 2= m 2( a - a1)<br />
m 3g - T 2= - m 3a 3= - m 3( a + a1)<br />
B , <br />
T 1- 2T 2= 0<br />
4 , <br />
23<br />
23 <br />
a 1 =<br />
m1m 2+ m1m 3- 4m 2m 3<br />
g <br />
m1m 2+ m1m 3+ 4m 2m 3<br />
0201+ 02005- 401005<br />
=<br />
0201+ 02005+ 401005 98<br />
= 196 m/ s 2<br />
2m1m 2- 2m 1m 3<br />
a =<br />
m 1m 2+ m1m 3+ 4m 2m g<br />
3<br />
20201- 202005<br />
=<br />
0201+ 02005+ 401005 98<br />
= 392 m / s 2<br />
<br />
a 1, a 2, a 3<br />
a 2= a - a 1= 392- 196= 196 m/ s 2<br />
a 3= a + a 1= 392+ 196= 588 m/ s 2<br />
, 23 <br />
21
( 2) T 1= m1( g - a 1) = 02( 98- 196) = 157 N<br />
T 2= m2( g - a 2) = 01( 98- 196) = 0784 N<br />
24 5000kg 1500kg <br />
060m/ s 2<br />
<br />
( 1) ?<br />
( 2) ?<br />
( 1) 24 <br />
, <br />
F - ( M+ m) g = ( M+ m) a <br />
F = ( M+ m) ( g + a )<br />
= ( 5000+ 1500)( 98+ 06)<br />
24<br />
= 67610 4 N<br />
24 ( 2) , <br />
T - mg = ma <br />
T = m( g + a ) = 1500( 98+ 06)<br />
= 15610 4 N<br />
2525 , <br />
<br />
( 1) , <br />
?<br />
( 2) 10% , <br />
? 75kg<br />
, <br />
2T - Mg = Ma<br />
T = M( g + a ) / 2<br />
( 1) , a = 0, <br />
T = Mg / 2= 7598/ 2= 368 N<br />
22<br />
25<br />
25
( 2) T = 11T = 11Mg / 2, <br />
2T <br />
a = - Mg ( 11- 1) Mg<br />
= = 01g = 098 m/ s 2<br />
M<br />
M<br />
26 m <br />
( 26) , <br />
( 1) ;<br />
( 2) <br />
( )<br />
2626 <br />
26 , , <br />
x : T 1cos = T 2<br />
y : T 1sin = mg / 2<br />
, <br />
( 1) <br />
( 2) <br />
T 1= mg / ( 2sin )<br />
T 2= mg / ( 2tan )<br />
27 A B m A = 150kg, mB = 285kg,<br />
, = 30( 27) A B<br />
kA = 015, kB = 021<br />
( 1) A B <br />
( 2) <br />
( 3) A B , ( 1) ( 2) ?<br />
23
A , <br />
2727 <br />
, x , <br />
B, <br />
<br />
m Ag sin - kA mgcos = mA aA <br />
mB gsin - k Bmgcos = mBa B <br />
a A = g ( sin - k A cos ) = 98( sin30 - 015cos30 ) = 363 m/ s 2<br />
a B = g ( sin - k Bcos ) = 98( sin 30 - 021cos30 ) = 312 m/ s 2<br />
( 1) 27 , A , B a A > a B<br />
, , aA = aB = a T T A <br />
B ( T = T ) , , x <br />
A :<br />
B:<br />
<br />
m A gsin - k A mA gcos - T = mA a<br />
m Bg sin - kB mBg cos + T = m Ba<br />
k Am A + k BmB<br />
a = g sin -<br />
g cos<br />
m A+ m B<br />
01515+ 021285<br />
= 98sin30 -<br />
98cos30<br />
15+ 285<br />
= 329 m/ s 2<br />
24
( 2) 27 <br />
T =<br />
mA gsin - kA m Ag cos - mA a<br />
= 1598sin30 - 0151598cos30<br />
- 15329 = 051 N<br />
( 3) , A , B , a A > a B , <br />
, T = 0, A B <br />
a A = a A = 363 m / s 2 , aB = aB = 312 m/ s 2<br />
28 M = 150k g , m =<br />
245k g, <br />
= 025, ?<br />
2828 <br />
28 , f A B = f BA = mg , f B =<br />
( M+ m) g m, , x <br />
a m= g<br />
mg = ma m<br />
M, , x <br />
F - ( M+ m) g - mg= MaM<br />
F = MaM + ( M+ 2m) g<br />
, aM a m<br />
F <br />
F Mam+ ( M+ 2m) g = 2 ( M+ m) g<br />
F m in= 2 ( M+ m) g = 2025( 150+ 245)98<br />
25
= 194 N<br />
29, v= 90km/ h <br />
s= 35m ,<br />
110 , <br />
?<br />
v= 90km/ h = 25m/ s, <br />
, f = mg,<br />
s= v 2 / 2a = v 2 / 2 g <br />
2929 <br />
, 29 , , <br />
x : mgcos - mg sin = ma <br />
<br />
<br />
a = g cos - g sin<br />
= v2<br />
2s cos - g sin<br />
s = v 2<br />
2a <br />
= v 2<br />
25 2<br />
=<br />
= 393 m<br />
v 2<br />
s cos 25 2<br />
- 2g sin 1- 2981<br />
35 10<br />
210k 1 k2<br />
210210 <br />
( 1) ( 210( a ) ) , k <br />
k= k 1k2<br />
k1+ k 2<br />
( 2) ( 210( b) ) , k <br />
26
k= k1+ k 2<br />
( 1) , F , x<br />
= x 1+ x 2F = k 1 x 1= k2 x 2 <br />
k= F x =<br />
F<br />
= 1<br />
x 1+ x 2<br />
x 1<br />
F + x 2<br />
F<br />
= 1<br />
1<br />
k1<br />
+ 1 k2<br />
= k 1k 2<br />
k1+ k2<br />
( 2) , x , F =<br />
F 1+ F 2, F 1= k1 x , F 2= k 2 x <br />
k= F x = F 1<br />
x + F 2<br />
x = k 1+ k 2<br />
211211 , m1 L 1 <br />
, <br />
m 2, L 2<br />
, m1, m2<br />
211 , m 2,<br />
<br />
T 21= m 2<br />
2 ( L 1+ L 2)<br />
m 1, <br />
T 1- T 12= m 1<br />
2 L 1<br />
T 12 =<br />
T 21, , <br />
T 1= m 1<br />
2 L 1+ m2<br />
2 ( L 1+ L 2)<br />
m 1 <br />
, <br />
T 2 1= T 12= m2<br />
2 ( L 1+ L 2) 211211 <br />
212212 , <br />
, , , <br />
s, r <br />
, ( r, , s ) ?<br />
f m<br />
, m , <br />
, 212 , <br />
27
x : N sin - f mcos = m<br />
2 m inr<br />
y : N cos + f msin - mg = 0<br />
f m= sN <br />
, <br />
<br />
m in=<br />
( sin - scos ) g<br />
( cos + s sin ) r<br />
m in= 1<br />
( sin - scos ) g<br />
2( cos + ssin ) r<br />
, , <br />
, f m<br />
212<br />
<br />
ma x= 1 ( sin + scos ) g<br />
2( cos - ssin ) r<br />
, , <br />
m ax min<br />
212<br />
212 <br />
213213 , m= 1200kg , <br />
, v= 25m/ sR= 400m, ,<br />
= 6<br />
213213 <br />
( 1) <br />
( 2) s= 09, <br />
, ?<br />
28
( 1) 213 , , <br />
x : N sin + f cos = m v 2<br />
R<br />
y : N cos - f sin - mg = 0<br />
<br />
f = m v2<br />
R cos - mg sin<br />
= 1200 252<br />
400 cos6 - 120098sin 6 = 635 N<br />
<br />
f n = m v 2<br />
2<br />
R = 120025 400 = 188103 N<br />
( 2) v m , f m a x= sN vm<br />
f m ax v f , <br />
v m=<br />
Rg ( sin + scos )<br />
cos - ssin<br />
=<br />
40098( sin 6 + 09cos6 )<br />
cos6 - 09sin 6<br />
= 660 m/ s<br />
214 5988kg,<br />
1829m, <br />
30577k m/ h g ?<br />
<br />
, <br />
, 1 , , <br />
?<br />
<br />
a n= v 2<br />
R = ( 30577103 ) 2<br />
3600 2 1829 = 3945 m/ s 2 = 402 g<br />
29
N 1 , , , <br />
<br />
<br />
, <br />
N - N 1- mg = 0<br />
N = N 1+ mg<br />
N = F = ma n<br />
N <br />
N 1=<br />
man<br />
- mg = m an - g<br />
= 5988 3945<br />
1<br />
- 98 = 17710 4 N<br />
215 73 000km <br />
136 000km 10 -<br />
6 m 10m <br />
142h, <br />
?<br />
m , M <br />
, , <br />
G Mm<br />
R 2<br />
= m 4<br />
2<br />
R<br />
T 2<br />
M= 4<br />
2 R 3<br />
4 ( 2 13610 8 ) 3<br />
=<br />
GT 2 66710 - 11 ( 1423600) 2<br />
= 5710 2 6 kg<br />
21616 , 4 <br />
1610 ( 244) 4 <br />
, 10710 6 k m, <br />
716d<br />
M m , <br />
, <br />
30
M= 4<br />
2 R 3<br />
=<br />
GT 2<br />
G Mm<br />
R 2<br />
= m 4<br />
2<br />
R<br />
T 2<br />
4 ( 2 10710 9 ) 3<br />
= 18910 27 kg<br />
66710 - 11 ( 71686400) 2<br />
217 : <br />
<br />
p =<br />
2 3 G<br />
2 R 2<br />
, R <br />
, 13<br />
10 3 k g/ m 3 , 7010 7 m ,<br />
( atm ) ( 1atm= 101310 5 P a) <br />
214 , r dr, dS <br />
dSdr, r <br />
<br />
214217 <br />
dF = G 4 3 r 3 dm/ r 2 = 4 3 G<br />
2 rdrdS<br />
31
, dm dS <br />
dp = dF<br />
dS =<br />
4 3 G<br />
2 rdr<br />
<br />
p = dp = <br />
R<br />
, , <br />
0<br />
4<br />
3 G<br />
2 r dr = 2 3 G<br />
2 R 2<br />
p =<br />
2 3 <br />
11 66710- ( 1310 3 ) 2<br />
( 7010 7 ) 2 / 101310 5<br />
= 1110 7 atm<br />
218<br />
<br />
( 1) T min = 3 / ( G ) , <br />
<br />
<br />
( 2) 3010 3 kg/ m 3 , <br />
( 3) 16ms, 10km , <br />
( ) ?<br />
( 1) M m <br />
, , <br />
<br />
m R <br />
G Mm = m 2<br />
2<br />
R 2 T<br />
R<br />
m in<br />
T m in=<br />
M= 4 3 R3 <br />
3 / ( G )<br />
( 2) = 3010 3 kg/ m 3 T m in, <br />
32
T m in=<br />
3<br />
G<br />
= 3<br />
= 6910 3<br />
66710 - 11 3010 3 s<br />
( 3) T min <br />
<br />
M= 4 3 R3 =<br />
=<br />
4<br />
2 R 3<br />
GT 2<br />
= 3<br />
GT 2<br />
4<br />
2 ( 10 4 ) 3<br />
= 23110 2 9 k g<br />
66710 - 11 ( 1610 - 3 ) 2<br />
= 012( )<br />
219<br />
, <br />
? ( )<br />
? <br />
18910 27 kg, 71410 4 km, <br />
10h <br />
r ( m) <br />
, <br />
<br />
<br />
r =<br />
=<br />
G Mm = m 2<br />
2<br />
r<br />
r 2 T<br />
219 <br />
GMT 2 1 / 3<br />
4<br />
2<br />
66710 - 11 18910 27 ( 103600) 2<br />
= 16110 8 m<br />
<br />
4<br />
2 1 / 3<br />
215<br />
33
h= r - R = 16110 8 - 71410 7<br />
= 89610 7 m<br />
215 <br />
S= 2 R 2 ( 1 -<br />
= 2 R 2 1 -<br />
= 2 R 2 h/ r<br />
cos )<br />
R<br />
r<br />
= 2( 71410 4 ) 2 89610 7 / ( 16110 8 )<br />
= 17710 10 km 2<br />
220: M <br />
, R, <br />
216 , <br />
<br />
, <br />
GM 2<br />
3<br />
F = 2<br />
( 3 R) 2 2<br />
GM 2<br />
=<br />
3 R 2<br />
<br />
GM 2<br />
3 R 2= M 2<br />
2<br />
R<br />
T<br />
<br />
216220 <br />
T =<br />
4<br />
48 R 3 / 2<br />
( GM) 1/ 2<br />
221 m <br />
M , <br />
, r<br />
<br />
34
, , <br />
, <br />
,<br />
G Mm<br />
r 2 +<br />
<br />
m 2<br />
= m 4<br />
2<br />
r<br />
( 2r ) 2 T 2<br />
T = 4 r 3/ 2 G( 4M+ m)<br />
222 , <br />
a , - 02v<br />
<br />
<br />
<br />
<br />
t 1 / 2 =dt = - v 0 / 2<br />
a = dv<br />
dt = - 02 v<br />
dt= - dv/ 02 v<br />
v 0<br />
dv<br />
02v =<br />
223<br />
, R<br />
( 217) , <br />
k<br />
A <br />
v 0, t <br />
A <br />
217 , <br />
<br />
N = m v2<br />
R <br />
ln2<br />
02 =<br />
347 s<br />
217223 <br />
35
v v 0<br />
f = kN<br />
- f = m dv<br />
dt<br />
dv<br />
dt = - v 2<br />
k<br />
R<br />
dv<br />
v 2<br />
v=<br />
= - <br />
t<br />
t <br />
t<br />
s= vdt =<br />
0<br />
= R ln 1 +<br />
k<br />
0<br />
k<br />
R dt<br />
v 0R<br />
R+ v 0 kt<br />
v 0R <br />
t<br />
0<br />
v 0 kt<br />
R<br />
dt<br />
R + v0 kt<br />
224510 4 r/ min, <br />
200cm, 100cm<br />
( 218)<br />
( 1) <br />
g <br />
( 2) 120g <br />
, <br />
? ?<br />
218224 <br />
( 3) 10 5 <br />
?<br />
( 1) <br />
510 4<br />
a n1/ g = 4<br />
2 2 r 1/ g = 4<br />
2 60<br />
36<br />
2<br />
002/ 98= 05610 5
a n 2/ g = 4<br />
2 2 r 2/ g = 4<br />
2 5104<br />
60<br />
2<br />
010/ 98= 28010 5<br />
( 2) 218 , r <br />
dm= Sdr<br />
, S ( <br />
) <br />
<br />
F + dF - F = dF<br />
dF = dm a= S<br />
2 r dr<br />
<br />
F r b<br />
2<br />
F b = dF =<br />
0<br />
S <br />
2 rdr = S<br />
2<br />
r 2 2 - r 2 1<br />
2<br />
r 1<br />
<br />
= S ( r 2 - r 1) <br />
2 ( r 2 + r 1)<br />
2<br />
= m<br />
2<br />
2 ( r 2 + r 1)<br />
= 1210- 3<br />
2<br />
= 19710 4 N<br />
510 4<br />
60<br />
2<br />
4<br />
2 ( 002 + 010)<br />
, 19710 4 N , <br />
201t <br />
( 3) <br />
F i= m<br />
2 r = 16710 - 2 7 10 5 4<br />
2 5104<br />
60<br />
= 4610 - 16 N<br />
2<br />
010<br />
225597m<br />
, 400r/ min , <br />
?<br />
37
219 , r <br />
dm= Sdr<br />
, S <br />
( <br />
) <br />
F - ( F + dF ) = - dF<br />
<br />
- dF = dma= S<br />
2 r dr<br />
L <br />
F 0 = F 0<br />
0<br />
dF = - L S <br />
2 r dr = -<br />
0<br />
219225 <br />
1<br />
2 S<br />
2 L 2 = -<br />
1<br />
2 m<br />
2 L<br />
r , , <br />
<br />
©¦F 0©¦<br />
mg = <br />
2 L<br />
2g = 4<br />
2 400597<br />
= 534<br />
29860 2<br />
226a = 70m/ s 2 <br />
, , <br />
l= 2m <br />
? k= 050<br />
220 , , <br />
f = kmg F 0= ma , , , <br />
<br />
220<br />
226 <br />
F 0- f = ma <br />
<br />
a = F 0- f<br />
m<br />
= a - kg<br />
l <br />
<br />
38
v = 2a l =<br />
2( a - kg ) l =<br />
= 29 m/ s<br />
2( 7- 0598)2<br />
227<br />
( ) , 18km <br />
g , <br />
? ?<br />
, <br />
=<br />
g<br />
r =<br />
m<br />
2 r = mg<br />
98<br />
1810 3 = 7410 -<br />
<br />
2<br />
rad/ s<br />
<br />
228 R <br />
( 221) <br />
( <br />
) , <br />
?<br />
221 , <br />
m, :<br />
mg, N F 0<br />
<br />
: N cos - mg = 0<br />
:<br />
<br />
N sin - F 0= 0<br />
F 0= m<br />
2 Rsin <br />
<br />
msin ( <br />
2 Rcos - g ) = 0<br />
221<br />
228 <br />
= 0, <br />
; = , ; = arccos<br />
g<br />
<br />
2 R 39
, <br />
<br />
F t = F 0cos - mg sin = m<br />
2 sin cos - mgsin<br />
, F t= 0, <br />
= <br />
dF t<br />
d <br />
= m<br />
2 R 2cos 2 - 1-<br />
dF t<br />
d =<br />
dF t d, <br />
= 0 <br />
:<br />
m<br />
2 R 1 +<br />
dF t<br />
d = m<br />
2 R 1-<br />
g<br />
<br />
2 R cos<br />
g<br />
<br />
2 R > 0<br />
g<br />
<br />
2 R<br />
<<br />
g<br />
R , dF t<br />
d, ;<br />
g R , dF t<br />
= arccos<br />
:<br />
d, dF t<br />
= 0, <br />
d<br />
g<br />
<br />
2 R <br />
dF t<br />
d = m<br />
2 R g 2<br />
- 1<br />
<br />
4 R 2<br />
><br />
g<br />
R , dF t<br />
d, ;<br />
g R , = 0, dF t<br />
= 0, <br />
d<br />
<br />
229 <br />
20km40k m , <br />
40
, <br />
50m, <br />
0062kg/ m 3 , 40m / s, <br />
0016, <br />
10mN / W, ? ( <br />
)<br />
<br />
, <br />
F = f =<br />
1 2 C Av 2<br />
= 1 2 00160062252<br />
40 2 =<br />
1560 N<br />
15610 3 / 1010 - 3 = 15610 5 W= 156 KW<br />
41
3 <br />
F = -<br />
t =<br />
31 ( 31) ,<br />
<br />
kx , x = Acos t, , k, A, t = 0<br />
/ ( 2 ) <br />
<br />
/ ( 2 )<br />
I = F dt = -<br />
0<br />
3131 <br />
k / ( 2 )<br />
Acos tdt = -<br />
0<br />
x <br />
kA<br />
<br />
32 m = 50g, v = 20m/ s <br />
, 1/ 4 ?<br />
3232 <br />
32 , v1 = v2 = v,<br />
I = mv2 - mv1 = 2 mv<br />
42
= 2 00520 = 141 N ¡¤s<br />
33 m = 014kg v 1 = 50m/ s<br />
, , = 45, <br />
v2 = 80m/ s<br />
t =<br />
?<br />
002s, <br />
3333 <br />
33 , x <br />
<br />
I = mv2 - mv 1<br />
= m v 2 1 + v 2 2 + 2v1v 2cos<br />
= 014 50 2 + 80 2 + 25080cos45<br />
= 169 N ¡¤s<br />
<br />
= 180 - arct an<br />
= 180 - arct an<br />
<br />
F =<br />
<br />
I t =<br />
mv2sin <br />
mv1 + mv 2cos<br />
80sin45<br />
50 + 80cos45<br />
= 152<br />
169<br />
002 =<br />
845 N<br />
43
F / ( mg ) = 845/ ( 01498)<br />
= 616 <br />
34120 , <br />
m = 790g , 735m/ s( ) <br />
<br />
, <br />
F =<br />
N mv<br />
t<br />
= 12000079735<br />
60<br />
= 116 N<br />
, , <br />
, 116N<br />
35 90 3<br />
10 3 k g/ s, 10m / s<br />
34 , t <br />
AA v BB<br />
<br />
p = p B B-<br />
p A A <br />
= p BA + p A B - p A B + p B A <br />
= p A B - p A B = mv A - mvA<br />
m AB A B,<br />
v A = v A = v<br />
<br />
F =<br />
, <br />
p = m ( v A - vA )<br />
t t<br />
3435 <br />
F = m t<br />
2 v<br />
= Q 2 v = 310 3 210 = 42410 4 N<br />
90 <br />
44
, 424<br />
10 4 N , 90 <br />
<br />
36 <br />
, <br />
v0 : l<br />
, F = llg + lv 2 0, <br />
l <br />
35 , dt <br />
dl = v 0dt , <br />
dt <br />
3536 <br />
v 0 l ( l + dl) - v0 ll = v0 ldl<br />
, ,<br />
<br />
( F - llg ) dt =<br />
F =<br />
l lg +<br />
2<br />
v0 l dl = v 0 ldt<br />
v 2 0 l<br />
37 , ,<br />
, <br />
3 <br />
3637 <br />
36 , t <br />
, l <br />
l, <br />
m = l l, l <br />
v =<br />
2g l dt , dm<br />
= l dl = l vdt ,<br />
v 0m + dm ,<br />
<br />
45
[ ( m + dm) g - N ] dt = dm( 0 - v)<br />
dmdt , <br />
= - lv 2 dt = -<br />
= - 2mg dt<br />
N = 3mg<br />
<br />
N = N = 3mg<br />
3 <br />
l 2g ldt<br />
<br />
3834 <br />
mv 1( 1 - cos<br />
f = )<br />
t<br />
t m <br />
37 , m <br />
t <br />
<br />
p = p 2 - p 1 = m( v 2 - v1)<br />
V <br />
p V = - m( v 2 - v 1cos )<br />
= - mv1( 1 - cos )<br />
m <br />
<br />
f =<br />
p V<br />
=<br />
dt<br />
- mv1( 1 - cos t<br />
, f <br />
f = - f = mv 1( 1 - cos )<br />
t<br />
3738 <br />
39, <br />
p 1= 92210 -<br />
46<br />
21 kgm/ s ,
p 2= 53310 - 2 1 k gm / s <br />
<br />
p 3 <br />
, <br />
p 1 + p 2 + p 3 = 0<br />
3839 <br />
38 , p 3<br />
<br />
p 3 = p 2 1 + p 2 2<br />
= 10 - 21 922 2 + 533 2<br />
= 10710 - 20 k g ¡¤m / s 2<br />
p 3 p 1 p 2 , p 1 <br />
= 90 + arctan p 1<br />
p 2<br />
= 90 + arct an 922<br />
533 =<br />
149 58<br />
310M ,<br />
, <br />
m, u<br />
, <br />
<br />
, , , <br />
2m( u - v1) - Mv1 = 0<br />
, <br />
47
v 1 =<br />
2mu<br />
M + 2m<br />
, , - v 2<br />
<br />
, <br />
m( u - v2 ) - ( M + m) v 2 = 0<br />
, - v 2 , <br />
<br />
v 2 =<br />
m( u - v 2) - Mv 2 = - ( M + m) v2<br />
mu + ( M + m) v 2<br />
= mu<br />
M + m<br />
v 1 v 2 , v1< v 2<br />
1<br />
M + m + 1<br />
M +<br />
311v 0= 7600m/ s <br />
m 1 = 2900kg m 2 =<br />
1500kg , <br />
u= 9100m/ s<br />
, <br />
, v0 , v 1 v2 <br />
<br />
<br />
( m 1 + m 2) v 0 = m 1v 1 + m 2v2<br />
, u= v 2- v1, v 2= u+ v 1 <br />
<br />
<br />
v 1, v 2<br />
v1 = v0 -<br />
( m1 + m2) v 0 = m 1v1 + m2( u + v 1)<br />
m2u<br />
m 1 + m 2<br />
= 7600 -<br />
150910<br />
150 + 290<br />
v2 = u + v 1 = 910 + 7290 = 8200 m/ s<br />
2m<br />
= 7290 m/ s<br />
, , v 0 <br />
48
312v 0 , <br />
, <br />
45 , 45 <br />
, <br />
?<br />
39 , <br />
v0cos , , <br />
v 1 v2 <br />
, <br />
<br />
39312 <br />
:<br />
mv 0cos= m 2 v 1cos45 + m 2 v 2cos45<br />
:<br />
, <br />
0 = m 2<br />
v 1sin 45 - m<br />
v2sin 45<br />
2<br />
v1 = v 2 = 2 v 0cos<br />
313, <br />
310313<br />
v =<br />
<br />
2 kg s =<br />
s= 25m <br />
<br />
k = 080 <br />
( 14m/ s) , <br />
?<br />
- kmg / m<br />
= - kg , <br />
<br />
2089825 = 198 m/ s<br />
, v l<br />
( 310)<br />
, <br />
49
v = 1 2<br />
( mv1) 2 + ( mv2) 2 = ( 2mv ) 2<br />
v 2 1 + v 2 2 =<br />
2<br />
2 vl = 2<br />
14 = 99 m/ s<br />
2<br />
v> v , , <br />
<br />
314 m 1= 20g, m 2= 50g, <br />
, v 1= 10icm/ s, v 2= ( 30i+ 50j ) cm/ s<br />
, <br />
v <br />
m1 v1 + m2 v2 = ( m 1 + m 2) v<br />
2010i + 50( 30i + 50j ) = ( 20 + 50) ( v xi + vyj )<br />
<br />
vx =<br />
2010 + 5030<br />
20 + 50<br />
vy = 5050<br />
20 + 50<br />
<br />
= 357 cm/ s<br />
= 50 cm / s<br />
v = v 2 x + v 2 y = 5 2 + 357 2 = 614 cm/ s<br />
x <br />
= arct an vy<br />
vx<br />
= arct an 357<br />
50 = 35 32<br />
315 6090kg, 105<br />
m / s253m/ s <br />
800kg , ?<br />
<br />
( ( 311) ) <br />
v f =<br />
50<br />
vi + uln M i<br />
M f<br />
= 105 + 253ln 6090<br />
6010<br />
= 108 m/ s
316, , <br />
, ?<br />
v f<br />
u<br />
, vf- u vf= v i+<br />
uln( M i/ M f) <br />
<br />
v f = 0 + uln Mi<br />
M f<br />
M i/ M f= e<br />
<br />
Mi - M f<br />
M i<br />
= 1 -<br />
M f<br />
M i<br />
= 1 -<br />
= u<br />
1<br />
e =<br />
0632<br />
31727210 6 kg , <br />
12910 3 kg/ s<br />
( 1) <br />
?<br />
( 2) 55010 4 m/ s , <br />
155s?<br />
( 3) ( 2) , , ?<br />
Mi = 27210 6 k g, =<br />
10 4 m / s, T = 155s, g = 98m/ s 2<br />
dM<br />
= 12910 3 kg/ s, u = 550<br />
dt<br />
<br />
( 1) , <br />
u 1<br />
dM<br />
dt<br />
= Mig<br />
<br />
u 1<br />
= M ig<br />
dM<br />
dt<br />
= 272106 98<br />
12910 3<br />
= 20710 4 m/ s<br />
( 2) , , <br />
udM + Mdv = - Mgdt<br />
51
dv<br />
dt = -<br />
t 0 T <br />
v = <br />
v<br />
0 dv = - M f<br />
= uln M i<br />
( 3) <br />
Mf<br />
M i<br />
u<br />
M<br />
dM<br />
dt<br />
u<br />
M dM - T 0 g dt<br />
- g T = uln<br />
= 5510 4 ln<br />
Mi<br />
Mi -<br />
- g<br />
T -<br />
gT<br />
27210 6<br />
27210 6 - 12910 3 155<br />
- 98155 = 26810 3 m/ s<br />
dv = -<br />
u<br />
M dM -<br />
gdt<br />
0 t v <br />
v = uln<br />
M i<br />
M i -<br />
t -<br />
0 T , , <br />
<br />
g t<br />
h = T 0 vdt = T 0<br />
uln<br />
M i<br />
M i -<br />
t -<br />
gt dt<br />
= uT lnM i + u ( M i - T ) ln( Mi - T ) - 1<br />
<br />
- Mi lnM i - 1 -<br />
h =<br />
1<br />
2 g T 2<br />
172 k m<br />
318 210m/ s , <br />
75kg , 30k g <br />
490m/ s <br />
52
v= 210m / s, dm 1 dM<br />
= 75kg/ s, = - 30k g/ s, u= 490m/ s<br />
dt dt<br />
, dt <br />
dm 10 + Mv = ( dm 1 - dM) ( v - u ) + ( M + dM) ( v + dv)<br />
<br />
<br />
F = M dv<br />
dt = -<br />
Mdv = - udM + ( u - v) dm1<br />
u dM<br />
dt<br />
+ ( u - v) dm1<br />
dt<br />
= - 490( - 30) + ( 490 - 210)75<br />
= 22510 4 N<br />
319311 <br />
00958nm, <br />
105 <br />
<br />
<br />
, B , <br />
<br />
AB= 00958cos 105 = 00583 nm<br />
2<br />
C <br />
311319<br />
ACm O = BC2mH = ( AB - A C)2mH<br />
<br />
AC =<br />
AB2m H<br />
m O + 2mH<br />
= 0058321<br />
16 + 21<br />
320<br />
<br />
= 000648 nm<br />
312 , R, m, A =<br />
2m/ ( R 2 ) x , <br />
53
x C<br />
x dm<br />
=<br />
m = m 1<br />
R x <br />
0 A 2 R 2 - x 2 dx<br />
= 4R<br />
3<br />
312320 <br />
313321 <br />
321, a <br />
a / 4 ( 336) <br />
<br />
313 <br />
, <br />
O <br />
, A <br />
AO , B <br />
, <br />
m1BO = m 2AO<br />
m 2= a 2<br />
<br />
a , m 1= a 3 - m2= a 3 1-<br />
4<br />
16 <br />
( ) m1 m 2 <br />
54
BO =<br />
m2<br />
m1<br />
A O =<br />
/ 16<br />
1 - / 16 AO = a<br />
4( 16 -<br />
0061a <br />
) = 0061a<br />
322 , <br />
8m , , <br />
? 3500kg, <br />
140kg<br />
, <br />
, , x , <br />
<br />
x3500 = ( 8 - x ) 140<br />
x =<br />
8140<br />
3500 + 140 = 031 m<br />
323 h= 25m, m= 75kg <br />
, ?<br />
l E l p <br />
, <br />
mEl E = mpl p<br />
, l p = h , <br />
<br />
l E = m p<br />
mE<br />
l p =<br />
m E l E = mp l p<br />
7525<br />
59810 24 = 31410 - 2 2 m<br />
31410 -<br />
22 m<br />
324 m= 20g , 1s <br />
m= 50g t( > 1) s ,<br />
<br />
55
v C =<br />
a C =<br />
m 1v 1 + m 2v 2<br />
m 1 + m 2<br />
m 1a 1 + m 2a2<br />
m 1 + m 2<br />
=<br />
=<br />
20g t + 50g ( t - 1)<br />
20 + 50<br />
20g + 50g<br />
20 + 50 = g<br />
= t -<br />
5<br />
7 g<br />
325 m= 2200kg v= 60k m/ h <br />
d = 50m <br />
? ?<br />
P 1<br />
314325 <br />
314 , d = 50m <br />
<br />
L 1<br />
P 2<br />
L 2<br />
= mvr 1sin 1 = mvd<br />
= 2200 6010 3<br />
3600 50<br />
= 18310 6 kg ¡¤m 2 / s<br />
<br />
= mvr 2sin 2 = mvr 2sin0 = 0<br />
326<br />
r 1 = 87510 10 m, v 1 = 54610 4<br />
m / s v2= 90810 2 m / s, <br />
r 2 ?<br />
, <br />
, , <br />
56
, <br />
<br />
r 2 =<br />
r 1v1<br />
v 2<br />
mr 1v1 = mr 2v 2<br />
= 875101 0 54610 4<br />
90810 2 = 52610 12 m<br />
327<br />
, 273d <br />
<br />
L M = mM R M v M = 2 mM R 2 M / T M<br />
<br />
dS<br />
dt =<br />
L M<br />
2mM<br />
= 273510<br />
22 ( 38210 8 ) 2<br />
27386400<br />
= 28610 3 4 kg ¡¤m 2 / s<br />
=<br />
28610 34<br />
273510 22 = 19410 1 1 m 2 / s<br />
3281988 12 <br />
, <br />
2055km, 358357k m <br />
102km / s<br />
( 1) ;<br />
( 2) ( : <br />
) <br />
315 , h P = 2055km, h A = 358357k m, vP =<br />
102k m/ s, R E= 6378km<br />
<br />
( 1) <br />
vA =<br />
vP<br />
r P<br />
r A<br />
= vP<br />
= 159 km/ s<br />
R E<br />
+ h P<br />
RE + h A<br />
6378 + 358357<br />
= 102<br />
6378 + 2055<br />
57
315328 <br />
( 2) S = <br />
2 ( r A + r P ) r A r P<br />
dS<br />
dt = 1 2 vP r P<br />
<br />
T =<br />
S<br />
dS / dt =<br />
( r A + r P ) r A r P<br />
vP<br />
r P<br />
= ( r A + r P )<br />
v P<br />
r A<br />
r P<br />
= ( 422137 + 65835)<br />
102<br />
422137<br />
65835 = 38057s =<br />
106 h<br />
329 ( <br />
316) , r 0, v0, <br />
r , v <br />
316329 <br />
58
, <br />
, m , <br />
<br />
mr 0v0 = mrv<br />
v = v 0<br />
330 m , a <br />
, , <br />
m <br />
, <br />
?<br />
r 0<br />
r<br />
( 1) ? <br />
( 2) , <br />
? , ?<br />
( 3) , ?<br />
( 1) 317 , C , <br />
, <br />
317330 <br />
<br />
2ml 1 = m( a - l 1)<br />
l 1 = a 3<br />
C a / 3<br />
, , <br />
59
, , C <br />
vC =<br />
mv + m( - v) + m ¡¤0<br />
m + m + m<br />
= 0<br />
( 2) , ( ) <br />
v= a/ 2C 0, <br />
a / 2, C <br />
L 1=<br />
m a 3 a / 2 + m 2a<br />
3 a / 2 + m a 3 0<br />
= 1 2 ma 2 <br />
, , <br />
, C , , , <br />
L 2=<br />
1 2 ma 2 <br />
<br />
( 3) <br />
C , <br />
<br />
L 2 = 2m a 3<br />
a<br />
3 + m 2a<br />
3<br />
= 3 4 <br />
2a<br />
3 = 1 2 ma 2 <br />
60
4 <br />
41<br />
( 41) ( ) M=<br />
1 200k g, m= 1 000k g<br />
, a =<br />
15m/ s 2 <br />
?<br />
( 1) <br />
( 2) t= 10s, <br />
? ( )<br />
( 3) t = 10s , <br />
h= 10m , <br />
?<br />
( 1) 41 , , <br />
M m <br />
<br />
T 1- Mg = Ma<br />
mg - T 2= ma<br />
41<br />
T 1= M( g + a ) = 1200( 98+ 15) = 13610 4 N<br />
T 2= m( g - a ) = 1000( 98- 15) = 08310 4 N<br />
<br />
41 <br />
( 2 ) t = 10s , h =<br />
1<br />
2 a t 2 , , <br />
61
A= ( T 1- T 2) h = ( 136- 083) 1 2 151 2 = 39510 3 J<br />
( 3) , T 1 =<br />
Mg , T 2 = mg h <br />
A = ( T 1 - T 2 ) h = ( M - m) g h<br />
= ( 1200 - 1000)9810 = 19610 4 J<br />
42 <br />
<br />
R, <br />
, <br />
m, <br />
k45 ,<br />
? <br />
?<br />
42 , F <br />
, , <br />
<br />
: F - mg sin - f = 0<br />
: N - mg cos = 0<br />
f = kN <br />
<br />
F = kmg cos + mg sin<br />
<br />
A F = ( kmg cos+ mg sin ) Rd<br />
0<br />
= R[ kmg sin - mg ( cos - 1) ]<br />
= Rmg [ ksin45 - cos45 + 1]<br />
4242 <br />
= mg R 1 -<br />
2<br />
2<br />
+<br />
2<br />
2 k<br />
62
A g= - mg sinRd = mg R( cos - 1)<br />
0<br />
= mg R<br />
2<br />
2<br />
<br />
- 1<br />
<br />
A f = - mg kcosRd= -<br />
0<br />
mg ksin R<br />
= -<br />
2<br />
2<br />
mg kR<br />
43, S = 50m 2 , h 1= 15m<br />
h 2<br />
= 5m<br />
, ? <br />
80% , P =<br />
35k W, <br />
?<br />
43 , dh<br />
<br />
Sg hdh , <br />
<br />
4343 <br />
A= <br />
h 1<br />
+ h 2<br />
h 2<br />
Sg hdh =<br />
h 1Sg h 1<br />
2 + h 2<br />
= 110 3 155098 15<br />
2 + 5<br />
= 4210 6 J<br />
T , A = P T <br />
T =<br />
A<br />
P <br />
= 42310 6<br />
351008 = 151 s<br />
3<br />
63
44 , <br />
q= 50kg/ s, v= 15m/ s<br />
, ? <br />
?<br />
4444 <br />
44 , dt dm <br />
, F 0 v <br />
, <br />
<br />
F dt= dm( v- 0)<br />
F = dm<br />
dt v = qv<br />
, F , <br />
, F <br />
<br />
P = F v= qv 2 = 5015 2 = 113 W<br />
<br />
dE k<br />
dt = 1 2 dm v 2 / dt= 1 2 qv 2 = 1 2 P<br />
dm 0 <br />
v , , s = vdt/ 2<br />
64
, F <br />
A = -<br />
F s<br />
dt = - qv 2<br />
2<br />
<br />
<br />
45 45 , A B <br />
mA = m B, B <br />
k = 020, <br />
A h=<br />
10m <br />
45 , <br />
<br />
- f h+ m Bgh = 1 2 ( m A + m B) v 2 4545 <br />
f = kmA g h, <br />
v= ( 1- k) gh = ( 1- 02)981= 28 m/ s<br />
4646 , M <br />
m v s <br />
( 1) ? <br />
?<br />
( 2) <br />
s <br />
46 , , <br />
, V , <br />
<br />
mv= ( m+ M) V<br />
V=<br />
m<br />
m+ M v 65
4646 <br />
( 1) s1 , <br />
s= s1+ s, f <br />
, <br />
- f ( s1+ s ) = 1 2 mV 2 -<br />
1<br />
= 1 2 mv2 2 mv m<br />
2<br />
m+ M<br />
2<br />
- 1<br />
, f <br />
f s1= 1 2 MV 2 = 1 2 M m<br />
m+ M<br />
( 2) f = f , , <br />
- f s =<br />
1<br />
2 mV 2 + 1 2 MV2 -<br />
2<br />
v 2<br />
1<br />
2 mv2<br />
<br />
s <br />
47S S u <br />
: S , <br />
( 46) , S , <br />
, A A B =<br />
1 2 m ( v B) 2 -<br />
) <br />
1<br />
2 ( mv A ) 2 ( : <br />
dr F S dt <br />
, dr S , dr 0= udt dt <br />
S S S , A B <br />
F <br />
66
A A B = B F ¡¤dr B = F ¡¤( dr - dr 0) = B F ¡¤dr B - F ¡¤udt<br />
A A A A<br />
= A A B - <br />
B<br />
A<br />
F dt ¡¤u<br />
( )<br />
<br />
B F dt = m( vB - vA )<br />
A<br />
A A B = A A B- m( vB - vA ) u<br />
S , A B <br />
1<br />
2 mv B 2 -<br />
1<br />
2 mv A 2<br />
= 1 2 m( v B - u) 2 -<br />
= 1 2 mv 2 B -<br />
1<br />
2 m( v A - u) 2<br />
1<br />
2 mv 2 A - m( vB - v A ) ¡¤u<br />
, , S , A A B =<br />
1<br />
2 mv 2 B -<br />
1<br />
2 mv 2 A , <br />
A A<br />
B =<br />
1 2 mv 1 2<br />
B-<br />
2 mv<br />
2 A<br />
S ( A A B A A B,<br />
1<br />
2 mv<br />
2 A 1 2 mv 2 A ,<br />
1<br />
2 mv<br />
2 B 1 2 mv 2 B) <br />
4847 , AB, k, <br />
A , m , <br />
a F <br />
F <br />
47 , <br />
67
, f = ka, <br />
<br />
F = ka + mg cos<br />
4748 <br />
, F <br />
A = F dr = <br />
<br />
F ad=<br />
0<br />
<br />
ka 2 d<br />
0<br />
+ <br />
0<br />
mg acos d <br />
= 1 2 ka 2 <br />
2 + mga sin <br />
49 ( k) <br />
, <br />
y , <br />
: y ,<br />
1 2 ky 2 <br />
48 <br />
y 0, <br />
mg = ky 0<br />
y , y 0<br />
<br />
48<br />
49 <br />
, <br />
68
E p 1= 1 2 k ( y + y 0) 2 -<br />
1<br />
2 ky 2 0= 1 2 ky 2 + ky 0y<br />
, <br />
E p2= - mgy= - ky 0y<br />
<br />
E p= E p1+ E p 2= 1 2 ky 2 + ky 0y - ky 0y = 1 2 ky 2<br />
410 l 0, k, , <br />
m , , <br />
, ? <br />
?<br />
v y , <br />
<br />
- mgy + 1 2 ky 2 + 1 2 mv 2 = 0<br />
, v= 0, y = y m ax , <br />
<br />
y m ax = 2mg / k<br />
f m a x= ky m a x= 2mg<br />
, mg = ky 0<br />
- mgy 0+ 1 2 ky 2 0+ 1 2 mv 2 0= -<br />
<br />
v 0= y 0( 2mg - ky 0) / m = y 0g =<br />
m 2 g 2<br />
k + 1 2 k m2 g 2<br />
k 2 + 1 2 mv2 0= 0<br />
m<br />
k g<br />
41149 , A( m= 05kg) <br />
B C s= 3m<br />
k= 400N / m = 45A <br />
, ?<br />
69
49411<br />
<br />
m 1, m2<br />
x ,<br />
<br />
mg ( s+ x ) sin = 1 2 kx 2<br />
0598( 3+ x ) sin 45 = 1 2 400x 2<br />
, <br />
m 1 m2<br />
m 1<br />
x = 023 m<br />
412410 , <br />
, <br />
,<br />
? k= 89<br />
N / m , m1= 500g, m 2= 300g<br />
m1 m2 , m 1+ m 2 <br />
, <br />
( m 1+ m2) g = ky 0<br />
410<br />
<br />
412 <br />
( m 1+ m 2) g ( 05+ 03)98<br />
y 0= = = 088 m<br />
k<br />
89<br />
, m 1 y 1<br />
m 1<br />
y 1= m 1g<br />
k = 0598 = 055<br />
89<br />
m<br />
, <br />
v m<br />
<br />
1<br />
2 m 1v2 m+ 1 2 ky 2 1- m1gy 1= 1 2 ky 2 0- m1gy 0<br />
vm=<br />
1<br />
m1<br />
[ k( y 2 0 - y 2 1) - 2m 1g ( y 0 - y 1) ]<br />
70
=<br />
1<br />
05 [ 89( 0882 - 055 2 ) - 20598( 088 - 055) ]<br />
= 140 m/ s<br />
413m 1 m2 A BC ( 411) <br />
m 1 ( m 1 ) , , m1 <br />
B m 2<br />
x 0<br />
k,<br />
?<br />
411413 <br />
( 1) m1 < m2, m1 x <br />
( 2) m1= m 2, x ?<br />
( 3) m1< m 2, m 2 h C ,<br />
x 0<br />
<br />
?<br />
( 1) , m 1<br />
v 1=<br />
k<br />
x 0<br />
m 1<br />
<br />
m 1< m 2 , m 1 <br />
<br />
m 2- m1<br />
v 1 = v 1=<br />
m 1+ m2<br />
m 2- m1<br />
m 1+ m2<br />
k<br />
x 0<br />
m 1<br />
<br />
71
x =<br />
m 1<br />
k v m 2- m1<br />
1 =<br />
m 1+ x 0<br />
m2<br />
( 2) m 1= m 2 , m 1 , , <br />
<br />
( 3) m2< m 1 , <br />
2m 1<br />
v 2 =<br />
m1+ m v 1=<br />
2<br />
2m 1<br />
( m 1+ m2)<br />
, m 2 , <br />
m 2gh=<br />
1 2 m 2v 2<br />
2 = 1 2 m 2<br />
<br />
x 0= ( m 1+ m 2)<br />
k<br />
m1 x 0<br />
4m 2 1kx 2 0<br />
( m1+ m 2) 2 m 1<br />
g h<br />
2m 1k<br />
414 412 , k, <br />
M A B, <br />
m v 0<br />
, <br />
<br />
412414 <br />
A , <br />
V 0 , , B A <br />
, A , <br />
<br />
mv0= MV 0+ mV 0<br />
72<br />
V 0=<br />
mv 0<br />
m+ M
B , B A <br />
, x m V A B <br />
, <br />
<br />
mv 0= ( M+ m+ M) V<br />
V=<br />
A V 0<br />
mv0<br />
2M+ m<br />
, <br />
<br />
A B V <br />
1<br />
2 ( m+ M) V 2 0= 1 2 ( 2 M+ m) V 2 + 1 2 kx 2 m<br />
x m= mv0<br />
M<br />
k( m+ M) ( m+ 2M)<br />
415m , M <br />
, <br />
R, / 2( 413) <br />
, <br />
( 1) ,<br />
?<br />
( 2) A B <br />
, A<br />
( 3) B <br />
1 / 2<br />
413415 <br />
( 1) 413 , , <br />
, N N , <br />
v V <br />
, <br />
mg R= 1 + 1 2 mv2 2 MV 2 73
, , <br />
v V , <br />
<br />
v=<br />
mv- MV= 0<br />
2Mg R<br />
M+ m , V= m<br />
2g R<br />
M( M+ m)<br />
( 2) , N , <br />
, <br />
, <br />
A N =<br />
1 2 MV 2 = m2 g R<br />
M+ m<br />
( 3) B , , <br />
, , <br />
<br />
<br />
<br />
v = v+ V=<br />
2MgR<br />
M+ m + m 2g R<br />
M( M+ m)<br />
N - mg = m v<br />
2<br />
R<br />
N = mg + m v<br />
2<br />
R = 3+ 2m M mg<br />
<br />
<br />
N = N = 3+ 2m M mg<br />
416 : <br />
, ( <br />
423 424) <br />
74
v 10 , v1 v 2 <br />
m 1= m2<br />
<br />
, <br />
v1 0= v 1+ v2<br />
v 2 1 0= v 2 1+ 2 v 1v 2+ v 2 2<br />
<br />
, <br />
v 2 1 0= v 2 1+ v 2 2<br />
v 1v 2= v1v 2cos = 0<br />
, <br />
v 1 v2 , 90<br />
417 : <br />
, , <br />
v 10- v2 0= - ( v1- v 2)<br />
<br />
v1= m1- m 2<br />
v 10+<br />
m1+ m 2<br />
2m2<br />
m 1+ m2<br />
v 20<br />
<br />
v 2= m 2- m 1<br />
v 0+<br />
m 1+ m 2<br />
2m1<br />
v 0<br />
m 1+ m2<br />
v 2 - v 1=<br />
m2 - m1<br />
m1 + m2<br />
-<br />
2m2<br />
m1 + m 2<br />
v 20<br />
+<br />
2m1<br />
m 1 + m 2<br />
-<br />
m 1 - m 2<br />
m 1 + m 2<br />
v 10<br />
<br />
= - v 20 + v 10<br />
v 10- v2 0= - ( v1- v 2) <br />
<br />
418 414 , , <br />
75
, m k, <br />
l 0m 1<br />
v 0<br />
<br />
l , <br />
v <br />
v 0<br />
<br />
414418 <br />
, , <br />
m 1v 0= ( m 1+ m) v0<br />
v 0 = m 1v0<br />
m 1+ m<br />
O<br />
, O , <br />
( m+ m 1) l 0v0 = ( m+ m 1) lvsin <br />
( ) , <br />
, <br />
1<br />
2 ( m+ m 1) v 0<br />
2 = 1 2 k ( l- l 0) 2 + 1 2 ( m+ m 1) v 2<br />
, <br />
k( l- l 0) 2<br />
v= v0<br />
2 -<br />
m+ m 1<br />
= arcsin v0 l 0<br />
=<br />
vl<br />
arcsin<br />
1/ 2<br />
=<br />
419: m, E k<br />
76<br />
m 2 1v 2 0<br />
( m+ m1) 2 -<br />
k( l - l 0) 2<br />
m+ m 1<br />
1 / 2<br />
m 1v 0l 0<br />
[ m 2 1v 2 0- k( m+ m 1) ( l - l 0) 2 ] 1/ 2 l<br />
M
, M<br />
M+ m E k<br />
m M , <br />
V=<br />
mv<br />
m+ M<br />
v m <br />
E av= 1 2 mv 2 -<br />
1<br />
2 ( m+ M) V 2 = 1 2 mv 2 1-<br />
m<br />
m+ M = M<br />
M+ m E k<br />
420m , <br />
2 ( 2R) m, R, G,<br />
M :<br />
( 1) ;<br />
( 2) ;<br />
( 3) <br />
( 1) <br />
GmM<br />
= mv2<br />
( 3R) 2 3R<br />
v <br />
( 2) <br />
E k=<br />
1 2 mv 2 = GmM<br />
6R<br />
E p= -<br />
( 3) <br />
GmM<br />
3R<br />
E = E k+ E p= GmM<br />
6R - GmM<br />
3R<br />
= - GmM<br />
6R<br />
421: <br />
E = -<br />
GMm<br />
r 1+ r 2<br />
M, m , r 1, r 2<br />
<br />
77
v1 v 2 <br />
, <br />
, <br />
mr 1v1= mr 2v2<br />
, , <br />
1<br />
2 mv 2 1-<br />
, <br />
<br />
GMm<br />
= 1 r 1 2 mv 2 2-<br />
1<br />
2 mv2 2=<br />
E = 1 2 mv 2 2-<br />
GMmr 1<br />
( r 1+ r 2) r 2<br />
GMm<br />
= -<br />
r 2<br />
GMm<br />
r 2<br />
GMm<br />
r 1+ r 2<br />
422 173kg, <br />
439km, 2 348km , <br />
421 <br />
E = -<br />
= -<br />
GMm<br />
r 1 + r 2<br />
= -<br />
GMm<br />
h 1 + h 2 + 2R<br />
66710 - 11 59810 2 4 173<br />
439 + 2384 + 63702<br />
= - 44310 9 J<br />
423 ( 415) <br />
500kg <br />
1 400k m , <br />
36 000km, <br />
<br />
( 1) ?<br />
( 2) ?<br />
78
415423 <br />
( 1 ) ( ) E s =<br />
GMm<br />
- GMm/ ( 2r 1) , ( ) E h= - <br />
r 1+ r 2<br />
<br />
E 1= E h - E s = GMm<br />
r 2 - r 1<br />
2r 1( r 1 + r 2)<br />
= 66710 - 11 59810 24 500<br />
<br />
42300 - 7800<br />
27800( 7800 + 42300)10 3<br />
= 88010 9 J<br />
E g= -<br />
<br />
GMm<br />
<br />
2r 2<br />
E 2= E g - E h = GMm<br />
r 2 - r 1<br />
2r 2( r 1 + r 2)<br />
79
= 66710 - 11 59810 24 500<br />
<br />
42300 - 7800<br />
242300( 7800 + 42300)10 3<br />
= 16210 9 J<br />
( 2) <br />
v s=<br />
<br />
GM<br />
r 1<br />
=<br />
66710 - 1 59810 1 24<br />
= 715 km/ s<br />
780010 3<br />
v hP , <br />
1<br />
2 mv 2 hP -<br />
GMm<br />
= -<br />
r 1<br />
GMm<br />
r 1+ r 2<br />
vh P =<br />
2GMr 2<br />
r 1( r 1 + r 2)<br />
=<br />
266710 - 11 59810 24 42310 7<br />
780010 3 ( 7800 + 42300)10 3<br />
= 929 km/ s<br />
v hA , <br />
vh A= v hP<br />
r 1<br />
= 929 7800<br />
r 2 42300 = 171 km / s<br />
<br />
vg=<br />
GM<br />
r 2<br />
=<br />
66710 - 11 59810 24<br />
= 307 km/ s<br />
4230010 3<br />
<br />
v 1= v hP - vs = 929- 715= 214 k m/ s<br />
<br />
v2= v g- v hA = 307- 171= 136 km/ s<br />
4243 500kg <br />
, 100km <br />
80
( 1) 100km <br />
<br />
( 2) , <br />
? ? 39810 5<br />
J/ kg, 10510 7 J/ kg<br />
( 1) 100km <br />
E 1 = -<br />
GMm<br />
= -<br />
2r<br />
= - 10810 11 J<br />
66710 -<br />
11 59810 24 3500<br />
2( 6370+ 100)10 3<br />
<br />
E 2 = -<br />
GMm<br />
R = - 66710 - 11 59810 24 3500<br />
637010 3<br />
= - 21910 11 J<br />
<br />
E = E 1- E 2= - 10810 11 - ( - 21910 1 1 ) = 11110 11<br />
( 2) <br />
Q 1= 39810 5 3500= 13910 9 J<br />
<br />
Q 2= 10510 7 3500= 36810 10 J<br />
E> Q 1, E > Q 1+ Q 2,<br />
<br />
425 10 30 kg, 20k m, <br />
10 10 m,<br />
( 1) , ?<br />
( 2) , ?<br />
( 1) , r <br />
, <br />
J<br />
81
-<br />
Gmm<br />
= -<br />
r<br />
Gmm<br />
r / 2 + 21 2 mv 2 1<br />
<br />
v 1=<br />
Gm<br />
=<br />
r<br />
66710 - 1 1 10 3 0<br />
10 10 = 8210 3 m/ s<br />
( 2) , , <br />
-<br />
Gmm<br />
= -<br />
r<br />
v2= Gm 1<br />
2R - 1<br />
r<br />
Gmm<br />
2R + 21 2 mv 2 2<br />
= 66710 - 11 10 30 1<br />
2210 4 -<br />
= 4110 7 m/ s<br />
1<br />
10 10<br />
426( ) <br />
6 500 <br />
10km, 6010 3 kg/ m 3 ( ) , <br />
?( <br />
42) ?<br />
<br />
E = -<br />
GM EmA<br />
r A<br />
- -<br />
GM EmA<br />
r A R E, <br />
RE<br />
E=<br />
GMEm A<br />
R E<br />
= GME 4 3 r 3 A <br />
RE<br />
= 66710 - 11 59810 24 4( 10 4 ) 3 6010 3<br />
640010 3 3<br />
82
= 1610 2 4 J<br />
( 10 18 J) 10 6 <br />
427 10 18 kg <br />
? 210 30 kg, 10km <br />
<br />
E = 0- -<br />
Gm1m 2<br />
R<br />
= Gm 1m 2<br />
R<br />
= 66710- 11 210 30 10 18<br />
1010 3<br />
= 1310 3 4 J<br />
428<br />
5010 1 0 m , 7510 4 m / s<br />
, <br />
<br />
<br />
416428 <br />
( 416) , ,<br />
0+ 1 2 mv2 0= -<br />
<br />
GMm<br />
+ 1 r m in 2 mv2<br />
83
v0= v 2 -<br />
2GM<br />
r m in<br />
= ( 7510 4 ) 2 -<br />
= 1810 4 m / s<br />
266710 - 11 19910 30<br />
5010 1 1<br />
, <br />
<br />
v0b= vr m in<br />
<br />
b= r m in<br />
v<br />
v 0<br />
= 510 10 51010<br />
1810 4 = 2110 11<br />
429 , <br />
, <br />
, , ( ve =<br />
m<br />
2GM/ R ) <br />
, ( R= 7<br />
10 8 m ) ? ?<br />
<br />
c , <br />
Rb = 2GM<br />
c 2 = 266710- 11 19910 30<br />
( 3010 8 ) 2 = 29510 3 m<br />
<br />
b= 3M =<br />
4 R 3 b<br />
319910 3 0<br />
= 18510 19<br />
4( 29510 3 ) 3 k g/ m 3<br />
430 <br />
, <br />
10 -<br />
6 K , <br />
10 67 <br />
<br />
84
3 , <br />
200 , <br />
?<br />
<br />
T M 3 ,<br />
<br />
M mi = M s<br />
T m i<br />
T s<br />
1/ 3<br />
= 510 11 kg<br />
( c=<br />
T m i<br />
=<br />
T s<br />
Mm i<br />
M s<br />
= 19910 3 0 <br />
3<br />
210<br />
10<br />
10 67 1/ 3<br />
2GM/ R) <br />
Rm i= 2GMm i<br />
c 2 = 266710- 11 510 11<br />
( 310 8 ) 2 = 7410 - 16 m<br />
431 235 , <br />
, <br />
, <br />
( 2 ) ( 12<br />
) <br />
, 1MeV <br />
, 003eV ?<br />
( m n) ( m ) <br />
v 10<br />
E 0<br />
<br />
<br />
v 1=<br />
E 1= 1 2 m nv 2 1= 1 2 m nv 2 10<br />
m- mn<br />
v1 0<br />
m+ mn<br />
m- m n<br />
m+ m n<br />
2<br />
= E 10<br />
m- mn<br />
m+ mn<br />
2<br />
85
E = E 10<br />
m- mn<br />
m+ mn<br />
2<br />
= 1 2<br />
<br />
= 1 2<br />
, 8 <br />
<br />
= 1 2<br />
, 52 <br />
lgE 10- lgE <br />
lg( m+ mn) - lg( m- mn )<br />
lg10 6 - lg003<br />
lg( 2+ 1) - lg( 2- 1) = 788<br />
lg10 6 - lg003<br />
lg( 12+ 1) - lg( 12- 1) = 518<br />
432 238 U 427MeV , <br />
238 U <br />
238 U 2 34 T h <br />
<br />
<br />
<br />
<br />
E =<br />
mT hv Th = m v <br />
1<br />
2 m T hv 2 T hm Th = 1 2 m v 2 m<br />
E<br />
1+ m / mT h<br />
E T hm Th = E m <br />
E Th + E = E<br />
=<br />
427<br />
= 420 MeV<br />
1+ 4/ 234<br />
433 1 4 N <br />
, 1 7 O <br />
119MeV <br />
( 14 N ) <br />
86
E a vE k <br />
E av=<br />
M N<br />
E k<br />
m+ M N<br />
<br />
E k, = m + M N<br />
MN<br />
E av=<br />
4+ 14<br />
119= 153 MeV<br />
14<br />
434<br />
E p( x ) = A x 1 2 -<br />
A , B , x <br />
B<br />
x 6<br />
<br />
<br />
F = 0 <br />
F = -<br />
dE p( x )<br />
dx<br />
= 12A<br />
x 13 -<br />
6B<br />
x 7<br />
x =<br />
6<br />
2A<br />
B<br />
<br />
435: , <br />
<br />
<br />
E k, r=<br />
<br />
1 2 v2 2 1= 1 2<br />
m1m 2<br />
( v2- v 1) 2<br />
m 1+ m 2<br />
E k , int =<br />
1 2<br />
<br />
m 1v 2<br />
1 + 1 2 m 2<br />
2v 2 = 1 2 m1( v1- vC) 2 + 1 2<br />
m2( v 2- vC)<br />
2<br />
<br />
v C=<br />
m 1v1+ m 2v2<br />
m1+ m 2<br />
v C<br />
<br />
87
E k, int = 1 m 2 2( v 2 - v 1) 2<br />
2 m1 + 1 m 2 1( v 2 - v 1) 2<br />
( m 1 + m2) 2 2 m2 ( m 1 + m 2) 2<br />
= 1 2<br />
m 1m 2<br />
m1 + m2<br />
( v 2 - v 1) 2<br />
<br />
E k , r= E k , in t<br />
<br />
436 M m <br />
, k <br />
m , v 0 <br />
<br />
M , <br />
1<br />
2 v2 mM = 1 2 kx 2 ma x<br />
= mM<br />
m+ M , vmM = v 0, <br />
x ma x=<br />
mM<br />
( m+ M) k v 0<br />
88
5 <br />
51 125 , <br />
v = 25m/ sR = 10m <br />
:<br />
( 1) ;<br />
( 2) ;<br />
( 3) ( ) <br />
( 1) <br />
= v/ R = 25/ 10 =<br />
( 2) <br />
=<br />
<br />
2<br />
2 = 25 2<br />
22125 =<br />
( 3) <br />
t =<br />
2<br />
=<br />
22125<br />
25<br />
25 rad / s<br />
398 rad / s2<br />
= 0628 s<br />
52 70s 200r/ min <br />
3 000r/ min<br />
( 1) ;<br />
( 2) ;<br />
( 3) r = 02m , <br />
70s <br />
( 1) <br />
<br />
0 = 2200/ 60 =<br />
209 rad/ s<br />
89
=<br />
=<br />
- 0<br />
=<br />
t<br />
( 2) <br />
=<br />
0 + t =<br />
2<br />
( 3) <br />
a t =<br />
<br />
<br />
23000/ 60 =<br />
314 - 209<br />
70<br />
314 rad/ s<br />
= 419 rad/ s 2<br />
209 + 314<br />
7 = 11710 3 rad = 186( )<br />
2<br />
R = 41902 = 838 m/ s 2<br />
an = <br />
2 R = 314 2 02 = 19710 4 m / s 2<br />
a = a 2 t + a 2 n = 837 2 + ( 19710 4 ) 2 = 19710 4 m/ s 2<br />
<br />
= arct an a n<br />
a t<br />
= arct an 19710 4<br />
837<br />
= 89 59<br />
53 1987 365 <br />
1900 114s1900 1987 , <br />
<br />
<br />
- <br />
= 0<br />
=<br />
t<br />
-<br />
3652<br />
-<br />
T 0 + t<br />
3652<br />
t<br />
= -<br />
87T 3 0<br />
= - 9610 - 22 rad/ s 2<br />
3652<br />
87T 0<br />
T 0<br />
3652114<br />
87( 31510 7 ) 3<br />
54 P , <br />
( 51) <br />
51 , <br />
90
v =<br />
<br />
<br />
a =<br />
5154 <br />
2<br />
Rcos =<br />
86400 6370103 cos<br />
<br />
2 Rcos =<br />
<br />
= 463cosm/ s<br />
2<br />
2<br />
637010 3 cos<br />
86400<br />
= 33710 - 2 cosm / s 2<br />
55 , h( <br />
52) , <br />
<br />
( 1) : <br />
h, <br />
( 2) : ,<br />
, <br />
h<br />
2h/ g <br />
52 55<br />
<br />
91
h =<br />
30m , ( <br />
<br />
, <br />
, ( 2h / 3) 2h / g )<br />
( 1) vt = ( R + h) , vb<br />
= Rvt - v b = h<br />
( 2) R , <br />
<br />
<br />
t =<br />
2h<br />
g<br />
<br />
<br />
h = 30 m, =<br />
s = ( vt - v b) t = h<br />
2h/ g<br />
2<br />
86400 = 72710- 5 rad / s<br />
s = 72710 - 5 30 230/ 98 = 5410 - 3 m<br />
56 53 <br />
AA <br />
J A A = 19310 -<br />
BB J B B =<br />
4 7 kg ¡¤m 2 , <br />
114<br />
10 - 4 7 kg ¡¤m 2 <br />
d <br />
<br />
<br />
J A A = 2m Hd 2 sin 2 <br />
2<br />
53 56 <br />
92
J B B = 2mH d 2 cos 2 <br />
2<br />
, <br />
d =<br />
J A A +<br />
, <br />
2mH<br />
J A A + J B B = 2mH d 2<br />
J BB <br />
=<br />
( 193 + 114)10 - 47<br />
216710 - 27<br />
= 95910 - 11 m<br />
J A A / J B B = t an 2 <br />
2<br />
= 2arctan<br />
J A A <br />
= 2arct an<br />
J B B<br />
193<br />
114 =<br />
104 54<br />
57C60( F ullerene, ) <br />
60 <br />
32 60 <br />
( 54) <br />
71n m<br />
( 1) , <br />
?<br />
( 2) C60 <br />
41410 - 21 J<br />
<br />
54 57 <br />
( 1) J = 2 3 mR 2<br />
= 2 3 1216710- 27 60<br />
7110 - 9<br />
2<br />
2<br />
= 10110 - 39 kg ¡¤m 2 93
( 2) E = 1 2 J <br />
2 = 1 2 J ( 2 ) 2 <br />
= 1 2E<br />
2 J<br />
=<br />
1 241410 - 21<br />
= 45610 8 Hz<br />
2 10110 - 39<br />
58 m, R <br />
l ( 55) , <br />
<br />
?<br />
5558 <br />
AA<br />
BB<br />
J A A = 2 2 5 mR 2 + m l 2 + R 2<br />
= m 14<br />
5 R2 + 2lR + l 2<br />
2<br />
J B B = 2 2 5 mR 2 = 4 5 mR 2<br />
59 R <br />
R , <br />
R/ 2 ( 56) , <br />
m <br />
<br />
, <br />
J <br />
94<br />
56 59
J 1 <br />
J 2 , a , <br />
<br />
J 1= 1 2 m 1 R<br />
2<br />
= 3 2 R 2<br />
2<br />
+ m 1<br />
2<br />
a R 2<br />
2<br />
R<br />
2<br />
2<br />
=<br />
3<br />
32 a R 4<br />
R - R 2<br />
J 2= 1 2 m 2R 2 = 1 2 a R 4<br />
J = J 2 - J 1 = 13<br />
32 a R 4<br />
2<br />
a = m , <br />
a R 2 = 4 3 m<br />
J , <br />
J = 13<br />
24 mR2<br />
510 m, R<br />
, ?<br />
57 , <br />
<br />
dm = mdS<br />
dS = Rd cos2Rcos<br />
<br />
2 R2 = 4 mcos 2 d<br />
AA , <br />
dJ =<br />
R 2 sin 2 dm =<br />
4 mR2 sin 2 cos 2 d<br />
57<br />
510 <br />
95
AA <br />
/ 2<br />
J = dJ =<br />
0<br />
4<br />
mR 2 sin 2 cos 2 d=<br />
511 58 , m1<br />
m, r , m 2<br />
1 4 mR2<br />
m2, <br />
<br />
k , m 1 ?<br />
, <br />
m 1<br />
m 2, <br />
, <br />
58511 <br />
, <br />
m 1g - T 1 = m 1a<br />
T 2 - km2g = m 2a<br />
( T 1 - T 2) r = 1 2 mr 2 <br />
, <br />
, <br />
a =<br />
= a / r<br />
m1 - km 2<br />
m 1 + m2 + m/ 2 g<br />
T 1 = ( 1 + k ) m2 + m/ 2<br />
( 1 + <br />
m1g , T 2 = k ) m 1 + km/ 2 m 2g<br />
m 1 + m 2 + m/ 2 m 1 + m 2 + m/ 2<br />
96
512 59 R 1 R2, <br />
M 1 M 2<br />
, <br />
,<br />
m1 m 2 <br />
, m 2 <br />
<br />
, <br />
m 1: T 1 - m 1g = m 1a 1<br />
m 2: m 2g - T 2 = m 2a 2<br />
, <br />
T 2R 2 - T 1R 1 =<br />
<br />
59512<br />
1<br />
2 M 1R 2 1 + 1 2 M 2R2 2) <br />
<br />
, <br />
= a1/ R1 = a 2/ R 2<br />
=<br />
( m2R 2 - m 1R 1) g<br />
( M1/ 2 + m1) R 2 1 + ( M 2/ 2 + m 2) R 2 2<br />
513 , 60cm , <br />
, <br />
?<br />
510 , m, <br />
<br />
I = 1 3 m 1l 2 1 + 1 3 m 2l 2 2<br />
= 1 3 2 5 m042 + 1 3 3 5 m06 2<br />
= 0093m<br />
97
510513 <br />
, , <br />
=<br />
mgOC<br />
I<br />
mgOC = I <br />
= m9801<br />
0093m<br />
, <br />
= 105 rad/ s 2<br />
mgOC =<br />
1 2 I <br />
2<br />
=<br />
2mgOC<br />
I<br />
=<br />
2m9801<br />
0093m<br />
= 458 rad/ s<br />
514 E k = 1 2 mv2 , <br />
E k = 1 2 J <br />
2 <br />
v =<br />
r m , <br />
r , <br />
E k = 1 2 mv2 =<br />
1 2 mr 2 <br />
2<br />
98
= 1 2 mr 2 <br />
2 = 1 2 J <br />
2<br />
515 , <br />
( 511) <br />
R , m, <br />
k , <br />
? ? <br />
, , ? <br />
?<br />
511515 <br />
511 , dS =<br />
dm = mrd dr / ( R 2 ) , <br />
dM =<br />
rdf = r kdmg =<br />
mg kr 2 d dr / ( R 2 )<br />
, <br />
M =dM =<br />
R 2 R dr<br />
2 dr =<br />
2<br />
0 0<br />
kmg<br />
<br />
2 3 kmg R<br />
rd dr , <br />
, 0 <br />
<br />
99
t =<br />
<br />
=<br />
M/<br />
<br />
<br />
= 3R<br />
1<br />
2 mR 4 kg<br />
2<br />
A = M ¡¤ = M ¡¤ t =<br />
1 2 mR 2 <br />
2<br />
<br />
E k = 1 2 J <br />
2 = 1 2<br />
1<br />
2 mR 2 = 1 4 mR 2 <br />
2<br />
516 k =<br />
20N / m <br />
, m1 = 80g<br />
( 512) , r =<br />
005m , m = 100gm1, <br />
, m 1 h = 05m ? <br />
, <br />
512516 <br />
<br />
- m 1gh + 1 2 kh 2 + 1 2 m 1v 2 + 1 2 J <br />
2 = 0<br />
J =<br />
1 2 mr 2 , = v/ r , <br />
100
v =<br />
2m 1g h - kh 2<br />
m 1 + m/ 2 = 20089805 - 205 2<br />
008 + 005<br />
= 148 m / s<br />
517 ( 515) <br />
, J 1 = 2k g ¡¤m 2 <br />
, 1 = 15r/ min , <br />
J 2 = 080kg ¡¤m 2 , 2 ? <br />
, ? ??<br />
<br />
, ,<br />
<br />
<br />
2 =<br />
1<br />
J 1 ¡¤21 = J 2 ¡¤22<br />
J 1<br />
J 2<br />
= 15 2<br />
08 =<br />
375 r / min<br />
, ( ) , <br />
<br />
A =<br />
= 1 2<br />
1 2 J 2<br />
2 2 -<br />
= 370 J<br />
1<br />
2 J 1<br />
2 1<br />
08 2 375 60<br />
2<br />
- 2 2<br />
15<br />
60<br />
518 513 , L M, <br />
m, <br />
v 0<br />
d <br />
( 1) ?<br />
( 2) ( t) , <br />
?<br />
2<br />
101
( 3) , ?<br />
( 1) , <br />
O , <br />
, <br />
mv0d =<br />
<br />
=<br />
1<br />
3 ML2 + md 2 <br />
3mv 0d<br />
ML 2 + 3md 2<br />
( 2) , <br />
<br />
mv - mv 0<br />
f =<br />
t<br />
<br />
f = -<br />
<br />
= m d - mv 0<br />
t<br />
x : F x + f = Ma Ct = M L<br />
2 t<br />
F x = - f + M L =<br />
2 t<br />
mv0 - m<br />
f = d<br />
t<br />
ML<br />
2 + md <br />
t - mv 0<br />
t<br />
y : F y - Mg - ( m<br />
2 d + mg ) = Ma Cn = M<br />
2 L/ 2<br />
F y =<br />
ML<br />
2<br />
+ md <br />
2 + ( M + m) g<br />
( 3) F x = 0, <br />
ML<br />
2 + md <br />
t -<br />
( 1) , <br />
d = 2L / 3<br />
mv0<br />
= 0<br />
t<br />
513<br />
518 <br />
519 514 L = 040m, M = 10kg, <br />
102
m = 80g <br />
v = 200m/ s ,<br />
d =<br />
3L/ 4 <br />
( 1) ;<br />
( 2) <br />
( 1) O <br />
<br />
mv 3 4 L= 1<br />
3 ML2 + m 3L 4<br />
3mv<br />
=<br />
4 1 3 ML + 9<br />
16 mL<br />
=<br />
2<br />
<br />
30008200<br />
4 1 3 104 + 9<br />
16 000804<br />
= 889 rad/ s<br />
( 2) , <br />
1<br />
2<br />
<br />
514<br />
519<br />
<br />
1<br />
3 ML 2 + 9<br />
16 mL 2 <br />
2 = Mg L 2 + mg 3 4 L ( 1 - cos )<br />
= arccos 1 -<br />
1<br />
3 M + 9<br />
16 m L<br />
2<br />
M +<br />
3 2 m g<br />
<br />
= arccos 1 -<br />
1<br />
3 1 + 9 0008 048892<br />
16<br />
1 + 3 0008 98<br />
2<br />
= 94 18<br />
520 , t =<br />
10s, J = 1200kg ¡¤m 2 M = 80k g<br />
103
, , , <br />
r = 2m ?<br />
, <br />
, <br />
<br />
2 =<br />
J<br />
J +<br />
<br />
Mr 2 1 =<br />
J 1 = ( J + Mr 2 ) 2<br />
1200<br />
2 = 0496 rad / s<br />
1200 + 802 2 10<br />
521 1200kg <br />
72k m/ h , <br />
05m, , , <br />
2500kgm 2 , :<br />
<br />
( 1) ;<br />
( 2) <br />
( 1) <br />
=<br />
2mvr<br />
I<br />
( 2) <br />
2 1 2 mv2 -<br />
2mvr = I <br />
= 2120020025<br />
2500<br />
1<br />
2 I <br />
2 = 120020 2 -<br />
= 4510 5 J<br />
= 48 rad / s<br />
1<br />
2 250048 2<br />
522<br />
<br />
( 1) ,<br />
? 25m,<br />
<br />
( 2) , , <br />
104
? 70kg, <br />
310 5 kgm 2 <br />
( 3) 30 , ?<br />
( 1) v 2 / r = g<br />
v = gr = 9825 = 495 m / s<br />
( 2) <br />
<br />
=<br />
3mvR<br />
J<br />
3mvR - J = 0<br />
= 37049525<br />
310 5 = 86710 - 3 rad/ s<br />
( 3) 30t = / ( 6 ) , <br />
+ v/ R, t <br />
= ( + v/ R) t/ ( 2 ) = 1 12 1 + v<br />
R<br />
= 1<br />
12 1 + 495<br />
86710 - 3 25<br />
= 19( )<br />
523 , <br />
52 <br />
?<br />
25d , <br />
J S =<br />
2 5 mR2 <br />
= 2 2<br />
0<br />
5 199103 ( 69610 8 ) 2 <br />
2586400<br />
= 1110 4 2 kg ¡¤m 2 / s<br />
<br />
01110 43<br />
( 011 + 32)10 43 = 33%<br />
524( 118) , PSR<br />
105
0531+ 21( 0033s) <br />
, , <br />
, 126<br />
10 - 5 s/ a <br />
( 1) <br />
( 2) 1510 30 kg( ) , <br />
10km( J/ s ) ( <br />
)<br />
( 3) , <br />
<br />
( 1) <br />
= d<br />
dt =<br />
= -<br />
d dt<br />
2<br />
T = - 2 dT<br />
T 2<br />
dt<br />
2<br />
( 0033) 2 12610 5<br />
31510 7 = - 2310 - 9 rad/ s 2<br />
( 2) <br />
dE<br />
dt =<br />
d dt<br />
<br />
1<br />
2 J <br />
2 = 1 2 J2d = 2 dt 5 mR 2 d<br />
dt<br />
= 2 5 15103 0 ( 10 4 ) 2<br />
2<br />
0033 ( - 2310- 9 )<br />
= - 2610 31 J/ s<br />
( 3) <br />
106<br />
t=<br />
=<br />
E<br />
dE<br />
dt<br />
= 1 2 J dE<br />
2<br />
dt<br />
21510 30 ( 10 4 ) 2 ( 2 ) 2<br />
25( 0033) 2 2610 31
= 41810 10 s = 1300 a<br />
525 033MR 2 , M <br />
, R <br />
, , <br />
16s , <br />
? ? ( : dE k/ E k =<br />
2d / = - 2dT / T )<br />
<br />
E =<br />
1 2 J <br />
2 = 1 2 033MR 2 2<br />
2<br />
T<br />
= 1 2 03359810 24 ( 6410 6 ) 2<br />
<br />
2<br />
2<br />
86410 4<br />
= 21410 29 J<br />
<br />
dE<br />
dt =<br />
d dt<br />
2<br />
1<br />
2 J 2<br />
= - J ( 2 ) 2<br />
dT<br />
T<br />
T 3<br />
dt<br />
= - 03359810 24 ( 6410 6 ) 2<br />
4<br />
2<br />
16<br />
<br />
( 86410 4 ) 3 10 6 31510 7<br />
= 2610 12 J/ s = - 2610 9 kW<br />
2610 9 k W, <br />
1999 <br />
2610 12 31510 7<br />
410 18<br />
<br />
M= J = J d<br />
dt = -<br />
20<br />
J2 dT<br />
T 2<br />
dt<br />
107
= -<br />
03359810 24 ( 6410 6 ) 2 216<br />
( 86410 4 ) 2 10 6 31510 7<br />
= - 3510 16 N ¡¤m<br />
526 , <br />
, <br />
?, <br />
26d <br />
<br />
T 2 = T 1<br />
J 2<br />
J 1<br />
= T 1<br />
J 1<br />
2<br />
= J 2<br />
T 1<br />
2<br />
,<br />
T 2<br />
R 2 2<br />
= 262460 ( 64106 ) 2<br />
R 2 1<br />
( 69610 8 ) 2<br />
= 31 min<br />
527 <br />
235 ( 515) , <br />
, 26 000a<br />
J = 80510 37 kg ¡¤m 2 <br />
, ©¦ dL/ dt©¦ , <br />
?<br />
<br />
dL<br />
dt<br />
= Lsin d<br />
dt<br />
= J sin d<br />
dt<br />
= 80510 37 2<br />
86400 sin235<br />
2<br />
<br />
2600031510 7<br />
= 17910 22 kg ¡¤m/ s 2<br />
<br />
108
M =<br />
515527 <br />
dL<br />
dt<br />
= 17910 2 2 N ¡¤m<br />
528 500t , <br />
200m 800r / min <br />
<br />
( 1) 74610 4 W , <br />
?<br />
( 2) 100 / s <br />
, ?<br />
( 1) P t =<br />
1 2 J <br />
2 <br />
t= J <br />
2<br />
2P = mR2 ( 2) 2<br />
22P<br />
= 5010 3 2 2 4<br />
2 800 2<br />
= 784 min<br />
2274610 4<br />
109
( 2) M = L = J = 1 2 mR 2 2<br />
= 5010 3 2 2 <br />
800 <br />
<br />
60 180<br />
= 14610 5 N ¡¤m<br />
529 034kg m 2 , <br />
036m 50m/ s , , <br />
60kg 004m <br />
<br />
M =<br />
L , <br />
= M L = dmg<br />
J v/ R =<br />
0046098036<br />
03450<br />
= 498 rad/ s<br />
530 h/ ( 4 )<br />
= 5310 - 3 5 J ¡¤s <br />
, = 2410 7 rad/ s, <br />
, 516 <br />
<br />
M =<br />
L = 5310 - 35 2410 7<br />
= 12710 - 2 7 N ¡¤m<br />
516<br />
<br />
530 <br />
<br />
110
6 <br />
61 S , l , x <br />
, S x <br />
x = x 1 -<br />
y = <br />
S <br />
u 2<br />
= lcos1 -<br />
c 2<br />
y = lsin<br />
l = ( x ) 2 + ( y ) 2 = l 1 - cos 2 u<br />
2<br />
lx <br />
= arct an<br />
u 2<br />
c 2<br />
lsin<br />
lcos1 - u 2 / c 2 = arctan tan 1 -<br />
c 2 1/ 2<br />
u 2 - 1/ 2<br />
c 2<br />
62 a , u <br />
S, S <br />
?<br />
S <br />
a = a 1 - u 2 / c 2 , a <br />
<br />
V =<br />
a a 2 = a 3 1 - u 2 / c 2<br />
63S x , <br />
Sx <br />
, S , S <br />
S S <br />
<br />
111
S S <br />
( x 1, t 1) ( x 2, t 2) ( x 1, t 1) ( x 2, t 2) ( 61) , ,<br />
6163 <br />
x <br />
2 - x <br />
1 =<br />
( x 2 - x 1) - u( t 2 - t 1)<br />
1 - u 2 / c 2<br />
t 2 = t 1, x 2 - x 1 = 1m, S <br />
x <br />
2 - x = 1/ 1 - u 2 / c 2 > 1m<br />
S , ,<br />
-<br />
x , x 2 , , x 1 <br />
, S <br />
1m <br />
64 , <br />
<br />
( v = 0998c) 22<br />
10 - 6 s, 8000m <br />
<br />
t=<br />
t/ 1 - v 2 / c 2 , <br />
l = v t =<br />
v t<br />
1 - v 2 / c = 0998310 8 2210 - 6<br />
2<br />
1 - 0998 2<br />
= 10410 4 > 8000 m<br />
<br />
112
65 S , <br />
2sS 3s<br />
S<br />
S , x 1 = x 2, <br />
<br />
t = t/ 1 - u 2 / c 2<br />
u = c 1 - ( t/ t ) 2<br />
S <br />
x = x - u t<br />
1 - u 2 / c = - u t = - c 1 - ( t/ t ) 2 t<br />
2<br />
= - 310 8 1 - ( 2/ 3) 2 3 = - 67110 8 m<br />
66 S x , <br />
1mS2mS <br />
<br />
<br />
S t =<br />
x =<br />
0, x =<br />
x<br />
1 - u 2 / c 2<br />
u = c 1 - ( x / x ) 2<br />
1m, <br />
S <br />
t=<br />
=<br />
67 l =<br />
u<br />
t - x<br />
c 2 = u x = x 1 - ( x / x ) 2<br />
c 2 c<br />
1 - u 2 / c 2<br />
2<br />
310 8 1 - ( 1/ 2) 2 = 57710 - 9 s<br />
[ ( x ) 2 +<br />
( y) 2 + ( z) 2 ] 1 / 2 ( x 1, y 1,<br />
z 1) ( x 2, y 2, z2) , : <br />
, <br />
113
( x ) 2 + ( y ) 2 + ( z ) 2 = ( x ) 2 +<br />
s = [ ( c t) 2 - ( x ) 2 -<br />
( y ) 2 -<br />
( y ) 2<br />
+ ( z ) 2<br />
( z) 2 ] 1/ 2 ( x 1,<br />
y 1, z 1, t 1) ( x 2, y 2, z 2, t 2) : <br />
, ( c t ) 2 - ( x ) 2 - ( y ) 2 - ( z ) 2 = ( c t) 2 -<br />
( x ) 2 - ( y) 2 - ( z ) 2 <br />
, ( y ) 2 = ( y ) 2 , ( z ) 2 = ( z ) 2 , <br />
( x ) 2 = ( x ) 2 - ( u t) 2 <br />
, t =<br />
0, ( x ) 2 = ( x ) 2 , <br />
( x ) 2 + ( y ) 2 + ( z ) 2 = ( x ) 2 +<br />
, <br />
( c t ) 2 - ( x ) 2 =<br />
c<br />
2<br />
u<br />
t - x<br />
c 2<br />
1 - u 2 / c 2<br />
= ( c t) 2 - ( x ) 2<br />
-<br />
( y ) 2<br />
+ ( z ) 2<br />
2<br />
x - u t<br />
1 - u 2 / c 2<br />
( ) ( y ) 2 = ( y ) 2 ,<br />
( z ) 2 = ( z ) 2 , <br />
( c t ) 2 - ( x ) 2 - ( y ) 2 - ( z ) 2<br />
= ( c t) 2 - ( x ) 2 - ( y) 2 - ( z ) 2<br />
68 , 4 5 c <br />
, , 60s<br />
<br />
?<br />
?<br />
( 1) , <br />
( 2) , <br />
( 1) , ,<br />
, , 30s <br />
114
, <br />
6268 <br />
c30 =<br />
910 9 m<br />
( 2) , , <br />
l = c30 -<br />
4<br />
c30 = 6c<br />
5<br />
, , <br />
l = l / 1 - u 2 / c 2 = 6c/ 1 - ( 4/ 5) 2 = 10c = 310 9 m<br />
, t =<br />
60s, , <br />
t =<br />
t / 1 - u 2 / c 2 = 60/ 1 - ( 4/ 5) 2 = 100 s<br />
, 10c , <br />
l 1<br />
= u t =<br />
4c 100 = 80c<br />
5<br />
, , , <br />
<br />
l + l 1 = 10c + 80c = 90c = 2710 1 0 m<br />
69 x ( S , ) , <br />
u =<br />
080c , ( S , <br />
) , t = - 6010 8 s, x = 18010 17 m, y =<br />
12010 17 m, z = 0 , <br />
, ?<br />
<br />
<br />
115
:<br />
x =<br />
x + ut<br />
1 - u 2 / c <br />
2<br />
= 18101 7 + 08310 8 ( - 6. 010 8 )<br />
1 - 08 2<br />
= 6010 16 m<br />
y = y = 1210 17 m, z = z = 0<br />
t =<br />
=<br />
t + u x <br />
c 2<br />
1 - u 2 / c 2<br />
- 6010 8 +<br />
= - 2010 8 s<br />
08<br />
310 8 1810 17<br />
1 - 08 2<br />
610 , <br />
, , <br />
<br />
( 1) ( S ) ?<br />
( 2) , <br />
( S ) ?<br />
( 3) ( S ) ?<br />
63 , 1, <br />
2, 3, <br />
4<br />
116<br />
t 1 = - 6010 8 s, x1 = 1810 17 m ,<br />
y 1 = 1210 17 m, z1 = 0<br />
t 1 = - 2010 8 s, x 1 = 6010 16 m,<br />
y 1 = 1210 17 m, z 1 = 0
63610 <br />
( 1) S <br />
t 2 = t 1 + t 12 = t 1 +<br />
x 1<br />
2 + y 1<br />
2<br />
c<br />
= - 6010 8 + 101 7 18 2 + 12 2<br />
310 8 = 1210 8 s<br />
( 2) <br />
t 3 = t 2 + t2 3 =<br />
=<br />
=<br />
t2 + u x 2<br />
c 2<br />
1 - u 2 / c + x 2<br />
2 c<br />
t 2<br />
1 - u 2 / c + ut 2<br />
2<br />
c 1 - u 2 / c 2<br />
t 2<br />
1 - u 2 / c 2 1 + u c<br />
= 12108 1 + 083108<br />
1 - 08 2 310 8<br />
= 3610 8 s<br />
( 3) <br />
t 4= t 1 + t 14 = t1 +<br />
x 2 1 + y 2 1<br />
c<br />
117
= - 2010 8 + 1017 06 2 + 12 2<br />
310 8 = 2510 8 s<br />
611 120km 9 <br />
9 0 00003 <br />
u = 08c <br />
, <br />
?<br />
1, 2, <br />
<br />
u<br />
t2 - t1 - ( x<br />
c 2 2 - x 1)<br />
t 2 - t 1 =<br />
1 - u 2 / c 2<br />
=<br />
00003 -<br />
= - 3310 - 5 s<br />
08<br />
310 8 1210 5<br />
1 - 08 2<br />
t 2 < t 1 , <br />
612 060c <br />
5s 080c <br />
<br />
( 1) <br />
<br />
( 2) , <br />
<br />
64 612 <br />
( 1) , <br />
<br />
v2 - v 1<br />
v 2 =<br />
=<br />
v2v 1<br />
1 -<br />
c 2<br />
118<br />
- 08c - 06c<br />
1 - ( - 0806) = - 095c
095c <br />
( 2) <br />
( 5s ) 1, <br />
2, <br />
, <br />
t = t 1 - v 2 1/ c 2 = 5 1 - 06 2 = 4 s<br />
613 S O , <br />
x y x , S <br />
, S c<br />
S v = c<br />
S <br />
v x =<br />
vx + u<br />
vx <br />
1 + u = v cos<br />
+ u<br />
1 + v cos u = ccos + u<br />
1 + ucos<br />
c 2 c 2 c<br />
v y = v y1 - u 2 / c 2<br />
1 + v x u = v sin1 - u 2 / c 2<br />
1 + v cos u<br />
c 2 c 2<br />
= csin1 - u 2 / c 2<br />
1 + ucos<br />
c<br />
S x <br />
<br />
= arct an vy<br />
vx<br />
= arct an<br />
sin 1 - u 2 / c 2<br />
cos + u/ c<br />
v= v 2 x + v 2 y<br />
=<br />
=<br />
c<br />
c + ucos ( u + ccos ) 2 + c 2 sin 2 1 -<br />
c +<br />
c<br />
ucos<br />
[ u<br />
2 cos 2 + 2uccos + c 2 ] 1/ 2 = c<br />
u 2<br />
c 2 1/ 2<br />
119
614 69 S S , <br />
S x v = v ( t) , a : S <br />
a <br />
a = ( 1 - u 2 / c 2 ) 3/ 2<br />
a<br />
( 1 - uv/ c 2 ) 3<br />
, u, v c , <br />
?<br />
, <br />
a = dv<br />
dt<br />
= dv dt<br />
dt dt = d dt<br />
=<br />
v - u d<br />
1 - uv/ c 2 dt<br />
( 1 - uv/ c 2 ) + u c 2 ( v - u )<br />
( 1 - uv/ c 2 ) 2 1 - uv/ c 2<br />
= ( 1 - u 2 / c 2 ) 3/ 2<br />
( 1 - uv/ c 2 ) 3 a<br />
1 - u 2 / c 2<br />
t - ux / c 2<br />
1 - u 2 / c 2<br />
S S x x , <br />
a a <br />
u, v c , a = a, <br />
615 m 0 F = F i <br />
, t, v x ?( t <br />
m 0c/ F ) ( t m 0c/ F ) , v x <br />
?<br />
F , , F =<br />
d ( mv) / dt t<br />
<br />
120<br />
v = <br />
t<br />
v =<br />
0<br />
F dt/ m = F t 1 - v 2 / c 2<br />
m0<br />
F t/ ( m0c)<br />
[ 1 + ( F t/ ( m 0c) ) 2 ] 1 / 2 c
t<br />
t<br />
x = vdt =<br />
0<br />
0<br />
F t/ m 0<br />
[ 1 + ( F t/ ( m 0c) ) 2 ] 1 / 2 dt<br />
= [ 1 + ( F t/ ( m0c) ) 2 ] 1/ 2 - 1 m 0c2<br />
F<br />
( t m 0c/ F ) ,<br />
v F t/ m 0<br />
x [ 1 + 1 2<br />
= a t<br />
F t<br />
m0c<br />
2<br />
- 1 m0c2<br />
F = F t 2<br />
2m 0<br />
= 1 2 a t 2<br />
a = F / m 0 , <br />
<br />
( t m 0c/ F ) ,<br />
vc<br />
x F t<br />
m 0c<br />
m0c 2<br />
F = ct<br />
c <br />
616 ?<br />
<br />
, <br />
<br />
<br />
m 0v<br />
= 2m 0v<br />
1 - v 2 2<br />
/ c<br />
v = 3 c/ 2 = 0866c<br />
mc 2 - m 0c 2 = 2 1 2 m 0v 2<br />
1 = 1 + v 2<br />
<br />
c 2 2<br />
1 -<br />
v 2<br />
c 2<br />
121
v =<br />
0786c<br />
617 , <br />
E k = 2810 9 eV <br />
( 1) m / s?<br />
( 2) ?<br />
( 3) 240m , <br />
??<br />
( 1) E k =<br />
c 2 - v 2 =<br />
m0<br />
1 - v 2 / c 2 - m 0 c 2 <br />
m0c 3<br />
E k + m0c 2 2<br />
c v, c 2 - v 2 = ( c + v) ( c - v) 2c( c - v) , <br />
<br />
c - v = 1 2c<br />
m 0c 3<br />
E k + m 0c 2 2<br />
E k = 2810 9 eV m0c 2 = 051110 6 eV , <br />
c - v = m 2 0c 5<br />
2E 2 k<br />
( 2) <br />
E k<br />
=<br />
p =<br />
m 0c 2 , <br />
( 091110 - 30 ) 2 ( 310 8 ) 5<br />
2( 2810 9 1610 - 1 9 ) 2 = 502 m/ s<br />
E 2 - m 2 0c 4<br />
c 2 =<br />
E k( E k + 2m 0c 2 )<br />
c<br />
p E k<br />
c = 28109 1610 - 19<br />
310 8 = 14910 - 18 kg ¡¤m/ s<br />
( 3) <br />
122<br />
F = mv 2<br />
R<br />
mc2 R = E R E k<br />
R<br />
= 2810 9 1610 - 19<br />
240/ ( 2 )<br />
= 1210 - 11 N
B = F ev F ec = 1210 - 11<br />
1610 - 19 310 8 = 025 T<br />
618 50J , <br />
, m/ s?<br />
E = m0c 2 / 1 - v 2 / c 2 <br />
v c, v +<br />
<br />
c - v = m2 0c 5<br />
c 2 - v 2 = m 2 0c 6<br />
c 2c, <br />
E 2<br />
2c( c - v) = m 2 0c 6<br />
E 2<br />
= ( 16710 - 2 7 ) 2 ( 310 8 ) 5<br />
2E 2 250 2<br />
= 13610 - 1 5 m/ s<br />
619 m p = 1672 6510 -<br />
27 kg, <br />
m n = 1674 9510 - 27 kg, <br />
m D = 3343 6510 - 2 7 kg <br />
MeV ? , <br />
?<br />
, 1358eV ,<br />
? <br />
m H = 1673 2310 - 27 kg<br />
<br />
( E ) D = ( m) D c 2 = ( 1672 65 + 1674 95 - 3343 65)<br />
10 - 27 ( 310 8 ) 2<br />
= 35510 - 1 3 J = 222 MeV<br />
<br />
123
D =<br />
( E ) D<br />
=<br />
m Dc 2<br />
35510 - 13<br />
3343 6510 - 27 ( 310 8 ) 2 = 012%<br />
<br />
H = ( E ) H<br />
=<br />
m H c 2<br />
= 14510 - 6 %<br />
13581610 - 1 9<br />
1673 2310 - 27 ( 310 8 ) 2<br />
620 , <br />
:<br />
1 1H + 1 1H + 1 1H + 1 1H 2 4He +<br />
2 0 1e<br />
( 1 1H ) mp = 1672 610 -<br />
27 kg, <br />
( 2 4He) mH e = 6642 510 - 27 kg( 0 1e) <br />
m e = 0000 910 - 27 kg<br />
( 1) ?<br />
( 2) ?<br />
( 3) 1kg ?<br />
( 4) P = 3910 2 6 W, <br />
?<br />
( 5) m = 1510 30 kg <br />
( 4) , ?<br />
( 1) <br />
E = mc 2 = ( 41672 6 - 6642 5 - 20000 9)10 - 27<br />
( 310 8 ) 2<br />
= 41510 - 12 J<br />
( 2) <br />
=<br />
E<br />
=<br />
4mpc 2<br />
41510 - 12<br />
41672 610 - 2 7 ( 310 8 ) 2 = 069%<br />
( 3) 1kg <br />
41510 - 12 ( 41672 610 - 2 7 ) = 62010 14 J/ k g<br />
124
( 4) <br />
3910 26 ( 62010 14 ) = 62910 1 1 k g/ s<br />
( 5) <br />
1510 30 ( 62910 11 ) = 23810 18 s = 75610 1 0 a<br />
6211996 <br />
( 618) 8m 2 , <br />
120V 10A <br />
1010 3 W / m 2 <br />
<br />
=<br />
10120<br />
1010 3 8 = 15%<br />
62220 60 <br />
<br />
<br />
<br />
( 1) 1kg ?<br />
( ) <br />
?<br />
( 2) 1kg <br />
? ( 10km) <br />
?620 <br />
?<br />
( 1) <br />
( E ) E = 0 -<br />
- GM Em<br />
RE<br />
= 66710- 1 1 59810 24 1<br />
63710 6<br />
= 6310 7 J<br />
125
E = ( E ) E<br />
m = 6310 7<br />
= 710 - 8 %<br />
1( 310 8 ) 2<br />
( 2) <br />
( E) N = 0 -<br />
<br />
- GMN m<br />
R N<br />
= 66710- 11 19910 3 0 1<br />
1010 3 = 1310 1 6 J<br />
=<br />
( E ) N<br />
m = 1310 1 6<br />
= 14%<br />
1( 310 8 ) 2<br />
( 069% ) 20 <br />
<br />
623 = 05 , :<br />
( 1) ;<br />
( 2) <br />
( 1) p 1 = m 1v1 = m 0 c 1 - <br />
2 = 05m 0c/ 1 - 05 2<br />
= 058m 0c<br />
E 1 = m 1c 2 = m 0c 2 1 - <br />
2 = m0c 2 1 - 05 2 = 115m 0c 2<br />
( 2) <br />
<br />
2 =<br />
+ <br />
=<br />
1 + <br />
2<br />
1<br />
125<br />
p 2 = m 2v2 = m0 2c 1 - <br />
2 2<br />
= m0c<br />
125<br />
1 -<br />
1<br />
125<br />
2<br />
= 133m 0c<br />
E 2 = m 2c 2 = m 0c 2 1 - <br />
2 2<br />
126
= m 0c 2 1 -<br />
1<br />
125<br />
2<br />
= 167m 0c 2<br />
624 05310 -<br />
110 -<br />
110 -<br />
34 J ¡¤s<br />
1 8<br />
m, <br />
18<br />
m, ,<br />
??<br />
, <br />
, <br />
<br />
L = J = 2 vm ax<br />
5 mR2 ¡¤<br />
R = 2 mRv ma x<br />
5<br />
vm ax = 5L<br />
2mR = 505310 - 3 4<br />
2091110 - 30 10 - 18<br />
= 14610 14 m / s<br />
, <br />
?<br />
625 22GeV , <br />
m =<br />
00005GeV/ c 2 , M <br />
1GeV/ c 2 , E k = 22GeV <br />
E av = 2Mc 2 E k + [ ( m + M) c 2 ] 2<br />
= 2122 + ( 0000 5 + 1) 2 = 67 GeV<br />
626 28GeV <br />
? <br />
, <br />
?<br />
<br />
, 282 =<br />
56GeV <br />
127
, <br />
<br />
E a v = 2Mc 2 E k + [ ( m + M) c 2 ] 2<br />
E k = E a v 2 - [ ( m + M) c 2 ] 2<br />
2Mc 2<br />
M = m = 0000 51GeV / c 2 E a v = 56GeV , <br />
E k = 562 - [ 20000 51] 2<br />
20000 51<br />
= 3110 4 GeV<br />
627 E 2 -<br />
c 2 p 2 <br />
( S S : E 2 - c 2 p 2 = E <br />
2 - c 2 p <br />
2 ) <br />
<br />
E <br />
2 - c 2 p <br />
2 = <br />
2 ( E - cp x ) 2 - c 2 <br />
2 p x -<br />
2<br />
<br />
+ p y 2 + p 2 z<br />
c<br />
= <br />
2 [ ( E - cp x) 2 - ( cp x - E ) 2 ] - c 2 ( p 2 y + p 2 z )<br />
= <br />
2 [ ( E - cp x + cp x - E ) ( E -<br />
+ E ] - c 2 ( p 2 y + p 2 z )<br />
= <br />
2 ( 1 - ) ( E + cp x ) ( 1 + ) ( E - cp x )<br />
- c 2 ( p 2 y + p 2 z )<br />
= E 2 - c 2 ( p 2 x + p 2 y + p 2 z ) = E 2 - cp 2<br />
cp x - cp x<br />
128
2 <br />
1 <br />
11 <br />
, 66510 3 Pa<br />
?<br />
( 1) 37315K , ?<br />
( 2) 22010 3 P a , K? <br />
( 1) , , <br />
, <br />
<br />
( 2) <br />
T 1/ T 3 = p 1/ p 3<br />
p 1 = p 3 T 1/ T 3 = 6. 6510 3 373. 15/ 273. 16<br />
= 9. 0810 3 P a<br />
T 2 = T 3 p 2/ p 3 = 273. 162. 2010 3 / ( 6. 6510 3 )<br />
= 90. 4 K<br />
= - 182. 8 <br />
12 l = 0. 7m , <br />
, <br />
h = 02m , <br />
, , , <br />
129
, p 0= 99810 4 Pa, <br />
?<br />
11 , , <br />
, <br />
p ( l -<br />
h) = p ( l - h )<br />
mmH g ( 1mmH g 133Pa ) <br />
, <br />
( p 0 + h) ( l - h) = ( p 0 - h ) ( l - h )<br />
( p 0= 0. 7510 3 mmHg)<br />
h<br />
2 - 1. 45h + 0. 05 = 0<br />
<br />
<br />
h = 0. 035 m<br />
( h= 1. 4m > l , )<br />
1112<br />
<br />
1328 7112cm ( 28 ) , <br />
3cm- 3 <br />
30cm, 15cm20 , , <br />
? 7<br />
T 1 = 273 -<br />
3 = 270K , V 1 = 201. 5 2 30cm 3 , p 1 =<br />
1atm , T 2= 273+ 7= 280K , V 2= 71. 121. 5 2 cm 3 <br />
<br />
p 2 =<br />
, <br />
p 1V 1T 2<br />
T 1V 2<br />
p 1V 1<br />
T 1<br />
= p 2V 2<br />
T 2<br />
= 1201.<br />
5 2 30280<br />
= 2. 8 at m<br />
27071. 121. 5 2<br />
14, <br />
290g/ mol<br />
130
km / 10 2 Pa / ( kg/ m 3 )<br />
20 5. 510 8. 810 - 2<br />
32 87 1210 - 2<br />
53 5810 - 1 7110 - 4<br />
90 1810 - 3 3210 - 6<br />
p V= m M RT<br />
<br />
T =<br />
p VM<br />
mR = p M R<br />
( ) , <br />
218 K, 253 K , 285 K , 196 K <br />
15 2110 4 m 3 , <br />
4510 3 kg, 20, ,<br />
?<br />
0 , 0= 1. 29kg/ m 3 1<br />
2 , <br />
( 1at m) <br />
1 = 0T 0/ T 1, 2 = 0T 0/ T 2<br />
<br />
<br />
( 1 - 2) Vg = mg<br />
0T 0<br />
1<br />
T 1<br />
-<br />
1<br />
T 2<br />
<br />
T 2 =<br />
V = m<br />
V 0T 0T 1<br />
V 0T 0 - mT 1<br />
131
=<br />
2. 110 4 1. 29273293<br />
2. 110 4 1. 29273 - 4. 510 3 293<br />
= 357 K = 84 <br />
16 , <br />
47, 86110 4 Pa , <br />
1/ 17, 42510 6 Pa, <br />
( K ) <br />
<br />
, <br />
T 2 = p 2V 2T 1<br />
p 1V 1<br />
p 1V 1<br />
T 1<br />
= p 2V 2<br />
T 2<br />
= 4. 25106 V 1320<br />
8. 6110 4 V 117<br />
= 929 K = 656 <br />
1720, 12atm, 15m<br />
, 10, 14m, <br />
11atm<br />
<br />
m= m 1 - m 2 = M R<br />
p 1V 1<br />
T 1<br />
-<br />
p 2V 2<br />
T 2<br />
= 210 - 3<br />
8. 31 1. 241.<br />
53 / 3<br />
293<br />
1. 0110 5 = 0. 32 kg<br />
-<br />
1. 141. 4 3 / 3<br />
283<br />
18, <br />
p 1, Vm 1T 1, <br />
, , p V m<br />
C ,<br />
p =<br />
CV m<br />
<br />
( 1) C( p 1, T 1 R ) <br />
( 2) T 1= 200K , 2V m1 , <br />
132
?<br />
( 1) <br />
<br />
p 1 = CVm 1<br />
V m 1<br />
p 1V m1 = RT 1<br />
C = p 1 2<br />
RT 1<br />
( 2) p = CV m, V m 2= 2V m1,<br />
1, 2 <br />
p 2 = p 1V m2/ V m 1 = 2p 1<br />
<br />
p 1Vm 1<br />
T 1<br />
= p 2V m 2<br />
T 2<br />
T 2 =<br />
p 2Vm 2T 1<br />
p 1V m 1<br />
= 4T 1 = 4200 = 800 K<br />
1910010 -<br />
1cm 3<br />
=<br />
18 atm<br />
? 20<br />
p<br />
kT = 1. 0010- 18 1. 0110 5<br />
1. 3810 - 23 293<br />
= 2. 510 7 m - 3 = 25 cm - 3<br />
1101997 7 26 <br />
: 671mbar ( 1bar = 10 5 Pa ) , <br />
- 133, 1cm 3 ?<br />
=<br />
p<br />
kT = 6. 7110 2<br />
1. 3810 - 23 ( 273. 15- 13. 3)<br />
= 1. 8710 23 m - 3 = 1. 8710 1 7 cm - 3<br />
11110 1 0 / m 3 , <br />
10 4 K <br />
133
p = kT = 10 10 1. 3810 - 23 10 4 = 1. 410 - 9 P a<br />
112( 1) 20% <br />
70% 30% 9010 6 K 36<br />
10 4 kg/ m 3 at m? ( <br />
)<br />
( 2) , , <br />
35% 65% 1510 7 K , <br />
1510 5 kg/ m 3 , atm ?<br />
p V =<br />
m RT <br />
M<br />
p ( 1) H =<br />
p =<br />
H RT<br />
M H<br />
RT<br />
M<br />
= 3. 6104 0. 78. 319. 010 6<br />
110 - 3<br />
= 1. 910 15 Pa<br />
p H e =<br />
H eRT<br />
MH e<br />
=<br />
= 3. 6104 0. 38. 319. 010 6<br />
410 - 3<br />
2. 010 14 Pa<br />
p = p H + p H e = 1. 910 15 + 0. 210 1 5<br />
= 2. 110 15 Pa = 2. 110 10 at m<br />
p ( 2) H = H RT<br />
M H<br />
= 1. 5105 0. 358. 311. 510 7<br />
110 - 3<br />
= 6. 510 1 5 Pa<br />
p H e =<br />
H eRT<br />
M H e<br />
= 1. 5105 0. 658. 311. 510 7<br />
410 - 3<br />
= 3. 010 15 Pa<br />
p = p H + p H e = ( 6. 5 + 30)10 15 = 9. 510 15 Pa<br />
= 9. 410 1 0 atm<br />
113, 50<br />
134
750mmH g , 590mmH g<br />
290g/ mol <br />
<br />
p = p 0exp -<br />
h =<br />
RT<br />
Mg ln p 0<br />
p =<br />
Mg h<br />
RT<br />
8. 31278 750<br />
ln<br />
2910 - 3 9. 8 590 = 1. 95103 m<br />
114, <br />
T T s<br />
( T - T s) , <br />
-<br />
, <br />
dT<br />
dt<br />
= A( T - T s)<br />
A , T s<br />
T 1<br />
, t, <br />
T = T s + ( T 1 - T s ) e - A t<br />
, <br />
25 , - 10<br />
40min 20, <br />
15?<br />
<br />
-<br />
<br />
<br />
dT<br />
dt<br />
= A ( T - T s )<br />
Adt = -<br />
- t 0 Adt = T T 1<br />
dT<br />
( T - T s)<br />
dT<br />
T - T s<br />
<br />
- At = ln T - T s<br />
T 1 - T s<br />
135
T = T s + ( T 1 - T s ) e - A t<br />
t 1= 40 min , <br />
20 = - 10 + ( 25 + 10) e - A t 1<br />
t 1 = 1 A<br />
t 2<br />
<br />
ln<br />
35<br />
30<br />
2520, <br />
15 = - 10 + ( 25 + 10) e - A t 2<br />
t 2 = 1 ln 35<br />
35<br />
ln<br />
A 25 = t 25<br />
1<br />
ln 35<br />
30<br />
2015<br />
t2 - t 1 = t 1<br />
= 40<br />
ln ( 35/ 25)<br />
ln ( 35/ 30) - 1<br />
ln ( 7/ 5)<br />
ln ( 7/ 6) -<br />
1 = 47 min<br />
115T y <br />
:<br />
T 0<br />
T = T 0 - y<br />
, <br />
( 1) , <br />
p = p 0exp Mg<br />
R ln 1 -<br />
y<br />
T 0<br />
( 2) 0 , ( 116) <br />
( 3) = 0. 6/ 100m, <br />
M= 29. 0g/ mol, T 0 = 273K , p 0 = 1. 00atm<br />
( 1) p y ( 115) , <br />
T = T 0- y , <br />
136
p p 0<br />
( 2) 0 , ln 1-<br />
( 116) <br />
dp<br />
p = - Mgdy<br />
R( T 0 - y )<br />
dp<br />
p = - y 0<br />
ln ( p / p 0) =<br />
Mg dy<br />
R( T 0 - y)<br />
Mg T 0 - <br />
ln y<br />
R T 0<br />
p = p 0exp Mg<br />
R ln 1 -<br />
y<br />
-<br />
T 0<br />
y<br />
T 0<br />
y<br />
, <br />
T 0<br />
p = p 0ex p -<br />
Mg y<br />
RT 0<br />
( 3) , y = 8848m, , <br />
p = p 0exp<br />
= 1. 00exp<br />
= 0. 29 atm<br />
T = T 0 - y = 273 - 0. 610 - 2 8848<br />
= 220 K = - 53 <br />
Mg<br />
R ln 1 -<br />
y<br />
T 0<br />
2910 - 3 9. 8<br />
0. 610 - 2 8. 31 ln 1 -<br />
0. 610 - 2 8848<br />
273<br />
137
2 <br />
21 , 85g, 17, <br />
65km / h :<br />
( 1) ( ) <br />
;<br />
( 2) ;<br />
( 3) <br />
( 1) <br />
t<br />
t =<br />
2 kT = 3 2 13810- 23 290<br />
= 60010 - 2 1 J<br />
( 2) E = 2 RT =<br />
<br />
<br />
r = r 2 kT = 2 2 13810- 23 290<br />
= 40010 - 2 1 J<br />
<br />
<br />
k = 2 kT = 5 23 2 13810- 290<br />
= 100010 - 21 J<br />
5<br />
2 85 28 831290 = 183103 J<br />
( 3) E k = 1 2 mv2 = 1 3 2 8510- 65000<br />
2<br />
= 139 J<br />
3600<br />
22 27 , 1mol ?<br />
1g ?<br />
E m, H e = 2 RT = 3 2 831300 = 374103 J/ mol<br />
138<br />
E m, H 2<br />
= 2 RT = 5 2 831300 = 623103 J/ mol
1g <br />
E m, O 2<br />
= 2 RT = 5 2 831300 = 623103 J/ mol<br />
E H e<br />
= E m, H e = 1 4 374103 = 093510 3 J<br />
E H 2<br />
= E m, H 2<br />
= 1 2 62310 3 = 31210 3 J<br />
E O 2<br />
= E m, O 2<br />
= 1<br />
32 62310 3 = 019510 3 J<br />
23 10 12 eV , <br />
001mol, <br />
, ?<br />
<br />
E =<br />
2 RT E =<br />
2 R T , <br />
T =<br />
2 E<br />
R = 2101 2 1610 - 19<br />
= 12810 - 6 K<br />
3001831<br />
24 10 8 K , <br />
, , : ( 1) <br />
?( 2) ?<br />
( 1) <br />
<br />
k = 3 2 kT = 3 23 2 13810- 10 8<br />
= 20710 - 15 J<br />
=<br />
12910 4 eV<br />
3RT<br />
( 2) v 2 =<br />
M = 383110 8<br />
= 15810 6 m/ s<br />
110 - 3<br />
25 , ,<br />
250K; , 310K <br />
<br />
, H e p 1V 1 = 1RT 1, O 2 p 2V2 =<br />
2RT 2p 1V1 = p 2V2, <br />
139
1T 1 = 2T 2<br />
E 0 = E 1 + E 2 = 3 2 1RT 1 + 5 2 2RT 2 =<br />
8 2 1RT 1<br />
, T , <br />
E =<br />
3 2 1RT +<br />
, , E 0<br />
<br />
T =<br />
5 2 2RT = 3<br />
2 + 5T 1<br />
2T 2<br />
8<br />
2 1RT 1 = 3<br />
2 + 5T 1<br />
2T 2<br />
8T 1<br />
3 + 5T 1/ T 2<br />
=<br />
= E , <br />
1RT<br />
1RT<br />
8250<br />
3 + 5250/ 310 = 284 K<br />
26N , <br />
f ( v) =<br />
( 1) ;<br />
( 2) v0 C;<br />
dN<br />
N dv =<br />
C( v 0 v 0)<br />
f ( v) = 0 ( v > v 0)<br />
( 3) <br />
<br />
( 1) 21<br />
( 2) <br />
<br />
0<br />
Cdv = <br />
v 0<br />
0<br />
Cdv = Cv 0 = 1<br />
C= 1/ v 0<br />
<br />
2126 <br />
( 3) v <br />
v 0<br />
= vf ( v) dv =<br />
0 vCdv =<br />
1 v 2 0<br />
0 v0 2 = v0<br />
2<br />
<br />
27 N , <br />
140
f ( v) = a v/ v 0( 0 v v0)<br />
f ( v) = a ( v 0 v 2v0)<br />
f ( v) = 0 ( v > 2v 0)<br />
( 1) <br />
a ;<br />
v 0<br />
( 2) v0 <br />
;<br />
( 3) <br />
( 1) <br />
22 <br />
<br />
<br />
0<br />
f ( v) dv = <br />
v 0<br />
0<br />
a v<br />
v0<br />
<br />
dv + <br />
2v 0<br />
2227 <br />
v 0<br />
a dv<br />
= a v 0<br />
2 + a v 0 = 3 2 a v0 = 1<br />
a =<br />
( 2) v > v0 <br />
v < v 0<br />
( N ) 1 = <br />
v 0<br />
dN = <br />
<br />
( 3) v <br />
= vf ( v) dv<br />
= <br />
v 0<br />
0<br />
0<br />
2<br />
3v 0<br />
v 0<br />
N f ( v) dv = 2 v 0<br />
( N ) 2 = N - ( N ) 1 = 1 3 N<br />
v av<br />
2v 0<br />
dv +<br />
v 0 va dv = 11v 0<br />
v 0<br />
9<br />
v 0<br />
N a dv = 2 3 N<br />
28 N <br />
, <br />
141
v 2<br />
v <br />
[ : ( v -<br />
( v - v ) 2 0, <br />
v ) ]<br />
( v - v ) 2 = v 2 + v 2 - 2vv = v 2 + v 2 - 2v v = v 2 - v 2<br />
<br />
<br />
v 2 - v 2 0<br />
v 2<br />
v <br />
29 300K , ( 1) v p<br />
; ( 2) 10v p ,<br />
( v = 1m/ s) <br />
? , 10 5 mol ? <br />
29g/ mol <br />
T =<br />
<br />
vp =<br />
N<br />
N<br />
300K , <br />
v = 1m / s,<br />
= 4m 2 kT<br />
=<br />
4<br />
v 2<br />
<br />
vp 3 e -<br />
3/ 2<br />
v 2 e - mv2 / 2kT<br />
v<br />
v2 / v 2 p<br />
v<br />
2kT<br />
m = 2RT<br />
M = 2831300<br />
2910 - 3 = 415 m / s<br />
( 1) v = vp <br />
N<br />
=<br />
N 1<br />
4<br />
<br />
v 2 p<br />
e -<br />
v 3 p<br />
( 2) v = 10 v p <br />
142<br />
=<br />
v2 p / v2 p<br />
v<br />
4 1<br />
415 e- 1 1 = 0002 = 02%
N<br />
N 2<br />
=<br />
=<br />
4<br />
<br />
( 10 vp) 2<br />
3 e - ( 10 v p ) 2 / v 2 p v<br />
vp<br />
4 100<br />
415 e- 100 1 = 2010 - 4 4 = 2010 - 42 %<br />
10 5 mol , vp<br />
, v= 1m / s <br />
N N N 1= 60210 23 10 5 02%<br />
10 v p<br />
, v =<br />
= 1210 2 6 ( )<br />
1m/ s <br />
N N N 2<br />
= 60210 23 10 5 210 - 4 2 %<br />
= 1210 - 15 = 0( ) <br />
210 t <br />
<br />
F ( t) d t =<br />
2<br />
( kT ) -<br />
3/ 2 <br />
1 / 2<br />
t e - t / kT d t<br />
, 1 2 mv 2 p<br />
<br />
t =<br />
1 2 mv 2 <br />
v =<br />
2 t<br />
m , dv =<br />
<br />
f ( v) dv = 4 m<br />
2 kT<br />
3 / 2<br />
v 2 e -<br />
( 2m t ) - 1<br />
2<br />
d t<br />
m v2 / 2kT dv<br />
<br />
F ( t ) d t = 2 ( kT ) - 3 / 2 1<br />
t<br />
2 e<br />
- / kT t<br />
d t<br />
t , F ( <br />
dF ( t )<br />
d t<br />
=<br />
t, p<br />
t ) t , <br />
1 ( kT ) 1<br />
- 3 / 2<br />
e - t / kT 2 <br />
- t , p 1/ 2<br />
+ <br />
1 / 2<br />
t , p -<br />
1<br />
kT<br />
= 0<br />
143
t , p = kT 2<br />
<br />
t , p 2 <br />
t ( vp ) = 1 2 mv2 p = 1 2 m 2kT<br />
m<br />
= kT<br />
211 210 6 K , <br />
27K , , <br />
1994 Na <br />
, 2410 -<br />
<br />
<br />
1 1<br />
K , N a <br />
v rm s, e =<br />
3kT<br />
me<br />
=<br />
313810 - 23 210 6<br />
9110 - 3 1<br />
= 09510 7 m / s<br />
<br />
v rm s, H =<br />
3RT<br />
MH<br />
=<br />
= 2610 2 m / s<br />
383127<br />
110 - 3<br />
Na <br />
vrm s , N a =<br />
3RT<br />
M N a<br />
=<br />
= 1610 - 4 m/ s<br />
38312410 - 11<br />
2310 - 3<br />
212 0108 , <br />
0531 , ? 240K , <br />
144
CO 2 H 2 ?CO 2<br />
H 2 ( , 96% CO 2 )<br />
318 , 112 , <br />
? 130K , H 2 <br />
? H 2 ( 78% <br />
H 2, H e, , <br />
)<br />
<br />
ve , M =<br />
2GM M<br />
RM<br />
=<br />
2G0108ME<br />
0531R E<br />
=<br />
vr ms , CO 2<br />
=<br />
v rms , H 2<br />
=<br />
266710 - 11 010859810 24<br />
053163710 6<br />
= 5010 3 m/ s<br />
3RT<br />
M CO 2<br />
=<br />
= 36810 2 m/ s<br />
3RT<br />
MH 2<br />
=<br />
= 17310 3 m/ s<br />
3831240<br />
4410 - 3<br />
3831240<br />
210 - 3<br />
CO 2 , H 2 , CO 2 H 2<br />
<br />
v e, J =<br />
2GMJ<br />
R J<br />
=<br />
2G318M E<br />
112R E<br />
=<br />
266710 - 1 1 31859810 2 4<br />
11263710 6<br />
= 6010 4 m/ s<br />
145
v rms , H 2<br />
=<br />
3RT<br />
MH 2<br />
=<br />
3831130<br />
210 - 3<br />
H 2<br />
= 12710 3 m/ s<br />
, H 2<br />
213 <br />
, <br />
1610 -<br />
16 kg, 300K <br />
300K , <br />
?<br />
vrm s =<br />
3kT<br />
m = 313810 - 23 300<br />
1610 - 16<br />
= 8810 - 3 m/ s<br />
, <br />
214 6210 -<br />
14 g 27 , <br />
14cm/ s R <br />
<br />
<br />
<br />
N A<br />
= 3RT<br />
v 2 m<br />
=<br />
v 2 =<br />
3kT<br />
m = 3RT<br />
N A m<br />
3831300<br />
( 1410 - 2 ) 2 6210 - 14 10 - 3<br />
= 61510 2 3 mol - 1<br />
215 89g/ mol 50<br />
10 4 g/ mol 37 <br />
?<br />
146
vr ms , a m =<br />
3RT<br />
M am<br />
<br />
v rm s, pr =<br />
=<br />
3RT<br />
M pr<br />
=<br />
3831310<br />
8910 - 3 = 2910 2 m/ s<br />
3831310<br />
510<br />
= 12 m/ s<br />
216 2 35 U 23 8 U :<br />
235 U F 6 23 8 U F 6 23 5 U F 6 <br />
, ( v ) , <br />
23 5 U F 6<br />
<br />
993% 238 U 07% 235 U , 235 U <br />
99% , 2 35 U F 6 2 38 U F 6 <br />
349 352<br />
<br />
1 2 238 U 23 5 U ,<br />
1/ 2 = 993235/ ( 07238)<br />
1 , 1v 1/ 2v 2, <br />
, ( 1v 1) v 1/ [ ( 2v 2) v 2] =<br />
1v 1 2 / ( 2v 2 2 ) , , 1v 1 / 2v 2 , <br />
1v 1<br />
<br />
238/ ( 2v <br />
2 235) , 235 U <br />
2v<br />
A =<br />
<br />
2 235<br />
1v 1<br />
238 + 2v <br />
2 235<br />
( v<br />
=<br />
2/ v 1) <br />
993/ 07 + ( v 2/ v 1) <br />
v 1 =<br />
8kT<br />
, v2 =<br />
m 1<br />
8kT<br />
m2<br />
147
A =<br />
A =<br />
099, <br />
= 2ln 99993<br />
07<br />
= 2ln 99993<br />
07<br />
( m 1/ m 2) / 2<br />
993/ 07 + ( m 1/ m 2) / 2<br />
ln m 1<br />
m 2<br />
ln 352<br />
349 = 223103<br />
217 <br />
<br />
RT<br />
ln 0<br />
N A =<br />
4 3 a 3 ( -<br />
) g h<br />
0 h , <br />
, , a <br />
( 1) ;<br />
( 2) a = 021210 - 6 m , <br />
- = 0206 7g/ cm 3 , t = 20, 3010 - 6 m <br />
7 160, 3 360, 1 620, 860 <br />
, <br />
, <br />
( 1) <br />
ln 0 =<br />
mg h<br />
kT<br />
mg h h , <br />
( m -<br />
h <br />
m W ) g , mg , <br />
( m - mW ) g h = 4 3 a 3 ( -<br />
) g h<br />
m W<br />
<br />
ln 0 = 1<br />
kT 4 3 a 3 ( -<br />
148<br />
) g h = N A<br />
RT 4 3 a 3 ( -<br />
) g h
RT<br />
ln 0<br />
N A =<br />
4 3 a 3 ( -<br />
( 2) <br />
) g h<br />
860/ 1620 = 053, 1620/ 3360 = 048, 3360/ 7160 = 047<br />
, <br />
N A =<br />
=<br />
3RT<br />
4 a 3 ( -<br />
1<br />
ln<br />
) gh 2<br />
3831293ln ( 7160/ 3360)<br />
4 ( 021210 - 6 ) 3 0206710 3 983010 - 6<br />
= 7610 23 mol - 1<br />
218 20L, 11k g CO 2 , <br />
13, ( a = 36410 5<br />
P a ¡¤L 2 / mol 2 , b =<br />
00427L/ mol) , <br />
CO 2 ?<br />
<br />
p V =<br />
=<br />
mRT<br />
MV - mb - m 2 a<br />
M 2 V 2<br />
11831286<br />
4410 - 3 2010 - 3 - 110042710 - 3<br />
-<br />
11 2 36410 5 10 - 6<br />
44 2 10 - 6 20 2 10 - 6<br />
= 25710 6 Pa<br />
<br />
p I =<br />
<br />
p in t =<br />
mRT<br />
MV =<br />
m 2 a<br />
M 2 V 2 =<br />
11831286<br />
4410 - 3 2010 - 3 = 29710 6 Pa<br />
11 2 36410 5 10 - 6<br />
( 4410 - 3 ) 2 ( 2010 - 3 ) 2 = 56910 5 Pa<br />
219 212 215, CO 2 <br />
149
K <br />
<br />
( 1) ( ( 236) ) p = f ( v) <br />
<br />
a = 3V 2 m , cp c , b = Vm , c<br />
3<br />
( 2) 212 K <br />
CO 2<br />
a b <br />
( 1) ( ( 236) ) <br />
<br />
p =<br />
p c =<br />
RT<br />
V m - b - a<br />
V 2 m<br />
RT c<br />
V m , c - b - a<br />
V 2 m , c<br />
, <br />
<br />
dp<br />
dV m c = - RT c<br />
( Vm , c - b) 2 +<br />
2a<br />
V 3 m , c<br />
= 0<br />
<br />
RT cV 3 m , c = 2a ( V m, c - b) 2 <br />
, <br />
<br />
/ , <br />
d 2 p<br />
dV 2 m c = 2RT c<br />
( V m, c - b) 3 -<br />
6a<br />
V 4 m , c<br />
= 0<br />
RT cV 4 m , c = 3a ( V m, c - b) 3 <br />
V m, c = 3 2<br />
( Vm , c - b)<br />
<br />
150
=<br />
RT c =<br />
, <br />
a =<br />
V m, c<br />
3<br />
8a<br />
9V m , c<br />
3V 2 m, cp c<br />
( 2) 212 V m, c = 95510 -<br />
10 6 Paa , b , <br />
a = 3V 2 m , cp c<br />
5 m 3 / mol, p c = 732<br />
= 3( 95510 - 5 ) 2 73210 6 = 0200 J ¡¤m 3 / mol 2<br />
b = Vm , c<br />
3<br />
= 95510- 5<br />
3<br />
= 31810 - 5 m 3 / mol<br />
220 , 100, <br />
1atm, 30110 4 cm 3 / mol<br />
( 1) cm 3 ?<br />
( 2) 1cm 2 ?<br />
( 3) , <br />
1cm 2<br />
?<br />
( 4) , <br />
?<br />
( 1) cm 3 <br />
= N A<br />
V m<br />
= 6021023<br />
30110 4 = 20010 19 cm - 3<br />
( 2) 1cm 2 <br />
= 1 4 v = 1 4 8RT<br />
M<br />
151
= 1 4 20010 8831373<br />
19<br />
10 6 1810 - 3<br />
= 33110 2 7 m - 2 ¡¤s - 1 = 33110 23 cm - 2 ¡¤s - 1<br />
( 3) , 1cm 2<br />
<br />
1cm 2 , 331<br />
10 2 3 cm - 2 ¡¤s - 1<br />
( 4) , <br />
, 1at m<br />
221 : , u <br />
v :<br />
u<br />
=<br />
[ : u 1 2 v1, v2<br />
<br />
v1<br />
<br />
2 v<br />
<br />
, ]<br />
v 2 , <br />
u 12 = v 1 - v 2<br />
u 2 1 2 = v 2 1 + v 2 2 - 2v 1v2 cos<br />
v1 v2 , <br />
u 2 1 2 = v 2 1 + v 2 2 - v 1 v2 cos<br />
, 0180, <br />
cos = 0<br />
u 2 12 = u 2 , v 2 1 = v 2 2 = v 2 , <br />
<br />
u 2 = 2 v 2<br />
u 2 = 2 v 2<br />
T <br />
, <br />
152
u<br />
=<br />
2 v<br />
<br />
222 3810 -<br />
<br />
<br />
=<br />
kT<br />
2 d 2 p<br />
13810 -<br />
23 273<br />
=<br />
2 ( 3810 - 10 ) 2 10110 5<br />
= 5810 - 8 m<br />
<br />
10 m <br />
<br />
=<br />
v =<br />
<br />
M<br />
8RT<br />
= 5810 - 8 2810 - 3<br />
8831273 = 1310- 10 s<br />
223 10 -<br />
2 m, 133<br />
10 - 3 Pa, 310 - 10 m, 27 <br />
<br />
=<br />
p<br />
kT = 13310 - 3<br />
13810 - 23 300 = 7 32101 m - 3<br />
<br />
<br />
1 =<br />
2 d 2 <br />
=<br />
( 10 -<br />
1<br />
= 78 m<br />
2 ( 310 - 10 ) 2 17<br />
3210<br />
2<br />
m) , <br />
, <br />
, <br />
= 10<br />
- 2 m, <br />
z = v<br />
=<br />
1 <br />
8RT<br />
M<br />
153
=<br />
1 8831300<br />
10 - 2 2910 - 3<br />
= 4710 4 s - 1<br />
224 160km , 1510 -<br />
500K 3010 -<br />
<br />
=<br />
=<br />
<br />
1 =<br />
2 d 2 =<br />
9 kg/ m 3 , <br />
1 0<br />
m , <br />
M<br />
2 d 2 A<br />
2910 - 3<br />
2 ( 310 - 10 ) 2 1510 - 9 60210 23<br />
80 m<br />
<br />
<br />
=<br />
v = <br />
M<br />
= 80 2910 - 3<br />
8RT 8831500 = 013 s<br />
225 , <br />
, <br />
d <br />
: ( 1) ; ( 2) <br />
( ) <br />
( 1) = d 2 + d e<br />
2<br />
d e d , <br />
v e<br />
2<br />
= d 2 / 4<br />
( 2) <br />
v e<br />
=<br />
z = u<br />
, z <br />
v e <br />
, u = ve <br />
154<br />
<br />
1 =<br />
= 4<br />
d 2
226 60km/ h, , <br />
500m/ s <br />
110 -<br />
??<br />
<br />
N =<br />
1 0 s1cm , <br />
s1<br />
vW =<br />
0013600<br />
6010 3 10 - 1 0 = 610 6<br />
<br />
s = N <br />
= N v <br />
= 610<br />
650010 - 10 = 03 m<br />
227 ( He) =<br />
10 - 5 Pa ¡¤s, M = 0004kg/ mol, v = 12010 3 m/ s, :<br />
( 1) ;<br />
( 2) <br />
( 1) = 1 3 v , <br />
= 3<br />
v = 318910 - 5<br />
000412010 3 / ( 22410 - 3 )<br />
= 26510 - 7 m<br />
( 2) <br />
= 1/ ( 2 d 2 ) =<br />
d =<br />
=<br />
1/ 2<br />
kT<br />
2 p <br />
<br />
kT<br />
2 d 2 p<br />
13810 - 23 1/ 2<br />
273<br />
<br />
2 10110 5 26510 - 7<br />
= 17810 - 1 0 m<br />
189<br />
228 l = 04cm, t = 27<br />
N 2, N 2 d = 3710 - 10 m, <br />
, N 2 ?<br />
155
k =<br />
1 3 mv <br />
<br />
cV <br />
1 = , <br />
2 d 2 <br />
, 1/ , k p = kT , , k <br />
<br />
<br />
= l , ,<br />
<br />
l , k , p <br />
:<br />
<br />
p =<br />
=<br />
kT<br />
2 d 2 l<br />
<br />
=<br />
kT<br />
2 d 2 p =<br />
13810 - 2 3 300<br />
= 17 Pa<br />
2 ( 3710 - 10 ) 2 - 2<br />
0410<br />
2291mm 20K , <br />
, <br />
, ? <br />
a ir = 23810 - 2 W / ( m ¡¤K) , gla ss = 072W / ( m ¡¤K ) <br />
<br />
<br />
Q 1<br />
= Q 2, <br />
<br />
<br />
Q 1 = - a ir<br />
S t<br />
x 1<br />
Q 2 = - gl as s<br />
l<br />
T<br />
S t<br />
x 2<br />
T T<br />
a ir = gl as s<br />
x 1 x 2<br />
156
x 2 = x 1<br />
gla s s<br />
ai r<br />
= 1 072 = 303 mm<br />
23810 - 2<br />
230 R , <br />
, <br />
, , <br />
D , W :<br />
( 1) W = 4 D( - ) R;<br />
( 2) t = W R 2 / ( 3D( - ) ) <br />
( 1) , r <br />
<br />
dM<br />
dt<br />
= - D d<br />
dr 4 r 2 = - 4 D d<br />
dr r 2<br />
, <br />
<br />
<br />
<br />
d=<br />
d<br />
dr r 2 = C<br />
C = ( -<br />
<br />
<br />
C dr<br />
R<br />
r 2<br />
) R<br />
W =<br />
dM dt<br />
= - 4 D C =<br />
4 D ( -<br />
) R<br />
( 2) <br />
t =<br />
4 3 R dM<br />
3<br />
W<br />
dt =<br />
W R 2 / ( 3D ( - ) )<br />
157
3 <br />
3131 <br />
, <br />
BC p V <br />
<br />
( 1) A <br />
T A = 300K , B, C D<br />
<br />
( 2) A D <br />
?<br />
( 3) VT <br />
3131 <br />
, <br />
V B<br />
( 1) AB : T B = T A<br />
V A<br />
BC : T C = T B = 600 K<br />
= 300 20<br />
10 = 600 K<br />
CD : T D<br />
= T C<br />
V D<br />
VC<br />
= 600 20<br />
40 = 300 K<br />
( 2) A = A A B + A B C + A C D<br />
= p A ( V B - V A ) + p B VB ln VC<br />
V B<br />
+ p C( V D - V C)<br />
= 2( 20 - 10) + 220ln 40<br />
20<br />
<br />
<br />
+ 1( 20 - 40) 10110<br />
2<br />
158<br />
= 28110 3 J
( 3) VT 32<br />
32 31 ( 3) <br />
321mol V 1 V 2 <br />
?a = b = 0 , <br />
<br />
<br />
p =<br />
<br />
A= <br />
V m2<br />
V m1<br />
p dV m<br />
RT<br />
V m - b - a<br />
V 2 m<br />
= <br />
V m2<br />
V m1<br />
= RT ln V m2 - b<br />
V m1 - b - a 1<br />
V m 1<br />
, a = b = 0, <br />
A =<br />
RT<br />
V m - b - a<br />
V 2 m<br />
RT ln V m2<br />
V m1<br />
<br />
-<br />
1<br />
V m2<br />
dV m<br />
33 33 a a cb <br />
b , 560J , 356J <br />
159
( 1) a d b b , 220J , <br />
?<br />
( 2) b ba <br />
a , 282J <br />
, ? <br />
, ?<br />
E b - E a = Q a cb - A a c b =<br />
560 - 356 = 204 J<br />
( 1) Q a d b = E b - E a + A a d b =<br />
204 + 220 = 424 J<br />
( 2) Q ba = E a - E b + A ba =<br />
- 204 + ( - 282) = - 486 J<br />
486J <br />
3333 <br />
3464g 050, ( 1) ;<br />
( 2) ? <br />
??<br />
( Q= 1) CV , mT = 64<br />
32 5 831( 50 - 0)<br />
2<br />
= 20810 3 J<br />
= Q = 20810 3 J<br />
A= 0<br />
( 2) Q= Cp , m T = 64<br />
32 5 + 2 831( 50 - 0)<br />
2<br />
= 29110 3 J<br />
= 20810 3 J<br />
A= Q - E = ( 291 - 208)10 3<br />
= 08310 3 J<br />
3510g 10 3 J , <br />
160
300K, ?<br />
Q = C p , m T =<br />
m M<br />
2QM<br />
T 2= T 1 +<br />
( + 2) Rm<br />
= 300 +<br />
+ 2<br />
R( T 2 - T 1)<br />
2<br />
210 3 4<br />
( 3 + 2)83110 = 319 K<br />
36 40010 5 Pa <br />
, 00 500 , 6010 4 J <br />
( 1) ?<br />
( 2) ?<br />
( 3) ?<br />
( 4) , <br />
?<br />
( 1) Q = C p , m T = + 2 R T <br />
2<br />
2Q<br />
=<br />
( + 2) R = 26010 4<br />
= 413 mol<br />
( 5 + 2)83150<br />
( 2) E =<br />
C V , m T =<br />
2 RT<br />
= 413 5 2 83150 = 429104 J<br />
( 3) A = Q - E = ( 60 - 429)10 4 = 17110 4 J<br />
( 4) Q = = 42910 4 J<br />
37 , 1at m, 10L, <br />
300K ( 1) ; ( 2) 400K<br />
, ? ?<br />
( Q= 1) C V , m T = 2 R T =<br />
p 1V 1<br />
T<br />
2 T 1<br />
= 5 1010 - 3<br />
2 1013105 100<br />
300<br />
161
= 084410 3 J<br />
( 2) Q= Cp , mT = + 2 R T = + 2<br />
2<br />
2<br />
p 1V 1<br />
T<br />
T 1<br />
= 7 5 2 101310 1010 - 3<br />
100<br />
300<br />
= 11810 3 J<br />
38 p V <br />
<br />
p V ( p , V) , <br />
dp<br />
dV T<br />
<br />
dp<br />
dV S<br />
=<br />
=<br />
dp<br />
dV S<br />
<br />
d<br />
dV<br />
d<br />
dV<br />
C<br />
V<br />
T<br />
C<br />
V <br />
S<br />
dp<br />
dV T<br />
= -<br />
p<br />
V ,<br />
= - p V<br />
= > 1<br />
393mol 2atm 40L, <br />
, <br />
;<br />
( 1) ;<br />
( 2) <br />
( 3) p V <br />
( 1) :<br />
p 2= p 1( V 1/ V 2) = 2( 40/ 20) 14 = 528 atm<br />
T 2= p 2V 2<br />
R = 5281013105 2010 - 3<br />
3831<br />
( 2) Q = 0 + RT 2ln V 1<br />
V 2<br />
162<br />
= 429 K
= 3831429ln 40<br />
20<br />
A=<br />
= 74110 3 J<br />
=<br />
1<br />
V1<br />
( p 1V 1 - p 2V 2) + RT 2ln<br />
- 1 V2<br />
1<br />
( 240 - 52820)1013102<br />
14 - 1<br />
+ 3831429ln 40<br />
20<br />
= 09310 3 J<br />
= Q - A = ( 741 - 093)10 3 = 64810 3 J<br />
( 3) 34 <br />
3439( 3) <br />
3102mol 300K 005m 3 ( 1)<br />
; ( 2) ; ( 3) , <br />
025m 3 <br />
?p V <br />
( 1) :<br />
T 2=<br />
T 1( V 1/ V 2) - 1<br />
A S= - E = CV , m( T 1 - T 2)<br />
163
35 310 <br />
= 2 5 2 831300[ 1 - ( 005/ 025) 1 4- 1 ]<br />
= 59110 3 J<br />
( 2) :<br />
A T = RT 1ln V 2<br />
V 1<br />
( 3) :<br />
= 80210 3 J<br />
A p= p 1( V 2 - V1)<br />
= RT 1<br />
( V 2 - V1)<br />
V 1<br />
= 2831300ln 025<br />
005<br />
= 2831300 ( 025 - 005) = 19910 3 J<br />
005<br />
, , <br />
, p V ( 35) : <br />
<br />
<br />
311 : p h <br />
<br />
164
p = p 0 1 -<br />
Mg h<br />
Cp , mT 0<br />
/ ( - 1)<br />
p 0, T 0 h = 0 , Cp , m <br />
<br />
<br />
, , <br />
, <br />
( 115) , <br />
dp = -<br />
p Mg<br />
RT dh<br />
, ( 325) , <br />
<br />
, <br />
<br />
, <br />
dp =<br />
dT = -<br />
p - 1 T - = C3<br />
T = T 0 -<br />
<br />
p<br />
dT <br />
( - 1) T<br />
- 1 Mg<br />
R dh<br />
dp<br />
p = - Mg dh<br />
= -<br />
- 1 Mg<br />
R T 0 -<br />
R h<br />
, <br />
<br />
ln p p 0<br />
=<br />
- 1 Mg<br />
R h<br />
<br />
- 1 ln 1 - - 1 Mg<br />
h<br />
RT 0<br />
Mg dh<br />
RT 0 1 -<br />
- 1 Mg<br />
h<br />
RT 0<br />
165
p = p 0 1 -<br />
- 1<br />
R<br />
Mg<br />
h<br />
T 0<br />
/ ( - 1 )<br />
= p 0 1 -<br />
Mg h<br />
Cp , m T 0<br />
/ ( - 1)<br />
312 366m , <br />
0152m, 454kg, <br />
098m, 311m/ s, 24310 8 Pa<br />
, :<br />
=<br />
( 1) ? <br />
12<br />
( 2) ( ) <br />
l = 366m, D = 0152m , m = 454kg, l 1 =<br />
098m , v 1 = 311m/ s, p 1 = 24310 8 P a, = 12<br />
( 1) :<br />
p 2= p 1<br />
A=<br />
V 1<br />
V 2<br />
<br />
= p 1<br />
= 050010 8 Pa<br />
=<br />
l 1<br />
l<br />
1<br />
( p 1V1 - p 2V 2)<br />
- 1<br />
<br />
= 24310 8 098<br />
366<br />
1<br />
( 243098 - 0500366)<br />
12 - 1<br />
<br />
4 01522 10 8<br />
= 49910 6 J<br />
( 2) A= 1 2 mv 2 -<br />
v =<br />
2A<br />
m + v 2 1 =<br />
1<br />
2 mv 2 1 , <br />
249910 6<br />
454<br />
12<br />
+ 311 2 = 563 m/ s<br />
313 : p 1, <br />
V 1, ( 312) p 2, <br />
V 2, <br />
166
E 1 + p 1V1 = E 2 + p 2V2<br />
E + p V H , , <br />
, , <br />
, p 1 <br />
, , <br />
p 2, , <br />
A = p 2V 2 - p 1V1<br />
, <br />
<br />
0 = E 2 - E 1 + A = E 2 + p 2V 2 - ( E 1 + p 1V 1)<br />
E 1 + p 1V1 = E 2 + p 2V2<br />
314: <br />
, p = p 1 = p 2<br />
Q= E 2 - E 1 + A = E 2 - E 1 + p ( V 2 - V 1)<br />
= E 2 - E 1 + p 2V 2 - p 1V 1<br />
= ( E 2 + p 2V 2) - ( E 1 + p 1V 1) = H 2 - H 1<br />
315 1mol :<br />
( 1) , , <br />
, CV , mT ( CV , m<br />
) <br />
( 2) , , ,<br />
, <br />
p in = a / V 2 m( <br />
( 235) ) <br />
: , V m, 0 Vm <br />
a / V m , 0 - a / V m<br />
( 3) <br />
E = CV , mT -<br />
a<br />
V m<br />
+ E 0<br />
167
E 0 <br />
( 1) E k = CV , mT <br />
( 2) , <br />
, <br />
E p0 - E p = - <br />
V m<br />
V m, 0<br />
p indV =<br />
a<br />
Vm<br />
-<br />
a<br />
V m, 0<br />
( 3) , <br />
E = E k + E p = CV , mT -<br />
E 0 E p0, a / V m , 0 <br />
a<br />
V m<br />
+ E 0<br />
<br />
316 : <br />
, T 0, p 0, V 0, <br />
, <br />
T 1 p 1 T 2<br />
V 1, <br />
<br />
= ( p 1 - p 0) V 0<br />
( V 1 - V 0) p 0<br />
T 0 = p 0V 0<br />
R<br />
<br />
T 1 = p 1V 1<br />
R = p 1V 0<br />
R<br />
<br />
T 2 = p 2V 2<br />
R = p 0V 1<br />
R<br />
, <br />
, <br />
<br />
168<br />
CV , m ( T 1 - T 0) = Cp , m( T 2 - T 0)
=<br />
Cp , m<br />
CV , m<br />
= T 1 - T 0<br />
T 2 - T 0<br />
=<br />
( p 1 - p 0) V0<br />
( V 1 - V 0) p 0<br />
317 <br />
p V =<br />
, <br />
( 1) = 0, 1, ?<br />
( 2) : <br />
p 2V2 - p 1V 1<br />
- 1<br />
( 3) : <br />
Cm<br />
= CV , m<br />
( 1) Cm<br />
<br />
- <br />
1 - <br />
( 1) = 0, p V = p = , ;<br />
= 1, p V = p V = , ;<br />
= , p V = p V = , ;<br />
= , p 1 V = p<br />
1<br />
V = V =<br />
( 2) <br />
A = - V 2<br />
p dV =<br />
V 1<br />
- V 2<br />
V 1<br />
=<br />
1<br />
( p 2V 2 - p 1V 1)<br />
- 1<br />
C<br />
V dV =<br />
, <br />
C<br />
- 1 ( V 1- <br />
2 - V 1- <br />
1 )<br />
( 3) 1mol T 1 T 2<br />
Q= E + A = E -<br />
= CV , m( T 2 - T 1) -<br />
<br />
Cm=<br />
Q<br />
T 2 - T 1<br />
= CV , m -<br />
= CV , m -<br />
CV , m - CV , m<br />
- 1<br />
A<br />
R<br />
- 1 ( T 2 - T 1)<br />
R<br />
- 1<br />
= CV , m<br />
<br />
- <br />
1 - <br />
169
= 0 , , Cp , m = CV , m;<br />
= 1 , , CT , m = , ;<br />
= , , CS , m = 0, ;<br />
= , , CV , m = CV, m<br />
318 10mol , <br />
, 209J, 1K<br />
, ?<br />
E =<br />
CV , m T = 10 3 8311 = 1247 J<br />
2<br />
Q = + W = 1247 - 209 = - 843 J<br />
Q<br />
Cm =<br />
T = - 843<br />
101 = - 843J/ ( mol ¡¤K)<br />
319 36 40L <br />
, , <br />
, A , B <br />
1mol , <br />
101310 3 Pa , <br />
B , A <br />
, :<br />
( 1) B , <br />
;<br />
( 2) ;<br />
( 3) B <br />
( 1) A , <br />
p A V <br />
A =<br />
C = p A 1V <br />
A 1<br />
<br />
170<br />
= 101310 5 002 1 4 = 4210 2<br />
p A = p B, VA = V - VB = 004 - VB<br />
36<br />
319
p B( 004 - V B) = 4210 2<br />
B , p B<br />
<br />
= RT B<br />
VB<br />
, <br />
( 2)<br />
T B ( 004 - V B) = 51V B<br />
T A 2= T A 1<br />
T B 2=<br />
= p A 1V A 1<br />
R<br />
= 322 K<br />
V A 1<br />
V A 2<br />
- 1<br />
V A 1<br />
V A 2<br />
- 1<br />
51V B 2<br />
( 004 - V B 2) 1 4 =<br />
( 3) Q B = E B + A B<br />
= 1013105 002<br />
002<br />
831<br />
001<br />
51003<br />
( 004 - 003) 14 = 965 K<br />
0 4<br />
= 2 R( T B 2 - T B 1) + V B2<br />
V B1<br />
p BdV B<br />
= 2 R T B 2 - p B 1V B 1<br />
R<br />
+ V B2<br />
4210 2<br />
dV<br />
V B1<br />
( 004 - V B) B<br />
= 2 R T B 2 -<br />
p B 1V B 1<br />
R<br />
+ 42102<br />
1 - <br />
( 004 - V B1) 1- - ( 004 - VB 2)<br />
1- <br />
= 5 2 831 965 - 101310 5 002<br />
831<br />
+ 4210 2<br />
1 - 14 [ 002 - 0 4 - 001 - 04 ]<br />
= 16610 4 J<br />
320 37 T V <br />
mol , CV , m<br />
a <br />
171
T 1, V 1, b V 2, ca :<br />
( 1) c :<br />
( 2) <br />
( 1) ca ,<br />
T c =<br />
T a<br />
Va<br />
V c<br />
- 1<br />
= T 1<br />
V 1<br />
V 2<br />
- 1<br />
( 2) a b , <br />
37 320<br />
<br />
Q 1 = RT 1ln V 2<br />
V 1<br />
bc , <br />
<br />
Q 2= CV , m ( T b - T c ) = CV , mT 1 1 -<br />
= CV , mT 1 1 -<br />
= 1 -<br />
Q2<br />
Q1<br />
= 1 -<br />
V 1<br />
V 2<br />
- 1<br />
CV , m<br />
R<br />
321 <br />
( ) <br />
a b cd bc<br />
d a ( 38) ,<br />
<br />
1 -<br />
V 1<br />
V 2<br />
ln V 2<br />
V 1<br />
T c<br />
T 1<br />
- 1<br />
= 1 -<br />
V 1<br />
V 2<br />
V <br />
1<br />
V2<br />
- 1<br />
<br />
- 1<br />
V <br />
1<br />
- 1<br />
V 2<br />
bc <br />
38321 <br />
Q 1 = Cp , m ( T c - T b)<br />
172
d a <br />
Q 2 = CV , m ( T d - T a )<br />
= 1 -<br />
Q 2<br />
Q 1<br />
= 1 -<br />
cd , <br />
a b , <br />
bc , <br />
<br />
T d<br />
T a<br />
CV , m( T d - T a )<br />
Cp , m ( T c - T b) = 1 - 1<br />
<br />
T c<br />
T d<br />
T b<br />
T a<br />
=<br />
=<br />
T c<br />
T b<br />
V 1<br />
- 1<br />
V 1<br />
V1<br />
V2<br />
- 1<br />
= V 1<br />
V 2<br />
= T d<br />
T b<br />
T c<br />
T c T a T b<br />
, <br />
= 1 -<br />
V 2<br />
- 1<br />
V1<br />
V2<br />
=<br />
V 1<br />
- 1<br />
V 1<br />
V 2<br />
V 1<br />
- 1<br />
V 2<br />
T b<br />
T a<br />
T d<br />
T a<br />
T c<br />
T b<br />
- 1<br />
- 1<br />
322 1854 39<br />
, ab, cd , ef T , T 2 T 1<br />
, bc, d e, f a <br />
cd ef <br />
, T 1, T 2, T , <br />
a b <br />
173
Q a b =<br />
cd <br />
Q cd<br />
ef <br />
Q ef<br />
RT ln V b<br />
Va<br />
= RT 2ln Vd<br />
V c<br />
= RT 1ln V e<br />
<br />
T V <br />
b<br />
- 1<br />
<br />
Vf<br />
= T 2V <br />
c - 1<br />
, T 2 = T 1<br />
V e<br />
Vd<br />
39 322 <br />
- 1<br />
, T = T 1<br />
V f<br />
V a<br />
- 1<br />
Q cd<br />
= Q ef , <br />
<br />
V b<br />
V a<br />
= V e Vc<br />
V f V d<br />
ln ( V d/ V c)<br />
ln ( V e/ V f ) = T 1<br />
T 2<br />
= 1 -<br />
Q ef<br />
Q a b +<br />
Q cd<br />
= 1 -<br />
R T ln V b<br />
V a<br />
RT 1ln Ve<br />
V f<br />
+ T 2ln V d<br />
V c<br />
= 1 -<br />
T<br />
ln Ve<br />
V f<br />
T 1ln V e<br />
V f<br />
- ln V d<br />
Vc<br />
+ T 2ln Vd<br />
V c<br />
= 1 -<br />
T 1T 2<br />
T ( T 2 - T 1) + T 1T 2<br />
323 , <br />
174
1 2<br />
:<br />
=<br />
1 + ( 1 - 1) 2<br />
<br />
<br />
<br />
T 1, T 2, T 3 , Q 1 Q2 <br />
, A 1 A 2 <br />
, <br />
A 1 =<br />
<br />
1Q1, A 2 = 2Q 2 = 2( Q 1 - A 1) = Q 1 2( 1 - 1)<br />
1 = 1 -<br />
= A 1 + A 2<br />
Q1<br />
T 2<br />
, 2 = 1 -<br />
T 1<br />
= 1 + ( 1 - 1) 2<br />
T 3<br />
, <br />
T 2<br />
= 1 -<br />
T 2<br />
T 1<br />
+ 1 - 1 -<br />
<br />
T 2<br />
T 1<br />
1 -<br />
T 3<br />
T 2<br />
= 1 -<br />
324 <br />
25, 300m 5<br />
( 1) ?<br />
( 2) <br />
1MW, ?<br />
( 3) 25 <br />
5 , 25 <br />
?<br />
T 2 278<br />
( 1) = 1 - = 1 -<br />
T 1 298 = 67%<br />
( 2) = 1 - Q 2/ Q 1 = 1 - Q2/ ( A + Q 2) <br />
T 3<br />
T 1<br />
175
Q 2 =<br />
A( 1 - )<br />
= 10 6 ( 1 - 0067)<br />
0067<br />
14MW <br />
( 3) Q 1 = A + Q2 = CmT<br />
= 1410 6 J<br />
m = A + Q 2<br />
C T = 1106 + 1410 6<br />
41810 3 ( 25 - 5) = 1810 2 kg<br />
1810 2 kg/ s =<br />
6510 2 t / h <br />
325 , -<br />
10, <br />
15 , 10 3 J <br />
, ?<br />
<br />
<br />
Q 2 =<br />
AT 2<br />
T 1 - T 2<br />
w = Q 2<br />
A = T 2<br />
T 1 - T 2<br />
= 10 3 263<br />
288 - 263 = 105104 J<br />
326 310 ( <br />
212 ) , d a bc <br />
a , b, c, d <br />
:<br />
T / p / kPa V/ m 3 E / kJ<br />
<br />
<br />
a 80 2 305 0068 2 1 969 0%<br />
b 80 2 305 0009 46 1 171 100%<br />
c 5 363 0220 2 1 015 54%<br />
d 5 363 0451 3 1 641 5%<br />
?<br />
( 1) , <br />
176
?<br />
310 326 <br />
( 2) , <br />
( 3) , ?<br />
( 4) , <br />
?<br />
( Q 1) cd = E d - E c + A cd<br />
= E d - E c + p c( V d - V c)<br />
= ( 1641 - 1015)10 6<br />
+ 36310 3 ( 04513 - 02202)<br />
= 71010 5 J<br />
( 2) - Q a b= - A a b - ( E b - E a )<br />
= p a ( V a - V b) - ( E b - E a )<br />
= 230510 6 ( 00682 - 000946)<br />
- ( 1171 - 1969)10 6<br />
= 93310 5 J<br />
( 3) <br />
A = A d a + A a b -<br />
A bc -<br />
A cd<br />
177
= E a - E d + p a ( V a - V b) - ( E b - E c) - p c( V d - V c)<br />
= ( 1969 - 1641)10 6 + 230510 6<br />
( 00682 - 000946) - ( 1171 - 1015)10 6<br />
- 36310 3 ( 04513 - 02202)<br />
= 22310 5 J<br />
( 4) w = Q 2<br />
A<br />
= Q cd<br />
A = 71010 5<br />
= 318<br />
22310 5<br />
<br />
w C =<br />
T 2<br />
T 1 - T 2<br />
=<br />
278<br />
80 - 5 = 371<br />
327 32, <br />
21 3810 4 kJ/ h , <br />
?<br />
A = Q 2<br />
w > Q 2<br />
w C<br />
<br />
=<br />
Q 2( T 1 - T 2)<br />
T 2<br />
= 38104 ( 305 - 294)<br />
294<br />
= 1410 3 K J/ h<br />
P m in = A m in<br />
t<br />
= 14106<br />
3600<br />
= 039 kW<br />
328 <br />
311 , <br />
1 2 ( T 1) 3 4<br />
( T 2) , <br />
<br />
, <br />
( <br />
4 1 <br />
2 3 <br />
178<br />
311328
, )<br />
12 <br />
34 <br />
Q 1 = RT 1ln V 1<br />
V 2<br />
Q 2 = RT 2ln V 1<br />
V 2<br />
41 23 ,<br />
<br />
w = Q A = Q2<br />
Q1 - Q2<br />
=<br />
T 2<br />
T 1 - T 2<br />
= w C<br />
329 : , <br />
, <br />
<br />
t 1 = 210,<br />
t 2 = 15, <br />
t 3 = 60<br />
<br />
, <br />
, <br />
1k g , <br />
? <br />
? <br />
33410 7 J/ k g<br />
312 329 <br />
312 , T 1 = 483K , T 2 = 333K , T 3 = 288K,<br />
Q 1 = 33410 7 J<br />
A = Q 1 = 1 -<br />
T 2<br />
T 1<br />
Q 1<br />
179
Q 2= Q 1 - A = T 2<br />
Q 1<br />
T 1<br />
Q 2 = Q 1 + A = A( + 1) = A<br />
T 3<br />
T 2 - T 3<br />
+ 1<br />
Q 2<br />
+ Q 2 =<br />
= A<br />
=<br />
T 2<br />
T 1<br />
+<br />
333<br />
483<br />
= 99810 7 J<br />
T 2<br />
T 2 - T 3<br />
T 2( T 1 - T 2)<br />
T 1( T 2 - T 3)<br />
<br />
Q1<br />
= ( T 1 - T 2) T 2<br />
T 1( T 2 - T 3) Q 1<br />
333( 483 - 333)<br />
+<br />
483( 333 - 288) 334107<br />
99810 7<br />
44310 7 = 299( )<br />
180
4 <br />
4. 11mol ( ) 4. 1 <br />
a b c<br />
<br />
4141 <br />
a bc , <br />
A= 1 2 ( p a + p b) ( Vb - V a ) + 1 2<br />
( p b + p c) ( Vc - V b)<br />
= 1 2 ( 8 + 6)10 5 ( 2 - 1)10 - 3<br />
<br />
+ 1 2 ( 8 + 4)105 ( 3 - 2)10 - 3<br />
= 1. 310 3 J<br />
Q= E c - E a + A = CV , m( T c - T a ) + A<br />
=<br />
<br />
2 R( T c - T a ) + A = <br />
2 ( p cVc - p a V a ) + A 181
= 5 2 ( 43 - 61) 105 10 - 3 + 1. 310 3<br />
= 2. 810 3 J<br />
S= CV ln T c<br />
T a<br />
= R 2 ln p c<br />
p a<br />
+ Rln V c<br />
V a<br />
=<br />
+ + 2 ln V c<br />
2 V a<br />
p cVc<br />
Rln<br />
2 p a V a<br />
= 8. 31 5 2 ln 4 6 + 5 + 2<br />
2 ln 3 1<br />
= 23. 5 J/ K<br />
+ Rln V c<br />
V a<br />
4. 2 30g, - 40 100 <br />
c1 = 2. 1J/ ( g K ) , , c2 = 4. 2<br />
J/ ( gK ) , 1. 01310 5 Pa = 334J/ g, <br />
L= 2260J/ g<br />
- 400<br />
d Q<br />
T = T 2 c1mdT<br />
R T<br />
S 1 = T 2<br />
R T 1<br />
0<br />
<br />
T 1<br />
S 2 = R<br />
d Q<br />
T<br />
2<br />
T 2<br />
= Q 2<br />
T 2<br />
0100<br />
d Q<br />
T = T 3 c2mdT<br />
R T 2<br />
T<br />
S 3 = T 3<br />
R T 2<br />
= c1mln T 2<br />
T 1<br />
= m<br />
T 2<br />
= c2mln T 3<br />
T 2<br />
100100<br />
d<br />
S 4 =<br />
Q<br />
= Q4<br />
= Lm<br />
R T 3 T 3 T 3<br />
T 3<br />
- 40100<br />
182<br />
S= S 1 + S 2 + S 3 + S 4
= m c1ln T 2<br />
T 1<br />
+<br />
<br />
+ c2ln T 3<br />
+ L T 3<br />
T 2<br />
T 2<br />
= 30 2. 1ln 273<br />
233 + 334<br />
273<br />
= 268 J/ K<br />
373<br />
+ 4. 2ln<br />
273 + 2260<br />
373<br />
4. 3 1mol 1. 01310 5 Pa 300K <br />
1200K Cp , m =<br />
a + bT , a = 2. 310 4 J/ ( mol ¡¤K ) , b = 592 J/ ( mol ¡¤K 2 ) <br />
S =<br />
T 2<br />
R T 1<br />
= a ln T 2<br />
T 1<br />
d Q<br />
T = R T 2<br />
T 1<br />
Cp , mdT<br />
T<br />
+ b( T 2 - T 1)<br />
= T 2<br />
R T 1<br />
( a + bT )<br />
dT<br />
T<br />
= 12. 310 4 ln 1200 + 15. 92( 1200 - 300)<br />
300<br />
= 3. 7210 4 J/ K<br />
4. 4 810 6 J , <br />
? , 273K<br />
<br />
T 1 = 36= 309K, T 2 =<br />
273K , <br />
S = S 1 + S 2 = - Q<br />
T 1<br />
= 3410 3 J/ K<br />
+ Q T 2<br />
= 810 6 - 1<br />
309 + 1<br />
273<br />
45210 8 J/ h<br />
20, - 20, ( J/ ( K <br />
s) ) ?<br />
S = S 1 + S 2 = - Q + Q - 1<br />
= 210 8<br />
T 1 T 2<br />
293 + 1<br />
253<br />
= 10810 5 J/ K<br />
<br />
183
S<br />
t =<br />
108105 / 3600 = 30 J/ ( K ¡¤s)<br />
46 , <br />
20k W ( J/ ( K ¡¤s) ) ? <br />
12<br />
<br />
S<br />
t =<br />
Q<br />
T t =<br />
20103<br />
2851 =<br />
70 J/ ( K ¡¤s)<br />
47 65m, <br />
23m 3 / s20, ?<br />
T 1<br />
:<br />
<br />
<br />
g h<br />
c =<br />
mg h = cm( T 2 - T 1)<br />
T 2 = g h<br />
c + T 1<br />
9865<br />
4210 3 = 015 T 1 = 293<br />
, 1 <br />
S= T 2<br />
R T 1<br />
d Q<br />
T = R T 2<br />
T 1<br />
= cmln 1 + gh<br />
cT 1<br />
cmdT<br />
T<br />
= 23109865<br />
293<br />
= cmln T 2<br />
T 1<br />
cm gh<br />
cT 1<br />
T 2 T 2<br />
= cmln T 1 + g h/ c<br />
T 1<br />
= mg h<br />
T 1<br />
= 5010 4 J/ K<br />
48 ( 1) 1kg, 0 100 , <br />
, , <br />
?<br />
184
( 2) 1kg , 0, 50 <br />
, 100<br />
( ) , ( 1) <br />
( 1) S =<br />
<br />
T 2<br />
S w a t er + S r es er voir =<br />
T 1<br />
= cmln T 2<br />
+<br />
T 1<br />
- cm( T 2 - T 1)<br />
T 2<br />
cmdT<br />
T<br />
+ Q T 2<br />
= 41810 3 1<br />
ln 373<br />
273 + - 41810 3 1( 373 - 273)<br />
373<br />
= 184 J/ K > 0<br />
( 2) S = S w 1 + S w 2 +<br />
= S w + S r 1 +<br />
S r1 + S r 2<br />
S r2<br />
= cmln T 2 - cm( T <br />
+ - T 1)<br />
T 1 T <br />
= 41810 3 1ln 373<br />
273<br />
-<br />
41810 3 1( 323 - 373)<br />
323<br />
-<br />
41810 3 1( 373 - 323)<br />
373<br />
= 97 J/ K ,<br />
- cm( T 2 - T <br />
+ )<br />
T 2<br />
, , <br />
, , <br />
<br />
49 25kg 07kg , 0<br />
<br />
( 1) 0 <br />
<br />
<br />
( 2) 100 <br />
185
( 1) , 09kg <br />
0<br />
S w = - Q<br />
T = - 334103 09<br />
= - 11010 3 J/ K<br />
273<br />
, ( 0) <br />
S e n = Q T = 33410 3 09<br />
273<br />
<br />
S w +<br />
( 2) <br />
S w = -<br />
<br />
S e n = -<br />
<br />
S w =<br />
S en = 0<br />
Q<br />
T <br />
= - 33410 3 09<br />
373<br />
= 11010 3 J/ K<br />
1. 1010 3 J/ K<br />
= - 08110 3 J/ K<br />
S w + S en = ( 110 - 081)10 3 = 02910 3 J/ K<br />
410 1mol ( = 14) <br />
42 , 13 <br />
, 14 <br />
S =<br />
S 3- S 1:<br />
( 1) 123;<br />
( 2) 13;<br />
( 3) 143<br />
( 1) S = S 12 + S 23<br />
42410 <br />
186
= T 2<br />
T 1<br />
Cp , mdT<br />
T<br />
+ T 3<br />
T 2<br />
CV , mdT<br />
T<br />
= Cp , mln T 2<br />
+ CV , mln T 3<br />
T 1<br />
T 2<br />
T 1 = T 3, Cp , m = CV , m + R, <br />
( 2) S = Q T 1<br />
( 3) S =<br />
S =<br />
=<br />
S 1 4 +<br />
1<br />
T 1<br />
= Cp , mln T 3<br />
T 4<br />
Rln T 2<br />
T 1<br />
RT 1ln V 2<br />
V 1<br />
= Rln V 2<br />
V 1<br />
T 3<br />
S 43 = 0 +<br />
T 4<br />
= Cp , mln T 1<br />
T 4<br />
= Rln V 2<br />
V 1<br />
Cp , mdT<br />
T<br />
p 1V 1 = p 3V 2 T 1/ T 4 = ( p 4/ p 1) 1 - <br />
1- <br />
= ( p 3/ p 1)<br />
=<br />
( V 1/ V 2)<br />
<br />
1- <br />
,<br />
S =<br />
Cp , mln T 1<br />
T 4<br />
= Cp , m<br />
S , <br />
S =<br />
Rln V 2<br />
V 1<br />
1 - <br />
ln V 1<br />
V 2<br />
= 18. 31ln 60<br />
20<br />
= Rln V2<br />
V1<br />
= 913 J/ K<br />
411 , , <br />
, m, , T 1<br />
T 2 ><br />
T 2, <br />
T 1 <br />
, cp<br />
<br />
T 0 = ( T 1 + T 2) / 2<br />
( m mol)<br />
<br />
S= S 1 + <br />
S 2 = <br />
T 0<br />
T 1<br />
mcp<br />
T dT + T 0<br />
T 2<br />
mcp<br />
T dT<br />
187
= mcpln T 2 0<br />
T 1T 2<br />
= mcp ln ( T 1 + T 2) 2<br />
4T 1T 2<br />
( T 1 + T 2) 2 > 4T 1T 2, S ><br />
0<br />
412 T 1 = 300K , p 1 = 3039<br />
10 5 Pa , V 1 = 4m 3 16m 3 , <br />
, <br />
<br />
14) <br />
( 1) p V T S <br />
( 2) ( =<br />
( 1) 43 <br />
<br />
43412 <br />
( 2) <br />
A T=<br />
RT 1ln V2<br />
V1<br />
= p 1V 1ln V2<br />
= 303910 5 4ln 16<br />
4 = 16910 6 J<br />
V1<br />
188
S T = Q Rln<br />
T 1= V2<br />
V1<br />
= p 1V 1<br />
ln V 2<br />
T 1 V 1<br />
= 3039105 4<br />
ln 16<br />
300 4 = 563103 J/ K<br />
A V = 0, <br />
T 3<br />
S V =<br />
T 2<br />
CV , mdT<br />
T<br />
= CV , mln T 3<br />
T 2<br />
T 3/ T 2 = T 3/ T 1 = ( V 1/ V 2) - 1 , <br />
S V =<br />
CV, mln V 1<br />
V 2<br />
= p 1V 1<br />
( - 1) CV , mln V1<br />
RT 1<br />
V2<br />
- 1<br />
= ( - 1) CV , mln V 1<br />
V 2<br />
= p 1V 1<br />
ln V 1<br />
T 1 V 2<br />
= 3039105 4<br />
ln 4 300 16 = - 563103 J/ K<br />
<br />
A S=<br />
<br />
1<br />
p 1V 1<br />
( p 2V 2 - p 1V 1) =<br />
- 1 - 1<br />
= 3039105 4<br />
14 - 1<br />
= - 13010 6 J<br />
4<br />
16<br />
14- 1<br />
S S = 0<br />
<br />
A = A T + A V + A S<br />
<br />
- 1<br />
V1<br />
V2<br />
- 1<br />
- 1<br />
= 16910 6 + 0 + ( - 13010 6 ) = 03910 6 J<br />
S =<br />
S T + S V + S S<br />
= 56310 3 + ( - 56310 3 ) + 0 = 0<br />
<br />
413 mol <br />
, p 1<br />
p 2, <br />
189
S > 0<br />
S = Rln ( p 1 + p 2) 2<br />
4p 1p 2<br />
T T , V1 V 2<br />
, <br />
, , <br />
<br />
1<br />
2 CV , mT +<br />
1<br />
2 CV , mT =<br />
1<br />
T = T<br />
2 ( + ) CV , mT <br />
<br />
<br />
, , <br />
, V = ( V 1 + V 2) / 2, <br />
V 1<br />
+ V 2<br />
p =<br />
2 RT<br />
V 1 + V 2<br />
=<br />
2 RT<br />
RT<br />
+ RT =<br />
p 1<br />
p 2<br />
2p 1p 2<br />
p 1 + p 2<br />
V , <br />
S= S 1 +<br />
= Rln<br />
S 2 = Rln V + Rln V<br />
V1 + V2<br />
2V 1<br />
= Rln ( V 1 + V 2) 2<br />
4V 1V 2<br />
= Rln ( p 1 + p 2) 2<br />
4p 1p 2<br />
V 1<br />
+ Rln V 1 + V 2<br />
2V 2<br />
, , , <br />
<br />
190<br />
V2
( p 1 + p 2) 2 > 4p 1p 2, S ><br />
0<br />
<br />
414 , <br />
( m, cp , T ) ( m , <br />
cp , T ) , <br />
, <br />
<br />
cpm( T - T ) = cp m ( T - T )<br />
T T <br />
<br />
<br />
S = cpmln T cp m ln<br />
T + T <br />
T <br />
d( S) = cpm<br />
T dT +<br />
<br />
<br />
<br />
m dT <br />
T = 0<br />
cp <br />
- cp mdT = cp m dT <br />
cpm<br />
T dT -<br />
cp mdT<br />
T = 0<br />
T = T <br />
<br />
<br />
415 ( Cp<br />
) <br />
T i( ) , <br />
T f: <br />
A min = Cp<br />
T i<br />
2<br />
T f<br />
+ T f - 2T i<br />
T f , <br />
<br />
191
A + Cp ( T i - T f) = Cp ( T f - T i)<br />
T f = A Cp<br />
+ 2T i - T f<br />
( , 0)<br />
S = Cpln T f<br />
T i<br />
S 0 <br />
+ Cp ln T f = Cpln<br />
T i<br />
T fT f<br />
1<br />
T i<br />
2<br />
T f <br />
<br />
A<br />
Cp<br />
A min = Cp<br />
+ 2T i - T f T 2 i<br />
T f<br />
T 2<br />
i<br />
T f<br />
+ T f - 2T i<br />
T fT f<br />
T 2 i<br />
416 ( ( 236) ) <br />
( 315) : 1mol ( <br />
CV , m<br />
)<br />
S = CV , mlnT + Rln( V -<br />
1mol <br />
( 416) <br />
E p , <br />
192<br />
E = CV , mT -<br />
p =<br />
a<br />
V m<br />
RT<br />
V m - b - a<br />
V 2 m<br />
T dS = dE + d A =<br />
+ E 0<br />
b) + S 0<br />
dE + p dV
T dS = CV , mdT +<br />
= CV , mdT +<br />
a<br />
dV<br />
V 2 m +<br />
m<br />
RT<br />
Vm - b dV m<br />
dS = CV , mdT / T + RdVm / ( V m - b)<br />
<br />
dS =CV , mdT / T + R<br />
V m - b dV m<br />
<br />
RT<br />
Vm - b dV m - a<br />
V 2 dVm<br />
m<br />
S - S 0 = CV, mlnT + Rln( V m - b) + C<br />
C , C + S 0 = S 0, <br />
S = CV , mlnT + Rln( V m - b) + S 0<br />
417 <br />
, 44 , <br />
( H m , S m ) <br />
:<br />
?<br />
?<br />
?<br />
( 1) 80K, 50MP a 20MPa , <br />
( 2) 70K, 20MPa 01MPa , <br />
( 3) 76K , 50MPa 01MPa , <br />
44 <br />
( 1) , T 1 = 95K ;<br />
( 2) , T 2 = 65K ;<br />
( 3) , T 3 = 20K, <br />
, <br />
193
194<br />
44
3 <br />
1 <br />
11 a , q, 2q,<br />
- 4q2q, , <br />
<br />
11 , 2q <br />
q 0 , q 0 q <br />
- 4q , <br />
F =<br />
=<br />
qq0<br />
+<br />
4 0r 2<br />
5q<br />
2 0a 2<br />
4qq0<br />
=<br />
4 0r 2<br />
12 -<br />
5qq0<br />
2 0a 2<br />
q <br />
r <br />
1111 <br />
, Q( Q > 0) <br />
, Q ?<br />
12 , Q 0, Q <br />
- q <br />
2F 1cos30 - F 3 = 2 q 2<br />
3<br />
4 0r 2 2<br />
-<br />
qQ<br />
4 0l 2<br />
195
=<br />
1212 <br />
q<br />
( 3 q - 3Q)<br />
4 0r 2<br />
Q = 3 q/ 3<br />
13 13 , ,<br />
- q, Q, - q Q <br />
, cot 3 = q 2 / Q 2 <br />
13 , -<br />
<br />
<br />
q <br />
q 2<br />
= 2qQcos<br />
4 0( 2r cos ) 2 4 0r 2<br />
q/ ( 2Q) = 4cos 3 <br />
, Q <br />
Q/ ( 2q) = 4sin 3 <br />
, ,<br />
cot 3 = q 2 / Q 2<br />
1313 <br />
14 u d u <br />
196
2 3 e , d 1 3 e , <br />
( 1010 -<br />
<br />
15 m) <br />
F =<br />
qdqu<br />
=<br />
4<br />
2 0r 2<br />
910 9 1 3 2 3 ( 1. 610- 19 ) 2<br />
( 1010 - 15 ) 2 = 512 N<br />
15, <br />
10 - 21 e , 10 - 21 e <br />
, ( <br />
8 8 8 ) ? <br />
, , <br />
?<br />
<br />
qm a x = ( 8 + 8 + 8)( 10 - 2 1 e) = 2410 - 21 e<br />
<br />
<br />
f G = G m 2<br />
f e/ f G =<br />
r 2<br />
©¦ f e ©¦=<br />
q 2 ma x<br />
4 0r 2<br />
qm 2 a x<br />
= ( 2410 - 2 1 1. 610 - 19 ) 2 910 9<br />
4 0Gm 2 66710 - 11 ( 161. 6710 - 27 ) 2<br />
= 2. 810 - 6 1<br />
<br />
16 p = ql, <br />
r ( r l ) E= 2p / ( 4 0r 3 ) <br />
+ q - q r <br />
<br />
197
E = E + - E - =<br />
=<br />
q<br />
4 0 r -<br />
2p r<br />
4 0 r 2 -<br />
l<br />
2<br />
l 2 4<br />
2 -<br />
2<br />
q<br />
4 0 r + l 2<br />
2<br />
r l, <br />
E =<br />
2p<br />
4 0r 3<br />
17 p <br />
, x <br />
x , xy <br />
E ( x , y ) r P ( x , y ) , p r <br />
r , 11 16 <br />
E ( x , y ) =<br />
p ( 2x 2 - y 2 )<br />
i +<br />
4 0( x 2 + y 2 ) 5 / 2<br />
14 , p <br />
p r<br />
P <br />
3p x y<br />
j<br />
4 0( x 2 + y 2 ) 5/ 2<br />
= p cos , p = p sin <br />
1417 <br />
198
E r<br />
= E rcos i + E rsin j<br />
=<br />
2p r<br />
cos i +<br />
4 0r 3<br />
= 2p cos 2 <br />
i +<br />
4 0r 3<br />
=<br />
E = -<br />
= -<br />
=<br />
2p x 2<br />
i +<br />
4 0( x 2 + y 2 ) 5/ 2<br />
2p r<br />
sin j<br />
4 0r 3<br />
2p cos<br />
sin j<br />
4 0r 3<br />
E sin i + E cos j<br />
p <br />
sin i +<br />
4 0r 3<br />
- p y 2<br />
i +<br />
4 0( x 2 + y 2 ) 5/ 2<br />
P <br />
E = E r + E =<br />
2p x y<br />
j<br />
4 0( x 2 + y 2 ) 5/ 2<br />
p <br />
cos j<br />
4 0r 3<br />
p ( 2x 2 - y 2 )<br />
i +<br />
4 0( x 2 + y 2 ) 5 / 2<br />
p x y<br />
j<br />
4 0( x 2 + y 2 ) 5/ 2<br />
3p x y<br />
j<br />
4 0( x 2 + y 2 ) 5/ 2<br />
18 , 2a , <br />
+ - , <br />
E = / ( 4 0a ) ,<br />
<br />
F =<br />
E =<br />
<br />
2<br />
4 0a<br />
, <br />
19L, <br />
L r( r > L/ 2) <br />
15 , dq= dx P <br />
1519 <br />
199
dE =<br />
dx<br />
4 0( r - x ) 2<br />
P <br />
L / 2<br />
E = dE <br />
dx<br />
= =<br />
- L/ 2 4 0( r - x ) 2<br />
x <br />
11016, <br />
, R, <br />
= 0sin <br />
<br />
16 , dq<br />
= Rd = 0sin Rd <br />
<br />
dE =<br />
0sin d<br />
4 0R<br />
<br />
L<br />
4 0( r 2 - L 2 / 4)<br />
dE x = dE cos = 0sin cos d<br />
4 0R<br />
dE y = - dE sin= -<br />
0 2, <br />
E x = dE x = 0<br />
E y = dE y<br />
= <br />
2 <br />
E = E xi + E yj = -<br />
0<br />
16110 <br />
0sin 2 d<br />
4 0R<br />
- 0sin 2 d<br />
= - 0<br />
4 0R 4 0R<br />
0<br />
4 0R j<br />
111, , <br />
05m, 2cm , 31210 -<br />
, <br />
200<br />
9 C
, <br />
, <br />
E =<br />
d<br />
=<br />
4 0r 2<br />
qd<br />
4 0r 2 ( 2 r - d )<br />
= 9109 3. 1210 - 9 0. 02<br />
05 2 ( 20. 5 - 0. 02)<br />
= 072 V/ m<br />
, <br />
112 17 , 2a , <br />
O <br />
<br />
<br />
, 17 , d<br />
dq dqO <br />
, dq= adO <br />
dE =<br />
dq<br />
=<br />
4 0a 2<br />
a d<br />
=<br />
4 0a 2<br />
d<br />
4 0a<br />
O dqdq = rd /<br />
sinO <br />
dq<br />
dE = =<br />
4 0r 2<br />
O dq<br />
r d<br />
4 0r 2 sin =<br />
17112 <br />
d<br />
4 0r sin =<br />
d<br />
4 0a<br />
dE = dE , <br />
, dO <br />
, O <br />
113 , <br />
: <br />
<br />
201
, <br />
, <br />
, <br />
, <br />
, <br />
<br />
114 ( 1) q a , <br />
?<br />
( 2) , <br />
?<br />
( 1) 6 , <br />
q/ ( 6 0) <br />
( 2) <br />
<br />
q/ ( 8 0) , <br />
1 3 q =<br />
8<br />
q/ ( 24 0) <br />
0<br />
115, 0, <br />
120V / m, , <br />
? <br />
, S , <br />
<br />
q =<br />
<br />
0 E ¡¤dS =<br />
0E S<br />
<br />
= q S = 0E<br />
202
= <br />
e =<br />
0E e = 88510- 12 120<br />
1. 610 - 1 9<br />
= 6. 6410 9 / m 2 = 6. 6410 5 / cm 2<br />
116, <br />
100m 150N / C, 300m <br />
100N / C ,<br />
<br />
100m 300m S <br />
, <br />
q =<br />
0 E ¡¤dS =<br />
0S ( E 1 - E 2)<br />
<br />
= q<br />
ehS =<br />
0( E 1 - E 2)<br />
eh<br />
= 1. 3810 7 / m 3<br />
q , <br />
= 88510 - 1 2 ( 150 - 100)<br />
1. 610 - 19 200<br />
117, a , <br />
, <br />
r, <br />
E r <br />
<br />
, , <br />
l r <br />
, <br />
E2 r l = qi nt / 0<br />
, r < a , q int = 0, E in t = 0<br />
, r > a , q int = 2 a l , E = a<br />
0r<br />
E r 18 <br />
18117 <br />
203
118 R 1 R 2, <br />
+ - <br />
, <br />
( ) :<br />
, r < R 1: E = 0<br />
<br />
, R 1< r < R2: E =<br />
2 0r<br />
, R< r: E = 0<br />
119 , <br />
1= 410 - 11 C/ m 2 2= - 210 - 11 C/ m 2 <br />
<br />
E 1 =<br />
E 2 =<br />
<br />
1<br />
=<br />
2 0<br />
2<br />
=<br />
2 0<br />
410 - 11<br />
28. 8510 - 12 = 2. 26 V / m<br />
210 - 11<br />
28. 8510 - 12 = 1. 13 V / m<br />
1 : E= E 1- E 2= 1. 13V / m, 1 ;<br />
: E = E 1+ E 2= 3. 39V / m , 2 ;<br />
2 : E= E 1- E 2= 1. 13V / m, 2 <br />
120 , D , ,<br />
E d d , <br />
<br />
, <br />
<br />
, 19( a) <br />
E ¡¤2S = qin t / 0<br />
d < D / 2 , qint = 2d S , E = d <br />
0<br />
204
19120 <br />
d > D / 2 , qint = DS , E = D <br />
2 0<br />
E d 19( b) <br />
121R , , <br />
0, <br />
x <br />
R ( <br />
) , <br />
E =<br />
0<br />
-<br />
2 0<br />
0<br />
1 -<br />
2 0<br />
x<br />
( R 2 + x 2 ) 1/ 2 =<br />
122 , <br />
R, , <br />
r ( r < R) , <br />
, <br />
, <br />
<br />
<br />
( <br />
0x<br />
2 0( R 2 + x 2 ) 1/ 2<br />
110) 110122 <br />
205
P , <br />
<br />
<br />
E + =<br />
E = E + + E - =<br />
= a<br />
3 0<br />
<br />
r +<br />
3 0<br />
E - = - r -<br />
3 0<br />
<br />
( r + - r - )<br />
3 0<br />
a O+ O - <br />
, <br />
123 : <br />
+ e ( r ) = - Ce - 2 r/ a 0 , a 0 <br />
, a 0= 05310 - 10 m, C - e <br />
a 0 ? a0<br />
<br />
<br />
a 0<br />
a 0<br />
E =<br />
<br />
<br />
e = ( r) 4 r 2 dr = 4 Ce -<br />
0<br />
C = e/ ( a 3 0)<br />
<br />
q= e - <br />
a 0<br />
206<br />
( r ) 4<br />
0<br />
r 2 dr = e - <br />
a 0<br />
= 5ee - 2 = 1. 0810 - 19 C<br />
<br />
0<br />
0<br />
?<br />
2 r<br />
a 0 r 2 dr = C a 3 0<br />
4e<br />
ex p -<br />
a 3 0<br />
2r<br />
a 0<br />
r 2 dr<br />
q<br />
= 5ee- 2<br />
= 9109 51610 - 19 e - 2<br />
4 0a 2 0 4 0a 2 0<br />
( 05310 - 1 0 ) 2
= 34610 11 V/ m<br />
124, <br />
, :<br />
=<br />
b , b= 0. 2310 -<br />
r = 1. 010 -<br />
e<br />
e -<br />
8 b 3<br />
r / b<br />
15<br />
m r <br />
15<br />
m <br />
, <br />
<br />
E =<br />
qint<br />
=<br />
04 r 2<br />
r = 1. 010 -<br />
=<br />
1<br />
4 r 0r 4 r 2 dr =<br />
2<br />
0<br />
r 0 r 2 e -<br />
e<br />
8 0b 3<br />
r / b dr<br />
e<br />
[ ( - r 2 - 2br - 2b 2 ) e - r / b + 2b 2 ]<br />
8 0b 2 r 2<br />
15<br />
m , <br />
E = 1. 210 2 1 N / C<br />
125 , <br />
2e/ 3, <br />
05010 -<br />
1 5 m ; - 2e/ 3, <br />
05010 - 1 5 m 1010 - 1 5 m <br />
1010 - 1 5 m, 07510 - 1 5 m, 05010 - 1 5 m 025<br />
10 - 1 5 m <br />
<br />
+ =<br />
2e/ 3<br />
=<br />
4<br />
3 R3 1<br />
<br />
- =<br />
- 2e/ 3<br />
=<br />
4<br />
3 ( R3 2 - R 3 1)<br />
1610 - 1 9<br />
= 2. 0410 26 C/ m 3<br />
2( 0. 510 - 15 ) 3<br />
- 1610 - 19<br />
2 [ ( 10 - 15 ) 3 - ( 0. 510 - 1 5 ) 3 ]<br />
207
= - 2. 9110 25 C/ m 3<br />
, <br />
r 1= 1. 010 - 15 m, E 1= 0;<br />
r 2= 0. 7510 -<br />
;<br />
1 5 m<br />
E 2 = [ 2 3 e + 4<br />
-<br />
3 ( r 3 2 - R 3 1) ] / ( 4 0r 2 2)<br />
= [ 2 3 1. 610- 19 - 2. 9110 25 4 3 <br />
( 0. 75 3 10 - 4 5 - 1. 2510 - 46 ) ]<br />
910 9 / ( 0. 7510 - 15 ) 2<br />
= 1. 1410 21 V / m<br />
r 3= 0. 510 - 15 m<br />
;<br />
E 3 = 2e/ 3 = 9109 21. 610 - 19<br />
4 0r 2 3 3( 0. 510 - 1 5 ) 2<br />
r 4= 0. 2510 -<br />
E 4 =<br />
<br />
= 3. 8410 21 V / m<br />
1 5<br />
m<br />
4<br />
+<br />
3 r 3 4<br />
= + r 4<br />
= 2. 0410 26 0. 2510 - 1 5<br />
4 0r 2 4 3 0 38. 8510 - 12<br />
= 1. 9210 21 V/ m<br />
126 <br />
31710 -<br />
27 kg, 3480 , <br />
, , <br />
2910 -<br />
7410 -<br />
15 m, <br />
15<br />
m , 92e <br />
<br />
208
=<br />
92e<br />
=<br />
4<br />
3 r 3 0<br />
<br />
E =<br />
- 1 9<br />
921. 210<br />
= 8. 6710 24 C/ m 3<br />
4<br />
3 ( 7. 15 410- ) 3<br />
r = 8. 671024 2. 910 - 1 5<br />
= 9. 4710 20 V / m<br />
3 0 38. 8510 - 1 2<br />
, <br />
v =<br />
<br />
E er<br />
m = 9. 4710 20 1. 610 - 19 2. 910 - 1 5<br />
3. 1710 - 2 7<br />
= 1. 210 7 m/ s<br />
<br />
<br />
E k = 1 2 mv 2 = 1 2 3. 1710- 27 ( 1. 210 7 ) 2<br />
= 2. 210 - 13 J<br />
L = mvr = 3. 1710 - 27 1. 210 7 2. 910 - 15<br />
= 1. 110 - 34 kg ¡¤m 2 / s<br />
=<br />
v<br />
2 r = 1. 210 7<br />
= 6. 510 20 H z<br />
22. 910 - 1 5<br />
127 , r 0= 0. 53<br />
10 - 1 0 m , - e, <br />
E = 310 6 V / m ( ) , <br />
( ) ? <br />
?<br />
=<br />
<br />
- e<br />
=<br />
4<br />
3 r 3 0<br />
- 1. 610 - 19<br />
= - 2. 5710 1 1 C/ m 3<br />
4<br />
3 ( 0. 510 - 1 0 ) 3<br />
209
, <br />
<br />
r =<br />
r<br />
e + E e = 0<br />
3 0<br />
3 0E<br />
- = 38. 8510 - 1 2 310 6<br />
= 3. 110 - 16 m<br />
2. 5710 1 1<br />
<br />
p = er = 1. 610 - 19 3. 110 - 1 6 = 5. 010 - 35 C ¡¤m<br />
128 , <br />
005nm , <br />
2e, , <br />
r <br />
<br />
<br />
e 2<br />
=<br />
4 0( 2r ) 2<br />
r = R/ 2<br />
<br />
1 2e 2<br />
r<br />
3 0 4<br />
3 R 3<br />
2r = R = 0. 05 nm<br />
1. 29111 <br />
E x = bx 1 / 2 , E y = E z = 0,<br />
b= 800Nm -<br />
1/ 2 / C:<br />
( 1) ;<br />
( 2) ?<br />
a = 10cm<br />
( 1) <br />
210<br />
111129
e = - E x , a a 2 + E x , 2a a 2 = - ba 1/ 2 a 2 + b( 2a ) 1/ 2 a 2<br />
= ( 2 - 1) ba 5 / 2<br />
= ( 2 - 1)80001 5/ 2<br />
= 1. 05 N ¡¤m 2 / C<br />
( 2) <br />
q = 0 e = 8. 8510 - 12 1. 05 = 9. 2910 - 12 C<br />
130x = + a x = - a + q <br />
( 1) O ( dE / dx ) 0= - q/ ( 0a 3 ) ; ( 2) <br />
p = p i , <br />
p ( dE / dx ) 0= - p q/ ( 0a 3 ) <br />
x <br />
E = -<br />
q<br />
+<br />
4 0( a - x ) 2<br />
<br />
dE<br />
dx x = 0<br />
= -<br />
q<br />
= -<br />
4 0( a + x ) 2<br />
q 4a 5 + 8a 3 x 2 - 12a x 4<br />
= -<br />
4 0 ( a 2 - x 2 ) 4 x = 0<br />
q 4a x<br />
4 0 ( a 2 - x 2 ) 2<br />
q<br />
0a 3<br />
p = q0l , <br />
+ q 0( + l/ 2 ) - q0( - l/ 2 ) , <br />
F = q0E + l / 2 - q0E- l / 2 = q0<br />
dE<br />
dx x = 0<br />
= p dE<br />
dx x = 0<br />
l<br />
= -<br />
p q<br />
0a 3<br />
131 : p E <br />
, <br />
, p Ecos = p E<br />
M= p E sin <br />
, d <br />
- Md = - p Esin d / 2 <br />
211
A = - Md= / 2<br />
<br />
- p Esin d= p E cos = p ¡¤E<br />
/ 2<br />
132 + 1. 010 - 6 C - 4. 0<br />
10 - 6 C, 10cm <br />
( 1) q0 , ?<br />
( 2) , q0 <br />
? q0 <br />
( 3) q0 ?<br />
( 1) 112 , q 0 q1 q2 , q0 <br />
q 1 q2 q 1 x q0 <br />
, q1 , <br />
112132 <br />
q1q0<br />
=<br />
4 0x 2<br />
©¦ q2©¦ q 0<br />
4 0( x + r ) 2<br />
x = r , - r / 3x = r= 0. 1m<br />
( 2) q0 x x , <br />
dF<br />
dx<br />
F =<br />
x = r<br />
q0<br />
q1<br />
-<br />
4 0 x 2<br />
= - q 0 q1<br />
-<br />
2 0 x 3<br />
= - q 0 1<br />
-<br />
2 0 r 3<br />
©¦ q2©¦<br />
( x + r ) 2<br />
©¦q2©¦<br />
( x + r) 3 x = r<br />
1<br />
2r 3 10 - 6<br />
q 0> 0 dF < 0, q0 ; q0 < 0 , dF<br />
dx x = r<br />
dx<br />
> 0, q 0 <br />
212<br />
x = r
( 3) q0 x = r y , <br />
x <br />
F =<br />
dF<br />
=<br />
dy y= 0<br />
q 0q 1<br />
y<br />
-<br />
4 0( y 2 + r 2 ) 2 ( y 2 + r 2 ) 1/ 2<br />
y<br />
<br />
( y 2 + 4r 2 ) 1 / 2<br />
= q0y q1<br />
-<br />
4 0 ( y 2 + r 2 ) 5/ 2<br />
=<br />
q0<br />
q1<br />
-<br />
4 0 ( y 2 + r 2 ) 5/ 2<br />
q0 1<br />
-<br />
4 0 r 5<br />
4<br />
( 2r ) 5 10 - 6<br />
©¦ q 2©¦<br />
( y 2 + 4r 2 ) 5/ 2<br />
©¦ q 2©¦<br />
( y 2 + 4r 2 ) 5/ 2 y = 0<br />
q 0©¦ q2©¦<br />
4 0( y 2 + 4r 2 ) 2<br />
q 0 > 0 , dF > 0, q 0 ; q0 < 0 ,<br />
dy y= 0<br />
dF<br />
< 0, q0 <br />
dy y= 0<br />
133: , <br />
( : P + q, <br />
, P ? <br />
) <br />
P q, <br />
P , P <br />
P P P<br />
P , <br />
, P P<br />
q , <br />
<br />
134113 <br />
, 10 -<br />
5 m( 10 5 <br />
213
, ) , <br />
<br />
, , <br />
, , <br />
<br />
1. 510 -<br />
10 k g, <br />
- 1410 - 13 C , 20m/ s , <br />
1. 6cm. 1. 610 6 N/ C, <br />
( <br />
, ) ?<br />
113134 <br />
<br />
= 1 2<br />
Eq<br />
m<br />
l<br />
v<br />
2<br />
= 1 2 1610 6 1. 410 - 13<br />
1. 510 - 10<br />
1610 - 2<br />
20<br />
= 4. 810 - 4 m = 0. 48 mm<br />
2<br />
214
2 <br />
21 , 2cm,<br />
20cm, 10cm, <br />
+ 2510 - 9 C - 2510 - 9 C , <br />
? ?<br />
08c , <br />
?? ? 06c <br />
, ?<br />
, <br />
<br />
E =<br />
N = q e = 2510- 9<br />
1610 - 19 = 1610 10 ( )<br />
=<br />
0<br />
q<br />
0S = 2510 - 9<br />
88510 - 12 201010 - 4<br />
= 1410 4 V / m<br />
08c ,<br />
l x = l x 1 - u 2 / c 2 = 20 1 - 08 2 = 12 cm<br />
l y = l y = 10 cm<br />
<br />
<br />
N = N = 1610 10 ( )<br />
E = q<br />
=<br />
0<br />
0S<br />
= 2510 - 9<br />
88510 - 12 121010 - 4<br />
= 2410 4 V / m<br />
06 c ,<br />
215
l x = l x = 20cm , l y = l y = 10 cm<br />
N = N = 1610 10 ( )<br />
E = q<br />
2510 - 9<br />
= =<br />
0<br />
0S 88510 - 1 2 201010 - 4<br />
= 1410 4<br />
V/ m<br />
22 , <br />
, <br />
x y , v = vi x <br />
?<br />
,<br />
<br />
<br />
E = k<br />
2 0<br />
<br />
E = rE = <br />
2 0 1 - v 2 / c k 2<br />
, <br />
23 099c <br />
10 -<br />
<br />
E =<br />
q<br />
( 1 -<br />
4 0r 2<br />
<br />
2 )<br />
10 m ?<br />
= 9109 1610 - 19<br />
( 10 - 10 ) 2 ( 1 - 099 2 )<br />
= 2910 9 V / m<br />
<br />
E =<br />
216<br />
q<br />
( 1 -<br />
4 0r 2<br />
<br />
2 ) - 1/ 2<br />
= 9109 1610 - 19<br />
( 10 - 10 ) 2 ( 1 - 099 2 ) - 1/ 2
= 1010 12 V / m<br />
24 : <br />
v a <br />
, <br />
E =<br />
<br />
2 0a<br />
<br />
2124 <br />
21 , x dx P <br />
dE =<br />
( 1 - <br />
) dx<br />
4 0r 2 ( 1 - <br />
sin 2 <br />
) 3/ 2 er<br />
, , x <br />
, P <br />
21 <br />
E = dE = <br />
+ <br />
r 2 =<br />
<br />
E =<br />
( 1 - <br />
2 )<br />
4<br />
- <br />
( 1 - <br />
) dx<br />
4 0r 2 ( 1 - <br />
sin 2 ) 3 / 2<br />
a 2 / sin 2 , x = acot , dx = -<br />
0a 0 <br />
sin d<br />
( 1 - <br />
2 sin 2 ) 3/ 2<br />
= ( 1 - <br />
2 )<br />
cos<br />
4 0a ( 1 - <br />
2 ) ( 1 - <br />
2 sin 2 <br />
=<br />
<br />
2 0a<br />
a d<br />
sin 2 <br />
) 1/ 2 0<br />
<br />
217
3 <br />
31 , 10cm 30cm , <br />
110 - 8 C, 1510 - 8 C<br />
( 1) 20cm , ( 2) 50cm <br />
<br />
q 1<br />
<br />
( 1) =<br />
4 0r + q 2<br />
4 0R2<br />
= 900 V<br />
= 910 9 110 - 8<br />
+ 1510- 8<br />
2010 - 2 3010 - 2<br />
q1 + q2<br />
( 2) = = 910 9 ( 1 + 15)10 - 8<br />
4 0r<br />
5010 - 2<br />
= 450 V<br />
32 , R 1 R 2( R 1 <<br />
R 2) , U 12, <br />
q, <br />
U 1 2 = R 2<br />
R 1<br />
Edr = R 2<br />
<br />
<br />
E =<br />
R 1<br />
q<br />
dr =<br />
4 0r 2<br />
q 1<br />
4 0<br />
q<br />
= U 1 2 R 1R 2<br />
4 0r 2 r 2 R 2 - R 1<br />
33 , R 1 = 50cm, R 2<br />
= 200cm, 1 = 60V , 2 =<br />
- 30V <br />
( 1) ;<br />
218<br />
R 1<br />
-<br />
1<br />
R 2
,<br />
( 2) ?<br />
( 1) q 1 q2<br />
1 =<br />
2 =<br />
<br />
1<br />
4 0<br />
q1<br />
R 1<br />
1 q 1 +<br />
4 0<br />
R2<br />
+ q2<br />
R 2<br />
q2<br />
= 60<br />
= - 30<br />
R 1 R 2 <br />
( 2) <br />
<br />
q1 = 6710 - 1 0 C, q 2 = - 1310 - 9 C<br />
r =<br />
q 1<br />
- q2<br />
=<br />
1<br />
4 0 r<br />
q1<br />
+ q2<br />
R 2<br />
= 0<br />
R 2 = 6710 - 1 0<br />
20 = 10 cm<br />
1310 - 9<br />
34 , R 1, R 2( R 1 < R 2) , <br />
q1, q 2 , <br />
q1<br />
, , <br />
; , <br />
<br />
<br />
1 =<br />
q1<br />
+<br />
4 0R 1<br />
q2<br />
4 0R 2<br />
<br />
1 R1<br />
-<br />
1<br />
R2<br />
2 =<br />
q1<br />
+<br />
4 0R 2<br />
U 12 = 1 - 2 =<br />
q2<br />
4 0R 2<br />
q1 1<br />
4 0<br />
R 1<br />
-<br />
1<br />
R 2<br />
> 0, U 12 q1 q1 > 0<br />
219
, U 1 2 > 0, q 1 < 0 , U 12 < 0, <br />
<br />
, q1<br />
35 z z = -<br />
<br />
a z = a , <br />
, , x x > 0 <br />
, P ( x , 0, 0) <br />
= a -<br />
= q d<br />
=<br />
<br />
ln<br />
4 0<br />
a<br />
dz<br />
4 0( x 2 + z 2 ) 1 / 2<br />
x 2 + a 2 + a<br />
x 2 + a 2 - a<br />
36 , l = 150cm, = 20<br />
10 -<br />
7 C/ m :<br />
( 1) a = 50cm ;<br />
( 2) b = 50cm <br />
( 1) x , x , <br />
, <br />
1= l 0<br />
<br />
dx<br />
4 0( l + a - x ) = <br />
ln a + l<br />
4 0 a<br />
= 910 9 2010 - 7 ln<br />
= 2510 3 V<br />
( 2) 35 , <br />
2=<br />
<br />
ln<br />
4 0<br />
b 2 + l 2 / 4 + l / 2<br />
b 2 + l 2 / 4 - l / 2<br />
= 910 9 2010 - 7 ln<br />
= 4310 3 V<br />
50 + 150<br />
50<br />
5 2 + 15 2 / 4 + 15/ 2<br />
5 2 + 15 2 / 4 - 15/ 2<br />
37118 <br />
220
U 12 = R 2<br />
R 1<br />
E dr = R 2<br />
R 1<br />
dr<br />
2 0r =<br />
<br />
ln R 2<br />
2 0 R 1<br />
38 20cm , <br />
12710 -<br />
110 3 V, :<br />
<br />
( 1) ;<br />
( 2) ;<br />
, <br />
U 1 2 = <br />
R 2<br />
D / 2<br />
Edr =<br />
R 1<br />
<br />
d / 2<br />
5 m <br />
dr<br />
2 0r =<br />
<br />
ln D 2 0 d<br />
= 2 0U 12<br />
ln D d<br />
E =<br />
( 1) <br />
2<br />
2 0d = 2U 1 2<br />
= 21410 7 V / m<br />
( 2) ,<br />
E =<br />
d ln( D / d ) = 210 3<br />
12710 - 5 ln<br />
2<br />
2 0D = 2U 1 2<br />
= 13610 4 V / m<br />
D ln( D/ d ) = 210 3<br />
002ln<br />
002<br />
12710 - 5<br />
002<br />
12710 - 5<br />
39 , , a <br />
( 1) ;<br />
( 2) , ;<br />
( 3) E r r <br />
( 1) r , l <br />
221
( ) <br />
E ¡¤2 rl =<br />
qi nt<br />
0<br />
r a , qin t = r 2 l , E i nt =<br />
<br />
r<br />
2 0<br />
r a , qint = a 2 l , E ou t = a 2 <br />
2 0r<br />
( 2) r a <br />
r a <br />
<br />
0<br />
0<br />
int = E in tdr =<br />
r<br />
a<br />
out = E r ou tdr 0 + E a int dr a = r<br />
= a 2 <br />
2ln a 4 0 r<br />
- 1<br />
r<br />
<br />
r dr = -<br />
2 0<br />
<br />
r 2<br />
4 0<br />
a 2 <br />
2 0r dr 0 + a<br />
<br />
r dr<br />
2 0<br />
3139 <br />
( 3) E r U r 31 <br />
310 R , <br />
: ( 1) 34 ;<br />
( 2) 1 16 <br />
222
( 1) r , dr <br />
x <br />
d=<br />
2 r dr<br />
4 0 r 2 + x 2<br />
, x <br />
= d= R 0<br />
<br />
2 r dr<br />
4 0 r 2 + x = <br />
( x 2 + R 2 - x )<br />
2 2 0<br />
( 2) x <br />
E =<br />
<br />
1 -<br />
2 0<br />
x <br />
= <br />
<br />
=<br />
x<br />
E dx =<br />
<br />
<br />
2 0 x<br />
x<br />
( R 2 + x 2 ) 1 / 2<br />
1 -<br />
<br />
( R 2 + x 2 - x )<br />
2 0<br />
x<br />
( R 2 + x 2 ) 1/ 2 dx<br />
311 , R, , <br />
R/ 2 <br />
, ?<br />
<br />
310 <br />
<br />
<br />
= ( R 2 + x 2 ) 1 / 2 - x -<br />
2 0<br />
=<br />
<br />
( R 2 + x 2 ) 1 / 2 -<br />
2 0<br />
, x = 0, <br />
R 2<br />
1 / 2<br />
2 0 4 + x 2<br />
R 2<br />
4 + x 2 1/ 2<br />
0 = R<br />
4 0<br />
, , <br />
- x<br />
223
312( 1) 040mm, 16pC,<br />
? ( 2) <br />
, ?<br />
<br />
( 1) 1 =<br />
q1<br />
= 9109 1610 - 1 2<br />
= 36 V<br />
4 0R 1 0410 - 3<br />
( 2) , 3 2 R 1 <br />
2=<br />
q2<br />
=<br />
4 0R 2<br />
4 3<br />
2q1<br />
2 0R1<br />
= 910 9 21610 - 12<br />
3<br />
2 0410 - 3 = 57 V<br />
313 , 79 e, <br />
7010 -<br />
1 5 m, ?<br />
<br />
1=<br />
q<br />
4 0R = 910 9 791610 - 19<br />
= 1610 7 V<br />
7010 - 15<br />
<br />
R<br />
2= <br />
0<br />
<br />
r<br />
dr +<br />
3 0 <br />
q<br />
dr = 3<br />
R 4 0r 2 2<br />
= 2410 7 V<br />
q<br />
4 0R =<br />
3 2 16107<br />
314 32 , , <br />
R, + q -<br />
q, l, l R <br />
( 1) O , x<br />
;<br />
ql<br />
( 2) : x R = <br />
4 0x 2<br />
( 1) <br />
224<br />
=<br />
1 q<br />
4 0 ( R 2 + r 2 ) 1/ 2
32 314 <br />
32 x <br />
=<br />
q<br />
4 0<br />
1<br />
R 2 + x -<br />
l<br />
2<br />
2 1/ 2 -<br />
1<br />
R 2 + x +<br />
l<br />
2<br />
2 1/ 2<br />
l R, <br />
q<br />
1<br />
=<br />
-<br />
4 0 ( R 2 + x 2 - xl ) 1/ 2<br />
1<br />
( R 2 + x 2 + xl ) 1/ 2<br />
=<br />
q<br />
4 0x<br />
1 -<br />
1<br />
l<br />
x + R 2 1/ 2 -<br />
x 2<br />
1 +<br />
1<br />
l<br />
x +<br />
1/ 2<br />
R2<br />
x 2<br />
( 2) x R , , <br />
=<br />
q<br />
4 0x<br />
1 -<br />
1<br />
l<br />
x<br />
1/ 2 -<br />
1 +<br />
1<br />
l<br />
x<br />
1/ 2<br />
x l , <br />
=<br />
q<br />
4 0x 1 + l<br />
2x - 1 - l<br />
2x<br />
=<br />
ql<br />
4 0x 2<br />
315 35 x x > 0 <br />
<br />
225
x , <br />
x <br />
E y = -<br />
=<br />
E = E x = -<br />
<br />
ln<br />
4 0<br />
x 2 + a 2 + a<br />
x 2 + a 2 - a<br />
<br />
y = 0, E z = - <br />
z = 0<br />
<br />
x =<br />
a<br />
2 0x x 2 + a 2<br />
<br />
316 q1 q2 x = -<br />
b <br />
x = + b , = 0 <br />
, ?<br />
33316 <br />
33 , x y , P ( x , y ) <br />
=<br />
1<br />
4 0<br />
= 0 <br />
<br />
q 2<br />
y 2 + ( b - x ) 2 1 / 2 +<br />
y 2 + ( b - x ) 2<br />
y 2 + ( b + x ) 2 =<br />
y 2 + x + b k + 1<br />
k - 1<br />
226<br />
2<br />
q1<br />
y 2 + ( b + x ) 2 1/ 2<br />
q2<br />
q1<br />
+ b 2 1 -<br />
2<br />
= k<br />
k + 1<br />
k - 1<br />
, k<br />
+ 1<br />
k + 1<br />
b, 0 , <br />
k - 1 k - 1<br />
2<br />
= 0<br />
2<br />
- 1<br />
1/ 2<br />
b
q1 q2 x , x <br />
x y x , <br />
, x x = -<br />
k + 1<br />
k - 1<br />
2<br />
- 1<br />
1 / 2<br />
b<br />
k + 1<br />
b , <br />
k - 1<br />
©¦ q 1©¦= ©¦ q 2©¦ , k = 1x , <br />
, yz ( , q1<br />
q2 , = 0 )<br />
<br />
317 -<br />
+ z , x x = -<br />
:<br />
a x = + a<br />
( 1) x y , <br />
;<br />
( 2) x y <br />
<br />
( 1) 34 , P ( x , y)<br />
<br />
= + + - = - ln r + +<br />
2 0<br />
= -<br />
<br />
ln r +<br />
2 0 r -<br />
+ C<br />
<br />
lnr - + C<br />
2 0<br />
<br />
= r + / r - = r + / r - = k, r + = kr - <br />
<br />
( a - x ) 2 + y 2 = k 2 [ ( a + x ) 2 + y 2 ]<br />
, 1 + k 2<br />
x 2 + y 2 - 2a 1 + k2<br />
1 - k 2 x + a 2 = 0<br />
1 - k 2 a , 0 , 2ka<br />
1 - k 2 , 34 <br />
227
E=<br />
( 2) P ( x , y) <br />
= -<br />
<br />
2 0r +<br />
er +<br />
+<br />
( a - x )<br />
2 0r 2 +<br />
34 317 <br />
- <br />
er<br />
2 0r -<br />
-<br />
+ - ( a + x )<br />
2 0r 2 -<br />
i +<br />
y<br />
+ - y<br />
2 0r 2 + 2 0r 2 j<br />
-<br />
E , : y = y ( x ) <br />
, <br />
dy<br />
dx =<br />
<br />
E y<br />
E x<br />
=<br />
1/ y 2 , <br />
228<br />
y<br />
+ - y<br />
2 0r 2 + 2 0r 2 -<br />
- ( a - x )<br />
+ - ( a + x )<br />
2 0r 2 + 2 0r 2 -<br />
x 2 dy - 2x ydx - y 2 dy - a 2 dy = 0<br />
=<br />
2x y<br />
x 2 - y 2 - a 2
x 2 dy - 2x ydx<br />
- dy -<br />
y 2<br />
d -<br />
<br />
x 2<br />
y + y - a 2<br />
c <br />
x 2 + y -<br />
c<br />
2<br />
a 2<br />
y 2 dy = 0<br />
x 2<br />
y - y + a2<br />
y = 0<br />
2<br />
y = c<br />
- a 2 + c2<br />
4 = 0<br />
, ( 0, c/ 2) , a 2<br />
+ c 2 / 434 <br />
, <br />
318 1010 9 V, <br />
30C<br />
( 1) ?<br />
( 2) 20kW h<br />
?<br />
( 1) <br />
W = qU = 301010 9 V = 3010 10 J<br />
( 2) <br />
t = W P = 3010 10<br />
2010 3 3600 =<br />
416( )<br />
319 , 35 K ,<br />
A , <br />
, , <br />
, , A - K = 25<br />
10 4 V , :<br />
( 1) ( ) ;<br />
( 2) <br />
229
35319 <br />
( 1) E k = e( A - K ) = 1610 - 1 9 2510 4<br />
= 410 - 15 J = 2510 4 eV<br />
2E k<br />
( 2) v =<br />
m = 2410 - 1 5<br />
= 9410 7 m/ s<br />
9110 - 31<br />
<br />
-<br />
v = 1 -<br />
1<br />
1 + E k / ( m 0c 2 )<br />
1/ 2<br />
c =<br />
6510 7 m/ s<br />
320 a , q, -<br />
2q , + Q <br />
, ?<br />
<br />
0=<br />
=<br />
<br />
q<br />
4<br />
0r + - q<br />
4 0r + - 2q<br />
4 0r<br />
3q<br />
4 0 3 a ( 1 - 1 - 2) = - 3 q<br />
2 0a<br />
q<br />
230<br />
A = - A = - Q( -<br />
0) = Q 0 = -<br />
3 qQ<br />
2 0a
321 36 , , <br />
1 = 1210 - 4 C/ m 2 , 2 = 20<br />
10 - 5 C/ m 2 , 3 = 1110 - 4 C/ m 2 A <br />
50cm, B 70cm<br />
( 1) A, B ;<br />
( 2) q0 = - 1010 - 8 C <br />
A B , ?<br />
( 1) 36 , <br />
<br />
E =<br />
1<br />
( 1 - 2 - 3)<br />
2 0<br />
<br />
E =<br />
U A B= E l A + E l B<br />
=<br />
=<br />
1<br />
( 1 + 2 - 3)<br />
2 0<br />
36 <br />
321 <br />
1<br />
( 1 - 2 - 3) l A + ( 1 + 2 - 3) l B<br />
2 0<br />
10 - 4<br />
288510 - 12 ( 12 - 02 - 11)005<br />
+ ( 12 + 02 - 11)007<br />
= 9010 4 V<br />
( A 2) A B = - A A B = - q0U A B<br />
= - ( - 1010 - 8 )9010 4<br />
= 910 - 4 J<br />
322 <br />
, 37 , <br />
, <br />
( ) ( <br />
, ) <br />
231
( 1) <br />
, L 1 1/ 2 , L 1 <br />
, ( )<br />
( 2) U 0, , L 1 <br />
( 3) , ?<br />
37322 <br />
( 1) v 1 = 2qU 0/ me , <br />
<br />
L 1 = v 1T / 2<br />
v2 = v 2 1 + 2qU 0/ me = 2 v1<br />
<br />
L 2 = v 2T / 2 = 2 L 1<br />
v3 = v 2 2 + 2qU 0/ me = 3 v1<br />
<br />
, <br />
L 3 = v 3T / 2 = 3 L 1<br />
L = L 1<br />
( 2) L 1 = v 1T / 2 = 1 2U 0e<br />
2 m e<br />
( 3) E k = 1 2 m e v 2<br />
= me<br />
2<br />
v 1<br />
2<br />
= eU 0<br />
232
323 ( 1) , <br />
?<br />
( 2) , m 0 <br />
E k = m 0c 2 1<br />
1 - v 2 / c 2 - 1<br />
<br />
?<br />
( 1) <br />
eU =<br />
U =<br />
1 2 m0c2<br />
m 0c2<br />
2e = 9110- 31 910 1 6<br />
21610 - 19 = 2610 5 V<br />
( 2) <br />
<br />
v<br />
c = 1 - 1<br />
2<br />
eU<br />
1 +<br />
m 0c 2<br />
<br />
eU = m 0c 2 1<br />
1 - v 2 / c 2 - 1<br />
1/ 2<br />
= 1 -<br />
1<br />
1 + 1 2<br />
2<br />
1/ 2<br />
= 75%<br />
324 , ,<br />
02010 -<br />
?( )<br />
<br />
W =<br />
1 e( - 2e)<br />
2 +<br />
4 0 r 2<br />
10 m<br />
( - e) ( - e)<br />
( 2r) 2<br />
= 910 9 - 4( 1610 - 1 9 ) 2<br />
+ ( 1610- 19 ) 2<br />
02010 - 10 0410 - 10<br />
= - 4010 - 17 J<br />
233
325 , <br />
, 12 C <br />
3 30<br />
10 - 1 5 m, 3 ?<br />
( )<br />
W = 3 ( 2e) 2<br />
9 4 0r = 3910 4( 1610 - 19 ) 2<br />
310 - 15<br />
= 9210 - 14 J = 58 MeV<br />
326 <br />
, e, a <br />
:<br />
ln( 1 + x ) )<br />
e 2<br />
( 2) -<br />
4 0a ln2<br />
( 1) <br />
1 = 2<br />
( 1) e<br />
2 0a ln2 ( : <br />
e<br />
4 0a - 1 + 1 2 - 1<br />
3 + = - e<br />
2 0a ln 2<br />
( 2) N ( N 1) , <br />
( )<br />
<br />
W =<br />
1 N<br />
2 <br />
= 1<br />
W1 = W / N = 1 2 e 1 = -<br />
e = 1 2 N e 1<br />
e 2<br />
4 0a ln2<br />
N , , <br />
<br />
327 R, e <br />
mec 2 , <br />
234
e m e R ?R <br />
?( R , <br />
10 -<br />
<br />
18 m )<br />
, <br />
, <br />
R=<br />
e 2<br />
4 0R = m ec 2<br />
R =<br />
e 2<br />
4 0mec 2<br />
( 16010 - 19 ) 2<br />
488510 - 1 2 91110 - 31 ( 30010 8 ) 2<br />
= 28110 - 15 m<br />
328 1010 -<br />
15 m <br />
, ? <br />
?<br />
<br />
W = 3 5<br />
e 2<br />
4 0R = 3( 1 9 1610- ) 2 910 9<br />
5110 - 15<br />
= 13810 - 1 3 J = 8610 5 eV<br />
( 938MeV ) <br />
086<br />
938 = 0092%<br />
<br />
329 92e, <br />
7410 -<br />
15 m <br />
, , 46e, <br />
, <br />
, ? <br />
?<br />
235
, 1kg <br />
?( )<br />
<br />
WU = 3 5<br />
( 92e) 2<br />
4 0RU<br />
= 1610 - 10 J<br />
<br />
WP d= 2 3 5<br />
= 3( 921610- 19 ) 2 910 9<br />
57410 - 15<br />
2<br />
46 e)<br />
(<br />
4 0RP d<br />
= 23( 19 461610- ) 2 910 9<br />
57410 - 15 3<br />
/ 2<br />
= 1010 - 1 0 J<br />
<br />
W 1 = WU - WP d = ( 16 - 10)10 - 10 = 6010 - 1 1 J<br />
1kg <br />
W = W1 1000<br />
235 60210 23 = 1510 1 4 J<br />
330 40MeV , <br />
2e, 79e, <br />
<br />
66810 -<br />
10 - 2 5 kg, ?<br />
<br />
<br />
r m in=<br />
236<br />
qqA u<br />
4 0r min<br />
= E k , <br />
27<br />
kg, 329<br />
q qA u<br />
= 910 9 279( 1610 - 19 ) 2<br />
4 0E k , 410 6 1610 - 1 9<br />
= 5710 - 14 m
, <br />
E p= -<br />
Gm m A u<br />
r 2 mi n<br />
= 66710 - 1 1 66810 - 27 32910 - 25<br />
5710 - 1 4<br />
= 25710 - 48 J<br />
= 1610 - 3 5 MeV<br />
331 , 317<br />
10 - 2 7 kg <br />
, <br />
?? <br />
92e , 7410 -<br />
, <br />
qqU<br />
4 0RU<br />
<br />
v1=<br />
=<br />
- 2qqU<br />
4 0R U m <br />
+ 1 2 mv 2 1 = 0<br />
15 m<br />
- 2( - 1610 - 1 9 )921610 - 19 910 9 1/ 2<br />
7410 - 15 31710 - 2 7<br />
= 4310 7 m/ s<br />
<br />
3<br />
2<br />
qU<br />
q + 1 4 0R U 2 m v 2 2 = 0<br />
v2 =<br />
- 2qqU<br />
3 4 0R U m 2 = v1 3 2 = 5210 7 m/ s<br />
332p 1<br />
p 2, <br />
r , , <br />
237
-<br />
p 1p 2<br />
<br />
2 0r 3<br />
l 1, l 2 , p 1 r<br />
<br />
p 2<br />
1 =<br />
q 1 1<br />
4 0 r - l 1/ 2 - 1<br />
r + l 1/ 2 = q1l 1<br />
=<br />
4 0r 2<br />
r , <br />
W = -<br />
= -<br />
q2 1 + q2 1 + d 1<br />
dr l 2 = q2l d 1<br />
2<br />
dr<br />
p 1p 2<br />
2 0r 3<br />
p 1<br />
4 0r 2<br />
333100V / m<br />
( 1) ?<br />
( 2) 10km <br />
, kW h ?<br />
( 1) w e =<br />
( 2) W=<br />
0E 2<br />
= 88510- 12 ( 100) 2<br />
2<br />
2<br />
= 4410 - 8 J/ m 3<br />
4 R 2 Ehw e<br />
= 4(<br />
64106 ) 2 1010 3 4410 - 8<br />
3610 6<br />
= 6310 4 kW ¡¤h<br />
334 , <br />
, , <br />
h = 10510 - 3 4 J ¡¤s, 2 h, 3 h <br />
r =<br />
( 1) : h( = 1, 2, 3, ) , <br />
4 0<br />
2 h 2 ;<br />
me e 2<br />
( 2) : , ( + )<br />
238
W = -<br />
mee 4<br />
1<br />
2( 4 0) 2 h 2 2<br />
( 3) = 1 ( eV ) <br />
( 1) <br />
<br />
, <br />
e 2<br />
=<br />
4 0r 2 me<br />
me rv = h<br />
r =<br />
( 2) <br />
v 2<br />
r<br />
4 0<br />
2 h 2<br />
m ee 2<br />
W = 1 2 mev 2 + - e2<br />
4 0r = - e 2<br />
8 0r<br />
= -<br />
( W1= 3) -<br />
= -<br />
mee 4<br />
2( 4 0) 2 2 h 2<br />
m ee 4<br />
2( 4 0) 2 h 2<br />
91110 - 3 1 ( 1610 - 19 ) 4 ( 910 9 ) 2<br />
2( 10510 - 34 ) 2<br />
= - 21810 - 19 J<br />
= - 136 eV<br />
239
4 <br />
41 <br />
, S , S <br />
S ( ) <br />
( S )<br />
, <br />
/ 0( ( 42) ) <br />
41 , <br />
S <br />
/ 2E 1E 2 , S<br />
S <br />
E , ,<br />
S <br />
<br />
E i nt = E + E 1 = 0<br />
E = - E 1 = E 2<br />
S , <br />
E ex t =<br />
2E 2<br />
4141 <br />
E e xt 2 / ( 2 0) = / 0, <br />
42 R 1, <br />
R 2 R 3 , 1, <br />
Q<br />
q1, -<br />
q1 + Q, <br />
q 1, <br />
240
1 =<br />
, <br />
1<br />
4 0<br />
q1<br />
R 1<br />
-<br />
q1<br />
R 2<br />
+ Q + q1<br />
R 3<br />
q1 = 4 0R1R 2R3 1 - R 1R 2Q<br />
R 2R 3 - R 1R3 + R1R 2<br />
r < R 1:<br />
R 1<br />
= 1, E = 0<br />
q 1<br />
1<br />
< r < R 2: =<br />
4 0 r<br />
+ - q1<br />
R2<br />
+ Q + q 1<br />
R 3<br />
,<br />
E=<br />
q1<br />
4 0r 2<br />
R 2 < r < R 3: = Q + q1<br />
, E =<br />
4 0R 3<br />
0<br />
r > R 3: = Q + q1 Q + q1<br />
, E =<br />
4 0r 4 0r 2<br />
43 R1 = 60cm A <br />
BB R 2 = 80cm, R 3 =<br />
100cmA QA = 310 - 8 C, B <br />
Q B = 210 - 8 C <br />
( 1) B A B<br />
;<br />
( 2) B , A A<br />
B A B <br />
( 1) <br />
Q B, int = - Q A = - 310 - 8 C<br />
<br />
Q B , e xt = Q B + QA = 510 - 8 C<br />
241
, A =<br />
1<br />
4 0<br />
QA<br />
R1<br />
+<br />
QB , i nt<br />
R 2<br />
+ Q B , ex t<br />
R 3<br />
= 910 9 310- 8<br />
= 5610 3 V<br />
B =<br />
1<br />
4 0<br />
QB , e xt<br />
R 3<br />
= 4510 3 V<br />
006<br />
+ - 310- 8<br />
008<br />
= 910 9 510- 8<br />
010<br />
+ 510- 8<br />
010<br />
( 2) B , Q B = Q B, int = - 3<br />
10 - 8 CA , A = 0A qA , <br />
<br />
qA =<br />
1<br />
A =<br />
4 0<br />
qA <br />
R1<br />
+<br />
- QB / R 3<br />
1/ R1 - 1/ R 2 + 1/ R 3<br />
= 2110 - 8 C<br />
qB , in t = - qA = - 2110 - 8 C<br />
qB , ex t = Q B + qA = - 0910 - 8 C<br />
B =<br />
QB <br />
- qA <br />
+ Q B + qA <br />
= 0<br />
R 2 R 3<br />
=<br />
310 - 8 / 010<br />
1/ 006 - 1/ 008 + 1/ 010<br />
+ qA ( - 3 + 21)10 - 8<br />
= 910 9<br />
4 0R 3<br />
01<br />
= 8110 2 V<br />
44 , R, <br />
q r , <br />
( ) , q<br />
q/ 4 0r , q , q<br />
q / 4 0R,<br />
<br />
242<br />
q<br />
4 0r +<br />
q = -<br />
q<br />
4 0R = 0<br />
R<br />
r q
4542 , , <br />
, <br />
13<br />
10 - 5 C/ m 2 <br />
?( <br />
)<br />
42 , <br />
1,<br />
2 A, B C , <br />
1 - 2 - 3 - 4 - 5 - 6 = 0<br />
1 + 2 + 3 - 4 - 5 - 6 = 0<br />
1 + 2 + 3 + 4 + 5 - 6 = 0<br />
A C , <br />
<br />
U A B<br />
= U C B<br />
( 1 + 2 - 3 - 4 - 5 - 6) d A B<br />
= ( 5 + 6 - 1 - 2 - 3 - 4) d C B<br />
: B <br />
A C <br />
3 + 4 = = 1310 - 5 C/ m 2<br />
1 + 2 + 5 + 6 = 0<br />
6 , <br />
1= 6510 - 6 C/ m 2<br />
2= - 3 = - 4910 - 6 C/ m 2<br />
4= - 5 = 8110 - 6 C/ m 2<br />
6= 6510 - 6 C/ m 2<br />
4245 <br />
46 A , <br />
243
, qb qc, <br />
r qd ( 43) qb, qc q d <br />
?<br />
4346 <br />
qb qc , <br />
, E = 0, qb qc <br />
<br />
, ( q b + qc) <br />
qd<br />
, <br />
, qb <br />
F d =<br />
( qb + qc) qd<br />
4 0r 2<br />
47 f =<br />
<br />
2<br />
en, , en <br />
2 0<br />
, <br />
41 , S<br />
, / ( 2 0) , <br />
, S S <br />
f = ( S ) ( / ( 2 0) ) = <br />
2 S / ( 2 0) , <br />
<br />
244
f =<br />
f<br />
S = <br />
2 / ( 2 0)<br />
, f , <br />
en<br />
S , <br />
f =<br />
<br />
2<br />
en<br />
2 0<br />
48 ( I <br />
) , <br />
<br />
915MV ,<br />
?<br />
( 1) 100MV / m, <br />
( 2) , , <br />
320 C/ s ?<br />
( 3) 485cm, 330m/ s<br />
<br />
( 1) 0 =<br />
q<br />
4 0R , E =<br />
q<br />
E b, <br />
4 0R 2<br />
R 0<br />
= 915106 = 91510 - 2 m<br />
E b 10010 6<br />
( 2)P mi n= Uq/ t = 0q/ t = 91510 6 32010 - 6<br />
= 29310 3 W<br />
q<br />
( 3) =<br />
vtb = 32010 - 6<br />
3300485 = 20010 - 5 C/ m 2<br />
E =<br />
<br />
=<br />
2 0<br />
20010 - 5<br />
288510 - 12 = 11310 6 V / m<br />
49 q h ,<br />
, <br />
, <br />
245
44 49 <br />
44 , q r a b, <br />
, q a b <br />
, <br />
q<br />
E a = E b =<br />
4 0r<br />
b , E b =<br />
2 er<br />
0, <br />
b E b = - E a <br />
, a <br />
44 E a , E a = E b = E b , E a <br />
E b , a<br />
E a = E a + E a , 44 , E a , <br />
<br />
E a =<br />
<br />
246<br />
= -<br />
2qh<br />
2E a cos =<br />
4 0( h 2 + r 2 ) 3/ 2<br />
0E a = -<br />
qh<br />
2 ( h 2 + r 2 ) 3 / 2
410 q h <br />
q , <br />
2h q - q , A = q 2 / ( 4 0<br />
¡¤2h ) q F dr , <br />
? ?<br />
q <br />
F = -<br />
q <br />
<br />
<br />
A = - F ¡¤dz =<br />
h<br />
q 2<br />
k<br />
4 0( 2z ) 2<br />
h<br />
q 2<br />
dz =<br />
16 0z 2<br />
q 2<br />
16 0h<br />
<br />
q , , <br />
, <br />
<br />
411 45 q <br />
?( )<br />
45 411 <br />
45 , ( <br />
) , <br />
q <br />
, <br />
247
, <br />
-<br />
= -<br />
q/ 2410 <br />
qh/ ( 2 ( r 2 + h 2 ) 3/ 2 ) , <br />
r 1<br />
0 2<br />
rdr = r 1<br />
0<br />
- qh2 rd r<br />
= -<br />
2 ( r 2 + h 2 ) 3/ 2<br />
, q <br />
q <br />
r 1 = 3 h<br />
412 , 1010 -<br />
q<br />
2<br />
8 C/ m, <br />
, 50m <br />
??<br />
<br />
, <br />
<br />
E = 2<br />
<br />
9<br />
2 0h = 22910 1010 - 8<br />
5<br />
<br />
= -<br />
= 72 V / m<br />
0E = - <br />
h = - 110 - 8<br />
= - 6410 - 10 C/ m 2<br />
5<br />
<br />
F 1 =<br />
<br />
2<br />
2 0( 2h ) = 110 - 16 910 9<br />
5<br />
= 1810 - 7 N / m<br />
413:<br />
, <br />
<br />
1cm 3 , 1g <br />
, <br />
= 1<br />
18 60231023 1610 - 1 9 / ( 910 9 6410 6 )<br />
248
10 6<br />
V<br />
414 R, q <br />
<br />
46 , <br />
<br />
2 / ( 2 0) , , Rd <br />
2 rsinx , <br />
dF x = <br />
2<br />
2 Rsin cos Rd<br />
2 0<br />
<br />
F x = dF x = <br />
2 R 2<br />
<br />
46414 <br />
0 / 2<br />
0<br />
sin cos d = R 2 <br />
2<br />
=<br />
2 0<br />
q 2<br />
32 0R 2<br />
: <br />
, , <br />
, <br />
, <br />
249
5 <br />
51H Cl , ( ) 0128nm,<br />
<br />
? <br />
HCl 3410 -<br />
? ( 17e )<br />
, HCl <br />
30<br />
Cm, H Cl <br />
p 0 = el 0 = 1610 - 19 012810 - 9 = 2010 - 29 C ¡¤m<br />
<br />
51 , H Cl<br />
<br />
l <br />
H Cl <br />
p = - 18el + el 0<br />
l = el 0 - p<br />
18e<br />
=<br />
5151 <br />
( 20 - 34)10-<br />
30<br />
181610 - 19 = 5910 - 12 m<br />
52 , R 1 =<br />
002m R2= 006m , <br />
r 1= 6 r 2= 3 R=<br />
004m Q= - 610 -<br />
8 C :<br />
( 1) D E , D r , E r ;<br />
( 2) ;<br />
( 3) <br />
( 1) D <br />
250
R 1: D = 0<br />
r > R 1: D =<br />
Q<br />
4 r 2<br />
E = D / 0 r, <br />
r < R1: E = 0<br />
R 1 < r < R: E =<br />
Q<br />
4 0 r 1r 2<br />
R < r < R2: E =<br />
Q<br />
4 0 r 2r 2<br />
r > R2: E =<br />
Q<br />
4 0r 2<br />
D r Er 52 <br />
5252 <br />
( 2) <br />
U = <br />
R<br />
= R R 1<br />
R 2<br />
Edr +<br />
R 1<br />
<br />
R<br />
Q<br />
4 0<br />
= Q 1<br />
-<br />
4 0 r 1R1<br />
E dr<br />
R 2<br />
dr +<br />
r1r 2 R<br />
Q<br />
4 0<br />
r2r 2 dr<br />
1<br />
r 1R + 1<br />
r2R - 1<br />
r2R 2<br />
251
= 910 9 ( - 610 - 8 )<br />
+<br />
1<br />
3004 - 1<br />
3006<br />
= - 3. 810 3 V<br />
( 3) = P ¡¤en = - P n = - 0( r 1 -<br />
= - 0( r 1 - 1)<br />
Q<br />
4 0 r 1r 2<br />
1<br />
6002 - 1<br />
6004<br />
1) E<br />
= - ( 6 - 1) - 8<br />
610- <br />
460. 02 2<br />
= 9. 910 - 6 C/ m 2<br />
53 R 1 R2, R 2<br />
< 2R 1, r 0<br />
r1, r2, r 2= r 1/ 2<br />
E m a x, ? <br />
?<br />
, <br />
U , ( r= R 1<br />
E 1 =<br />
U<br />
R1ln R 2 2<br />
R 1r 0<br />
( r= r 0 ) <br />
<br />
E 2 =<br />
2U<br />
r 0ln R 2 2<br />
R1r 0<br />
E 2/ E 1 = 2R1/ r 0<br />
) <br />
r 0< R2, R2< 2R1, E 2/ E 1> 0, ,<br />
E ma xE 2= E m ax<br />
<br />
252
U m ax =<br />
E ma xr 0<br />
ln R 2 2<br />
2 R1r 0<br />
54 r <br />
Q: <br />
<br />
Q = 1 -<br />
1<br />
Q<br />
r<br />
, E 0= / 0= Q/ ( 0S) <br />
r , E<br />
= E 0/ r= Q/ ( 0 rS ) , <br />
Q = S = S =<br />
0( r - 1) ES = 1 -<br />
1<br />
Q<br />
r<br />
55 3kV / mm, <br />
10cm , 10mm, 01mm <br />
?<br />
E b = m a x/ ( 2 0r ) , m ax = 2 0r E bE b = 3<br />
10 3 kV / mm= 310 6 V/ m r <br />
r 1 = 1. 0cm , ma x , 1 = 1. 710 - 6 C/ m<br />
r 2 =<br />
r 3 =<br />
1. 0mm , ma x , 2 = 1. 710 - 7 C/ m<br />
0. 1mm , ma x , 3 = 1. 710 - 8 C/ m<br />
56<br />
5210 - 9 m , 05210 - 3<br />
C/ m 2 , 60,<br />
: ( 1) ; ( 2) <br />
( 1) E = / ( 0 r ) = 05210 - 3 / ( 88510 - 12 60) =<br />
9810 6 V / m <br />
( 2) U= E d = 9. 810 6 5. 210 - 9 = 5. 110 - 2 V = 51 mV<br />
<br />
57E 0<br />
<br />
253
, , 53 <br />
r, <br />
<br />
53 , <br />
<br />
tan 2 = rt an 1 = rcot<br />
, <br />
E sin 2 = E 0sin 1 = E 0cos<br />
<br />
E =<br />
E 0cos / sin 2 = E 0<br />
r<br />
<br />
5357 <br />
sin 2 + rcos 2 <br />
= P cos 2 = 0( r - 1) E cos 2 = 0( r - 1)<br />
r<br />
58 <br />
, <br />
( <br />
54) , <br />
, <br />
, <br />
500mm 2 , 0600mm<br />
E 0sin <br />
54<br />
58 <br />
0250pF, <br />
?<br />
<br />
<br />
254<br />
C =<br />
d 1 =<br />
0S 1 d 1<br />
-<br />
0Sd 0<br />
d 0 C +<br />
1<br />
d 0<br />
0S
=<br />
8. 8510 - 1 2 5010 - 6 0. 60010 - 3<br />
0. 25010 - 12 0. 60010 - 3 + 8. 8510 - 12 5010 - 6<br />
= 0. 44810 - 3 m = 0. 448 mm<br />
<br />
d = d 0 - d 1 = 0. 600 - 0. 448 = 0. 152 mm<br />
59 510 -<br />
2 mm, <br />
23 , 30 F, <br />
?<br />
S = Cd = 3010- 6 510 - 5<br />
2. 38. 8510 - 12 = 7. 4 m 2<br />
510 310 3 kV / m <br />
50kV , <br />
?<br />
E b= U/ d C= 0S<br />
d<br />
<br />
C/ S = 0E b<br />
U = 8. 8510 - 1 2 310 6<br />
= 5. 310 - 10 F / m 2<br />
5010 3<br />
51118cm<br />
( 1) ?<br />
( 2) 2010 5 V , ?<br />
( 1) C= 4 0R= 0. 18/ ( 910 9 ) = 2. 010 - 1 1 F<br />
( 2) Q= CU= 2. 010 - 1 1 2. 010 5 = 4. 010 - 6 C<br />
512<br />
2510 -<br />
2 mm, 25mm, <br />
100mm, ( <br />
)<br />
C=<br />
2 0l<br />
ln R = 28.<br />
8510 - 12 0. 1<br />
= 8. 010 - 1 3 F<br />
2<br />
25<br />
ln<br />
R 1 2. 510 - 2<br />
255
51355 <br />
<br />
, , <br />
,<br />
S, <br />
d <br />
<br />
C =<br />
( - 1) 0S<br />
d<br />
55513 <br />
, C1<br />
= 0S / d ( - 1) , ,<br />
<br />
C = ( - 1) C1 = ( - 1) 0S / d<br />
514 002m 2 , <br />
05mm, ( 56) <br />
025mm , , <br />
, ?<br />
<br />
56514 ( )<br />
57( a) <br />
C = CA B +<br />
CA K CBK<br />
CA K + CB K<br />
C= 0S/ d , <br />
256
C = 7. 0810 - 10 F<br />
( B ) , 57( b) <br />
, <br />
C = CA K + CA B = 1. 0610 - 9 F<br />
57514 <br />
( )<br />
58515 <br />
515 ( 58) , <br />
a , b , <br />
d , l( l d ) <br />
<br />
58 x y , y= lx a + d <br />
C = <br />
a<br />
0<br />
0bdx<br />
y<br />
= a 0<br />
0a b<br />
l<br />
0bdx<br />
lx / a + d = 0a b ln 1 +<br />
l<br />
l<br />
d - l 2<br />
= 0a b<br />
2d 2 d<br />
516 , <br />
15cm 20cm <br />
, , <br />
60% , ?<br />
, <br />
, E 0<br />
E 0/ r<br />
1 -<br />
l d<br />
l<br />
2d<br />
<br />
257
U = E 0( d 0 - d ) + E 0d / r = E 0d 0 1 -<br />
= U 0 1 -<br />
d<br />
d 0<br />
U = 0. 60U 0, <br />
1 -<br />
+<br />
d<br />
rd 0<br />
d<br />
d 0<br />
1 -<br />
d 0= 2. 0cm, d = 1. 5cm <br />
r = 2. 1<br />
1<br />
= 0. 60<br />
r<br />
d<br />
d 0<br />
+<br />
d<br />
rd 0<br />
517 , R1<br />
R= ( R 2- R 1) R1<br />
<br />
Q 1<br />
-<br />
4 0 R 1<br />
R2,<br />
<br />
Q, U =<br />
1<br />
R2<br />
<br />
C = Q U = 4 R2R 1<br />
0<br />
R2 - R 1<br />
R= ( R 2- R 1) R 1<br />
, R 1R 2R 2 1, <br />
R 2 1<br />
C 4 0<br />
R<br />
4 R 2 1= S , R= d <br />
, <br />
C =<br />
0S<br />
d<br />
<br />
51812 F 2 F <br />
3 F 200V , <br />
?<br />
3 F , 2 F <br />
258
, 12 F U , 2 F<br />
U/ 4, 12 F 3U/ 4<br />
, 12 F U b , 3U / 4<br />
U b, <br />
U 4U b/ 3 = 4200/ 3 = 267 V<br />
276V <br />
519 S, <br />
d , <br />
r 1 r2( 59) <br />
<br />
0 r1 S<br />
1<br />
2 d 0 r2 S<br />
<br />
C =<br />
0 r 1S<br />
0 r2S<br />
d / 2 d / 2<br />
510520<br />
<br />
1<br />
d , <br />
2<br />
0 r1S<br />
d / 2 +<br />
0 r 2S =<br />
d / 2<br />
59519<br />
2 0 r1 r2S<br />
d ( r 1 + r2)<br />
<br />
520 <br />
510 <br />
r , eff<br />
( <br />
) <br />
a, <br />
, r <br />
( r = 1. 95) ( r= 33) , <br />
?<br />
, <br />
C =<br />
b d <br />
0 rhb + 0( a - h ) b = 0b h( r - 1) + a = 0<br />
d d d<br />
d<br />
r , effa b<br />
259
, e ff = 1 + ( r - 1)<br />
r , , r, eff , <br />
<br />
521<br />
r , ?<br />
C = C- C0= 4 0R 1R 2<br />
R 2- R 1<br />
= 4 0R 1R2 r<br />
R2- R 1 2 - 1<br />
2<br />
( r- 1) / 2 <br />
h<br />
a<br />
0R 1R2<br />
1<br />
2 + r<br />
2 - 4<br />
R2- R 1<br />
= C0( r- 1) / 2<br />
522 4 F 6 F <br />
200V , , <br />
, ?<br />
( 1) ;<br />
( 2) , <br />
, Q 0, <br />
Q 0 =<br />
C1C2<br />
C1 + C2<br />
U 0 = 46 200 = 480 <br />
4 + 6 C<br />
( 1) , <br />
, , <br />
( 2) , Q= 2Q 0 <br />
, C= C1+ C2= 10 F, <br />
U = Q C = 2480<br />
10<br />
= 96 V<br />
523 100pF 100V , <br />
, , 30V <br />
? ? ?<br />
260
, <br />
<br />
C2 =<br />
<br />
C1( U 1 - U 2)<br />
U 2<br />
C1U 1 = ( C1 + C2) U 2<br />
=<br />
- W = 1 2 C1U 2 1 -<br />
100( 100 - 30)<br />
30<br />
1<br />
2 ( C1 + C2) U 2 2<br />
= 233 pF<br />
= 1 2 10010 - 1 2 100 2<br />
-<br />
1<br />
2 ( 100 + 233)10- 12 30 2<br />
= 3. 510 - 7 J<br />
<br />
<br />
524 , S , d ( <br />
511) <br />
( 1) Q ,<br />
b <br />
, <br />
?<br />
( 2) , ( ) 511524 <br />
? ?<br />
( 3) U , ( 1) , ( 2) <br />
?<br />
C0 = 0S/ d , <br />
b, C= 0S / ( d - b) <br />
( 1) W= 1 Q 2<br />
2 C - 1 Q 2<br />
= Q 2<br />
d - b<br />
2 C0 2 0S - d<br />
0S = - Q 2 b<br />
2 0S<br />
( 2) A e xt = W < 0, , <br />
, <br />
261
( 3) U , , <br />
Q = ( C - C0) U<br />
U , <br />
<br />
<br />
W = 1 2 CU 2 -<br />
WS = Q ¡¤U = ( C - C0) U 2<br />
1<br />
2 C0U 2 = 1 2 ( C - C0) U 2 =<br />
A , <br />
<br />
WS<br />
+ A = W<br />
0U 2 S b<br />
2d ( d - b)<br />
A = W - W S = 1 2 ( C - C0) U 2 - ( C - C0) U 2<br />
= -<br />
1<br />
2 ( C - C0) U 2 = -<br />
0U 2 S b<br />
2d ( d - b)<br />
525 512 , <br />
7cm , <br />
5cm , <br />
5kV , <br />
( )<br />
512 x <br />
<br />
C =<br />
2 0x<br />
ln( R2/ R1)<br />
U , <br />
262<br />
Q = CU =<br />
2 0xU<br />
ln ( R2/ R1)<br />
512525
W C = 1 2<br />
Q 2<br />
C = 1 2<br />
Q 2 ln ( R 2/ R 1)<br />
2 0x<br />
, , <br />
<br />
F = -<br />
=<br />
W C<br />
x = 1 2<br />
0U 2<br />
ln( R 2/ R 1)<br />
Q 2<br />
ln( R 2/ R 1)<br />
2 0x 2<br />
= 8. 8510- 12 ( 510 3 ) 2<br />
ln ( 7/ 5)<br />
= 2. 110 - 3 N<br />
F > 0, x <br />
<br />
526 a , b, <br />
( 513) Q <br />
513526 <br />
( 1) , ?<br />
( 2) b, , r <br />
x , <br />
?<br />
?<br />
( 3) x , <br />
( 4) x 0 a , <br />
? ( )<br />
263
( 5) U<br />
, , ( 2) ( 4) ?( <br />
)<br />
( 1) <br />
W = 1 2<br />
Q 2<br />
C =<br />
Q2<br />
2 0ab<br />
( 2) x , <br />
C =<br />
, <br />
WC = 1 2<br />
0b [ a + ( r - 1) x ]<br />
Q 2<br />
C =<br />
Q 2<br />
2 0b[ a + ( r - 1) x ]<br />
( 3) , <br />
Q <br />
F = -<br />
dW C<br />
dx = ( r - 1) Q 2<br />
2 0b[ a + ( r - 1) x ] 2<br />
0, F x , , <br />
( 4) , <br />
, <br />
F dx = -<br />
dW C<br />
( 5) U , U <br />
WC = 1 2 CU 2 = 1 2<br />
0b[ a + ( r - 1) x ]<br />
<br />
dx , , <br />
, <br />
dQ =<br />
UdC<br />
U , <br />
, <br />
264<br />
dA E = UdQ = U 2 dC<br />
U 2
dWC = 1 2 U 2 dC<br />
dA E = dWC + F dx<br />
F dx = dA E - dWC = 1 2 U 2 dC<br />
F = 1 2 U 2 dC<br />
dx =<br />
0( r - 1) b<br />
2 U 2<br />
Q , <br />
F =<br />
0( r - 1) b<br />
2<br />
Q 2<br />
C 2 =<br />
( r - 1) Q 2<br />
2 0b[ a + ( r - 1) x ] 2<br />
F > 0, F x , , <br />
F Q ( 3) , <br />
x , Q , <br />
<br />
<br />
527: , <br />
R 1, 2R1R 2/ ( R1 + R 2) , R1<br />
R 2<br />
<br />
<br />
?<br />
Q , <br />
<br />
w e =<br />
E =<br />
0E 2<br />
=<br />
2<br />
Q<br />
4 0r 2<br />
Q 2<br />
32<br />
2 0r 4<br />
R , <br />
R <br />
4<br />
32<br />
2 0r 4<br />
R 1<br />
Q 2<br />
r 2 dr = 1 2 R 2<br />
4 r 2 dr<br />
32<br />
2 0r 4<br />
R 1<br />
Q 2<br />
265
1<br />
R 1<br />
-<br />
1<br />
R<br />
= 1 2<br />
1<br />
R1<br />
-<br />
1<br />
R2<br />
<br />
R =<br />
2R1R 2<br />
R1 + R2<br />
, R2, <br />
R = 2R 1<br />
528 S , y 0, <br />
y = 0 , y = y 0<br />
y , <br />
( 1) ?<br />
<br />
r = 1 + 3 y<br />
y 0<br />
( 2) Q( + Q) , <br />
?<br />
( 3) <br />
( 4) <br />
( 1) dy, <br />
r , <br />
C , <br />
<br />
266<br />
1<br />
C = 1<br />
dC<br />
= y 0<br />
0<br />
dy<br />
0<br />
dC =<br />
rS y =<br />
0<br />
0<br />
0 rS<br />
dy<br />
dy<br />
0S 1 + 3 y 0y<br />
=<br />
y 0<br />
3 0S ln 4
C =<br />
3 0S<br />
y 0ln4<br />
( 2) , 1 = P 1= - 0( r , y 0<br />
- 1) E = - 0( r, y 0<br />
- 1)<br />
= -<br />
r, y 0<br />
- 1<br />
= -<br />
r, y 0<br />
3Q<br />
4S<br />
, 2 = P 2= 0( r, 0- 1) E = 0( 1- 1) E= 0<br />
D<br />
0<br />
( 3) y dy,<br />
, <br />
dq int<br />
= dy =<br />
= -<br />
= -<br />
Q<br />
S d 1<br />
r<br />
Q<br />
S<br />
d<br />
dy<br />
0[ ( E + dE ) - E ] = 0dE =<br />
1<br />
= 3Q<br />
r y 0S 1 + 3 y<br />
y 0<br />
<br />
y 0<br />
0<br />
Sdy = -<br />
Q <br />
r, y0<br />
d<br />
r, 0<br />
( 4) <br />
1 S = -<br />
- 2<br />
d( D / r)<br />
1<br />
= - Q 1 r<br />
4 - 1 = 3Q 4<br />
3<br />
4 Q<br />
<br />
<br />
52930 ,<br />
2010 -<br />
?<br />
r, y 0<br />
6<br />
C, <br />
<br />
Q1 Q 2 <br />
U 1 =<br />
Q 1/ ( 4 0R) , U 2= Q 2/ ( 4 0 rR) ,<br />
, <br />
267
Q 1<br />
4 0R = Q 2<br />
4 0 rR<br />
rQ 1 = Q 2<br />
Q 1 + Q 2 = Q<br />
<br />
<br />
Q 1 =<br />
Q<br />
r + 1<br />
=<br />
2. 010-<br />
6<br />
3 + 1<br />
= 0. 5010 - 6 C<br />
Q 2 = Q - Q1 = ( 2. 0 - 0. 5)10 - 6 = 1. 510 - 6 C<br />
530 , <br />
, <br />
<br />
;<br />
( 1) 334 , <br />
( 2) r = 158, <br />
<br />
?<br />
( 1) , <br />
1/ r, 334 , <br />
<br />
W = -<br />
r =<br />
4 0 r<br />
2 h 2<br />
m ee 2<br />
m ee 4<br />
1<br />
= W0<br />
2( 4 0 r h) 2 2 <br />
2<br />
r<br />
W 0 <br />
( 2) <br />
1/ <br />
2<br />
r <br />
268<br />
W 1 = W01<br />
= 13. 6 = 0. 054 eV<br />
r 2 15. 8 2
6 <br />
61 240m <br />
8mA , <br />
? <br />
N 1 , I = N 1ev<br />
<br />
N = l N 1 = lI<br />
ev = 240810 - 3<br />
1610 - 19 310 8 = 410 1 0 ( )<br />
62 , 30cm <br />
20cm/ s , , <br />
1210 6 V / m <br />
, ?<br />
I =<br />
w v =<br />
2 0Ew v<br />
= 288510 - 12 1210 6 0302<br />
= 1310 - 6 A<br />
63 , <br />
1mm 30A , ?<br />
, , <br />
20, <br />
, ?<br />
I<br />
v =<br />
Se = I M<br />
<br />
4 D 2 N A e<br />
M = 100g/ mol= 01kg/ mol, = 10g/ cm 3<br />
= 10 4 k g/ m 3 , <br />
269
v =<br />
43001<br />
( 10 - 3 ) 2 10 4 610 23 1610 - 1 9<br />
= 410 - 3 m/ s<br />
v = 160<br />
= 1110 5 m/ s<br />
kT<br />
m = 160 13810- 23 293<br />
9110 - 31<br />
64 20mm80mm, 2m, <br />
50mV = 17510 - 8 ¡¤m, <br />
8510 28 / m 3 : ( 1) ; ( 2) <br />
; ( 3) ; ( 4) ; ( 5) <br />
; ( 6) <br />
( 1) R = l S = 2<br />
8<br />
17510- <br />
208010 - 6<br />
= 21910 - 5 <br />
( 2) I = U/ R = 5010 - 3 / ( 21910 - 5 ) = 22810 3 A<br />
( 3) J = I / S = 22810 3 / ( 208010 - 6 )<br />
= 14310 6 A/ m 2<br />
( 4) E = J = 17510 - 8 14310 6 = 25010 - 2 V / m<br />
( 5) P = I U = 22810 3 5010 - 3 = 11410 2 W<br />
( 6) v = J / ( e) = 14310 6 / ( 8510 28 1610 - 1 9 )<br />
= 10510 - 4 m/ s<br />
65 , 20cm 25cm, <br />
<br />
20A , ?<br />
001¡¤m, 8710 -<br />
I 1<br />
I 2<br />
I 1<br />
= R 2<br />
R 1<br />
=<br />
8 ¡¤m<br />
I 2 , <br />
2r 2 1<br />
1( r 2 2 - r 2 1) = 8710 - 8 2 2<br />
001( 25 2 - 2 2 ) = 5<br />
15510-<br />
I 1 I 2 , I 2 20A , I 1 0<br />
270
66 , <br />
( 61) 5m , <br />
AB , CD <br />
30 , 70<br />
P , <br />
AP<br />
CP = R A B / 2<br />
R CD / 2<br />
= 30<br />
70 = 3 7<br />
AP + CP = 5 m<br />
AP =<br />
A 15m <br />
15 m<br />
6166 <br />
67 <br />
<br />
( 1) , 120V / m, <br />
410 - 12 A / m 2 ?<br />
( 2) 410 5 V , <br />
?<br />
<br />
( 1) = E J = 120<br />
= 310 13 ¡¤m<br />
410 - 12<br />
( 2) R = U U<br />
410 5<br />
=<br />
=<br />
I J4 R 2 E 410 - 1 2 4( 63710 6 ) 2<br />
= 196 <br />
68 62 , r 1 = 05cm ,<br />
62 68 <br />
<br />
, r 2 =<br />
2cm , =<br />
110 12 ¡¤<br />
m <br />
<br />
( 1) L = 1000m <br />
;<br />
271
( 2) 100V , <br />
?<br />
( 1) R =<br />
<br />
2 L ln r 2 2<br />
r 2 1<br />
=<br />
110 12<br />
22<br />
ln = 2210 8 <br />
21000 05 2<br />
( 2) I = U/ R = 100/ ( 2210 8 ) = 4510 - 7 A<br />
69r 1 r 2, <br />
<br />
R = r 2<br />
r 1<br />
dr<br />
=<br />
4 r 2<br />
R =<br />
1<br />
4r 1<br />
1<br />
4r 1<br />
-<br />
<br />
610, , 200A<br />
, , <br />
100m , 10m, <br />
13m<br />
-<br />
1<br />
r 2<br />
, <br />
, r J =<br />
I / ( 2 r 2 ) , E =<br />
<br />
U = <br />
r 2<br />
r 1<br />
Edr =<br />
=<br />
I 1<br />
2r 1<br />
-<br />
1<br />
r 2<br />
1<br />
r 2<br />
J =<br />
= I r 2 - r 1<br />
2r 2r 1<br />
100200( 13 - 10)<br />
21310<br />
I / ( 2 r 2 ) , <br />
= 73 V<br />
611 63 , E 1 = 30 V, r 1= 05 , E 2= 60 V , r 2 =<br />
10 , R 1= 20 , R 2= 40 , R1 R2 <br />
63 , :<br />
b: I 1- I 2+ I 3= 0<br />
a bR 1a : - I 3r 3- E1+ I 1R 1= 0<br />
a R 2ba : I 2r 2- E 1+ I 3r 1+ E 2+ I 2R 2= 0<br />
272
, , <br />
I 1 = 3 4 A , I 2 = 2 3 A <br />
63611 <br />
64612 <br />
61264 , E 1= 30 V , E 2= 10 V , r 1= 05 ,<br />
r 2= 10 , R 1= 45 , R2= 190 , R 3= 100 , R 4= 50 <br />
<br />
64 , <br />
b: - I 1+ I 3+ I 2= 0<br />
a R 1bR3a : - E 1+ I 1( r 1+ R1+ R 4) + I 3R 3= 0<br />
a R 3bR2a : - I 3R 3+ I 2( R 2+ r 2) + E 2= 0<br />
, ,<br />
<br />
I 1 = I 4 = 016 A , I 2 = 002 A,<br />
I 3 =<br />
014 A<br />
613 65 , I 1,<br />
I 2, I g<br />
3 <br />
, I g, R 1/ R 2 =<br />
R 3/ R 4<br />
I g = 0, 4 <br />
<br />
65 , :<br />
R 1GR2 : I 1R 1 + I gR g - I 2R 2 = 0<br />
65613 <br />
R 3R4G : ( I 1 - I g) R3 - ( I 2 + I g) R 4 - I gRg = 0<br />
273
R 2R4E : - E + I 2R 2 + ( I 2 + I g) R 4 = 0<br />
<br />
I g =<br />
(R2R3 - R1R4)E<br />
R1R3(R2 + R4) + R2R4(R1 + R3) + Rg( R1 + R3)(R2 + R4)<br />
, R1/ R2 = R 3/ R4 , I g<br />
= 04 <br />
<br />
614 66 <br />
E = 6 V, 0, U e c =<br />
196V , U e b = 02V , I c = 2mA , I b =<br />
20 A, I 2= 04mA , R c= 1kR 1,<br />
R 2, R e <br />
66 , <br />
, <br />
, <br />
66614 <br />
I 1 = I 2 + I b = 04 + 002 = 042 mA<br />
I e = I b + I c = 002 + 20 = 202 mA<br />
U bc = U ec - U e b = 196 - 02 = 176 V<br />
R 1R c: I 1R1 - I cRc - U bc = 0<br />
R 1<br />
= 90 k<br />
R eRcE: I cRc - E + I e Re + U e c = 0<br />
Re = 10 k <br />
R 2R e: I 2R 2 + U b c - I e Re = 0<br />
R 2 = 56 k<br />
<br />
615 : C , R <br />
, t =<br />
, Q =<br />
0, <br />
? R, C , <br />
274
U 0 , <br />
<br />
<br />
=<br />
Q t / ( R C)<br />
e-<br />
RC<br />
R <br />
<br />
<br />
W = 2 Rdt =<br />
0<br />
0<br />
Q 2<br />
RC 2 e - 2t / ( RC ) dt = Q 2<br />
<br />
<br />
- t/ ( R C)<br />
q = Qe<br />
1 <br />
2C = W C<br />
t = RCln Q e = RCln CU e<br />
C = 10 - 7 F, U = 10 2 V , R = 10 3 , <br />
t = 10 3 10 - 7 ln( 10 - 7 10 2 / 1610 - 1 9 ) = 310 - 3 s<br />
<br />
<br />
<br />
616 2000 F <br />
4000V , <br />
1A , <br />
, 05 , <br />
<br />
I m a x<br />
<br />
Rm in = U / I m ax = 410 3 / 1 = 40 k<br />
min = Rm inC = 410 3 210 - 3 = 80 s<br />
<br />
275
I m a x = U R = 4103<br />
05<br />
= 8010 3 A<br />
= RC = 05210 - 3 = 1010 - 3 s<br />
617 400V 200A <br />
, 20, <br />
80, ( L/ min) ?<br />
Q( L/ min ) , <br />
Q( kg/ min) , <br />
<br />
Q =<br />
UI60 = cQ( t 2 - t 1)<br />
UI60<br />
( t 2 - t 1) c = 40020060<br />
= 19 L/ min<br />
( 80 - 60)4210 3<br />
<br />
618( 615) : <br />
, ( ) <br />
, <br />
<br />
, , <br />
qin t =<br />
0E ¡¤dS =<br />
0 J ¡¤dS<br />
, , <br />
qi nt<br />
= 0 J ¡¤dS<br />
, , <br />
qin t = 0<br />
<br />
, , <br />
, qint 0, <br />
276
7 <br />
71 0. 5g, 2510 -<br />
8 C <br />
6010 4 m / s, <br />
, <br />
?<br />
<br />
, , <br />
B =<br />
qvB = mg<br />
mg<br />
qv = 0. 510 - 3 9. 8<br />
= 3. 3 T<br />
2. 510 - 8 610 4<br />
, <br />
7. 2 7. 1, A <br />
, v0= 110 7 m/ s<br />
( 1) A C <br />
, ;<br />
7172 <br />
( 2) A C <br />
<br />
( 1) <br />
<br />
B =<br />
ev0B = m v2 0<br />
R<br />
mv0<br />
eR = 9. 1110- 31 110 7<br />
1. 610 - 19 0. 05<br />
<br />
= 1. 110 - 3 T<br />
277
( 2) <br />
t = T 2 = 2 R = 0. 05<br />
= 1. 610 - 8 s<br />
2v 0 110 7<br />
7. 3 2. 010 3 eV , B =<br />
0. 1T , B 89, , <br />
B T h r <br />
v =<br />
<br />
2E k<br />
m = 2210 3 1. 610 - 1 9<br />
9. 1110 - 31 = 2. 610 7 m/ s<br />
<br />
<br />
<br />
T =<br />
2 m<br />
eB = 2<br />
31<br />
9. 1110-<br />
1. 610 - 1 9 0. 1 = 3. 610 - 1 0 s<br />
h = vcos89 T =<br />
r =<br />
= 1. 610 - 4 m<br />
2. 610 7 cos893. 610 - 10<br />
mvsin 89<br />
= 9. 1110- 31 2. 610 7 sin 89<br />
eB<br />
1. 610 - 19 0. 1<br />
= 1. 510 - 3 m<br />
7. 4<br />
2. 010 4 V , 0. 2m , <br />
0. 510 -<br />
, ?<br />
<br />
v =<br />
4 T ? <br />
2E k<br />
m = 2eU<br />
m = 21. 610 - 1 9 210 4<br />
9. 110 - 31<br />
= 8. 410 7 m/ s<br />
<br />
278
R =<br />
mv<br />
eB = 9. 110 - 31 8. 410 7<br />
1. 610 - 1 9 0. 510 - 4 = 9. 6 m<br />
72 , <br />
x = R - R 2 - l 2 l 2<br />
2R = 0. 2 2<br />
29. 6<br />
= 210 - 3 m = 2 mm<br />
, <br />
, <br />
7. 5 7274 <br />
240m <br />
1. 4910 -<br />
<br />
R= mv/ ( eB) = p / ( eB) <br />
18<br />
kgm/ s, <br />
B = p eR = 1. 4910 - 18<br />
= 0. 244 T<br />
1. 610 - 19 240/ ( 2 )<br />
7. 6 10 -<br />
10 -<br />
1 6 kg m/ s, <br />
8<br />
T , ? <br />
, 10 8 T , <br />
?<br />
R 1=<br />
p =<br />
eB 1<br />
10 - 16<br />
= 610 10 m<br />
1. 610 - 19 10 - 8<br />
10 - 16<br />
= 610 - 6 m<br />
1. 610 - 19 10 8<br />
R 2=<br />
p =<br />
eB 2<br />
7. 7 , 20T , <br />
3. 5m <br />
p = eRB = 1. 610 -<br />
<br />
E =<br />
p 2<br />
2m 0, p<br />
= 1. 1210 - 17 kg ¡¤m / s<br />
=<br />
19 3. 520<br />
( 1. 1210 - 17 ) 2<br />
21. 6710 - 2 7 = 3. 7510 - 7 J = 234 GeV<br />
279
( 1GeV ) , <br />
, <br />
E = c 2 p 2 - m 2 0, pc 4 cp = 310 8 1. 1210 - 1 7<br />
= 3. 3610 - 9 J = 21 GeV<br />
7. 80. 8010 8 m/ s <br />
, 410 -<br />
7 T <br />
? <br />
210 -<br />
, ?<br />
R 1= mv = 9. 110 - 31 0. 810 8<br />
= 1. 110 3<br />
eB 1 1. 610 - 1 410 9 - 7 m<br />
5 T <br />
R 2= mv = 9. 110 - 31 0. 810 8<br />
= 23<br />
eB 2 1. 610 - 1 210 9 - 5 m<br />
7. 9 D 75cm,<br />
1. 5T ( 7. 30) <br />
3. 3410 - 2 7 kg, :<br />
( 1) ?<br />
( 2) MeV ?<br />
( 1) = 1 T = eB = 1. 610- 19 1. 5<br />
= 1. 110 7 Hz<br />
2 m D 23. 3410 - 2 7<br />
( 2) E k = 1 2 m Dv2 = p 2<br />
2m D<br />
= e2 B 2 R 2<br />
2m D<br />
= ( 1. 610- 19 ) 2 ( 1. 5) 2 ( 0. 75/ 2) 2<br />
23. 3410 - 27<br />
= 1. 210 - 12 J= 7. 6 MeV<br />
7. 10 7. 3 m <br />
q ( E <br />
B) B , <br />
<br />
280
73710 <br />
( 1) l <br />
m =<br />
qBB l<br />
2E<br />
( 2) 16 O 29. 20cm , <br />
32. 86cm 16 O <br />
16. 00u, ?<br />
<br />
( 1) <br />
qvB = qE<br />
v = E / B<br />
B <br />
<br />
m =<br />
R = l 2 = mv<br />
qB<br />
qB l<br />
2v = qBB l<br />
2E<br />
( 2) m l , <br />
<br />
281
32. 86<br />
16. 00 = 18. 01 u<br />
29. 20<br />
7. 117. 4 , d = 1. 0mm, B= 1. 5T<br />
, <br />
8. 4<br />
10 22 , <br />
- e= - 1. 610 -<br />
I = 200A ,<br />
U a a ;<br />
19 C, <br />
( 1 ) <br />
( 2) b U a a ? ?<br />
74711 <br />
( 1) U a a = I B<br />
qd<br />
2001. 5<br />
=<br />
8. 410 22 ( - 1. 610 - 19 )1. 010 - 3<br />
a <br />
= - 2. 2310 - 5 V<br />
( 2) b U a a = U H U H = E H b= vb/ B<br />
b , I , v= I / ( qbd ) <br />
b <br />
7. 127. 5 , abc, <br />
x I , z B <br />
a = 0. 10cm , b= 0. 35cm , c= 1. 0cm, I = 1. 0mA, B = 3000G , <br />
U A A = 6. 55mV <br />
( 1) ( P ) ( N ) ?<br />
( 2) <br />
( 1) A A<br />
<br />
<br />
282
75712 <br />
I B<br />
( 2) =<br />
U A A qa = 1. 010 - 0. 3 3<br />
6. 5510 - 1. 3 610 - 19 10 - 3<br />
= 2. 8610 2 0 / m 3<br />
7. 13 N , <br />
210 2 1 / m 3 , 1. 610 -<br />
2 m <br />
, , abc= 0. 5cm0. 2cm<br />
0. 005 cm1V <br />
, 0. 2cm<br />
1. 05mV <br />
a , b, c <br />
B =<br />
qU Hc<br />
I<br />
=<br />
qU H c a =<br />
Ubc<br />
qU H a<br />
Ub<br />
= ( 210 21 1. 610 - 19 1. 0510 - 3<br />
1. 610 - 2 0. 510 - 2 ) / ( 10. 210 - 2 )<br />
= 1. 3410 - 2 T<br />
7. 14, <br />
7. 6 , l <br />
B, , <br />
J <br />
( 1) : l p =<br />
283
J lB, ;<br />
( 2) l 1. 00atm , ?<br />
B= 1. 50T , l = 2. 00cm<br />
76714 <br />
( 1) p = F S = I Bl<br />
S = J Bl<br />
( 2) J = p 1. 001. 013105<br />
=<br />
Bl 1. 502. 0010 - 2<br />
= 3. 3810 6 A / m 2<br />
= 338 A / cm 2<br />
7. 157. 7 <br />
, <br />
2. 0mm, 0. 080T , 0. 10mV , <br />
? ( )<br />
, <br />
284<br />
77715
v =<br />
E H<br />
B =<br />
qvB = qE H<br />
U H<br />
dB = 0. 1010 - 3<br />
0. 080210 - 3 = 0. 63 m/ s<br />
7. 167. 8 , <br />
, <br />
B , l, B <br />
I , <br />
; ,<br />
m ,<br />
( g = 9. 80<br />
m / s 2 )<br />
;<br />
( 1) B <br />
( 2 ) l = 10. 0 cm, = 5, I =<br />
0. 10A , m= 8. 78g , B= ?<br />
78716 <br />
( 1) M<br />
<br />
, <br />
<br />
, <br />
Mg =<br />
M g -<br />
I Bl<br />
( M + m) g = M g + I Bl<br />
B =<br />
mg<br />
2I l<br />
8. 789. 8010 - 3<br />
( 2) B=<br />
= 0. 860<br />
250. 110. 010 - 2 T<br />
7. 17 20mm, 10mm, <br />
, 1000 , B= 1000G , <br />
100mA , 7. 9 <br />
, <br />
285
( 7. 22) <br />
79717 <br />
( 1) B ( 7. 9( a) ) ;<br />
( 2) B ( 7. 9( b) ) <br />
( 1) , <br />
F 1<br />
= F 1 = N I l 1B = 10 3 0. 10. 010. 1 = 0. 1 N<br />
<br />
, <br />
F 2<br />
= F 2 = N I l 2B = 10 3 0. 10. 020. 1 = 0. 2 N<br />
<br />
<br />
4 , , <br />
( 722) M = mBsin , <br />
m B 0 , M= 0, <br />
<br />
( 2) <br />
, <br />
F 2<br />
= F 2 = N I l 2B = 10 3 0. 10. 020. 1 = 0. 2 N<br />
, , <br />
, F 2 F 1 2 <br />
M = F 2l 1 = N I l 2l 1B = 0. 20. 01 = 210 - 3 N ¡¤m<br />
B <br />
286
N I l 1l 2= N I S = m , <br />
B , m B 90 , <br />
( 722) M= mBsin , mB <br />
<br />
7. 18 , 200<br />
, 150mm, B= 4. 0T , I<br />
= 8. 0A , :<br />
( 1) m ;<br />
( 2) <br />
( 1) m= N I S = 2008. 0( 15010 - 3 ) 2 = 36 A m 2<br />
( 2) M ma x= mB= 364. 0= 144 N m<br />
7. 19 M R <br />
, <br />
, ©¦m©¦=<br />
1 4 R 4 , m <br />
L m=<br />
q L, q <br />
2M<br />
710 dr <br />
<br />
d©¦m©¦=<br />
¡¤2 rdr r 2 = r 3 dr<br />
T<br />
<br />
©¦m©¦=d©¦m©¦= R r 3 dr<br />
0<br />
= R 4 / 4<br />
©¦m©¦= 1<br />
2M R 2 MR2<br />
2 <br />
R 2 = q, MR 2 / 2= L, <br />
©¦m©¦=<br />
qL<br />
2M<br />
710719 <br />
287
m L , <br />
<br />
m =<br />
q<br />
2M L<br />
7. 20 <br />
+ 2e/ 3 - e/ 3 ,<br />
, , <br />
r v<br />
, , <br />
;<br />
( 1) <br />
( 2) r= 1. 2010 - 15 m, <br />
v m = 9. 6610 - 2 7<br />
A m 2 <br />
( 1) 711 , <br />
m = m= v q<br />
v + = - v -<br />
2 r r 2 = r 2 v+ ¡¤ 2 3 e + 2v - ¡¤ - 1<br />
3 e = 2 3 r ve<br />
= v, <br />
711720 <br />
( 2) v= 3m<br />
2re = 39. 6610 - 27<br />
21. 2010 - 15 1. 610 - 1 9 = 7. 5510 7 m / s<br />
288
7. 210. 92810 - 2 3 J/ T <br />
, R, e <br />
, ? <br />
10 -<br />
18 m , , <br />
? ?<br />
712 , <br />
<br />
m = ¡¤2 Rsin ¡¤ <br />
0<br />
2 ¡¤ ( Rsin ) 2 Rd<br />
= <br />
0<br />
R 4 sin 3 d<br />
= 1 3 e R 2<br />
e= 4 R 2 , <br />
712721 <br />
R= 10 -<br />
v =<br />
R =<br />
18 m , <br />
3m<br />
eR = 30. 92810 - 2 3<br />
1. 610 - 1 9 10 - 1 8 = 1. 710 14 m / s<br />
, <br />
<br />
7. 22 , <br />
2 P 3/ 22. 3910 -<br />
23 J/ T <br />
289
, <br />
, 39. 2 , 75 , 105 ,<br />
140. 8<br />
B= 2. 0T , <br />
?<br />
Wm = - m B= - mBcos<br />
, - 3. 7010 - 2 3<br />
J, - 1. 2410 - 23 J, + 1. 2410 - 2 3 J, + 3. 7010 - 23 J<br />
<br />
7. 23( 7. 29) :<br />
( 1) S , B = 0, <br />
S , <br />
B =<br />
vE<br />
c 2<br />
( 2) S , E = 0, <br />
S , <br />
E = -<br />
( 1) ( 729) ,<br />
B x = B x, B y = B y + <br />
c E z<br />
B = 0, <br />
B x = 0, By = -<br />
vB<br />
, B z = B z - <br />
c E y<br />
v<br />
c 2 E z , B z = v c 2 E y<br />
v = vi, B <br />
B = -<br />
( 2) ( 729) <br />
v<br />
E zk + v E yj = vE<br />
c 2 c 2 c 2<br />
E x = E x, E y = ( E y - cBz ) , E z = ( E z + cBy )<br />
E = 0, <br />
E x = 0, E y = vBz , E z = - vBy<br />
v = vi, <br />
290
E = -<br />
vB<br />
7. 24S x , <br />
, , v 0 = v0i , <br />
- z z = a v = vi <br />
<br />
( 1) S <br />
F =<br />
0 ev 0v<br />
k<br />
2 a<br />
( 2) S, , <br />
<br />
+ = 1 - v 2 / c 2 , - = - 1 -<br />
<br />
= v0v c 2 1 - v 2 / c 2<br />
( 3) S <br />
ev0v<br />
F =<br />
2 0a c 2 1 - v 2 / c 2<br />
v 0v<br />
c 2 1 - v 2 / c 2<br />
( 4) ( 2. 16) F F ( 1) <br />
( 1) S ( 713( a) ) <br />
I = - v - = v0, - x p <br />
B= ( 0I / ( 2 a ) ) j , <br />
F = evB =<br />
0 ev 0v<br />
k<br />
2 a<br />
, <br />
<br />
( 2) S ( 713( b) ) , l + , 0<br />
l+ = l + , 0 1- v 2 / c 2 , <br />
+ = 1 - v 2 / c 2 291
713724 <br />
S l - l - , 0= l -<br />
1- v 2 0/ c 2 ,<br />
S , <br />
, l -<br />
v - = v - , x =<br />
v 0 - v<br />
1 - v 0v/ c 2<br />
, 0<br />
l - = l - , 0 1 - v - 2<br />
/ c 2 =<br />
l -<br />
1 - v 2 0/ c 2 1 -<br />
v0 - v<br />
1 - v0v/ c 2 2<br />
c 2<br />
=<br />
l -<br />
1 - v 2 0/ c 2 ¡¤<br />
1 - v 2 0/ c 2 ¡¤ 1 - v 2 / c 2<br />
1 - v 0v/ c 2<br />
= l - 1 - v 2 / c 2<br />
1 - v 0v/ c 2<br />
, q= q , <br />
- l - = - l -<br />
- = - l - / l - = - ( 1 - v0v/ c 2 ) 1 - v 2 / c 2<br />
, S <br />
= + + - = v 0v c 2 1 - v 2 / c 2<br />
( 3) S p , <br />
292
z a , <br />
<br />
<br />
E =<br />
2 0a k =<br />
<br />
F = E e =<br />
v 0v<br />
2 0a c 2 1 - v 2 / c 2k<br />
ev 0v<br />
2 0ac 2 1 - v 2 / c k 2<br />
( 4) [ ( 216 ] ,<br />
F z =<br />
F z / <br />
1 + vv x / c 2<br />
v x S S <br />
, v x = 0, F z = Fz / F z = ev0v<br />
2 0a c 2 1- v 2 / c 2 <br />
F z =<br />
( 1) <br />
ev0v 1 - v 2 / c 2<br />
2 0a c 2 1 - v 2 / c = 0 ev 0v<br />
2 2 a<br />
293
8 <br />
8. 181 P B <br />
8181 <br />
( a) P <br />
, P <br />
<br />
B = 1 2<br />
0I<br />
2 a =<br />
0I<br />
4 a<br />
( b) P <br />
, r , 0I /<br />
( 2 r ) P ,<br />
0I / ( 4r ) P , <br />
<br />
P =<br />
0I<br />
2 r +<br />
0I<br />
4r<br />
( c) P a / ( 2 3 ) P <br />
, <br />
294
B =<br />
0I<br />
3<br />
4 a / ( 2<br />
3 ) ( cos30 - cos150<br />
) = 9 0I<br />
2 a<br />
8. 2 25m , 1. 8<br />
10 3 A <br />
( 1) ?<br />
( 2) , 0. 610 - 4 T , <br />
?<br />
( 1) B= 0I<br />
2 r = 410-<br />
1. 7 810 3<br />
= 1. 410 - 5 T<br />
225<br />
( 2) B/ B E= 1. 410 - 5 / ( 0. 610 - 4 ) = 0. 24<br />
8. 3 , 0. 80m , <br />
20A <br />
( 1) ? ( <br />
)<br />
( 2) ( ) 0. 1810 - 4 T <br />
, <br />
, ? <br />
, <br />
( 1) B= 0I<br />
2 r = 410-<br />
20<br />
7 = 5. 010 - 6 T<br />
20. 80<br />
( 2) B , <br />
1 = arctan B BE<br />
= arctan<br />
6<br />
5. 010-<br />
= 15 31<br />
0. 1810 - 4<br />
, <br />
2 = arcsin B B E<br />
= arcsin<br />
6<br />
5. 010-<br />
= 16 8<br />
0. 1810 - 4<br />
8. 4 A , C , <br />
82 O ?<br />
I 1<br />
<br />
295
B 1 = 0I 1<br />
2r<br />
l 1<br />
2 r =<br />
0I 1l 1<br />
4 r 2<br />
I 2 <br />
B 2 = 0I 2<br />
2r<br />
l 1<br />
I 1<br />
I 2<br />
l 2<br />
2 r =<br />
0I 2l 2<br />
4 r 2<br />
l 2 , <br />
= R2<br />
R1<br />
= l 2<br />
l 1<br />
I 1l 1= I 2l 2B1 B2 , , <br />
<br />
8284 <br />
8385 <br />
8. 5d = 40cm, I 1= I 2<br />
= 20A , 83 :<br />
;<br />
( 1) <br />
( 2) ( r 1= r 3= 10cm, l =<br />
25cm )<br />
( 1) <br />
B 0 = 2<br />
0I<br />
2 d / 2 =<br />
( 2) <br />
296<br />
24<br />
7 10- 20<br />
0. 4<br />
= 4. 010 - 5 T
= 2B ¡¤dS = 2 r 1 + r 2<br />
r 1<br />
0I<br />
2 r ldr =<br />
= 4<br />
7 10- 200. 25<br />
ln<br />
<br />
= 2. 210 - 6 Wb<br />
0I l<br />
ln r 1 + r 2<br />
r 1<br />
0. 10 + 0. 20<br />
0. 10<br />
8. 684 , I <br />
x B<br />
8486 <br />
<br />
84 , , I dl P <br />
dB = 0I dlr<br />
= 0I dl( x i - R)<br />
4 r 3 4 r 3<br />
= 0I [ ( dy j + dz k)x i - dlR]<br />
4 r 3<br />
= 0I [ - x dy k + x dz j - Rdli]<br />
4 r 3<br />
P <br />
B = dB =<br />
=<br />
0I<br />
4<br />
r Ṟ - x dyk + 3 R<br />
0 x dz j - 0<br />
R<br />
- 0I R<br />
[ 2x k + Ri]<br />
4 ( x 2 + R 2 ) 3 / 2<br />
0 Rdli<br />
297
: 84 , I dl P dB<br />
dB= 0I dl/ ( 4 r 2 ) dB dBx<br />
dB,<br />
dBx = - dBsin , dB = dBcos<br />
x <br />
dBR dB dBy dBz , dBz =<br />
- dB cos = - dBcos cos<br />
<br />
z , <br />
By = dB y = 0<br />
R<br />
Bx = dB x = - dBsin= -<br />
= -<br />
B z = dB z<br />
= -<br />
0I R 2<br />
4( x 2 + R 2 ) 3/ 2<br />
0<br />
0I<br />
dlsin = -<br />
4 r 2<br />
R<br />
0I dl<br />
= - dBcos cos= - cos cos<br />
0 4 r 2<br />
/ 2<br />
0I<br />
cos<br />
4 r 2<br />
- / 2<br />
Rdcos= -<br />
P <br />
B = -<br />
0I Rx<br />
2 ( x 2 + R 2 ) 3/ 2<br />
0I R<br />
[ Ri + 2x k]<br />
4 ( x 2 + R 2 ) 3 / 2<br />
0I sin 4 r R<br />
dl<br />
2<br />
0<br />
8. 7 , I = 5. 010 3 A <br />
: 5. 0cm , <br />
7. 0cm, 9. 0cm ( <br />
) <br />
( <br />
) , <br />
, :<br />
298<br />
r 0. 05m, B =<br />
0. 4r T
0. 05m r 0. 07m, B = 10 - 3 / r T<br />
0. 07m r 0. 09m, B = 0. 31( 8. 110 - 3 - r 2 ) / r T<br />
0. 09m r , B = 0<br />
r 85 <br />
8587 <br />
8. 8( 84) , :<br />
( 1) I ;<br />
( 2) ( j ) <br />
( 1) 86( a ) , I = 2 Rj , <br />
P P d dI 1 =<br />
j Rd 1= j r 1d / cos , dI 2 = j Rd 2= j r 2d / cos P <br />
<br />
dB1 = 0dI 1<br />
= 0j Rd 1<br />
=<br />
2 r 1 2 r 1<br />
dB2 = 0dI 2<br />
= 0j Rd 2<br />
=<br />
2 r 2 2 r 2<br />
0j r 1d<br />
2 r 1cos =<br />
0j r 2d<br />
2 r 2cos =<br />
0j d<br />
2 cos<br />
0j d<br />
2 cos<br />
dB 1= dB2, , , dB1+ dB2=<br />
0P <br />
Bint = ( I )<br />
( dB1 + dB2) = 0<br />
299
300
86( b ) , P , r<br />
d, dB 1= dB2= 0j d / ( 2 cos ) , dB1 dB2<br />
OP P<br />
OP dB1 dB2 <br />
OP P B <br />
dB =<br />
2dB1cos = 0j cos d / ( cos )<br />
86( b) rsin = Rsin , rcos d = Rcos d<br />
, <br />
dB =<br />
P <br />
/ 2<br />
B = dB =<br />
- / 2<br />
0j R d<br />
r<br />
0j R<br />
d = 0j R =<br />
r r<br />
<br />
0I R<br />
2 Rr =<br />
0I<br />
2 r<br />
( 2) 87 , z j dy P<br />
dB= 0j dy / ( 2 r ) x <br />
, P x <br />
P <br />
B = By =dB y = + 0j dy<br />
- 2 r<br />
cos= + 0j x<br />
dy<br />
- 2<br />
r 2<br />
87 , y = xt an , dy = x d / cos 2 , r 2 = x 2 / cos 2 , <br />
<br />
y <br />
+ / 2<br />
B =<br />
- / 2<br />
0j<br />
2<br />
d=<br />
0j<br />
2<br />
8. 984 I ( 85) <br />
- + <br />
[ ( 818) ] ?<br />
301
8788( 2) <br />
+ <br />
B <br />
- <br />
B ¡¤dx i = <br />
+ <br />
= -<br />
- <br />
0I R 2 dx<br />
= 0I<br />
2( x 2 + R 2 ) 3 / 2<br />
0I<br />
2 0 <br />
sin d = 0I<br />
2R + - dx<br />
[ ( x / R) 2 + 1] 3/ 2<br />
, <br />
, dB= 0I dl/ ( 4 r 2 ) , <br />
, , r 2<br />
+ <br />
, <br />
- <br />
+ <br />
B ¡¤dr <br />
- <br />
<br />
d©¦ r©¦ / r 2 0, <br />
r =<br />
B <br />
8. 10 ( 88) <br />
B= 0I <br />
302<br />
88810
, 0, <br />
( b) , <br />
<br />
B ¡¤dr = B ¡¤a = 0aI<br />
B = 0I<br />
<br />
8. 11 <br />
( 89) ,<br />
89811 <br />
( 1) <br />
;<br />
( 2) abc <br />
;<br />
( 3) , d ef<br />
;<br />
303
( 4) r 0 <br />
r =<br />
2 r 0<br />
( 1) <br />
, <br />
, <br />
, <br />
<br />
, , <br />
/ 2<br />
( 2) , ( 3) , , <br />
, ( <br />
) ( ) , , <br />
<br />
( 4) r 2<br />
r 2 0 , r 0 <br />
, <br />
B= B0/ 2, r =<br />
r 2 0B 0<br />
2 r 0<br />
= r 2 B<br />
8. 12 , <br />
<br />
2. 0m, 1. 0m , 10km <br />
7. 310 4 A , <br />
? ( )<br />
B =<br />
N = l/ ( 2 r ) <br />
B ¡¤2 R = 0N I =<br />
0lI<br />
2 r<br />
0lI<br />
4<br />
2 rR = 4<br />
7 10- 1010 3 7. 310 4<br />
= 11. 6 T<br />
4<br />
2 1. 02. 0<br />
8. 13810 , <br />
304
( R 1 R2, h, <br />
) , N , I , <br />
?<br />
810813 <br />
<br />
, , , B= 0<br />
, r( R1< r < R 2) , <br />
B ¡¤dr = 2 rB = 0N I<br />
, ,<br />
B = 0N I / ( 2 r )<br />
, <br />
dr , h <br />
<br />
= d=<br />
d= Bhdr = 0N I h dr<br />
2 r<br />
0N<br />
2 I h<br />
R 2<br />
1<br />
R 1<br />
r dr =<br />
0N I h<br />
2 ln R 2<br />
R 1<br />
8. 14 , <br />
j , <br />
, 0j / 2, <br />
811 B, , <br />
305
, B= B1+ B 2= 0j , <br />
, B= B 1- B2= 0<br />
811814 <br />
8. 15 I , <br />
, Rl <br />
?<br />
<br />
, r R, B= 0I r<br />
2 R 2<br />
, r R, B= 0I<br />
2 r<br />
<br />
, <br />
=B ¡¤dS = R 0<br />
0I r<br />
¡¤ldr = 0I<br />
2 R 2 4<br />
l<br />
8. 16, R<br />
, r , <br />
8. 12 <br />
306
, J , <br />
d <br />
812816 <br />
J <br />
J J ( J = - J )<br />
812 , J <br />
P <br />
B1 = 0<br />
2 Jr 1<br />
J P <br />
B2 =<br />
P <br />
0<br />
2 J r 2 = - 0<br />
2 Jr 2<br />
B = B1 + B2 = 0<br />
<br />
J( r 1 - r 2) = 0<br />
2 2 Jd<br />
, , 0J d / 2, <br />
<br />
8. 17( H elmholtz) <br />
307
( 813) <br />
R, R, <br />
<br />
813817 <br />
( 1) z ;<br />
( 2) z= 0 dB<br />
2<br />
dz d B<br />
<br />
dz 2<br />
( 1) <br />
<br />
B =<br />
<br />
2<br />
0I R2<br />
( 2) dB = -<br />
dz z = 0<br />
d 2 B<br />
dz 2 z = 0<br />
1<br />
[ ( z + R/ 2) 2 + R 2 ] 3 / 2 +<br />
+<br />
= -<br />
0I R 2<br />
3( z + R/ 2)<br />
2 [ ( z + R/ 2) 2 + R 2 ] 5 / 2<br />
3( z - R/ 2)<br />
= 0<br />
[ ( z - R/ 2) 2 + R 2 ] 5/ 2 z = 0<br />
+<br />
3 0I R 2<br />
2<br />
1<br />
[ ( z - R/ 2) 2 + R 2 ] 3/ 2<br />
4( z + R/ 2) 2 - R 2<br />
[ ( z + R/ 2) 2 + R 2 ] 7/ 2<br />
4( z - R/ 2) 2 - R 2<br />
[ ( z - R/ 2) 2 + R 2 ] 7 / 2 z = 0<br />
= 0<br />
8. 18 , R, q <br />
: , <br />
308
B= 0 q<br />
2 R <br />
r ( r < R) , dr <br />
<br />
dB =<br />
0dI<br />
2r<br />
= 0<br />
2r ¡¤2 rdr <br />
2 =<br />
<br />
B = dB = <br />
R<br />
0<br />
0<br />
2 dr<br />
0<br />
dr = 0 R = 0 q<br />
2 2 2 R<br />
8. 19814 , <br />
, <br />
l, b, <br />
a , I <br />
I 1<br />
, <br />
? <br />
?<br />
<br />
814 , <br />
F l = BlI 1l = 0I I 1<br />
2 a l<br />
; <br />
F r = BrI 1l =<br />
0I I 1l<br />
2 ( a + b)<br />
814819 <br />
<br />
<br />
F = F l - F r =<br />
, <br />
0I I 1lb<br />
2 a ( a + b)<br />
, <br />
309
8. 20, , <br />
j A / m<br />
815 , dl dL d <br />
Rd<br />
dF =<br />
0j Rd<br />
j dldL =<br />
2 a<br />
, <br />
0j Rd<br />
4 Rsin( / 2) j dldL<br />
815820 <br />
<br />
dF 1 =<br />
dF<br />
dldL =<br />
0j 2 d<br />
4 sin( / 2)<br />
, <br />
<br />
<br />
F 1 = F R 1 = dF R 1 = dF 1sin <br />
2 2<br />
= 0<br />
<br />
0j 2 d<br />
4 =<br />
0j 2<br />
2<br />
8. 21<br />
, <br />
B1<br />
B2( 816) , <br />
<br />
310
B l= Br= 0j<br />
2 , <br />
B0 <br />
816 B B 2 ><br />
B 1, Bl, Br<br />
B0 , j <br />
,<br />
B 0 - B l= B 1, B0 + Br = B 2 B 0<br />
= ( B1+ B 2) / 2, Bl = Br = ( B 2- B 1) / 2, <br />
j = 2B l/ 0= ( B 2- B1) / 0<br />
<br />
F = j B 0 = ( B 2 2 - B 2 1) / ( 2 0)<br />
B1<br />
<br />
816821 <br />
8. 22 5. 0cm , 30A <br />
? <br />
, , 30A <br />
? 1. 0<br />
10 -<br />
3 m/ s<br />
<br />
F m = 0I 1I 2<br />
2 d = 410<br />
- 7 3030<br />
= 3. 610 - 3 N / m<br />
2510 - 2<br />
, <br />
F e =<br />
1 2<br />
2 0d =<br />
0c2 I 1I 2<br />
2 d v 1v 2<br />
= 3. 210 20 N / m<br />
= c2<br />
v 2 F m =<br />
( 310 8 ) 2<br />
( 110 - 3 ) 2 3. 610 - 3<br />
, <br />
<br />
8. 23817 , R ,<br />
( z ) <br />
311
, I <br />
( 1) ;<br />
( 2) <br />
( <br />
I ) , <br />
, ?<br />
( 1) 817 , <br />
j RdI <br />
, <br />
dF = dB ¡¤I =<br />
0j Rd I<br />
2 R<br />
x <br />
817823 <br />
, y <br />
<br />
F = dF x<br />
x <br />
<br />
= dF sin = 0j I sin d = 0j I<br />
20<br />
=<br />
0I 2<br />
<br />
2 R<br />
( 2) x , d<br />
, <br />
<br />
0I 2<br />
<br />
2 R = 0I 2<br />
2 d<br />
d =<br />
R/ 2<br />
8. 24 ( <br />
10k m/ s) 8. 18 ,<br />
I <br />
, r ( ) , a <br />
, <br />
312
F =<br />
0I 2<br />
2 ln a + r<br />
r<br />
L = 5. 0m , a = 1. 2cm, r = 6. 7cm, m =<br />
317g, 4. 2k m/ s<br />
818824 <br />
( 1) ?<br />
( )<br />
?<br />
( 2) ?<br />
( 3) 40% , <br />
( B1<br />
F =<br />
2 a + r<br />
r<br />
I B1dr =<br />
2 a + r<br />
( 1) <br />
r<br />
0I 2<br />
4 r dr =<br />
)<br />
0I<br />
2<br />
2 ln a + r<br />
r<br />
a = v 2 / ( 2L) = ( 4. 210 3 ) 2 / ( 25. 0) <br />
= 1. 7610 6 m/ s 2<br />
<br />
( 2) F = m a , <br />
<br />
a / g = 1. 7610 6 / 9. 8 = 1. 810 5<br />
I =<br />
0I 2<br />
2 ln a +<br />
r<br />
r<br />
= ma<br />
2 ma<br />
0ln [ ( a + r ) / r ]<br />
1 / 2<br />
313
=<br />
231710 - 3 1. 7610 6<br />
410 - 7 ln[ ( 1. 2 + 6. 7) / 6. 7]<br />
= 4. 110 6 A<br />
( 3) <br />
P = 1 2 mv2 / ( 0. 4t) = 1 2 mv2 / ( 0. 42L/ v) = mv3<br />
1. 6L<br />
= 31710- 3 4. 2 3 10 9<br />
1. 65. 0<br />
= 2. 910 9 W = 2. 9 Mk W<br />
8. 25B I , <br />
T( 819) , <br />
<br />
819825 <br />
( 1) : r = T / ( BI ) <br />
( 2) , P <br />
p = qT / I - q , <br />
( <br />
)<br />
( 1) 819 , dl= r d <br />
dF m= I Bdl = I Brd , T 1= T 2= T<br />
T1 T2 - d , dF T =<br />
314
T d , dF m = dF T<br />
r = T / ( BI )<br />
( 2) P , <br />
, <br />
r =<br />
p<br />
qB =<br />
qT<br />
qBI =<br />
, <br />
<br />
<br />
8. 26( 816) <br />
( v ) , <br />
:<br />
( 1) ( ( 83) ) <br />
B =<br />
0I cos 1<br />
-<br />
4 r ( 1 - <br />
2 sin 2 1) 1 / 2<br />
T BI<br />
cos 2<br />
( 1 - <br />
2 sin 2 <br />
2) 1/ 2<br />
( 2) [ ( 8. 4) ] , <br />
B =<br />
0I<br />
2 r<br />
( 816) q <br />
B1 =<br />
0q( 1 - <br />
) vr<br />
4 r<br />
( 1 - <br />
sin 2 ) 3 / 2<br />
r I dl <br />
r dB<br />
, <br />
dB = B=<br />
0( 1 - <br />
2 ) vr <br />
Sqdl<br />
4 r<br />
3 ( 1 - <br />
2 sin 2 ) 3 / 2<br />
Sqv= I v dl , <br />
dB =<br />
0I ( 1 - <br />
) dlr <br />
4 r <br />
( 1 - <br />
sin 2 ) 3/ 2<br />
<br />
315
( 1) ( 820) , P <br />
<br />
B =<br />
0I ( 1 - <br />
2 ) r dlsin <br />
4r <br />
3 ( 1 - <br />
2 sin 2 ) 3/ 2<br />
l= - r cot , dl= rd / sin 2 , r = r / sin , <br />
B = 0I 2 ( 1 - <br />
2 ) sin d<br />
= -<br />
4<br />
1<br />
( 1 - <br />
2 sin 2 ) 3/ 2<br />
r <br />
= 0I cos 1<br />
-<br />
4 r ( 1 - <br />
2 sin 2 1) 1/ 2<br />
0I cos<br />
4 r ( 1 - <br />
sin 2 <br />
cos 2<br />
( 1 - <br />
2 sin 2 <br />
2) 1 / 2<br />
2<br />
) 1/ 2 <br />
1<br />
820826( 1) <br />
( 2) , 1= 0, 2= <br />
B =<br />
0I / ( 2 r )<br />
8. 27811 , <br />
<br />
e ( 827) B<br />
( 817) ( <br />
) <br />
, <br />
316
821 , ,<br />
Rq R q <br />
:<br />
=<br />
2 ( 1 - cos )<br />
821827 <br />
( )<br />
e =<br />
t , <br />
q <br />
0 4 =<br />
d e<br />
=<br />
dt<br />
q<br />
( 1 - cos )<br />
2 0<br />
q<br />
sin d<br />
2 0 dt<br />
821 , dt , <br />
d= vsin dt/ r<br />
d<br />
<br />
dt = vsin<br />
r<br />
B <br />
B ¡¤dr =<br />
B ¡¤2 R =<br />
d e<br />
( 827) B ¡¤dr = 0 0<br />
dt<br />
<br />
2 Br sin=<br />
0q<br />
2 sin 2 v r<br />
2 Brsin <br />
317
B = 0qvsin<br />
4 r 2<br />
( 817) <br />
8. 28 5. 0cm <br />
, , dE<br />
dt = 1. 010 12 V/ ms<br />
( 1) ;<br />
( 2) B<br />
dE<br />
( 1) I d = 0 R 2<br />
dt<br />
= 8. 8510 - 1 <br />
2 0. 051. 2 010 - 12<br />
= 7. 010 - 2 A<br />
( 2) B= 0I d<br />
2 R = 410-<br />
710 7 - 2<br />
= 2. 810 - 7 T<br />
20. 05<br />
8. 29 ( C= 1<br />
10 - 1 2 F ) , 50H z, 1. 7410 5 V , <br />
<br />
<br />
e =<br />
ES = S / 0 = Q/ 0 = CU / 0<br />
d e<br />
I d = 0 = C dU<br />
dt dt<br />
I d, ma x = 2CU m a x = 250110 - 12 1. 7410 5<br />
= 5. 510 - 5 A<br />
8. 30 c/ 3( c ) , <br />
110 -<br />
1 0 m <br />
, <br />
F e = E e =<br />
e 2<br />
4 0r 2 ( 1 -<br />
, <br />
318<br />
<br />
2 ) 1/ 2
F m = ev 1B2 = ev 1<br />
=<br />
e 2 v 2<br />
4 0c 2 r 2 ( 1 -<br />
E 2v2<br />
c 2 =<br />
<br />
2 ) 1 / 2<br />
e 2 v 1v2<br />
4 0c 2 r 2 ( 1 -<br />
F e> F m , , <br />
F = F e - F m =<br />
e 2<br />
4 0r 2 ( 1 -<br />
1 -<br />
<br />
2 ) 1 / 2<br />
= ( 1. 610- 19 ) 2 910 9<br />
2 1/ 2 1 -<br />
( 110 - 10 ) 2 1<br />
1 -<br />
3<br />
= 2. 210 - 8 N<br />
<br />
2 ) 1/ 2<br />
8. 31a , 1 <br />
2, v 1 2 <br />
v2<br />
<br />
? ( <br />
<br />
<br />
, <br />
, )<br />
822 , 1( p 1) <br />
2( p 2) <br />
F 1e = eE 2 =<br />
e 2<br />
4 0a 2 ( 1 -<br />
<br />
2 2) 1/ 2<br />
2<br />
1 2 <br />
v 2<br />
c 2<br />
1<br />
3<br />
2<br />
822831 <br />
F 1m = eB 2v1 =<br />
e 2 v1v 2<br />
4 0a 2 c 2 ( 1 -<br />
<br />
2 2) 1/ 2<br />
, v 2 <br />
1 2 <br />
319
F 1 = F 1e + F 1m<br />
=<br />
e 2<br />
4 0a 2 ( 1 -<br />
, <br />
= arct an F 1m<br />
F 1e<br />
2 1 <br />
1 + v 2 1v 2 2<br />
<br />
2 2) 1/ 2 c 4<br />
= arct an v 1v 2<br />
c 2<br />
F 2e = eE 1 = e2 ( 1 - <br />
2 1)<br />
4 0a 2<br />
1 2 , 2 2 <br />
F 2 F 2e, 1F 1 F 2 <br />
<br />
320
9 <br />
<br />
9. 1 , N , <br />
mB <br />
: , Wm = - mB <br />
: -<br />
mB + mB ( <br />
) W <br />
e -<br />
:<br />
W / ( kT ) B <br />
/ ( kT )<br />
M = N m emB - e<br />
e mB / ( kT ) + e<br />
( 1) mBkT ,<br />
M = N m 2 B/ ( kT )<br />
MB/ T <br />
( 2) mBkT ,<br />
<br />
M = N m<br />
- mB / ( kT )<br />
- mB / ( kT )<br />
, <br />
W- = - mB, N - = N e - mB / ( kT ) /<br />
( e mB / ( kT ) + e - m B/ ( kT ) ) ; W+<br />
= mB, N + = N e m B / ( kT ) / ( e mB / ( kT ) + e - mB / ( kT ) ) <br />
, <br />
M = N + m + N - ( - m) = N m em B/ ( kT ) - e<br />
e m B/ ( kT ) + e<br />
( 1) mBkT ,<br />
- mB / ( kT )<br />
- mB / ( kT )<br />
321
M =<br />
N m<br />
1 + mB<br />
kT - 1 - mB<br />
kT<br />
1 + mB<br />
kT + 1 - mB<br />
kT<br />
( 2) mBkT ,<br />
= N m2 B<br />
kT<br />
M = N m emB / ( kT ) ( 1 - e - 2m B/ ( kT ) )<br />
e mB / ( kT ) ( 1 + e - 2m B/ ( kT ) ) = N m<br />
9. 291 , L B <br />
<br />
( 1) <br />
BeL sin ;<br />
2m e<br />
( 2) Be ,<br />
2me<br />
1T <br />
9192 <br />
<br />
( 1) 91 , <br />
m =<br />
e<br />
r 2 =<br />
ev<br />
2 r r 2 = evr<br />
2 = eL<br />
2me<br />
, L <br />
<br />
M =<br />
©¦mB©¦= mBsin= BeLsin / ( 2m e)<br />
L B <br />
dL<br />
( 2) M= = Lsin , M , <br />
dt<br />
<br />
B= 1T ,<br />
322<br />
=<br />
= Be/ ( 2me )<br />
11. 610-<br />
19<br />
29. 110 - 31 = 8. 810 10 rad/ s
9. 3, , r =<br />
0. 5310 - 1 0 m, v= 2. 210 6 m / s<br />
( 1) B ?<br />
( 2) S = h/ 2= 0. 5310 - 3 4<br />
Js, m= 1. 4110 -<br />
26 Am 2 , <br />
, ?<br />
( 1) B = 0ev = 410-<br />
1. 7 610 - 19 2. 210 6<br />
4 r 2 4( 0. 5310 - 10 ) 2<br />
= 12. 5 T<br />
( 2) M = mBsin , M =<br />
S sin , <br />
=<br />
mB<br />
S = 1. 4110 - 2 6 12. 5<br />
0. 5310 - 34 = 3. 310 9 rad / s<br />
9. 4 , <br />
1. 0cm, 12cm, <br />
7. 8g/ cm 3 , <br />
( ) 55. 85g/ mol<br />
( 1) ?<br />
( 2) ?<br />
( 3) ?<br />
( 4) ?<br />
( 1) N = 120. 5<br />
2 7. 86. 02310 23 2/ 55. 85<br />
= 1. 610 2 4 ( )<br />
( 2) m= N m B= 1. 610 24 9. 2710 - 24 = 15 A m 2<br />
( 3) I = m/ S = 15/ ( ( 0. 005) 2 ) = 1. 910 5 A<br />
( 4) B= 0I / l= 410 -<br />
7 1. 910 5 / 0. 12= 2. 0 T<br />
9. 5 , <br />
8. 5cm, 1. 0cm, 0. 02cm , <br />
dS<br />
dt<br />
=<br />
323
7. 8g/ cm 3 , <br />
( ) 55. 85g/ mol<br />
( 1) ?<br />
( 2) , ? <br />
0. 5210 -<br />
?<br />
4 T <br />
( 3) , <br />
8. 51. 00. 027. 8<br />
( 1) m = N m B= 6. 02310 2 3<br />
55. 85<br />
29. 2710 - 2 4 = 0. 27 Am 2<br />
( 2) M = ©¦mBE©¦= mBE = 0. 270. 5210 - 4<br />
= 1. 410 - 5 N m<br />
( 3) Wm = - mBE = mBE = 0. 270. 5210 - 4 = 1. 410 - 5 J<br />
9. 6 l = 10cm, N = 20, <br />
I = 0. 1A <br />
( 1) B0 H 0;<br />
( 2) r = 4200 , <br />
B H ?<br />
( 3) B0 <br />
B ?<br />
( 1) B 0 = 0I = 0N I / l= 410 - 200. 7 1/ 0. 1<br />
= 2. 510 - 5 T<br />
H 0= I = N I / l= 200. 1/ 0. 1= 20 A / m<br />
( 2) B= rB0= 42002. 510 -<br />
H = H 0= 20 A / m<br />
5 = 0. 11 T<br />
( 3) B 0= 2. 510 - 5 T , B = B- B0= 0. 11 T<br />
9. 7, 30cm, 1cm 2 ,<br />
300 0. 032A , <br />
324
210 - 6 W b:<br />
( 1) ( ) ;<br />
( 2) ;<br />
( 3) ( ) ;<br />
( 4) ;<br />
( 5) <br />
( 1) B= / S = 210 - 6 / ( 110 - 4 ) = 210 - 2 T<br />
( 2) H = I = N I / l= 3000. 032/ 0. 3= 32 A / m<br />
( 3) J = M= B - H = 210- 2<br />
- 32= 1. 610 4 A / m<br />
0 410 - 7<br />
( 4) = B/ H = 210 - 2 / 32= 6. 310 - 4 H / m<br />
r= / 0= 6. 310 - 4 / ( 410 - 7 ) = 5. 010 2<br />
( 5) M= J = 1. 610 4 A / m<br />
9. 8, <br />
1000 , 15. 0cm, 2. 0A ,<br />
B= 1. 0T , :<br />
( 1) H ;<br />
( 2) r ;<br />
( 3) <br />
( 1) H = I = N I / ( 2 r) = 10002. 0/ ( 20. 15)<br />
= 2. 110 3 A / m<br />
( 2) = B/ H = 1/ ( 2. 110 3 ) = 4. 710 - 4 H / m<br />
r= / 0= 4. 710 - 4 / ( 410 - 7 ) = 3. 810 2<br />
( 3) J = M= ( r - 1) H = ( 3. 810 2 - 1)2. 110 3<br />
= 8. 010 5 A / m<br />
9. 99. 2 <br />
6. 0A , 1. 2T <br />
, , <br />
325
?<br />
9299 <br />
92 B = 1. 2T , H = 2. 2<br />
10 2 A / m H = I 1, = H / I 1 , <br />
B, <br />
I =<br />
B<br />
0 = BI 1<br />
0H = 1. 26. 0<br />
= 2. 610 4 A<br />
410 - 7 2. 210 2<br />
9. 10800 <br />
, 1. 0T , ? ( <br />
9. 2 BH )<br />
BH B = 1. 0T , H = 1. 7<br />
10 2 A / m <br />
I = H / = 1. 710 2 / 800 =<br />
0. 21 A<br />
9. 11 ( ) <br />
93( a ) , <br />
9. 3( b) <br />
, 0. 8mm , 0. 5mm , <br />
0. 3mm<br />
326
, 9. 3( b ) , , <br />
? H c =<br />
2A / m<br />
93911 <br />
, , <br />
, H c=<br />
m a x<br />
= 2 r in tH c =<br />
4<br />
2<br />
510- 2 =<br />
2<br />
m ax<br />
r in t<br />
, <br />
2<br />
3. 1 mA<br />
9. 12 61cm, 1cm, <br />
1000 1. 5A , <br />
B 0. 18T r ( <br />
)<br />
<br />
r =<br />
=<br />
l<br />
0N I / B -<br />
<br />
0. 61<br />
= 1.<br />
410 - 7 10 3 3103<br />
1. 5/ 0. 18 - 0. 01<br />
9. 13 94 <br />
l 1= 500mm, l 2= 20mm, <br />
r= 5000 B= 3T ,<br />
N I <br />
327
94913 <br />
N I = B l 1<br />
+ l 2<br />
0 r 1 = 3 0. 5<br />
+ 0. 02<br />
410 - 7 510 3<br />
= 4. 910 4 ( )<br />
9. 14 , 14. 4cm,<br />
2. 0mm , 0. 60cm 2 , <br />
r= 16004. 810 - 6 W b, <br />
N I 220V , <br />
20W , N <br />
N I =<br />
l 1<br />
+ l 2<br />
0S r 1<br />
=<br />
4. 810 - 10 6 - 2<br />
14. 4- 0. 2<br />
+ 0. 2<br />
410 0. 7 610 - 4 1600<br />
= 1. 3310 2 ( )<br />
N = ( N I ) / I = 1. 3310 2 220/ 20 = 1. 4610 3 ( )<br />
328
10 <br />
10. 1I = 5A ab, <br />
l= 20cm, d = 10cm ( 101) <br />
v= 10m/ s , <br />
? a , b ?<br />
101101 <br />
101 <br />
Ea b = d E = ( vB) ¡¤dr = - vBdr = -<br />
= -<br />
0I v<br />
2 ln d +<br />
d<br />
l<br />
= -<br />
= - 1. 110 - 5 V<br />
E a b< 0, a <br />
410 -<br />
v<br />
d + l<br />
7<br />
510<br />
ln<br />
2<br />
d<br />
0I<br />
2 r dr<br />
10 + 20<br />
10<br />
10. 2 12cm 410 3 , 0. 5G<br />
30 , <br />
329
? , ?<br />
E m a x= N BS<br />
= 410 0. 3 510 - <br />
4 0. 122<br />
2 30<br />
= 1. 7 V<br />
, <br />
<br />
<br />
10. 310. 2 , <br />
I = 5. 0A , <br />
110 3 , a = 10cm, L =<br />
20cm, v = 2m/ s ,<br />
d = 10cm <br />
<br />
102 , <br />
102103 <br />
, <br />
, <br />
E = E 1 - E<br />
<br />
2 = N ( B 1 - B 2) Lv = N Lv 0I 1<br />
2d - 1<br />
d +<br />
= 110 3 0. 22 410-<br />
7 5. 0<br />
2<br />
= 210 - 3 V<br />
a<br />
1<br />
0. 1 - 1<br />
0. 1 + 0. 1<br />
10. 4 , =<br />
5sin 100 t A , ?<br />
<br />
= N = N B ¡¤dS =<br />
E = -<br />
d<br />
= -<br />
dt<br />
N <br />
d + a<br />
0N L<br />
2 ln d +<br />
d<br />
d<br />
0<br />
2 r ¡¤Ldr =<br />
a<br />
d<br />
dt<br />
0N L<br />
2 ln d +<br />
d<br />
a<br />
330
= -<br />
410 - 7 110 3 0. 2<br />
2<br />
= - 4. 410 - 2 cos 100 t<br />
ln<br />
0. 1 + 0. 1<br />
0. 1<br />
d( 5sin 100 t)<br />
dt<br />
10. 5R , B <br />
L <br />
, 103 <br />
, dB , <br />
dt<br />
, <br />
103 , Oba <br />
S , S <br />
= BS , 103105 <br />
O <br />
<br />
-<br />
d<br />
= - S dB<br />
dt dt<br />
= E idr = <br />
b<br />
= 0 + E ba + 0 = E ba<br />
Eba = -<br />
dB<br />
S<br />
dt<br />
dB<br />
= -<br />
O E idr + a b E idr + O a E idr<br />
1<br />
2 L R 2 - L 2 / 4 dB<br />
dt<br />
> 0,<br />
dt<br />
E<br />
ba < 0, b <br />
: dl <br />
E i = 1 2<br />
dB<br />
dt<br />
, 103 <br />
Ea b b = E i ¡¤dl =<br />
a b E idlcos =<br />
a<br />
b a<br />
r cos dB<br />
2 dt dl<br />
= h dB<br />
2 dt b dl = hL dB<br />
= 1<br />
a 2 dt 2 L R2 - L 2 / 4 dB<br />
dt<br />
E<br />
a b> 0, b <br />
10. 650 FBC1 <br />
<br />
331
12. 705m 0. 4210 - 4 T , <br />
M 1. 70( M , ) <br />
, ?<br />
U = E= Blv= 0. 4210 -<br />
= 0. 30 V<br />
4 12. 7051. 70330<br />
, <br />
10. 7 , <br />
<br />
0. 7010 - 4 T , 200m , <br />
7. 010 -<br />
<br />
3 V , <br />
v = E/ ( Bl ) = U/ ( Bl ) = 7. 010 - 3 / ( 0. 7010 - 4 200)<br />
= 0. 50 m/ s<br />
10. 8, <br />
2. 010 -<br />
2 T <br />
10. 0cm20. 0cm, 120 , <br />
12. 0V , <br />
?<br />
, Ema x= N BS = 2 N BS<br />
=<br />
E m ax<br />
2 N BS = 12. 0<br />
21202. 010 - 2 0. 10. 2<br />
= 40 s - 1<br />
10. 9 : , <br />
N , S , <br />
R, <br />
, , <br />
qN , S , q, R <br />
<br />
332
q = dt = 1 REdt = -<br />
= <br />
R =<br />
N BS<br />
R<br />
B = qR/ ( N S )<br />
1<br />
R d<br />
dt dt = - 1<br />
R 0 d<br />
10. 10, , b<br />
, r a 2<br />
<br />
B( 104) <br />
<br />
1041010 <br />
, <br />
E = Blv = Ba r<br />
,, <br />
a / ( a b) = / b<br />
I = Eb/ = Bab r/ <br />
F = BI l= B 2 a 2 b r / <br />
M = F r =<br />
( Bar ) 2 b / <br />
10. 11, <br />
, B B <br />
333
B , <br />
R , <br />
eE = mea t = me<br />
evB = m ean = me<br />
2 eB= m ev/ R( B ) , dv<br />
dt =<br />
1 <br />
dv<br />
dt<br />
v 2<br />
R<br />
eR<br />
m e<br />
, <br />
dB<br />
= E dt R<br />
1 d<br />
E = = R2 dB <br />
2 R dt 2 R dt = R dB <br />
( B <br />
2 dt<br />
) , <br />
dB<br />
= 1 dB <br />
dt 2 dt<br />
<br />
B = B / 2<br />
10. 12 1011( a) <br />
, r :<br />
v <br />
F ( ) , B , v+ v <br />
( ) <br />
<br />
<br />
v v+ v , <br />
F n =<br />
me ( v + v) 2<br />
r<br />
-<br />
m ev 2<br />
B <br />
334<br />
r<br />
v =<br />
2m ev<br />
v ( )<br />
r<br />
er<br />
B<br />
2me
B =<br />
<br />
2m e v<br />
er<br />
F m = e( v + v) B 2mev v ( )<br />
r<br />
F m = F n<br />
B , B <br />
v , <br />
, <br />
<br />
10. 13 l R <br />
N 1, N 2<br />
<br />
N 1 I 1<br />
2 1 = N 2 1 = N 2 0N 1I 1S / l =<br />
M =<br />
21<br />
= 0N 1N 2 R2<br />
I 1 l<br />
, N 2 <br />
0N 1N 2 R 2 I 1/ l<br />
10. 14a 50 , 4. 0cm 2 ,<br />
100 , 20. 0cm b <br />
, :<br />
( 1) ;<br />
( 2) a 50A / s , b <br />
;<br />
( 3) b <br />
( 1) b I b , a b <br />
, a <br />
a b =<br />
<br />
N b<br />
0I b<br />
N aS a<br />
2R b<br />
335
M = a b<br />
I b<br />
= 0N a N bS a<br />
2Rb<br />
= 4<br />
7 10- 501004. 010 - 4<br />
20. 2<br />
= 6. 310 - 6 H<br />
( 2) d ba<br />
= 1 d ba<br />
= 1 M da<br />
dt N b dt N b dt = 1<br />
100 6. 310- ( 6 - 50)<br />
= - 3. 110 - 6 Wb / s<br />
( 3) E ba = - M da<br />
dt = - 6. 310 - 6 ( - 50)<br />
= 3. 110 - 4 V<br />
a <br />
I a I a a , a b <br />
1, b 2 = 1+ 2,<br />
b - 1= 2= ba <br />
R b> R a , 2 I a <br />
b a r B= 0m/<br />
( 4 r 3 ) = 0I aS a N a / ( 4 r 3 ) <br />
ba = <br />
2 = B ¡¤dS = <br />
<br />
<br />
M =<br />
<br />
R b<br />
0I a S a N a<br />
4 r 3<br />
ba<br />
= N b 0I aS a N a<br />
I a 2R bI a<br />
¡¤2 rdr =<br />
= 0N aN bS a<br />
2Rb<br />
0I a S a N a<br />
2R b<br />
10. 15 2. 0cm , 30. 0cm, <br />
1200 , <br />
( 1) ?<br />
( 2) 3. 010 2 A / s , <br />
?<br />
336
( 1) L = 0N 2 S/ l = 0N 2 R 2 / l<br />
= 410 -<br />
= 7. 610 - 3 H<br />
( 7 1. 210 3 ) <br />
2 0. 02 2 / 0. 3<br />
( 2) ©¦E©¦= L d = 7. 610- 3. 3 010 2 = 2. 3 V<br />
dt<br />
10. 16 10. 0A ,<br />
20Wb; 4. 0A/ s <br />
, 3. 2mV <br />
<br />
<br />
<br />
L =<br />
E d<br />
dt = 3. 210- 3 / 4. 0 = 0. 810 - 3 H<br />
L = N / I ,<br />
N = LI / = 0. 810 - 3 10. 0/ ( 2010 - 6 ) = 400 ( )<br />
10. 17105 , N <br />
1051017 <br />
( 1) ;<br />
( 2) <br />
M 12M2 1, ?<br />
( 1) I =<br />
0N I h<br />
2 ln R 2<br />
R 1<br />
<br />
337
L =<br />
= N = 0N 2 h<br />
I I 2 ln R 2<br />
R 1<br />
( 2) , 1<br />
I 1<br />
<br />
, <br />
M2 1 = 21<br />
I = 1<br />
= 0N I 1h<br />
1 I 1<br />
I 2<br />
<br />
R 2<br />
12 = B2hdr =<br />
R 1<br />
M 12<br />
<br />
2 ln R 2<br />
R 1<br />
/ I 1 = 0N h<br />
2 ln R 2<br />
R 1<br />
, B 2 = 0I 2/ ( 2 r ) <br />
R 2<br />
0I 2h<br />
2<br />
R 1<br />
dr<br />
r<br />
= 12<br />
I = N 12<br />
= 0N h<br />
2 I 2 2 ln R 2<br />
R 1<br />
M 12 = M2 1<br />
= 0I 2h<br />
2<br />
ln<br />
R2<br />
10. 18 a , D , <br />
, <br />
<br />
L 1 = 0 <br />
ln D -<br />
a<br />
, <br />
I , <br />
<br />
= 2 D - a<br />
a<br />
B1dr ¡¤1 = 2 D -<br />
<br />
a<br />
a<br />
a<br />
0I<br />
2 r dr =<br />
L 1 = = 0<br />
I <br />
ln D -<br />
a<br />
a<br />
R1<br />
0I<br />
ln D -<br />
a<br />
10. 19, , <br />
338<br />
a
L 1 L 2, L <br />
, :<br />
( 1) ,<br />
( 2) ,<br />
L = L 1 + L 2<br />
1<br />
L = 1 L 1<br />
+ 1 L 2<br />
( 1) , E= E 1 + E 2, = 1 = 2 E=<br />
- L d<br />
dt , E 1 = - L 1<br />
d<br />
dt E 2 = - L 2<br />
L = L 1 + L 2<br />
d<br />
dt <br />
( 2) , = 1+ 2, E= E 1= E 2d dt = - E, d 1<br />
L dt<br />
= -<br />
E 1<br />
L 1<br />
d2<br />
dt = - E 2<br />
L 2<br />
d<br />
dt = d1<br />
dt + d2<br />
dt<br />
1<br />
L = 1 + 1 L 1 L 2<br />
<br />
, , <br />
, <br />
, <br />
10. 20L 1 L 2, M<br />
( 106) <br />
( 1) , 2, 3 <br />
, 1, 4 , <br />
L= L 1+ L 2+ 2M;<br />
( 2) , 2, 4 <br />
, 1, 3 , <br />
L=<br />
1061020 <br />
L 1+ L 2- 2M<br />
( 1) , <br />
339
, <br />
<br />
<br />
=<br />
1 + 12 + 2 + 2 1<br />
= LI , 1= L 1I 1, 12 = MI 2, 2= L 2I 2, 21 = MI 1, I<br />
= I 1= I 2<br />
L = L 1 + L 2 + 2M<br />
( 2) , <br />
, <br />
21 12 , <br />
, <br />
L = L 1 + L 2 - 2M<br />
10. 21 10 8 T , <br />
? ( , kg/ m 3<br />
)<br />
w m=<br />
B 2<br />
=<br />
2 0c 2<br />
44 <br />
( 10 8 ) 2<br />
= 4. 410 4 kg/ m 3<br />
2410 - ( 7 310 8 ) 2<br />
10. 22 2. 0T , <br />
110 6 V / m ? <br />
?<br />
w m= B 2 / ( 2 0) = ( 2. 0) 2 / ( 2410 - 7 ) = 1. 610 6 J/ m 3<br />
w e= 0E 2 / 2= 8. 8510 - 12 ( 10 6 ) 2 / 2= 4. 4 J/ m 3<br />
, <br />
10. 23<br />
1kW h , 1. 0T , ?<br />
500A , <br />
?<br />
<br />
340
Vm = W / w m = 3. 610 6 2410 - 7 = 9. 0 m 3<br />
<br />
L = 2W / I 2 = 23. 610 6 / 500 2 = 29 H<br />
10. 24 5. 5mm, 20A <br />
?<br />
1. 6910 -<br />
8 m<br />
w m = B 2<br />
= 1<br />
2<br />
0I<br />
=<br />
2 0 2 0 2 R<br />
= 0. 21 J/ m 3<br />
410 - 20 7 2<br />
24 ( 2 5. 510 - 3 ) 2<br />
, <br />
E = J = I / ( R 2 ) , <br />
E = w e =<br />
0<br />
2 E 2 = 0( I )<br />
2<br />
2( R 2 ) 2<br />
= 8. 8510 - 1 2 ( 1. 6910 - 8 20) 2<br />
2[ ( 5. 510 - 3 ) 2 ] 2<br />
= 5. 610 - 17 J/ m 3<br />
10. 25, <br />
R 1<br />
R2, , <br />
r 1, I ( , <br />
) , , <br />
<br />
W m1 = B 2<br />
0 R 1<br />
0<br />
= 1<br />
2<br />
dV<br />
2 0<br />
0I r<br />
2 R 2 1<br />
2<br />
R 2<br />
¡¤2 r dr ¡¤1 +<br />
R 1<br />
2<br />
0I<br />
2 r<br />
= 0I 2<br />
1 R2<br />
+ ln<br />
44 R1<br />
W m1= L 1I 2 / 2, <br />
L =<br />
0 1<br />
24 + ln R 2<br />
R 1<br />
¡¤2 r dr ¡¤1<br />
341
10. 26 a , <br />
D 1a ( 107) I <br />
;<br />
( 1) <br />
( 2) , <br />
D 2<br />
<br />
A m ;<br />
( 3) <br />
Wm ;<br />
( 4) <br />
E <br />
A E ;<br />
( 5) A m, Wm A E <br />
( 1) <br />
L = =<br />
I<br />
2 D 1 -<br />
= 0 <br />
ln D 1 - a<br />
a<br />
( 2) <br />
a<br />
a<br />
0I<br />
¡¤dr ¡¤1<br />
2 r<br />
I<br />
0<br />
<br />
ln D 1<br />
a<br />
A m = F m ¡¤dr = <br />
D 2<br />
( 3) <br />
W m = 1 2 L 2I 2 -<br />
= I 2<br />
2<br />
D 1<br />
0I 2<br />
dr ¡¤1 =<br />
<br />
2 r<br />
1<br />
2 L 1I 2<br />
0<br />
<br />
ln D 2<br />
a - 0<br />
<br />
ln D 1<br />
a<br />
1071026 <br />
0I<br />
2<br />
2 ln D 2<br />
D 1<br />
= 0I 2<br />
2 ln D 2<br />
D 1<br />
( 4) , <br />
E <br />
342
A E = EI dt = -<br />
= -<br />
0I 2<br />
ln D 2<br />
D 1<br />
( 5) <br />
d<br />
dt I dt = - I d= - I D 2<br />
- A E = Wm + A m<br />
2 0I dr ¡¤1<br />
D 1<br />
2 r<br />
E , <br />
, , <br />
- A E , D 1 D 2 , <br />
, <br />
<br />
<br />
10. 27 S , <br />
, 108 1<br />
I 1<br />
I 2<br />
F m = 012SI 1I 2<br />
2, <br />
1081027 <br />
, , <br />
108 I 1 I 2<br />
<br />
M =<br />
01I 1x 2S<br />
I 1<br />
<br />
= 012Sx<br />
Wm = 1 2 L 1I 2 1 + 1 2 L 2I 2 2 + MI 1I 2<br />
, <br />
343
I 1 I 2 , 2 x , <br />
<br />
W m = ( M) I 2I 2<br />
, E 1 =<br />
-<br />
( MI 2)<br />
= -<br />
t<br />
M<br />
t I 2, E 2= -<br />
M<br />
t I 1I 1 I 2 <br />
, <br />
x t , <br />
A e xt = - (E1I 1 t + E2I 2 t) = 2( M) I 1I 2<br />
x , 2 F m <br />
<br />
A m = F m x<br />
A e xt = Wm + A m<br />
2( M) I 1I 2 = ( M) I 1I 2 + F m x<br />
F m = I 1I 2( M/ x ) = 012SI 1I 2<br />
F m> 0, 2 x , <br />
<br />
344
11 <br />
11. 1 <br />
, : , <br />
( : ( 111) q= 0 e,<br />
d e<br />
, ( <br />
dt<br />
L) )<br />
S( 111) , B <br />
LS , L <br />
, ( 111) <br />
L<br />
B ¡¤dr = 1 c 2 d<br />
dt S<br />
E ¡¤dS<br />
, L= 0, <br />
L<br />
B ¡¤dr = 0<br />
111111 <br />
<br />
<br />
d<br />
dt E ¡¤dS = 0<br />
t<br />
( 111) E ¡¤dS = qint / 0, dqin = 0,<br />
dt<br />
q , <br />
11. 2 : 112 <br />
( <br />
) , B= 0<br />
112 , r P <br />
345
Br<br />
, B<br />
r S , <br />
S<br />
B ¡¤dS =<br />
4 r 2 B r<br />
( 111) , S B ¡¤dS = 0 B r = 0<br />
112112 <br />
Br P , <br />
S I S = J ¡¤dS = 0, e<br />
<br />
= S <br />
E ¡¤dS = S <br />
<br />
S <br />
J ¡¤dS = J ¡¤dS = 0 ( 111) <br />
, , <br />
, B = 0<br />
L<br />
B ¡¤dr =<br />
2 rB =<br />
0I + 1 d e<br />
= 0<br />
c 2 dt<br />
B , B= 0<br />
P , , B= 0<br />
<br />
11. 32. 010 24 m/ s 2<br />
45, 20cm , <br />
? , ?<br />
346
E = easin 1. 19 610-<br />
=<br />
4 0c 2 r<br />
= 0. 11 V / m<br />
t = r / c =<br />
210 24 sin( / 4)910 9<br />
( 310 8 ) 0. 2 2<br />
0. 2<br />
310 8 = 6. 710 - 10 s<br />
11. 4X , <br />
( X ) 2<br />
10 4 eV , 510 - 9 m <br />
, 0. 3m <br />
E = easin<br />
4 0c 2 r = eE k<br />
4 0c 2 msr<br />
= 9109 1. 610 - 19 210 4 1. 610 - 19<br />
( 310 8 ) 2 0. 9110 - 3 0 510 - 9 0. 3<br />
= 3. 810 - 2 V/ m<br />
<br />
11. 5( ) , <br />
v = v 0cos t, v0 = 8. 010 - 3 m / s, = 6. 0<br />
10 6 rad/ s<br />
( 1) ?<br />
( 2) , 1. 0k m , <br />
? <br />
1. 0km ?<br />
( 1) a ma x= v0= 6. 0108. 6 010 - 3 = 4. 810 4 m / s 2<br />
( 2) E , m a x=<br />
ea ma xsin<br />
4 0c 2 r<br />
= 1. 19 610- 4. 810 sin 4 ( / 2)910 9<br />
( 310 8 ) 10 2 3<br />
= 7. 710 - 25 V / m<br />
t = r/ c = 10 3 / ( 310 8 ) = 3. 310 - 6 s<br />
11. 6 , 1. 110 1 4<br />
m / s 2 <br />
347
( 1) 45 , 0. 50m <br />
;<br />
( 2) ( 1) <br />
<br />
ea sin <br />
( 1) E =<br />
4 0c 2 r<br />
= 1. 610 - 1 1. 9 110 14 sin ( / 4)910 9<br />
( 310 8 ) 0. 2 5<br />
= 2. 510 - 12 V / m<br />
B = E / c = 2. 510 - 12 / ( 310 8 ) = 8. 310 - 2 1 T<br />
( 2) a , E , B113 <br />
113116 <br />
<br />
11. 7 0. 26cm 3. 910 - 3<br />
V / m , 12. 0A <br />
( 1) ?<br />
( 2) 4. 0m <br />
?<br />
( 3) 5. 0cm <br />
, 4. 0m ?<br />
( 4) 12. 0A ? <br />
? ?<br />
348
( 1) a = E e = 3. 910- 1. 3 610 - 19<br />
= 6. 810 8 m/ s 2<br />
me 9. 110 - 3 1<br />
( 2) E 1= easin<br />
4 0c 2 r<br />
= 1. 19 610- 6. 810sin( 8 / 2)910 9<br />
( 310 8 ) 4<br />
2<br />
= 2. 710 - 1 8 V / m<br />
B 1=<br />
E 1 / c = 2. 710 - 1 8 / ( 310 8 ) = 910 - 27 T<br />
( 3) <br />
( 4) B s<br />
= D M N A = 8. 910 3<br />
6. 310 - 3 6. 02310 23<br />
= 8. 510 2 8 m - 3<br />
E = E 1 r 2 l<br />
= 2. 710 - 18 8. 510 28 0. 13 2 10 - 4<br />
5. 010 - 2 = 6. 110 6 V / m<br />
B= E / c = 6. 110 6 / ( 310 8 ) = 2. 010 - 2 T<br />
= 0I l = 410-<br />
12. 7 05. 010 - 2<br />
4 r 2 44 2<br />
= 3. 810 - 9 T<br />
, , <br />
, , E 1<br />
<br />
<br />
B 1, <br />
11. 8 1. 3810 3 W/<br />
m 2 <br />
<br />
E r ms=<br />
I =<br />
c 0E 2 rm s<br />
I / ( c 0) = 1. 3810 3 / ( 310 8 8. 8510 - 12 )<br />
= 7. 210 2 V / m<br />
Br ms= E r ms / c = 7. 210 2 / ( 310 8 ) = 2. 410 - 6 T<br />
349
11. 9 60 m, <br />
300kW <br />
?<br />
S =<br />
P =<br />
R 2<br />
E m = S / ( c 0)<br />
30010 3<br />
= 1. 110 14 W/ m 2<br />
( 3010 - 6 ) 2<br />
= 1. 110 1 4 / ( 310 8 8. 8510 - 12 )<br />
= 2. 810 8 V / m<br />
Bm = E m/ c = 2. 810 8 / ( 310 8 ) = 0. 93 T<br />
11. 10 ( 514. 5nm ) 3. 8kW<br />
0. 880 rad<br />
3. 8210 5 km :<br />
( 1) ;<br />
( 2) <br />
( 1) R = r / 2= 3. 82100. 8 88010 - 6 / 2<br />
= 168 m<br />
( 2) I = P / S = 3. 810 3 / ( 168 2 ) = 0. 043 W / m 2<br />
<br />
11. 11 , l, a , , <br />
I ( 114) , :<br />
( 1) , <br />
, ( : <br />
)<br />
( 2) <br />
, <br />
S ¡¤dA = I 2 R<br />
dA , R <br />
, , <br />
350
, <br />
( 1) E <br />
B 114 S= E<br />
B/ 0 S <br />
<br />
( 2) B = 0I / ( 2 a) , E = J =<br />
I / ( a 2 ) , A= 2 a l<br />
A<br />
S ¡¤dA = - A<br />
= -<br />
E B<br />
dA<br />
0<br />
0I I<br />
¡¤2 al<br />
2 a<br />
0 a 2<br />
= - I 2 l / ( a 2 ) = -<br />
I 2 R<br />
<br />
1141111 <br />
<br />
11. 12E R <br />
r 1 r 2( 115) <br />
1151112 <br />
( 1) r 1< r < r 2 E B S , <br />
S ;<br />
( 2) S , <br />
E 2 / R, R <br />
( 1) , <br />
U= E , <br />
115 S= E<br />
351
B/ 0 S R<br />
<br />
B =<br />
0I<br />
2 r =<br />
, ( r 1 < r < r 2)<br />
2 rR<br />
0 E<br />
l l, <br />
r ( r 1< r < r 2) e= 2 rlE <br />
, r E = e/<br />
2 E l<br />
r 2<br />
( 2 rl ) E = U = Edr =<br />
r 1<br />
E <br />
S r <br />
I <br />
S =<br />
E =<br />
e<br />
2 l ln r 2<br />
r 1<br />
E<br />
rln( r 2/ r 1)<br />
EB = E 2<br />
0 2 r 2 Rln( r 2/ r 1)<br />
( 2) S <br />
r 2<br />
r 1<br />
S 2<br />
rdr = <br />
r 2<br />
r 1<br />
E 2 dr<br />
rRln ( r 2/ r 1) = E 2<br />
R<br />
, e =<br />
ln( r 2/ r 1)<br />
ln( r 2/ r 1) = E 2<br />
R<br />
ln( r 2/ r 1) ,<br />
11. 133. 0 cm, E <br />
30V / m , :<br />
( 1) ?<br />
( 2) ?<br />
( 3) , 0. 5m 2 <br />
?<br />
( 1) = c/ = 310 8 / ( 3. 010 - 2 ) = 1. 010 10 Hz<br />
( 2) B m= E m / c= 30/ ( 310 8 ) = 1. 010 - 7 T<br />
( 3) F = p A = 0E 2<br />
A= 1 2 0E 2 mA<br />
352
= 1 2 8. 8510- 12 30 2 0. 5= 210 - 9 N<br />
<br />
11. 14 1. 110 3 W / m 2 <br />
? 0. 5m 2 , <br />
50% <br />
p = S c ( 1 + 50% )<br />
F = p A = SA c ( 1 + 50% )<br />
= 1. 1103 0. 5<br />
310 8 1. 5 = 2. 810 - 6 N<br />
11. 15<br />
, <br />
1. 510 9 W , 1. 3mm 2 <br />
?<br />
p m<br />
= 2S m<br />
c<br />
= 2P m<br />
cA<br />
= 7. 710 6 Pa<br />
=<br />
21. 510 9<br />
310 8 1. 310 - 6<br />
11. 16 10m , <br />
10k W 100kg, <br />
, <br />
?<br />
, I / c, <br />
F = I / ca<br />
= F / m= I / ( cm) <br />
t =<br />
2l<br />
a =<br />
2lcm<br />
I<br />
= 7. 7510 3 s = 2. 15 h<br />
=<br />
210310 8 100<br />
1010 3<br />
11. 17 , <br />
353
1. 0g/ cm 3 r , <br />
?( <br />
6. 910 7 W/ m 2 ) ?<br />
R , <br />
<br />
F g = GM S 4<br />
R 2 3 r 3 <br />
F g= F r<br />
<br />
F r = S c A = P SR2 S<br />
r 2<br />
cR 2<br />
r =<br />
=<br />
3P SR 2 S<br />
4GMS c<br />
36. 910 7 ( 710 8 ) 2<br />
46. 6710 - 1 1 210 30 310 8 1. 010 3<br />
= 6. 310 - 7 m = 6. 310 - 4 mm<br />
, <br />
R , <br />
, , <br />
354
4 <br />
1 <br />
11, <br />
<br />
;<br />
<br />
x = 0. 05cos 8 t +<br />
<br />
3<br />
( 1) <br />
( 2) t= 1s, 2s, 10s ;<br />
( 3) <br />
( 1) x = Acos ( t + ) <br />
= 8= 25. 1 s - 1 ;<br />
T =<br />
2 / = 0. 25 s;<br />
A = 0. 05 m;<br />
=<br />
/ 3;<br />
v m = A = 80. 05 = 1. 26 m/ s;<br />
a m = <br />
2 A = ( 8 ) 2 0. 05 = 31. 6m/ s 2 <br />
( 2) 1= t1+ = 81+ / 3= 25 / 3,<br />
2= t2+ = 82+ / 3= 49 / 3,<br />
3= t3+ = 810+ / 3= 241 / 3<br />
355
( 3) x , v, a t 11 <br />
1111 <br />
12 , x A <br />
t= 0 , <br />
: ( 1) x 0= - A; ( 2) x ; ( 3) <br />
x = A / 2 , x <br />
<br />
( 1) = ; ( 2) = - / 2; ( 3) = / 3<br />
1212 <br />
1313 <br />
( 1) a , b, c, d , e ;<br />
( 2) ;<br />
( 3) <br />
356
1313 <br />
( 1) x = A cos, x :<br />
x a =<br />
A, a = 0;<br />
x b =<br />
A 2 , b = / 3;<br />
x c =<br />
x d = -<br />
x e = -<br />
0, c =<br />
/ 2;<br />
A<br />
2 , d = 2 / 3;<br />
A<br />
2 , e =<br />
4 / 3<br />
( 2) t= 0 , x = A 2<br />
, = arccos( 1/ 2) = / 3 ; <br />
v> 0, = - / 3 T = 1. 2s,<br />
2<br />
= 2 / ( T / 2) = 5 / 6<br />
<br />
x =<br />
0. 05cos<br />
5<br />
6 t -<br />
<br />
3<br />
( 3) 14 <br />
1413 <br />
14 , v m= 3cm/ s, A<br />
= 2cm , <br />
( 1) ;<br />
357
( 2) ;<br />
( 3) <br />
( 1) vm = A= 2 A / T , <br />
T =<br />
2 A/ vm = 20. 02/ 0. 03 =<br />
4. 2 s<br />
( 2) a m= <br />
2 A = v 2 m/ A = 0. 03 2 / 0. 02= 4. 510 - 2 m/ s 2<br />
( 3) t = 0 , v= + v m, = - / 2, = vm = 0. 03/<br />
A<br />
0. 02= 1. 5s - 1 , <br />
x = A cos( t +<br />
) = 0. 02cos( 1. 5t - / 2)<br />
15 , A = 2. 010 - 2 m, T =<br />
0. 50st= 0 ,<br />
( 1) x = 1. 010 - 2 m , ;<br />
( 2) x = - 1. 010 - 2 m , <br />
<br />
( 1) x = Acos<br />
2 t+ = 2. 2 010-<br />
T<br />
( 2) x = 2. 010 - 2 cos( 4 t- 2 / 3)<br />
cos 4 t+ <br />
3<br />
1610g , 24cm, <br />
4s, t= 0, + 24cm:<br />
( 1) t= 05s , ;<br />
( 2) x = 12cm <br />
= 0, <br />
( 1) t= 0. 5s ,<br />
x = 0. 24cos<br />
F = ma = -<br />
358<br />
x = Acos<br />
= - 4. 210 - 3 N<br />
2<br />
<br />
t + = 0. 24cos<br />
T 2 t<br />
<br />
0. 5 = 0. 17 m<br />
2<br />
m<br />
2 x = - 1010 - 3 ( / 2) 2 0. 17
( 2) x = 0. 12m , arccos( 1/ 2) = / 3<br />
<br />
2 t m in= <br />
3 <br />
tm in = 2 3 s<br />
17<br />
x 1= Acos( t + ) , <br />
, <br />
( 1) ;<br />
( 2) t= 0 , x 1= - A/ 2, x , <br />
x t <br />
( 1) / 2 , , <br />
2- 1= 0- / 2, 2= 1- / 2= - / 2<br />
<br />
x 2<br />
= Acos( t +<br />
2) = A cos( t +<br />
- / 2)<br />
( 2) t= 0 , x 1= A/ 2 v< 0, = 2 / 3<br />
x 1<br />
= Acos( t + 2 / 3) , x 2 = Acos( t +<br />
x t 15 <br />
/ 6)<br />
1517 <br />
359
18<br />
, , <br />
, <br />
16 ,<br />
A<br />
2<br />
= Acos( t +<br />
t +<br />
1 = / 3, t +<br />
1) = A cos( t +<br />
©¦ ©¦= ©¦ 2- 1©¦= 0, 2 / 3, 2 / 3<br />
2)<br />
2 = / 3<br />
1618 <br />
19 , k= 25N / m, <br />
02J 06J , :<br />
( 1) ?<br />
( 2) , ?<br />
( 3) , ?<br />
( 1) A = 2E / k = 2( E k+ E p ) / k<br />
= 2( 0. 2+ 0. 6) / 25= 0. 25m<br />
( 2) E p= E k , E p= 1 2 kx 2 = 1 2 E= 1 2 kA 2 / 2<br />
360<br />
x = 2<br />
2<br />
2<br />
A= 0. 25= 0. 18 m<br />
2
( 3) E p= 1 2 k A 2<br />
= 1 1<br />
2 4 2 kA 2 = 1 4 ( 0. 2+ 0. 6) = 0. 2 J<br />
110 k , <br />
m , b<br />
, <br />
A , 1 2 kA 2 <br />
mg = kb, k= mg / b<br />
, x , <br />
<br />
mg = kb , <br />
mg - k( x + b) = m d 2 x<br />
dt 2<br />
m d 2 x<br />
dt 2 = - kx<br />
, T =<br />
2m/ k , <br />
, <br />
<br />
E p , e = 1 2 k( x + b) 2 -<br />
<br />
, <br />
E p , g = - mg x<br />
1<br />
2 kb2 = 1 2 kx 2 + kbx<br />
E = E k + E p = E k + E p , e + E p, g<br />
= 1 2 mv 2 + 1 2 kx 2 + ( kb - mg ) x<br />
E = 1 2 mv2 + 1 2 kx 2<br />
x = A , v= 0<br />
361
E = 1 2 kA 2<br />
<br />
111, 10g , <br />
49cm 80g , <br />
10cm , v0= 50cm/ s<br />
<br />
m 1g = kx 1 <br />
k = m 1g / x 1 = 0. 019. 8/ ( 4. 910 - 2 ) = 2. 0 N / m<br />
<br />
T =<br />
2m2/ k = 20. 08/ 2. 0 = 1. 26 s<br />
= k/ m 2 = 2. 0/ 0. 08 = 5. 0 s - 1<br />
x , , x 0 = 0. 01m , v 0 =<br />
- 0. 05m / s, <br />
A = x 2 0 + v 2 0<br />
= 0. 01 2 +<br />
<br />
2<br />
0 = arct an -<br />
v 0<br />
= arctan -<br />
x 0<br />
x 0> 0, v0< 0, 0= / 4<br />
0. 052<br />
( 5. 0) 2 = 2 10 - 2 m<br />
x = 2 10 - 2 cos( 5t + / 4)<br />
- 0. 05<br />
5. 00. 01 = <br />
4 , 5<br />
4 <br />
112 k 1 k2 <br />
, , m , <br />
, <br />
k <br />
k = 1<br />
1<br />
k 1<br />
+ 1 k2<br />
<br />
362<br />
=<br />
k1k 2<br />
k1 + k 2
T = 2m/ k = 2m( k1 + k2) / ( k 1k2)<br />
113k 1 k2<br />
m <br />
, 17 , <br />
<br />
T = 2 m<br />
k 1 + k 2<br />
17113 <br />
17 , , <br />
x 1<br />
x 2, k 1x 1= k 2x 2<br />
x , <br />
k 1( x 1 + x ) - k 2( x 2 - x ) = - m d 2 x<br />
dt 2<br />
<br />
m d 2 x<br />
dt<br />
<br />
= - ( k 1 + k2) x<br />
T = 2m/ ( k1 + k2)<br />
114 <br />
005k g ( 18) 110 3 N / m<br />
<br />
18 , , B , <br />
B x , A x , <br />
363
18114 <br />
2x B <br />
m d 2 x<br />
dt 2 = - k( 2x ) = - 2kx<br />
B , A <br />
= 1 2k<br />
2m = 1 2110 3<br />
2 0. 05<br />
= 31. 8 Hz<br />
115 11 , <br />
, m , <br />
, mv <br />
, <br />
( 1) : 1 2<br />
m+ m<br />
3 <br />
m<br />
m+ v 2 , <br />
3<br />
( 2) : k m+ m<br />
1 / 2<br />
<br />
3<br />
( 1) L l, <br />
dm = m dl/ L 1 2 dm v 2 l = 1 2<br />
l 2 dl<br />
L<br />
E k =<br />
0<br />
<br />
364<br />
m v 2<br />
l 2 dl = 1 2L 3 6 m v2<br />
E k = 1 2 m + m v 2<br />
3<br />
l<br />
L v 2<br />
= m v2<br />
dm<br />
2L 3
( 2) <br />
E = E k + E p = 1 2 m + m v 2 + 1 3 2 kx 2 = <br />
x , <br />
m +<br />
m v dv<br />
3 dx = m + m dv<br />
3 dt = m + m a = -<br />
3<br />
<br />
= [ k/ ( m + m / 3) ] 1/ 2<br />
116dT / T <br />
dg / g g = 9800m/ s 2<br />
kx<br />
<br />
, 10s, <br />
<br />
T = 2l/ g , <br />
dT<br />
T = - dg<br />
2g<br />
T = 2s T = 286400/<br />
( 86400- 10) <br />
dT<br />
T =<br />
T - T<br />
T<br />
g = g + dg = g ( 1 - 2dT / T )<br />
=<br />
86400<br />
86400 - 10 - 1 = 10<br />
86390<br />
= 9. 800( 1 - 210/ 86390) = 9. 798 m / s 2<br />
117m, l, 0 <br />
<br />
=<br />
0cos( t +<br />
)<br />
( ) <br />
<br />
19 , <br />
=<br />
t <br />
0cos( t +<br />
)<br />
365
E k = 1 2 mv2 = 1 2 m l d<br />
2<br />
= 1 dt 2 ml 2 <br />
2 <br />
2 0sin 2 ( t + )<br />
( 0 )<br />
E p = mg l( 1 - cos )<br />
= mg l[ 1 - ( 1 - <br />
2 / 2) ]<br />
= 1 2<br />
mg l<br />
2 0cos 2 ( t +<br />
)<br />
<br />
2 = g / l, <br />
E k = 1 2<br />
mg l<br />
2 0sin 2 ( t +<br />
)<br />
<br />
E = E k + E p = 1 2<br />
mg l<br />
2 0<br />
19117 <br />
118 ( 110) , <br />
m , x <br />
, ME , RE<br />
110118 <br />
( 1) ( : <br />
)<br />
( 2) , <br />
366
( 3) ?<br />
( 1) 110 , <br />
F =<br />
Gm M<br />
r 2 E<br />
r 3<br />
R 3 E<br />
= GmME<br />
R 3 E<br />
( 2) x , F x = ma x<br />
r<br />
F x= - F sin = -<br />
GmME<br />
R 3 E<br />
r x r , <br />
a x = -<br />
GME<br />
R 3 E<br />
, <br />
T =<br />
2R 3 E/ ( GM E) = 2 R E RE / ( GM E)<br />
( 3) , <br />
mv 2<br />
RE<br />
x<br />
= GMEm<br />
R 2 E<br />
v = GME / R E<br />
<br />
T =<br />
2 RE / v =<br />
2 R E R E/ ( GM E)<br />
<br />
<br />
119 v r= dr<br />
dt<br />
( ) v= r d , m <br />
dt<br />
<br />
E =<br />
1 2 m dr<br />
dt<br />
2<br />
+ 1 2<br />
2 mr d<br />
2 -<br />
dt<br />
GmM S<br />
r<br />
M S , r <br />
( 1) : L , <br />
367
E =<br />
1 2 m dr<br />
dt<br />
2<br />
+ 1 2<br />
L 2<br />
mr 2 -<br />
GmM S<br />
r<br />
( 2) r= r 0 , r = r 0+ x , x r 0<br />
: <br />
E =<br />
1 2 m dx<br />
dt<br />
2<br />
+ 3 2<br />
L 2<br />
x 2 -<br />
mr 4 0<br />
GmM S<br />
x 2 -<br />
r 3 0<br />
GmMS<br />
2r 0<br />
( 3) , ( 130) , <br />
, :<br />
<br />
k =<br />
GM Sm<br />
r 3 0<br />
( 4) : <br />
<br />
2<br />
d<br />
( 1) L = mrv = mr 2 dt , d =<br />
dt<br />
, <br />
E =<br />
1 2 m dr<br />
dt<br />
2<br />
+ 1 2<br />
L 2<br />
mr 2 -<br />
GmM S<br />
r<br />
( 2) , v v 0, v 0 r 0<br />
L 2<br />
( mr 2 ) 2 <br />
<br />
L 0<br />
<br />
L = m( r 0 + x ) vmr 0v0 = L 0<br />
L 2 m 2 r 2 0v 2 0 = mr 3 0mv 2 0/ r 0 = mr 3 0GMSm/ r 2 0 = m 2 r 0GM S<br />
r = r 0+ x ( 1) , x / r 0<br />
E = 1 2 m d dt ( r 0 + x ) 2<br />
= 1 2 m dx<br />
dt<br />
-<br />
GmM S<br />
r 0<br />
368<br />
2<br />
+ 1 2<br />
1 -<br />
x<br />
r 0<br />
L 2<br />
mr 2 0<br />
+ 1 2<br />
1 -<br />
+ x 2<br />
r 2 0<br />
L 2<br />
mr 2 0( 1 + x / r 0) 2 -<br />
2x<br />
r 0<br />
+ 3x 2<br />
r 2 0<br />
2 , <br />
GmM S<br />
r 0( 1 + x / r 0)
1 2<br />
L 2<br />
mr 2 0<br />
1-<br />
2x<br />
r 0<br />
m2 r 0GM S<br />
2mr 2 0<br />
= GmM S GmMS<br />
-<br />
2r 0 r 2 x<br />
0<br />
E x <br />
E =<br />
1 2 m dx<br />
dt<br />
2<br />
+ 3 2<br />
L 2<br />
x 2 -<br />
mr 4 0<br />
( 3) L 2 m 2 r 0GM S, x 2<br />
, E <br />
1-<br />
GmMS<br />
x 2 -<br />
r 3 0<br />
2x<br />
r 0<br />
GmM S<br />
2r 0<br />
<br />
E = 1 2 mv2 x + 1 2<br />
<br />
GmM S<br />
x 2 -<br />
r 3 0<br />
GmMS<br />
2r 0<br />
E = 1 2 mv2 + 1 2 kx 2<br />
, t<br />
, E , <br />
m dvx<br />
dt<br />
= -<br />
GmMS<br />
x<br />
r 3 0<br />
, <br />
<br />
k = GmM S/ r 3 0<br />
( 4) <br />
<br />
T = 2m/ k =<br />
2 r 0 r 0/ ( GmM S)<br />
111119 <br />
<br />
111 ( ) <br />
120 , <br />
050<br />
369
( 1) 20H z , <br />
, ?<br />
( 2) , 50cm, <br />
, ?<br />
( 1) , <br />
smg = ma m = mA<br />
2 = mA( 2 ) 2<br />
A = sg / ( 2 ) 2 = 0. 509. 8/ ( 22. 0) 2 = 3. 110 - 2 m<br />
( 2) , <br />
mg = ma m = mA( 2 ) 2<br />
= 1 g<br />
2A = 1 9. 8<br />
= 2. 2 Hz<br />
20. 05<br />
121112 , m, <br />
l = 20cm , <br />
= 05<br />
<br />
112121 <br />
112 , <br />
x , <br />
, <br />
F = F 1 - F 2 = - mg l/ 2 +<br />
l<br />
= -<br />
2mg x<br />
l<br />
x<br />
+ mg l/ 2 -<br />
l<br />
x , <br />
, <br />
370<br />
x
T =<br />
2 ml<br />
2 mg = 2 0. 20<br />
20. 59. 8 =<br />
0. 90 s<br />
122m= 121g U , S =<br />
030cm 2 , T ? <br />
136g/ cm 3 <br />
U , ,<br />
, <br />
y , <br />
E p<br />
= ySg ¡¤ y 2 -<br />
ySg - y<br />
2<br />
= gSy 2<br />
E k=<br />
1 2 mv 2 , <br />
E = 1 2 mv2 + g Sy 2<br />
, U <br />
, <br />
T = 2m/ k =<br />
2m/ ( 2 g S)<br />
= 20. 121/ ( 213. 69. 80. 30)<br />
= 0. 77s<br />
123, R, Q<br />
m, - q <br />
, <br />
- q <br />
F = -<br />
Qqx<br />
4 0( R 2 + x 2 ) 3/ 2<br />
x ©¦ x ©¦R , <br />
F = -<br />
Qqx<br />
4 0R 3<br />
, <br />
371
= <br />
2 = 1 Qq<br />
24<br />
0R 3 m<br />
124 a 0 =<br />
0053nm , : <br />
, <br />
3810 15 Hz <br />
<br />
r , <br />
<br />
E = - er<br />
4 0a 3 0<br />
F = -<br />
e 2 r<br />
4 0a 3 0<br />
, <br />
= 1 e 2<br />
24<br />
0a 3 0m p<br />
m p , <br />
<br />
m p =<br />
m em p<br />
m e + m p<br />
= me<br />
= e 1<br />
24<br />
0m ea 3 0<br />
=<br />
1. 610-<br />
19<br />
2<br />
= 6. 610 15 Hz<br />
910 9<br />
9. 110 - 31 ( 0. 05310 - 9 ) 3<br />
3. 810 1 5 Hz , <br />
<br />
372
125H Cl 1310 -<br />
<br />
E p ( r) = -<br />
r <br />
e 2<br />
4 0r + B r 9<br />
10 m, <br />
( 1) HCl ( Cl <br />
, Cl )<br />
( 2) ( 135) , H Cl ( = 1) ,<br />
, <br />
,<br />
dE p( r )<br />
dr r= r 0<br />
=<br />
e 2<br />
-<br />
4 0r 2<br />
9B<br />
r 10 r = r 0<br />
=<br />
e 2<br />
-<br />
4 0r 2 0<br />
9B<br />
r 10<br />
0<br />
= 0<br />
( 1) <br />
B = e2 r 8 0<br />
36 0<br />
d 2 E p( r )<br />
dr 2 r = r 0<br />
= -<br />
e 2<br />
+ 90B =<br />
2 0r 3 r 11 r = r 0<br />
2e 2<br />
> 0<br />
0r 3 0<br />
H Cl , <br />
= 1<br />
2<br />
d 2 E p<br />
dr 2 m p = 1 2e 2<br />
r = r 0<br />
2<br />
0r 3 0m p<br />
= 1 8910 9 ( 1. 610 - 19 ) 2<br />
= 1. 110 14 Hz<br />
2( 1. 310 - 10 ) 3 1. 6710 - 27<br />
( 2) ( 135) , = 1, <br />
E = 3 2 h = 1 2 m<br />
2 A 2<br />
A =<br />
3h <br />
= 1 3h<br />
m<br />
2 2m<br />
373
= 1 36. 6310 - 34<br />
= 1. 710 - 11 m<br />
21. 6710 - 27 1. 110 14<br />
126 m <br />
O , 113 C<br />
O b, O I <br />
O , OC <br />
, <br />
T =<br />
2 I<br />
mg b<br />
113 , <br />
- mgbsin , <br />
<br />
I d 2 <br />
dt 2 = - mg bsin<br />
, sin , <br />
I d 2 <br />
dt 2 = - mgb<br />
, <br />
T = 2I / ( mg b)<br />
113126 <br />
127m, R, <br />
<br />
, - mgRsin , <br />
2mR 2 , , , <br />
<br />
2mR 2<br />
d 2 <br />
dt 2 = - mg Rsin - mg R<br />
374<br />
T =<br />
2 2mR2<br />
mg R =<br />
22R g
128 1 14 , K , <br />
, , L <br />
L = 0010H , C= 10 F , E= 14V , L<br />
<br />
( )<br />
<br />
114 , <br />
E = -<br />
E L + u = 0<br />
114128 <br />
L d<br />
dt , u = q C , = - dq<br />
dt , <br />
L d 2 q<br />
dt 2 = -<br />
, q , <br />
q =<br />
q<br />
C<br />
Qcos t<br />
= 1/ LC= 1 0. 01110 - 6 = 10 4 s - 1 , Q = CE= 1. 0<br />
10 - 6 1. 4= 1. 410 - 6 C, <br />
= -<br />
dq<br />
dt =<br />
m ax = Q= 1. 410 - 2 A<br />
Qsin t = 1. 410 - 2 sin ( 10 4 t)<br />
129, 100m , 0=<br />
5100s, 1= 4, 2<br />
= 2 ? Q ?<br />
1= 0e - t , <br />
2= 1e -<br />
=<br />
<br />
t =<br />
ln 0 t = ln 5 1 4 100 = 2. 3 210- s - 1<br />
t<br />
, 1 2 <br />
ln 1 = ln 4 2 2 ( 2. 210 - 3 ) = 311 s<br />
375
Q =<br />
<br />
2 =<br />
<br />
T =<br />
g<br />
2 l<br />
=<br />
1 g<br />
2 l<br />
=<br />
1<br />
9. 8<br />
22. 210 - 3 1. 00 = 712<br />
130 : , <br />
<br />
x = Acos( t+ ) <br />
v =<br />
dx<br />
dt<br />
v ma x = A =<br />
= - Asin( t + ) = - vm a xsin( t +<br />
h<br />
[ ( <br />
0 - <br />
) 2 + 4<br />
<br />
2 ] 1/ 2<br />
)<br />
dvma x<br />
d =<br />
h<br />
[ ( <br />
0 - <br />
) 2 + 4<br />
<br />
]<br />
[ ( <br />
2 0 - <br />
2 ) 2 + 4<br />
2 <br />
2 ] 1 / 2<br />
-<br />
- 2<br />
2 ( <br />
2 0 - <br />
2 ) + 4<br />
2 <br />
2<br />
[ ( <br />
2 0 - <br />
2 ) 2 + 4<br />
2 <br />
2 ] 1 / 2<br />
=<br />
=<br />
h<br />
{( <br />
[ ( <br />
0 - <br />
) 2 + 4<br />
<br />
] 3 / 2 0 - <br />
) 2 + 2<br />
( <br />
0 - <br />
) }<br />
h<br />
( <br />
[ ( <br />
0 - <br />
) 2 + 4<br />
<br />
] 3 / 2 0 - ) ( 0 + ) ( <br />
0 + <br />
)<br />
dvm ax<br />
v ma x = 0, <br />
d<br />
= 0<br />
131 , <br />
, <br />
4 576kg, <br />
1800r/ min ( ) , <br />
5 , 90% 5 , <br />
?<br />
376
d= 1800r / min= 30 H z<br />
4 , <br />
k 1 4 k= 4k1 d= 5 0 <br />
k 1<br />
d = 5 0/ ( 2 ) = 5 k/ m/ ( 2 ) = 5 k1/ m <br />
= 2 d<br />
2 m/ 25 = 30 2 <br />
2 576/ 25 = 2. 0510 5 N/ m<br />
1320994m, 12k g<br />
( 1) , 150min , <br />
<br />
( 2) 8 , <br />
<br />
( 1) = 0e - t , = ln 0 t = ln 2 1<br />
( 15. 060) = 7. 7<br />
10 - 4 s - 1<br />
( 2) P in= -<br />
dE<br />
= 2 E 0e -<br />
dt t = 0<br />
2 t = 2 E 0= 2<br />
1<br />
t= 0<br />
2 mgl<br />
2 0<br />
<br />
= 27. 710 - 1 4 1. 29. 80. 994<br />
2<br />
( 8 / 180) 2 = 1. 7510 - 4 W<br />
133 , <br />
<br />
<br />
x 1 = 0. 04cos 2t + <br />
6<br />
x 2 = 0. 03cos 2t -<br />
A = A 2 1 + A 2 2 + 2A 1A 2cos( 2 - 1)<br />
<br />
6<br />
= 0. 04 2 + 0. 03 2 + 20. 040. 03cos( - / 6 - / 6)<br />
377
= 0. 06 m<br />
= arct an<br />
= arct an<br />
= 0. 08<br />
<br />
A 1sin 1 + A 2sin 2<br />
A 1cos 1 + A 2cos 2<br />
0. 04sin ( / 6) + 0. 03sin( - / 6)<br />
0. 04cos( / 6) + 0. 03cos( - / 6)<br />
x = Acos( t + ) = 0. 06cos( 2t + 0. 08)<br />
134 R, <br />
L, <br />
u <br />
u 1= 90 2 cos100 t V<br />
u 2= 200 2 cos 100 t +<br />
u u 1 u 2<br />
V<br />
2<br />
1= 0, 2= / 2<br />
U = U 2 1 + U 2 2 + 2U 1U 2cos( 2 - 1) = U 2 1 + U 2 2<br />
= ( 90 2 ) 2 + ( 200 2 ) 2 = 310 V<br />
= arctan U 2<br />
U 1<br />
u = Ucos( t +<br />
= arctan 200<br />
90<br />
= 0. 37<br />
) = 310cos( 100 t + 0. 37 ) V<br />
135<br />
x 1 = 0. 08cos 314t + <br />
6<br />
x 2 = 0. 08cos 314t + <br />
2<br />
x 3 = 0. 08cos 314t + 5<br />
6<br />
: ( 1) ;<br />
378
( 2) x =<br />
<br />
<br />
115135 <br />
= 12. 5ms <br />
2<br />
2 A ( A ) <br />
( 1) 115 <br />
= 314s - 1 ,<br />
A = A 1<br />
2 + A 2 + A 3<br />
2<br />
= / 2,<br />
x = 0. 16cos( 314t +<br />
= 0. 16m,<br />
/ 2)<br />
( 2) 115 A <br />
x =<br />
2 A/ 2 , <br />
+ / 4 = 5 / 4, t 1 =<br />
5 / ( 4 ) = 5 / ( 3144) = 0. 0125s<br />
<br />
136 01kg <br />
, <br />
x =<br />
y =<br />
0. 06cos<br />
0. 03cos<br />
<br />
3 t + <br />
3<br />
<br />
3 t - <br />
3<br />
, , <br />
= x - y= / 3- ( - / 3) = 2 / 3 <br />
<br />
x 2<br />
+ y 2<br />
- 2 x y<br />
A 2 B 2 AB cos = sin 2 <br />
<br />
x 2 + 2x y + 4y 2 = 2. 710 - 3<br />
> 0, 116 <br />
379
116136 <br />
<br />
137 <br />
, 117 , <br />
27010 4 H z, <br />
117 y / x = 23<br />
y = 2 x / 3 = 22. 7010 4 / 3 =<br />
138 118 C1<br />
1. 8010 4 H z<br />
100V , C2<br />
K 1 K 2 C2 400V <br />
117137 <br />
118 , LC1<br />
118138 <br />
<br />
380
LC2<br />
T 1 = 2LC1 = 2 10160010 - 6 = 0. 80 s<br />
<br />
T 2 = 2LC2 = 21010010 - 6 = 0. 20 s<br />
LC , <br />
/ 2K 1, t 1= T 1/ 4= 0. 20s <br />
I m , K 1, K 2 I m C2 K 2 t 2=<br />
T 2/ 4= 0. 05s, q2<br />
<br />
K 2, C2 U 2 C2 <br />
C1 , 1 2 C2U 2 2= 1 2 C1U 2 1, U 2=<br />
100= 400V , <br />
C1<br />
C2<br />
U 1=<br />
1600<br />
100<br />
<br />
139119 <br />
( ) A B <br />
, , ( A, B ) <br />
C ( ) <br />
L 1 L 2 S , <br />
( kHz) A , B C , <br />
<br />
50kH z, <br />
10 -<br />
5 m, ? A, B C <br />
?<br />
119139 <br />
381
A ( ) C <br />
( ) / 2, L 1 L 2 <br />
, , , <br />
L 1<br />
, <br />
vm a x = r = 2 A =<br />
L 2 <br />
25010 3 10 - 5 = 3. 14m/ s<br />
382
2 <br />
21 740km/ h, <br />
300km? 8000km <br />
?<br />
= u/ = 74010 3 / ( 30010 3600) 3 = 6910 - 4 Hz<br />
t= s/ u= 8000/ 740= 108 h<br />
2208m/ s x =<br />
01m , y = 005sin ( 10<br />
- 40t) <br />
x = 01m <br />
= 40s - 1<br />
y = 005sin ( 10 - 40t)<br />
= 2 u/ = 208/ 40 =<br />
04m<br />
x x = 01m <br />
, <br />
= 2 ( x - 01) / = 5x - 05<br />
y = 005sin ( 10 - 40t + )<br />
= 005sin ( 5x - 40t + 05)<br />
= 005sin ( 40t - 5x + 264)<br />
x <br />
<br />
y = 005sin ( 10 - 40t - )<br />
= 005sin ( 15 - 40t - 5x )<br />
= 005sin ( 40t + 5x + 164)<br />
383
x <br />
23, <br />
y = 210 - 2 sin2 ( 200t - 20x )<br />
( 1) ;<br />
( 2) <br />
( 1) <br />
, <br />
y =<br />
Asin2 t -<br />
x<br />
<br />
= 1/ 20 = 050 m, = 200 H z, u = = 100 m/ s<br />
t x , x <br />
<br />
( 2) <br />
vm a x<br />
v =<br />
= 2 A =<br />
dy<br />
dt =<br />
2 Acos2 t -<br />
x<br />
<br />
2200210 - 2 = 25 m / s<br />
24, 1976 , <br />
2m , 1Hz, <br />
3km/ s, ? ?<br />
, <br />
<br />
vm = 2gh<br />
A = v m/ ( 2 ) = 2gh / ( 2 )<br />
= 2982/ ( 21) =<br />
= u/ = 3/ 1= 3 km<br />
10 m<br />
25t= 0 21 <br />
( 1) u= 008m/ s, ;<br />
( 2) t= T / 8 <br />
384
2125 <br />
( 1) 21 , = 04m, u = 008m/ s, = u/ =<br />
008/ 04= 02 Hz<br />
, , t = 0, x = 0 , y = 0, <br />
= / 2<br />
y =<br />
Acos 2 t -<br />
x<br />
+ = 004cos( 04<br />
t -<br />
5 x +<br />
/ 2)<br />
( 2) t= T / 8 x / 8=<br />
005m , 22 <br />
2225( 2) <br />
26y= Acos ( 4t+ 2x ) <br />
( 1) t= 42s , <br />
, ?<br />
<br />
( 2) t= 42s <br />
( 1) t = 42s y = A , <br />
( 4t + 2x ) = 2¡¤<br />
385
t= 42s <br />
x = - 84, = 0, 1, 2, <br />
©¦ x ©¦, 8, x = - 04m<br />
= 8 x = 0 t , <br />
<br />
( 4t + 20) = 28<br />
t = 4 s<br />
( 2) = 2 / ( 2 ) = 1m - 04m<br />
23 <br />
2326( 2) <br />
?<br />
( 2)<br />
2. 7500H z , 350m / s<br />
( 1) , 60 ?<br />
( 2) , 10 - 3 s , <br />
( 1) = u/ = 350/ 500= 07 m = 2 x / <br />
x =<br />
¡¤ / ( 2 ) = 0. 7 <br />
3 ( 2 ) = 012 m<br />
= 2 t/ T = 2<br />
t= 250010 -<br />
3 = <br />
2. 8 , 3. 17210 2<br />
m / s, ?<br />
u=<br />
RT / M<br />
= Mu 2<br />
RT = 3210- 3 3172 2<br />
831273<br />
= 142<br />
2. 9 5100m/ s, ( <br />
386
= 7. 810 3 k g/ m 3 ) <br />
u=<br />
Y/ <br />
Y =<br />
u 2 = 7. 810 3 ( 5110 3 ) 2 = 2. 0310 11 N/ m 2<br />
2. 10 p <br />
1 2 K<br />
V V<br />
2<br />
, , VV<br />
, p , <br />
S , V0, p = p 0= 0 , V 0 p = p -<br />
p 0= p = - K ( V- V 0) / V0, V 0<br />
<br />
r<br />
r<br />
A = - p dSdr = -<br />
S<br />
<br />
r 0<br />
r 0<br />
p Sdr = - <br />
V<br />
V ,<br />
V 0<br />
p dV<br />
= K<br />
V ( V - V0) dV = K ( V - V 0) 2<br />
V 0 V 0<br />
2V0<br />
= 1 2 K ( V) 2<br />
V 0<br />
V Wp <br />
VV 0, <br />
w p = W p<br />
V = 1 2 K V V<br />
2. 11 ( 2. 17) , K = -<br />
( 2. 23) , <br />
2<br />
V dp<br />
dV <br />
: ,<br />
<br />
u =<br />
u =<br />
V dp<br />
dV<br />
RT<br />
M<br />
387
u =<br />
RT<br />
M<br />
<br />
332m/ s ? ( = 1. 4,<br />
M= 29g/ mol )<br />
, p V= C, ©¦dp / dV ©¦= p / V, <br />
, <br />
u T =<br />
Vp<br />
V =<br />
p<br />
=<br />
, p V = C, ©¦dp / dV©¦= p / V, ,<br />
<br />
RT<br />
M<br />
u S =<br />
V p<br />
V =<br />
, ,<br />
p<br />
=<br />
RT<br />
M<br />
uT =<br />
831273<br />
2910 - 3 = 280 m / s<br />
, u S<br />
uS =<br />
14831273<br />
2910 - 3 = 331 m / s<br />
, <br />
, <br />
, , <br />
<br />
2. 12 u = 10 3 m/ s, A =<br />
1. 010 - 4 m , = 10 3 Hz = 800kg/ m 3 ,<br />
:<br />
( 1) ;<br />
( 2) S= 410 - 4 m 2 <br />
388
( 1) I =<br />
1 2 ( 2 ) 2 A 2 u<br />
= 1 800( 2<br />
2 103 ) ( 2 1. 010 - 4 ) 10 2 3<br />
= 1610 5 W / m 2<br />
( 2) W = I S t= 1610 410 5 - 60= 4 3810 3 J<br />
<br />
2. 13 <br />
2. 13, x S <br />
, , <br />
( 230) <br />
<br />
y =<br />
Acos( t - kx )<br />
, x S <br />
F = -<br />
<br />
Y dy<br />
dx S = -<br />
v =<br />
dy<br />
dt<br />
<br />
P = F v =<br />
YkA Ssin( t - kx )<br />
= - Asin ( t - kx )<br />
YkA 2 S sin 2 ( t - kx )<br />
Y= u 2 , k= 2 / = 2 / u= / u, <br />
P =<br />
<br />
2 A 2 u Ssin 2 ( t - kx )<br />
( 230) <br />
2. 14 , <br />
, ?<br />
, l <br />
r 1 r 2<br />
, <br />
2 r 1lI 1 = 2 r 2lI 2<br />
I 1r 1 = I 2r 2<br />
389
I A 2<br />
, A <br />
r <br />
2. 15P , Q , <br />
3 / 2, R P Q Q , P , Q <br />
R <br />
= 2<br />
P R -<br />
, P = Q , P Q=<br />
2<br />
QR + P - Q = 2<br />
P Q + P - Q<br />
3<br />
2 , <br />
= 2<br />
3 2 = 3 <br />
2. 16 A, B , , <br />
100Hz, , A, B 30m, 400m/ s, AB <br />
<br />
AB A x , A B <br />
<br />
= A -<br />
= A -<br />
2<br />
x -<br />
B - 2<br />
<br />
( l - x )<br />
B + 2<br />
u ( l - 2x )<br />
= + 2100<br />
( l - 2x )<br />
400<br />
= + ( l - 2x ) / 2<br />
= ( 2+ 1) , <br />
+<br />
( l - 2x ) / 2 = ( 2+ 1) <br />
x = l/ 2 - 2= 15 - 2<br />
, 0< x < 30, x = 1, 3, 5, , 29 m<br />
2. 17<br />
y =<br />
0. 02cos 20x ¡¤cos 750t<br />
: ( 1) ?<br />
390
?<br />
( 2) ?<br />
( 3) t = 2. 010 - 3 s , x = 5. 010 - 2 m <br />
( 1) y= 2Acos kx cos t , A= 001 m<br />
u =<br />
/ k = 750/ 20 = 375 m/ s<br />
( 2) = 2 / k, <br />
x =<br />
/ 2 = / k = / 20 = 0157 m<br />
( 3) v = dy<br />
dt = - 002750 cos 20x sin 750t<br />
= - 002750cos( 20005) sin ( 7502010 - 3 )<br />
= - 808 m/ s<br />
2. 18 x , 2. 4 , <br />
A , , u<br />
2. 42. 18 <br />
( 1) t = 0 , O x <br />
, ;<br />
( 2) , <br />
, x <br />
<br />
( 1) O <br />
y 0 = Acos( 2 t -<br />
/ 2)<br />
391
y i =<br />
Acos 2 t -<br />
2<br />
u x -<br />
<br />
2 , 0 x 3 4 = 3u<br />
4<br />
( 2) , <br />
y i y r<br />
y r = Acos 2 t -<br />
/ 4 <br />
= Acos 2 t +<br />
2 3<br />
u 4 - <br />
2 + - 23<br />
u 4 - x<br />
2<br />
u x -<br />
<br />
2<br />
, P , P / 2, x =<br />
2. 19 , <br />
( 2. 5) , <br />
, <br />
d = 2. 0mm, u= 5. 74<br />
10 3 m/ s , <br />
?<br />
2. 52. 19 <br />
= 2d <br />
= u/ = u/ ( 2d ) = 57410 3 / ( 22010 - 3 )<br />
= 1. 4410 6 Hz<br />
2. 20 , <br />
210 4 W 12km <br />
, 12k m <br />
? 2. 3 ?<br />
392
12km <br />
L = 10lg I<br />
I 0<br />
= 10lg<br />
<br />
= 10lg<br />
P<br />
I 04 r 2<br />
210 4<br />
= 70 dB<br />
10 - 12 4( 1210 3 ) 2<br />
2. 21, 115dB<br />
?<br />
I = I 010 L / 1 0 = 10 - 12 10 1 15/ 10 = 032 W/ m 2<br />
2. 22, <br />
, <br />
( 2. 6) , <br />
<br />
; P S <br />
, P <br />
150m/ s, S 50m/ s <br />
35ms, ?<br />
2. 62. 22 <br />
<br />
393
d =<br />
tuSuP<br />
u P - u S<br />
t = d<br />
1<br />
uS<br />
-<br />
1<br />
u P<br />
= 3. 510- 3 15050<br />
150 - 50<br />
= 0. 26 m<br />
2. 23 , <br />
4. 0s, 60cm, 25m <br />
( 1) <br />
( 2) , <br />
<br />
<br />
( 1) u= / T = 25/ 4. 0= 6. 25 m/ s<br />
( 2) v= 2 r / T = 2 A / T = 20. 6/ 4. 0= 0. 94 m/ s< u<br />
2. 24 1080Hz, 30m/ s <br />
65m/ s <br />
331m/ s:<br />
( 1) ;<br />
( 2) <br />
( 1) <br />
b = ( u - v S) / S = ( 331 - 30) / 1080 = 0. 279 m<br />
<br />
a = ( u + vS ) / S = ( 331 + 30) / 1080 = 0. 334 m<br />
( 2) <br />
<br />
u<br />
R =<br />
u -<br />
=<br />
394<br />
R =<br />
v R<br />
R = u + vR<br />
u - v S<br />
S<br />
u( u + vR )<br />
( u - vS ) ( u - vR ) S<br />
331( 331 + 65)<br />
( 331 - 30) ( 331 - 65) 1080 = 177103 Hz
a = u/ R = 331/ ( 17710 3 ) = 0187 m<br />
2. 25 120m, 10s <br />
24m / s ? <br />
? , ? <br />
?<br />
u= / T = 120/ 10= 12 m/ s<br />
, <br />
f = ( u + v) / = ( 24 + 12) / 120 = 0. 30 H z<br />
T f = 1/ f = 1/ 0. 30 = 3. 3 s<br />
, <br />
a = ( v - u) / = ( 24 - 12) / 120 = 0. 10 H z<br />
T a = 1/ a = 1/ 0. 10 = 10 s<br />
2. 26 , <br />
<br />
, ?<br />
= ( u- v S) T = ( u- vS) / S<br />
u- vS<br />
R=<br />
= u - v S<br />
u - v S= S<br />
S<br />
, <br />
, <br />
2. 27 , <br />
1. 810 4 Hz <br />
220Hz, 1. 54<br />
10 3 m / s<br />
S, <br />
S = u+ v<br />
u- v S <br />
= S - S =<br />
u + v<br />
u - v - 1 S =<br />
2v<br />
u -<br />
v S<br />
395
, uv, = 2v S / u, <br />
v = u / ( 2 S ) = 1. 5410 3 220/ ( 21810 4 )<br />
= 94 m / s<br />
2. 280. 32m/ s <br />
4. 0MHz , <br />
? 1. 5410 3 m/ s<br />
= 1 -<br />
=<br />
u - v<br />
u + v<br />
= 2v u + v =<br />
2v<br />
u<br />
20. 324. 0106<br />
1. 5410 3 = 1. 6610 3 H z<br />
2. 29 ,<br />
5. 010 10 H z<br />
, 1. 110 4 H z <br />
100km/ h<br />
= 2v / u <br />
v = u / ( 2 ) = 310 8 1. 110 4 / ( 2510 10 )<br />
= 33 m/ s = 119 km/ h > 100 km/ h<br />
<br />
2. 30 , <br />
2. 3 <br />
5000m , 330m/ s <br />
( 1) <br />
( 2) <br />
?<br />
( 1) 27 , <br />
( 2) tan = h / s= h/ ( vt)<br />
396<br />
= arcsin u v = arcsin 1<br />
2. 3<br />
= 25. 8<br />
t= h/ ( vt an ) = 5000/ ( 2. 3330tan 258 ) = 136 s
27230 <br />
<br />
, C <br />
<br />
2. 31, <br />
y 1 = Asin ( 5x - 10t)<br />
y 2 = A sin( 4x - 9t)<br />
: ( 1) , ;<br />
( 2) ;<br />
( 3) <br />
( 1) y = y 1+ y 2= A sin( 5x - 10t) + Asin( 4x - 9t)<br />
= 2Acos( 05x - 0. 5t) sin( 4. 5x - 9. 5t)<br />
( 2) vg= <br />
k = 10- 9<br />
5- 4 = 1 m/ s<br />
( 3) L= 1 2 2<br />
= = 2<br />
2- 1 k 1- k 2 5- 4 = 2 = 6. 3 m<br />
<br />
2. 32 ( <br />
, ) <br />
=<br />
k 2<br />
, <br />
<br />
u g= d<br />
dk = d<br />
dk ( k2 ) = 2 k 2<br />
k<br />
= 2<br />
k = 2u<br />
<br />
397
2. 33 , <br />
<br />
<br />
2 = <br />
2 p + c 2 k 2<br />
c , p <br />
u u g, uu g= c 2 <br />
u = <br />
k =<br />
, uug= c 2<br />
<br />
2 p+ c 2 k 2<br />
k<br />
, u g= d<br />
dk = d<br />
dk<br />
<br />
2 p+ c 2 k 2 =<br />
c 2 k<br />
<br />
2 p + c 2 k 2<br />
2. 34<br />
3/ 2 <br />
=<br />
c- v<br />
c+ v S , =<br />
c+ v<br />
c- v S= 3 2 S<br />
c+ v<br />
<br />
c- v = 3 2 , v= 5<br />
13 c= 12108 m/ s<br />
<br />
2. 352. 39 <br />
<br />
x =<br />
<br />
2<br />
<br />
x k = 2 ( 2. 351)<br />
t , , t<br />
= x / u g, <br />
t = 1 ( 2. 352)<br />
( ) , <br />
<br />
( 2. 351) ( 2. 352) , <br />
<br />
k <br />
, :<br />
398
y = y 1 + y 2<br />
= A sin( t - kx ) + Asin ( + ) t - ( k + k) x<br />
= 2Acos <br />
2 t - k<br />
<br />
x sin + t - k + k x<br />
2 2<br />
2<br />
cos , <br />
x <br />
<br />
<br />
x = 1 2<br />
2<br />
k/ 2 = 2<br />
k = 1<br />
x k =<br />
1 <br />
2<br />
u g= / k, x = u g t= <br />
k t<br />
<br />
<br />
x k =<br />
<br />
k t k = t =<br />
<br />
t = 1<br />
= <br />
2<br />
<br />
2<br />
t = 2<br />
2. 36 17 : <br />
<br />
( = ) [ ( 236) ] <br />
2. 8, Q 1 Q 2 <br />
( 1) 28 , A, B <br />
Q 1Q1<br />
, Q 1C= Q 1 C<br />
t Q 1<br />
A Q 2<br />
=<br />
Q 1A + AQ2<br />
c<br />
= Q 1 A + AQ2<br />
c<br />
Q 1 Q 2 B, Q 1 B Q 2 <br />
<br />
399
2. 82. 36 ( 1) <br />
t Q 1<br />
B Q 2<br />
=<br />
Q 1Q2<br />
Q 1B + BQ2<br />
c<br />
, Q 1BQ 2<br />
, = <br />
= Q 1 B + BQ 2<br />
c<br />
= Q Q 2<br />
< Q 1 A + AQ2<br />
c<br />
c<br />
Q 1 Q 2 , t Q B Q 1 2<br />
,<br />
, <br />
( 2) 29 , Q1 Q 2 <br />
400<br />
29236 ( 2)
t =<br />
Q 1A<br />
u 1<br />
+ AQ2<br />
u 2<br />
t , dt = 0, <br />
dx<br />
dt<br />
dx = x<br />
-<br />
h 2 1 + x 2 u 1<br />
<br />
<br />
=<br />
h 2 1 + x 2<br />
u 1<br />
D -<br />
x<br />
+<br />
h 2 2 + ( D - x ) 2 u<br />
sin<br />
sinr = u 1<br />
u 2<br />
h 2 2 + ( D - x ) 2<br />
u 2<br />
= sin -<br />
u 1<br />
sinr<br />
u 2<br />
= 0<br />
401
3 <br />
31589. 3nm10 -<br />
, <br />
<br />
= c t/ = 310 8 10 - 8 / ( 589. 310 - 9 ) = 510 6<br />
32<br />
d = 0. 60mm, D = 2. 5m, <br />
x = 2. 27mm , <br />
<br />
x = D d <br />
= d x / D = 06010 - 3 22710 - 3 / 25<br />
= 5. 4510 - 7 m = 545 nm, <br />
33 31 , = 7. 2<br />
10 - 7 m, <br />
8 s<br />
3. 133 <br />
x = 1 2<br />
D<br />
d = 1 30<br />
20+<br />
2 0. 22 7210- 7 m = 4. 510 - 5 m<br />
402
34 015mm, 10m <br />
1 10 36mm <br />
<br />
= d 3<br />
D 0. 3<br />
1510-<br />
x = 3610- 1. 0 10- 1<br />
= 6010 - 7 = 060 m<br />
35 30km , <br />
2010 5 Hz <br />
/ 2( <br />
) <br />
<br />
32 , <br />
= 2 dsin<br />
+<br />
<br />
2<br />
= 2 , <br />
3235 <br />
2 d sin + <br />
c 2 = 2<br />
sin = 2-<br />
1<br />
2<br />
c<br />
2d <br />
403
1<br />
2<br />
310 8<br />
= 1 23010 3 210 5 4 2- 1<br />
2<br />
= 2-<br />
<br />
-<br />
2 < < , - 1, 0, 1, 2, sin <br />
2<br />
- 5/ 8, - 1/ 8, 3/ 8, 7/ 8, - 39 ,<br />
- 72 , 22 , 61<br />
, <br />
<br />
36 ( = 632. 8nm) <br />
20m 1 <br />
14cm<br />
( 1) ;<br />
( 2) ?<br />
( 1) d = D<br />
9<br />
2. 0632. 810-<br />
= = 9. 010 - 6 m<br />
x 0. 14<br />
( 2) < = , <br />
2 2<br />
k = d sin / = D / x = 2. 0/ 0. 14 = 14. 3<br />
14 14 <br />
37 ( 35) , <br />
12cm, 50cm <br />
45cm25cm/ s, <br />
= x d<br />
D<br />
= u = uD<br />
x d = 2550<br />
4512 = 23 Hz<br />
38d , <br />
( 1) :<br />
d sin - d sin= k , k = 0, 1, 2, <br />
( 2) , <br />
404
3338 <br />
( 1) 33 , d sin -<br />
d sin, <br />
d sin - d sin = k , = 0, 1, 2, <br />
( 2) , sin , <br />
= k / d + sin<br />
= k+ 1 - k = [ ( k + 1) / d + sin ] - [ k / d + sin ] = / d<br />
<br />
, ( ) ,<br />
<br />
39 ,<br />
, <br />
60m <br />
, 98 MH z, <br />
( ) ? ( <br />
)<br />
, <br />
<br />
<br />
2 h 2 + D 2 / 4 - D = m , m = 0, 1, 2, 3, <br />
405
3439 <br />
D = 2h 2<br />
m -<br />
m<br />
2<br />
dD<br />
dm = - <br />
2h2 / ( m 2 ) - < 0, m , D D <br />
2<br />
m= 1 , <br />
D = 2h 2<br />
-<br />
<br />
2 = 2h2 c<br />
-<br />
c 2<br />
= 260 2 9810 6<br />
310 8 -<br />
310 8<br />
29810 6 = 2410 3 m<br />
310 , <br />
<br />
, ( 35) <br />
6010 7 H z, 25m <br />
<br />
35310 <br />
35 , <br />
406
=<br />
2 2hsin<br />
+ <br />
= ( 2k+ 1) , <br />
k= 1 <br />
sin=<br />
k = kc/ ( 2<br />
2h h)<br />
m in = arcsin c<br />
2 h = arcsin 310 8<br />
26010 7 25 = 57<br />
311<br />
=<br />
<br />
2d<br />
<br />
<br />
, <br />
I = I m axcos 2<br />
<br />
2<br />
I = I m a x/ 2 , cos 2<br />
<br />
<br />
=<br />
= / 2<br />
2 d sin / <br />
I = I m a x/ 2 , / 2= 2 d sin 1/ 2/ = 2 d 1/ 2/ ,<br />
1 / 2 = / ( 4d )<br />
<br />
2 = 1 2 <br />
, <br />
= 2 1 / 2 = / ( 2d )<br />
312180m, <br />
, ?<br />
= k , k= 1, 2, 3, <br />
407
= / k= 1. 80/ k m<br />
077 m 0. 35 m , 060 m, 045 m,<br />
036 m; 5010 1 4 H z, 6710 14 H z, 8310 14 H z<br />
31336 M 1<br />
<br />
, M 2 M 1, <br />
G , M 1<br />
M 2 <br />
45 , A 1A 2= 21<br />
6328nm<br />
3. 6313 <br />
36 , <br />
, <br />
x =<br />
<br />
V = I m a x - I m in<br />
I m a x + I m in<br />
/ cos45 = 632. 8 2 = 895 n m<br />
= ( 2 + 1) 2 - ( 2 - 1) 2<br />
( 2 + 1) 2 + ( 2 - 1) 2 = 08<br />
314 = 6328nm, <br />
( ) = 1310 9 H z<br />
? ?<br />
L = <br />
2 / = c/ <br />
408<br />
= 310 8 / ( 1310 9 ) = 023 m
= L/ c= 1/ = 1/ ( 1310 9 )<br />
<br />
= 7710 - 10 s<br />
315 10 -<br />
2 rad, <br />
550nm , <br />
? <br />
d 0= / 0= 55010 - 9 / 10 - 2 = 5510 - 5 m = 55 m<br />
316 , <br />
7 <br />
= 550n m, = 158, <br />
t, S 2<br />
7 <br />
r 1- r 2= 7, <br />
r 1- ( t+ r 2- t) = 0<br />
t = 7 / ( - 1) = 755010 - 9 / ( 158 - 1)<br />
= 6610 - 6 m = 66 m<br />
317, = 152 = 5893nm <br />
, L= 50mm, <br />
Lsin = / ( 2) <br />
sin=<br />
/ ( 2L)<br />
= 589310 - 9 / ( 21525010 - 3 )<br />
= 3910 - 5 rad = 8<br />
318 , <br />
, , <br />
, Si 342, SiO 2<br />
15, 5893nm, 7 ( 37<br />
) SiO 2<br />
e ?<br />
2e= ( 2k+ 1) / 2 <br />
e = ( 2k +<br />
1) / ( 4)<br />
= ( 26 + 1)589310 - 9 / ( 415)<br />
409
37318 <br />
= 12810 - 6 m = 128 m<br />
319, <br />
, , <br />
38 , G1 , G2 G1 <br />
, <br />
5893nm ,<br />
<br />
;<br />
( 1) L = 050mm, G1, G2 <br />
( 2) G2 G1 ?<br />
( 3) L 1 = 050mm, L 2 = 030mm , <br />
G 2 ? G2<br />
?<br />
, <br />
38319 <br />
410
( 1) 38 , , <br />
G 1G 2 <br />
h = l = l / ( 2L)<br />
= / ( 2L)<br />
= 005589. 310 - 9 / ( 20. 5010 - 3 )<br />
= 2. 9510 - 5 m<br />
( 2) G2 , , G2 G 1<br />
; , G2 G1 <br />
( 3) L 2< L 1, G2 2 G1 1, <br />
G 2 , G2<br />
, G 2 G1<br />
<br />
<br />
, , 1= 2= 0, <br />
320, 04 m, 150, <br />
, , ? <br />
?<br />
<br />
=<br />
2e -<br />
/ 2 = k , k = 0, 1, 2, <br />
4e<br />
2k + 1 = 41500410 - 6<br />
2k + 1<br />
, k= 2, = 480nm , <br />
<br />
2e = k , k = 1, 2, 3, <br />
=<br />
2. 410-<br />
6<br />
2k + 1<br />
= 2e/ k = 21500410 - 6 / k = 1. 210 - 6 / k<br />
, k= 2, = 600nm ; k= 3, = 400nm , <br />
321 , ( = 15) <br />
, ( = 20) <br />
560nm , ?<br />
, <br />
m<br />
411
2e+ / 2= kk= 1 <br />
emin<br />
= / ( 4) = 56010 - 9 / ( 42. 0)<br />
= 7. 010 - 8 m = 70 nm<br />
322( = 15) ( = 132) , <br />
485nm ,<br />
679nm , <br />
<br />
, , <br />
2e= ( 2k+ 1) / 2<br />
=<br />
2e = ( 2k + 1) 1/ 2 = ( 2k - 1) 2/ 2<br />
2 1<br />
2e( 2 - 1) = 679485<br />
2132( 679 - 485)<br />
= 643 nm<br />
323 133 , 45 <br />
( 500n m) , <br />
, ?<br />
, <br />
k= 1 <br />
emi n =<br />
2e 2 - sin 2 + / 2 = k , k = 1, 2, 3, <br />
<br />
4 2 - sin 2 = 50010 - 9<br />
4 1. 33 2 - sin 2 45 = 11110- 7 m<br />
, 2e= / 2<br />
= 4e = 41. 331. 1110 - 7<br />
= 5. 910 - 7 m = 590 nm, <br />
324 1= 152 2 =<br />
138 MgF 2<br />
?<br />
, = 550nm , <br />
<br />
412<br />
2e -<br />
/ 2 = k , k = 0, 1, 2,
e = k + 1 2<br />
<br />
2 = k + 1 - 9<br />
2 55010 2138<br />
= ( 1993k + 99. 6)10 - 9 m<br />
e= 996 nm<br />
32539 <br />
<br />
39325 <br />
<br />
, 162, <br />
, <br />
, , <br />
39 <br />
326 310( a) ( b) <br />
, <br />
( ) <br />
310( a ) , k= 0<br />
/ 2, 11 / 4= 5 / 2+ / 4, 5 , k<br />
= 1, 2, 3, 4, 5, 310( b ) , <br />
, k= 0, 5 , = 1, 2, 3, 4, 5,<br />
, 310( b ) <br />
413
310326 <br />
327 , <br />
300mm , 5 460mm, <br />
103m, <br />
r 2 k= 2k- 1 Rr k 2 + 5=<br />
2<br />
= r 2 k+ 5 - r 2 k<br />
5R<br />
= d 2 k + 5 - d 2 k<br />
20R<br />
= 5. 9010 - 7 m = 590 nm<br />
2( k+ 5) - 1<br />
R<br />
2<br />
= ( 4. 6010 - 3 ) 2 - ( 3. 0010 - 3 ) 2<br />
20103<br />
328 , d <br />
, ?<br />
, <br />
2( - 1) d <br />
329 , <br />
L = 03220mm , <br />
1204 , <br />
L= N / 2, <br />
= 2L/ N = 20322010 - 3 / 1204<br />
= 5. 34910 - 7 m = 534. 9 n m<br />
330 ( 329) , <br />
414
M 1 M2 , <br />
( G1<br />
M1<br />
) , <br />
, <br />
M 1 , M 1 <br />
02073mm 15140, <br />
<br />
M 1<br />
, <br />
, M1 M1 <br />
, <br />
<br />
2l = 2( - 1) d<br />
d = l/ ( - 1) = 0. 2073/ ( 1. 5140 - 1) = 0. 4033 mm<br />
331 <br />
, 311 S , L , G1,<br />
G 2 , , T 1, T 2 <br />
, d , , <br />
, E , <br />
, T 2<br />
, <br />
, E 98 <br />
= 5893nm , d = 20cm, <br />
3. 11331 <br />
415
, <br />
N , <br />
<br />
( - 1) d = N <br />
= N <br />
d + 1 = 98589310- 9<br />
2010 - 2 + 1 = 100029<br />
416
4 <br />
41 , a = 010mm, 50cm<br />
, = 546. 1nm , <br />
<br />
x = 2f tan 12f sin 12f 1= 2f / a<br />
= 25010 - 2 ( 546110 - 9 ) / ( 0110 - 3 )<br />
= 5. 4610 - 3 m<br />
42 = 632. 8nm , <br />
1 5 , <br />
a sin 1= , <br />
a = / sin 1 = 632. 810 - 9 / sin5 = 7. 2610 - 6 m<br />
43, 3 <br />
600nm 2 <br />
, <br />
a sin = ( 2k+ 1) / 2 , <br />
( 23 + 1) 1/ 2 = ( 22 + 1) 2/ 2<br />
1 = 5 2/ 7 = 5600/ 7 = 429 nm<br />
4420m 50m <br />
?<br />
a sin 1= , <br />
2 1 = 2arcsin( / a ) = 2arcsin( 20/ 50) = 47<br />
45, <br />
<br />
HeNe , <br />
417
6328nm, 265m <br />
137mm , 10 ?<br />
a sin k= k<br />
l = 2D k = 2D arcsin k<br />
a<br />
= 2265arcsin 10632810- 9<br />
13710 - 3<br />
= 2. 4510 - 2 m<br />
46, <br />
<br />
( 1) 70mm, 550nm <br />
?<br />
?<br />
( 2) 23mm <br />
( 3) ( 025mm) <br />
1510 5<br />
( 1) <br />
= 2 1 = 2122 / D<br />
?<br />
= 21. 2255010 - 9 / ( 7010 - 3 ) = 1910 - 4 rad<br />
( 2) <br />
D i = l = 1. 910 - 4 23 = 4. 410 - 3 mm<br />
( 3) <br />
N =<br />
D 2 i / 4 =<br />
( 4410 - 3 ) 2 1. 510 5 / 4 = 23( )<br />
47 3510 4 k m <br />
, <br />
10cm, <br />
15km? <br />
?<br />
418
sin 1= 1. 22 / D 1, <br />
<br />
= 2 1 = 2arcsin( 1. 22 / D 1)<br />
= 2arcsin [ 1. 2201/ ( 1510 3 ) ]<br />
= 1. 610 - 4 rad<br />
41 <br />
D 2 = r + D 1 = 3. 510 7 1610 - 4 + 1. 510 3<br />
= 7. 110 3 m<br />
4147 <br />
48( 414) , <br />
, <br />
( ) , <br />
<br />
( 1) <br />
, <br />
( 2) 05 <br />
5 , ? 450n m<br />
<br />
419
( 1) , <br />
( ) <br />
, , <br />
, <br />
<br />
( 2) 1 ,<br />
<br />
=<br />
D = 2122 v/ <br />
2 1 = 2122 v/ D<br />
= 212245010 - 9 / ( 505<br />
/ 180)<br />
= 2. 510 - 5 m<br />
49, 120cm <br />
, ? <br />
50mm, 550nm , <br />
<br />
c= d / l= 1. 22 / D <br />
l = d D / ( 1. 22 ) = 1. 200. 510 - 3 / ( 12255010 - 9 )<br />
= 8. 910 3 m<br />
410<br />
<br />
( 1) 5cm, <br />
160km ?<br />
( 2) ? 500nm <br />
( 1) <br />
c = d / l = 510 - 2 / ( 16010 3 ) = 310 - 7 rad<br />
( 2) <br />
D = 1. 22 / c = 1. 2250010 - 9 / ( 310 - 7 ) = 2 m<br />
411 ( <br />
420
425) 300m, 300m <br />
4cm , <br />
?<br />
c = 1. 22 / D = 122410 - 2 / 300= 1. 610 - 4 rad<br />
= 0. 56<br />
412 , <br />
( 10 4 km) <br />
, ( <br />
) <br />
10 4 km, , <br />
?<br />
= 5cm, <br />
c / d = 510 - 2 / 10 7 = 510 - 9 rad 110 - 3 <br />
413 750 7, <br />
50mm <br />
( 1) , ? <br />
550nm<br />
( 2) 70mm<br />
, 7, , <br />
<br />
( 1) c =<br />
1. 22 / D = 12255010 - 9 / ( 5010 - 3 )<br />
= 1310 - 5 rad<br />
( 2) c = 1. 22 / D = 12255010 - 9 / ( 710 - 3 )<br />
= 9610 - 5 rad<br />
c / 7= 13710 - 5 rad<br />
c / 7> c, , ,<br />
<br />
414 484<br />
421
10 - 6 rad, 550nm <br />
, ?<br />
D = 1. 22 / c = 1. 2255010 - 9 / ( 48410 - 6 )<br />
= 0139m<br />
<br />
415 <br />
05<br />
( 1) 01mm, 550nm <br />
, ?<br />
?<br />
( 2 ) 001mm , , <br />
( 3) 01mm , ?<br />
1= / d <br />
( 1) 1 = / d = 55010 - 9 / ( 0110 - 3 ) = 5. 510 - 3 rad<br />
= 03 < 05 , ;<br />
( 2) 1 = / d = 55010 - 9 / ( 00110 - 3 ) = 5. 510 - 4 rad<br />
= 3 > 05 , ;<br />
( 3) 1 = re d/ d = 7510 - 7 / ( 0110 - 3 ) = 7. 510 - 3 rad<br />
= 04 < 05 , <br />
416 , d = 0. 10mm, a = 002mm, <br />
= 480n m , <br />
50cm , :<br />
( 1) ;<br />
( 2) ;<br />
( 3) <br />
( 1) <br />
x = f / d = 5010 - 2 48010 - 9 / ( 01010 - 3 )<br />
= 2410 - 3 m<br />
( 2) <br />
422
x = 2f / a = 25010 - 2 48010 - 9 / ( 00210 - 3 )<br />
= 2410 - 2 m<br />
( 3) <br />
N =<br />
x <br />
x - 1 = 24<br />
2. 4 - 1 = 9<br />
41742 , <br />
:<br />
42417 <br />
423
( 1) ? ?<br />
( 2) a ? ( )<br />
( 3) d / a ? ?<br />
( 4) / d / a <br />
( 1) , <br />
N , N - 1 , 42 , ( a ) <br />
; ( b ) ; ( c) ; ( d) <br />
( 2) , sin a = / a , ( c) <br />
<br />
( 3) ( a ) d / a = sin d/ sin = 2, 2 ;<br />
( b ) d / a = 4, 4 ;<br />
( d ) d / a = 3, 3 <br />
( 4) 42<br />
418, 20cm, 6000 <br />
, ?<br />
<br />
= arcsin( k / d ) = arcsin ( k l/ N )<br />
= arcsin( k589310 - 9 2010 - 2 / 6000)<br />
= arcsin( 01768k)<br />
sin 1, k = 0, 1, 2, 3, 4, 5 0 ,<br />
10 11 , 20 42 , 32<br />
, 45 , 62 7<br />
4196000 ,<br />
1 20 , 2 <br />
?<br />
= d sin 1 = 10 - 2 sin20 / 6000<br />
424<br />
= 5. 7010 - 7 m = 570 nm<br />
2 = arcsin ( 2 / d )<br />
= arcsin ( 25. 7010 - 7 6000/ 10 - 2 )
= 43. 2<br />
4204000 , <br />
?<br />
k k r= ( k+ 1) v<br />
k =<br />
v/ ( r - v) = 400/ ( 750 - 400) = 1. 1<br />
k 1, 1 <br />
, , <br />
<br />
r =<br />
arcsin( r/ d ) = arcsin( 75010 - 9 4000/ 10 - 2 ) = 17. 5<br />
421 3000 , 555nm <br />
30 , <br />
d ( sin - sin) = k , , = 0, <br />
k = -<br />
d sin/ = - 10 - 2 sin 30 / ( 55510 - 9 3000) = - 3<br />
3 <br />
422 600nm , 2, 3<br />
sin = 020 sin = 030 , 4 <br />
:<br />
= 10<br />
( 1) ;<br />
( 2) ;<br />
( 3) <br />
( 1) d = 2 / sin 2= 260010 - 9 / 0. 2= 6. 010 - 6 m<br />
( 2) d / a = 4, a = d / 4= 1510 - 6 m<br />
( 3) m ax =<br />
km ax = dsin ma x/ <br />
2 = 6. 6 010- / ( 60010 - 9 )<br />
0, 1, 2, , 9( km ax )<br />
423 = 656. 3nm , <br />
= 0. 18nm 1 <br />
425
, <br />
/ = kN <br />
N =<br />
/ ( k ) = 656. 3/ ( 1018) = 3646<br />
424 60cm, 6000 , 3<br />
, = 500nm, ?<br />
= / ( kN ) = 50010 - 9 / ( 3606000)<br />
= 4. 610 - 12 m = 0. 0046 nm<br />
425<br />
28 ( 427, ) <br />
( <br />
) , <br />
232MHz 6m,<br />
192 <br />
? <br />
<br />
? <br />
?<br />
, <br />
<br />
dsin = m / N , m= 1 <br />
<br />
= arcsin( / ( N d ) ) = c/ ( N d )<br />
= 310 8 / ( 19262. 3210 8 )<br />
= 1. 1210 - 3 rad = 3. 85<br />
d sin = m , m= 1 <br />
<br />
= arcsin( / d ) = arcsin( 310 8 / ( 62. 3210 8 ) )<br />
= 0. 217 rad = 12. 4<br />
426
426 420 , = 45 , X <br />
0095nm 0130nm d =<br />
0275nm, X ? , <br />
X ?<br />
<br />
2d sin = k X <br />
= 2dsin / k = 20275sin 45 / k = 0389/ k nm<br />
<br />
3 = 0389/ 3 = 0130 nm<br />
4 = 0389/ 4 = 0097 nm<br />
4271927 <br />
( ) <br />
= 50 ( 43) <br />
d = 0215nm, <br />
<br />
43427 <br />
43 , <br />
= d sin<br />
= = d sin = 0215sin50 = 0165 nm<br />
4. 1444 , <br />
P <br />
( A) , ( B, <br />
427
) : P <br />
( <br />
) <br />
44414 <br />
44 , , <br />
, <br />
E 1 , <br />
, <br />
E 2 <br />
, 44 , E 0 <br />
, <br />
, , <br />
E 0 = E 1 + E 2<br />
<br />
<br />
44 , a , ( <br />
) , E 0= 0, <br />
<br />
428<br />
E 1 = - E 2
I 1 = I 2<br />
( <br />
) 45 , ( a) ( b) , ( a1) <br />
( b1) , , <br />
45<br />
429
5 <br />
51 60 , <br />
I 1, <br />
30, ?<br />
I 0, <br />
I 0/ 22 I 0cos 2 60 / 2= I 1<br />
I 0 =<br />
2I 1/ cos 2 60 = 8I 1<br />
, <br />
I = 1 2 I 0cos2 30 cos 2 30 = 1 2 8I 1 3 4 3 4 = 9 I 1 = 2. 25I 1<br />
4<br />
52<br />
( 1) , ( 2) ,<br />
?<br />
( 1) , , , <br />
I 0/ 2( I 0/ 2) / 3 , <br />
<br />
I 0cos 2 / 2 = ( I 0/ 2) / 3<br />
= arccos<br />
( 2) I <br />
<br />
1<br />
3 = 54 44<br />
I = I 0cos 2 / 2 = I 0/ 3<br />
430<br />
= arccos<br />
2<br />
3 = 35 16
53P 1 P 2 ( 51) <br />
I 0<br />
P 1, P 2 ,<br />
P 2 ?<br />
5. 153 <br />
52 , y , E 1<br />
<br />
5253 <br />
431
P 1 , z OA P 2 <br />
, E 1<br />
<br />
, P 2 E 1 OA ( xz <br />
) , <br />
cos=<br />
OC<br />
OA <br />
= OC<br />
OC 2<br />
+ OB<br />
= cos<br />
2<br />
cos 2 + sin 2 cos 2 <br />
P 2<br />
E 2<br />
= E 1cos= E 1cos / cos 2 + sin 2 cos 2 <br />
<br />
I 2 = E 2 2 = E 2 1cos 2 / ( cos 2 + sin 2 cos 2 )<br />
= 1 2 I 0cos2 / ( cos 2 + sin 2 cos 2 )<br />
5453 , <br />
, 0<br />
, 0, <br />
<br />
53 <br />
5. 354 <br />
55133, 150, <br />
432
, ? <br />
, ? ?<br />
, <br />
0, 12 = arct an 2<br />
, <br />
t an 0 , 12 = 2<br />
<br />
1<br />
0, 21 = arct an 1<br />
1<br />
2<br />
= arct an 1. 5<br />
1. 33 = 48 26<br />
= arct an<br />
1. 33<br />
1. 50 = 41 34<br />
= ( tan 0 , 21 ) - 1 , 0, 12 + 0, 2 1 = / 2, <br />
56 45 , <br />
?<br />
sin = 2/ 1<br />
<br />
0<br />
= arctan 2<br />
1<br />
= arctan( sin ) = arctan( sin45 ) = 35 16<br />
57<br />
0= 58 , <br />
t an0= 2/ 1<br />
<br />
2 = 1t an0 = 1. 00t an58 = 1. 60<br />
58,<br />
, ?<br />
= arctan<br />
, = 0 = arct an 2 1<br />
1. 33<br />
1. 00 = 53 4 = 90 - = 36 56<br />
59<br />
, 53 , e <br />
433
, , o <br />
<br />
e r e = 90 - 60 = 30e <br />
, sin= esinr e<br />
= arcsin ( esinr e) = arcsin ( 1. 4864sin30 ) = 48<br />
r o o , osinr o= sin, <br />
r o<br />
= arcsin( sin/ o) = arcsin( sin48 / 16584) = 26 37<br />
o o = 60 - r o= 33 23o <br />
osino = sinr o <br />
o 54 <br />
r o = 65 51<br />
5459 <br />
510 ABCD 45<br />
( 55<br />
) , ABD AB, BCD <br />
A B , o e <br />
<br />
434<br />
55510
55 <br />
<br />
511 56 , P 1, P 2<br />
<br />
C , P 1 60<br />
I i P 1<br />
, P 2<br />
( 1) , , ;<br />
( 2) <br />
( 1) 56 , P 1<br />
<br />
, C <br />
A 1<br />
5. 6511( 1) <br />
( 2) P 1 I 1= I i/ 2, A 1( 57) , C <br />
A e = A 1cos , A o = A 1sin , / 2, <br />
A 2<br />
A 2 2 = A 2 e + A 2 o + 2A eAocos( / 2) = A 2 1cos 2 + A 2 1sin 2 = A 2 1<br />
57511( 2) <br />
<br />
435
P 2<br />
I 2 = I 1 = I i / 2<br />
A 3e= A e sin = A 1cos sin ,<br />
A 3o= A ocos = A 1sin cos / 2+ , <br />
<br />
A 2 3 = A 2 3e + A 2 3o + 2A 3eA3ocos<br />
= 2A 2 1sin 2 cos 2 =<br />
<br />
2 + <br />
2A 2 1sin 2 60 cos 2 60 = 3A 2 1/ 8<br />
I 3 = 3I 1/ 8 = 3I i/ 16<br />
512 6328n m o= 1. 66, e =<br />
1. 49, ?<br />
?<br />
d mi n( o- e ) = / 4, <br />
d mi n<br />
= / [ 4( o - e ) ]<br />
= 6328/ [ 4( 1. 66 - 1. 49) ] = 931 nm<br />
<br />
<br />
513 o e <br />
, 800nm 400nm <br />
, 45<br />
, ?<br />
d ( o- e ) = 1/ 4= 2 2/ 4= 2/ 2, 800 nm( 1)<br />
, 400nm ( 2) <br />
<br />
, <br />
45, <br />
, , <br />
, , <br />
<br />
514 1823 <br />
436
( <br />
155) , 58 <br />
, <br />
, <br />
? ( <br />
51 )<br />
5. 8514 <br />
<br />
22 , o <br />
r o =<br />
arcsin<br />
o <br />
o <br />
sin 22<br />
= 13. 1<br />
1. 658<br />
= 90 - 131 = 76. 9<br />
= arcsin<br />
1. 55<br />
1. 658<br />
= 69. 2<br />
> , o <br />
e , , , <br />
e ( 1486) , <br />
<br />
437
5153968nm <br />
R = 1. 55810, L = 1. 55821 <br />
<br />
= ( L - R) / <br />
= ( 1. 55821 - 1. 55810) / ( 396. 810 - 9 )<br />
= 0. 870910 3 rad/ m = 49. 9 / mm<br />
516, <br />
, <br />
<br />
+ x - x , y z <br />
x = 0 , y 45<br />
+ x / 8 , <br />
<br />
, x<br />
= / 8 , , + x / 4, <br />
- x / 4 /<br />
2( x ) x =<br />
/ 4 , x = 3 / 8<br />
x = / 2 <br />
, 59<br />
59516 <br />
438
5 <br />
1 <br />
11<br />
- 5, , <br />
?<br />
<br />
M =<br />
T 4 = 5. 6710 - 8 268 4 = 292 W / m 2<br />
12 M m =<br />
3. 410 14 H z ( 1) ( 2) <br />
M<br />
( 1) m = CT , <br />
T =<br />
m / C= 3. 410 14 / ( 5. 8810 10 ) = 5. 810 3 K<br />
( 2) M= T 4 = 5. 6710 - ( 8 5. 810 3 ) 4 = 6410 7 W / m 2<br />
13, 1010 3 W / m 2 <br />
, <br />
? <br />
T =<br />
, , I = T 4<br />
4<br />
I / =<br />
4<br />
1010 3 / ( 56710 - 8 ) = 364 K = 91<br />
14P S = 3910 26 W ( 1) r <br />
: <br />
T <br />
439
T 4 =<br />
P S<br />
16 r 2<br />
( ) ( 2) <br />
, r E= 1510 11 m, <br />
r P = 5910 12 m<br />
( 1) R , P a b=<br />
P S<br />
R 2 , <br />
4 r 2<br />
P e j= T 4<br />
4 R 2 P ab = P e j,<br />
T 4 =<br />
P S<br />
16 r 2<br />
P S<br />
4 r 2 R 2 = T 4<br />
4 R 2<br />
( 2) T E=<br />
3. 910 26<br />
1/ 4<br />
= 279<br />
1656710 ( 8 1510 11 ) 2 K<br />
T P =<br />
3. 910 26<br />
1 / 4<br />
= 45<br />
1656710 ( 8 5910 1 2 ) 2 K<br />
15Procyon B 11 l. y. , <br />
1710 -<br />
<br />
1 2 W / m 2 , 6600K <br />
r = 9. 4610 15 11= 1. 0410 1 7 m <br />
, <br />
<br />
D = 2R = 2<br />
= 2. 610 7 m<br />
I 4 r 2 = T 4 4 R 2<br />
I r 2<br />
= 2 1. 710 - 12 ( 1. 0410 17 ) 2<br />
T 4 5. 6710 - 8 ( 6600) 4<br />
16<br />
3K <br />
( 1) M?<br />
( 2) ?<br />
( 1) m= CT = 58810 10 3= 17610 11 Hz<br />
( 2) P = M4 R 2 E= 4 T 4 R 2 E<br />
440
= 456710 -<br />
8 3 4 ( 6410 6 ) 2 = 2. 3610 9 W<br />
17[ <br />
( 13) ] , <br />
M=<br />
2 hc2<br />
e M ©¦ d ©¦= M d<br />
d<br />
M = M <br />
d =<br />
= 2 hc2<br />
e 1<br />
5 hc / ( <br />
1<br />
5 hc / ( <br />
2 h<br />
3<br />
c 2 ( e h / ( kT ) - 1)<br />
kT )<br />
- 1<br />
kT ) - 1<br />
c<br />
=<br />
<br />
2<br />
2 hc 3<br />
c 2 <br />
3 hc / ( <br />
( e kT ) - 1)<br />
c<br />
<br />
2<br />
18w <br />
w M <br />
<br />
M =<br />
c 4 w <br />
c <br />
11 <br />
, dV dV<br />
d dVd / ( 4 ) <br />
dS dV dS cos / r 2 , dV <br />
dS dN = dVdScos / ( 4 r 2 ) dV =<br />
1118 <br />
441
2 sin drd d <br />
dN = r 2 sin dr d dScos<br />
4 r 2<br />
= <br />
sin cos drd d dS<br />
4<br />
dt , rcdt dS dS<br />
, dt dS <br />
N = dN = <br />
c dt<br />
0<br />
dr <br />
2<br />
<br />
2<br />
d<br />
0 0<br />
dsin cos d<br />
dS<br />
4 =<br />
c 4 dSdt<br />
E , <br />
, , <br />
M =<br />
E N <br />
=<br />
dS dt<br />
c E <br />
= c 4 4 w <br />
w = E , <br />
<br />
<br />
19 [ ( 13) ] <br />
m = CT<br />
( : m/ T , C )<br />
m , <br />
d 2 h<br />
3<br />
dc 2 ( e h / ( kT ) - 1) <br />
=<br />
= m<br />
2 h <br />
2 m<br />
e h <br />
c 2 ( e h m / ( kT ) - 1) 2 m / ( k T ) 3 -<br />
h m<br />
kT - 3 = 0<br />
m m= 0, <br />
e h m / ( k T ) 3 -<br />
h m<br />
kT - 3 = 0<br />
m/ T C , <br />
m/ T = C<br />
( h m/ ( kT ) = x , e x ( 3- x ) - 3= 0, <br />
x = 2822C= 2822k/ h= 58810 10 H z/ K )<br />
<br />
110[ ( 13) ] 0 <br />
442
M = T 4<br />
( : M/ T 4 , )<br />
M = <br />
M 0 d <br />
= 2 h 3 d<br />
0 c 2 ( e h / ( kT ) - 1)<br />
h / ( kT ) = x , <br />
M =<br />
2 k 4<br />
T 4<br />
c 2 h 3<br />
<br />
0<br />
x 3 dx<br />
e x - 1<br />
, <br />
M = T 4<br />
k, c, h <br />
( <br />
4 / 15 = 2<br />
5 k 4 / ( 15c 2 h 3 ) = 5. 6710 - 8<br />
W / m 2 K 4 )<br />
, :<br />
111 4. 2eV, 200nm <br />
( 1) ;<br />
( 2) ;<br />
( 3) <br />
( 1) E k, m = h - A= h c <br />
- A<br />
= 6. 6310- 34 310 8<br />
20010 - 9 1610 - 19 - 42= 2. 0 eV<br />
( 2) U c= E k, m / e= 2. 0/ 1= 2. 0 V<br />
( 3) 0 = c = hc<br />
0 A<br />
= 6. 6310 - 3 4 310 8<br />
4. 21610 - 19 = 29610 - 7 m= 296 nm<br />
11210 - 1 5 J/ m 3 ,<br />
? 500nm<br />
443
N = w h<br />
= w<br />
hc = 10 - 15 50010 - 9<br />
= 2. 510 3 / m 3<br />
66310 - 34 310 8<br />
113 10W 10m <br />
( 225eV) <br />
, ? <br />
1310 -<br />
10 m( ) ? ( <br />
, 10 -<br />
, <br />
<br />
t =<br />
A =<br />
P<br />
r 2 t<br />
4 R 2<br />
9 s )<br />
4R2 A<br />
P r 2 = 41 2 2. 251. 610 - 19<br />
1. 0( 1. 310 - 1 0 ) 2 = 85 s<br />
1145eV c/ 2<br />
, <br />
?<br />
S O , <br />
+ x , 0x > 0 + x u<br />
= c/ 2 , - x u= c/ 2 <br />
, <br />
<br />
=<br />
1 - u/ c<br />
1 + u/ c 0<br />
h =<br />
1 - u/ c<br />
1 + u/ c h 0 = 1 - 1/ 2<br />
1 + 1/ 2 5 = 5<br />
3<br />
= 2. 9 eV<br />
115X 060MeV <br />
20% <br />
, =<br />
444
12 0, <br />
E = hc/ = hc/ ( 1. 2 0) = h 0/ 1. 2 = E 0/ 1. 2<br />
, <br />
E e = E 0 - E 0/ 1. 2 = E 0/ 6 = 0. 60/ 6 = 0. 10 MeV<br />
1164010 3 eV ,<br />
?<br />
, <br />
= 0+ 2h/ ( mec) , <br />
E = hc = hc<br />
0 + 2h/ ( m ec) = hc<br />
hc/ E 0 + 2h/ ( mec) = E 0me c 2<br />
m ec 2 + 2E 0<br />
, , <br />
E e = E 0 - E = E 0 1 -<br />
= 4. 010 3 1 -<br />
m ec 2<br />
mec 2 + 2E 0<br />
0. 51110 6<br />
051110 6 + 2410 3 = 62 eV<br />
117 : <br />
<br />
, <br />
, <br />
m 0c 2<br />
+ h = mc 2<br />
mv = h / c<br />
h , <br />
m 0 = m( 1 - v/ c) =<br />
m0( 1 - v/ c)<br />
1 - v 2 / c 2 = 1 - v/ c<br />
1 - v 2 / c 2<br />
v= 0 v= c, <br />
<br />
<br />
445
118 5010 4 eV 20<br />
10 4 eV <br />
?<br />
E p , E e p e<br />
, <br />
<br />
<br />
E 0 + E e 0 = E + E e<br />
p 0 - p e 0 = - p + p e<br />
p 0<br />
= E 0/ c, p = E / c<br />
p e 0 = 1 c<br />
E 2 e0 - ( m ec 2 ) 2 , p e = 1 c<br />
E 2 e - ( m ec 2 ) 2<br />
, , <br />
E e =<br />
2E 0 + E e 0 - E 2 e0 - m 2 e c 4 2<br />
+ m<br />
2<br />
e c 4<br />
2 2E 0 + E e 0 - E 2 e0 - m 2 e c 4<br />
mec 2 = 5. 1110 5 eV , E e 0= E k0 + mec 2 = 2. 010 4 + 5. 1110 5<br />
= 5. 3110 5 eV , E 0= 510 4 eV , <br />
E e = {[ 25. 010 4 + 5. 3110 5<br />
- ( 5. 3110 5 ) 2 - ( 5. 1110 5 ) 2 ] 2 + ( 5. 1110 5 ) 2 }<br />
/ {2[ 25. 010 4 + 5. 3110 5<br />
- ( 5. 3110 5 ) 2 - ( 5. 1110 5 ) 2 ] }<br />
= 51210 5 eV<br />
<br />
E ek = E e - m ec 2 = 51210 5 - 51110 5 = 0110 4 eV<br />
<br />
E = E 0 + E e 0 - E e = 510 4 + 53110 5 - 51210 5<br />
= 6910 4 eV<br />
446
119 020nm <br />
?<br />
<br />
<br />
E e = ( pc) 2 + ( m0c 2 ) 2<br />
p = h/ = 6. 6310 - 34 / ( 0. 2010 - 9 )<br />
= 3. 3210 - 24 kg ¡¤m/ s<br />
= ( 3. 3210 - 24 310 8 ) 2 + ( 0. 91110 - 30 910 16 ) 2<br />
= 8. 1910 - 14 J = 5. 1210 5 eV<br />
<br />
E = p c = 3. 3210 - 24 310 8<br />
= 9. 910 - 16 J = 6. 1910 3 eV<br />
120( 300 K ) <br />
<br />
<br />
E k = 3 2 kT = 3 2 13810 - 2 3 300 = 62110 - 21 J<br />
<br />
E 0 = mnc 2 = 16710 - 27 910 1 6 = 15010 - 10 J<br />
E kE 0, <br />
=<br />
h<br />
2mnE k<br />
=<br />
66310 - 34<br />
216710 - 2 7 62110 - 21<br />
= 14610 - 10 m = 0. 146 nm<br />
12140keV <br />
?<br />
40k eV 511k eV , <br />
<br />
447
=<br />
h<br />
2me E k<br />
=<br />
= 6110 - 12 m<br />
66310 - 34<br />
209110 - 30 410 4 1610 - 1 9<br />
122 m =<br />
m 0/<br />
1- v 2 / c 2 = E / h = mc 2 / h = h/ p = h/ ( mv) , <br />
v g v<br />
v g= d<br />
dk = d<br />
d( 1/ )<br />
d = d( mc 2 / h) = c2<br />
h dm<br />
d<br />
1<br />
= d mv<br />
h<br />
vg =<br />
=<br />
= 1 h<br />
d<br />
d( 1/ ) = c2<br />
h<br />
dm<br />
c 2<br />
dv<br />
v dm<br />
dv + m<br />
m = m0/ 1 - v 2 / c 2<br />
<br />
dm<br />
dv =<br />
m 0v<br />
c 2 ( 1 - v 2 / c 2 ) 3/ 2<br />
v g= v<br />
( vdm + mdv)<br />
dm/ [ ( vdm + mdv) / h ]<br />
123r <br />
, <br />
<br />
<br />
<br />
L = mer v = h, = 1, 2, 3, <br />
<br />
448
2 r = , = 1, 2, 3, <br />
= h/ ( mev) , <br />
m evr = h/ ( 2 ) = h<br />
L mevr, <br />
L = m evr = h<br />
124 <br />
10 -<br />
1 2 m050kg <br />
, , ?<br />
v =<br />
x = 210 -<br />
p<br />
m =<br />
12 m<br />
h<br />
2m x = 1. 0510 - 34<br />
= 5. 310 - 23 m/ s<br />
20. 5210 - 12<br />
125 9kV , <br />
050mm , 030m<br />
?<br />
y = 0. 50mm<br />
p x = 2meE<br />
<br />
d = 2 p y<br />
l =<br />
=<br />
p x<br />
h l<br />
yp x<br />
=<br />
y<br />
p y = h / ( 2 y )<br />
h l<br />
2meE<br />
10510 -<br />
34 030<br />
0510 - 3 29110 - 31 910 3 1610 - 19<br />
= 1. 210 - 9 m = 1. 2 nm<br />
<br />
, <br />
d = 2 l =<br />
1. 22<br />
2 l =<br />
y<br />
2. 44hl<br />
yp<br />
=<br />
2. 442h l<br />
y<br />
2meE<br />
449
h l<br />
y 2meE<br />
126 77MeV <br />
6710 -<br />
10 -<br />
?<br />
2 7 kg ? <br />
10<br />
m , , <br />
<br />
E 0 = mc 2 = 6710 - 27 910 1 6 = 3. 810 4 MeV<br />
E E 0, , <br />
=<br />
h<br />
2mE = 66310 - 34<br />
26710 - 27 7710 6 1610 - 1 9<br />
= 5. 210 - 1 5 m<br />
10 -<br />
1 0 m, <br />
127 , <br />
22GeV <br />
? 10 -<br />
?<br />
15 m<br />
( 22GeV ) <br />
( 051MeV) , , p = E / c<br />
<br />
= h/ p = hc/ E<br />
10 -<br />
= 66310 - 3 4 310 8 / ( 2210 8 1610 - 1 9 )<br />
= 5. 710 - 17 m<br />
15<br />
m, , <br />
<br />
128 : , <br />
h 2 / ( 8m ed 2 ) d =<br />
0091nm, ?<br />
450
= 2dsin<br />
, p =<br />
2me E , = h 2m eE <br />
, <br />
2d sin= h<br />
2meE<br />
<br />
E =<br />
h 2 / ( 8m ed 2 sin 2 )<br />
sin1, <br />
E min = h 2 / ( 8m ed 2 )<br />
d = 0091n m ,<br />
E min =<br />
( 66310 - 34 ) 2<br />
89. 1110 - 31 ( 009110 - 9 ) 2 1610 - 19<br />
= 45. 5 eV<br />
129 7210 -<br />
15 m( 1) ( m =<br />
6. 710 - 27 kg) ? ( 2) <br />
MeV ?<br />
( 1) <br />
p h / ( 2 x ) = 1. 0510 - 34 / ( 27210 - 15 )<br />
p p , <br />
= 7. 2910 - 21 kg ¡¤m/ s<br />
p 72910 -<br />
21 k g ¡¤m / s<br />
<br />
E k , = p 2 / ( 2m )<br />
( 7. 2910 - 21 ) 2 / ( 26. 710 - 27 1. 610 - 19 )<br />
= 2. 4810 4 eV<br />
( 2) , p 7. 2910 -<br />
21 kgm/ s<br />
451
E e, min = p 2 e / ( 2me )<br />
p e p = 7. 2910 - 2 1 kg ¡¤m/ s<br />
= ( 7. 2910 - 21 ) 2 / ( 29. 110 - 31 1. 610 - 1 9 )<br />
= 1. 8210 8 eV = 182 MeV<br />
0511MeV , <br />
E e, , <br />
E e, min = (p ec) 2 + ( mec 2 ) 2<br />
= ( 7. 2910 - 21 310 8 ) 2 + ( 9. 1110 - 31 910 16 ) 2<br />
= 2. 1910 - 12 J = 137 MeV<br />
Ek, e = E e - mec 2 = 13. 7 - 0. 5 = 13. 2 MeV<br />
130: m a <br />
, ( ) <br />
E m in = 3 h 2<br />
8ma 2<br />
x = a , p x h/ ( 2 x ) = h/ ( 2a ) <br />
p x p x, <br />
,<br />
<br />
p x h / ( 2a )<br />
p y h / ( 2a ) , p z h / ( 2a )<br />
E m in = p 2 m in<br />
2m = p 2 x , min + p 2 y , m in + p 2 z , min<br />
2m<br />
= 3 h 2<br />
8ma 2<br />
452
2 <br />
21 10 - 5 m, 10 - 14 g<br />
, 1= 100 2 = 101 <br />
?<br />
E 1<br />
E 2<br />
= <br />
2 h 2<br />
2<br />
2ma 2 1 = 2 ( 10510 - 34 ) 2<br />
100 2<br />
210 - 17 10 - 10<br />
= 5410 - 3 7 J<br />
= <br />
2 h 2<br />
2<br />
2ma 2 2 = 2 ( 10510 - 34 ) 2<br />
101 2<br />
210 - 17 10 - 10<br />
= 5510 - 3 7 J<br />
E = E 2 - E 1 = ( 55 - 54)10 - 37<br />
= 110 - 3 8 J<br />
22<br />
, 10 cm<br />
( 1) ?<br />
(2) T = 300K <br />
3kT / 2, ? + 1 <br />
?<br />
<br />
( 1) E 1 = <br />
2 h 2<br />
=<br />
2ma 2<br />
m= 3210- 3<br />
6. 0210 23 = 5. 310 - 26 k g<br />
= 1010 - 4 0 J<br />
( 2 10510 - 34 ) 2<br />
25310 - 26 01 2<br />
453
( 2)<br />
3<br />
2<br />
<br />
2 h 2<br />
kT = E = 2 = E 1 2<br />
2ma 2<br />
=<br />
3kT<br />
2E 1<br />
=<br />
= 7810 9<br />
313810 - 2 3 300<br />
21010 - 40<br />
E = E 1[ ( + 1) 2 - 2 ] = E 1( 2+ 1)<br />
= 1010 - 4 ( 27810 9 + 1)<br />
= 1. 610 - 3 0 J<br />
2321 <br />
= 5 <br />
E k= E - U, = h/ p = h 2mE , <br />
k<br />
, E k , E k , , <br />
, , <br />
, , 23 <br />
, x - 1 ( ) <br />
, 21 <br />
2123 <br />
24<br />
1/ 4 ?<br />
454
( 233) , <br />
=<br />
2<br />
a sin<br />
<br />
a x<br />
x = 0 x = a / 4 <br />
P = <br />
a / 4<br />
0<br />
<br />
= 1 4 - 1<br />
2 =<br />
2<br />
dx = 2 a a / 4<br />
0<br />
0091<br />
sin 2<br />
<br />
a x dx<br />
25 , <br />
( 233) x x 2 <br />
x 2<br />
x <br />
=<br />
a<br />
x<br />
<br />
x 2<br />
0<br />
= <br />
a<br />
x <br />
2 dx = 2 a a <br />
0xsin 2 a x dx = a 2<br />
0<br />
x 2 <br />
2 dx =<br />
a 2<br />
a <br />
0x 2 sin 2 a x dx<br />
1<br />
= a 2 3 - 1<br />
2 2 <br />
2<br />
26 : m( x , t) ( x , t) <br />
, <br />
a 0 m ( x , t) ( x , t) dx = 0<br />
<br />
<br />
( 233) , <br />
a 0 m ( x , t) ( x , t) dx<br />
= a 0<br />
2<br />
a<br />
E m t / h ei2 sin<br />
m<br />
a x 2<br />
a e-<br />
i2 E t/ h sin <br />
455<br />
a x dx
= 2 i( E a e2 m - E <br />
) t/ h<br />
a sin<br />
0<br />
m<br />
a x <br />
sin<br />
a x dx<br />
= 2 sin ( ( m - ) x / a )<br />
i( E<br />
a e2 m - E ) t/ h 2( m - ) / a<br />
-<br />
sin( ( m + ) x / a )<br />
2( m + ) / a<br />
m, , <br />
a<br />
0<br />
a 0 m ( x , t) ( x , t) dx = 0<br />
27, E ,<br />
?<br />
E = <br />
2 h 2 2 / ( 2ma 2 ) , <br />
F = -<br />
dE <br />
da =<br />
<br />
2 h 2 2<br />
ma 3<br />
28<br />
, a <br />
<br />
<br />
E =<br />
<br />
2 h 2<br />
2<br />
2ma 2<br />
= 2a / , = 1, 2, 3, <br />
p = h/ = h/ ( 2a ) = h / a <br />
E =<br />
p 2 <br />
2m =<br />
<br />
2 h 2<br />
2<br />
2ma 2<br />
29 , a <br />
<br />
E =<br />
<br />
2 h 2<br />
( 2<br />
2ma 2 x + 2 y + 2 z )<br />
x, y , z <br />
<br />
, 3 , <br />
456
x = 2a / x, y = 2a / y, z = 2a / z<br />
<br />
p x = h<br />
a<br />
<br />
E = p 2<br />
2m = p 2 x + p 2 y + p 2 z<br />
2m<br />
, x, y, z<br />
h<br />
x, p y = y, p z =<br />
h<br />
a<br />
a z<br />
= <br />
2 h 2<br />
( 2<br />
2ma 2 x + 2 y + 2 z )<br />
<br />
210, 0= A e - a x 2 , A , a <br />
( 251) <br />
x <br />
( 251) <br />
d 2 <br />
+ 2m E -<br />
dx 2 h 2<br />
0= Ae - a x 2 , <br />
4a 2 -<br />
E 0 = 1 2 h<br />
m 2<br />
<br />
2 x 2 = 2 a -<br />
h 2<br />
1<br />
2 m<br />
2 x 2 = 0<br />
x , x 2<br />
<br />
4a 2 -<br />
m 2<br />
<br />
2 = 0, a -<br />
h 2<br />
a , <br />
211H 2<br />
E 0<br />
= h <br />
2 = h <br />
2<br />
m<br />
h 2 E 0<br />
, <br />
m<br />
h 2 E 0 = 0<br />
, <br />
k= 11310 3 N / m, m= 16710 -<br />
2 7 kg<br />
( eV ) ? <br />
457
, ?<br />
<br />
<br />
= 1 k<br />
2m<br />
E = + 1 2 h = + 1 2<br />
h k<br />
2m<br />
= + 1 2<br />
= + 1 2<br />
66310 - 3 4<br />
2<br />
054 eV<br />
11310 3<br />
16710 - 27 1610 - 1 9<br />
<br />
E = E - E - 1 = + 1 2 - [ ( - 1) + 1 2 ] h = 054 eV<br />
<br />
= hc<br />
34 E = 66310- 310 8<br />
0541610 - 1 9<br />
= 23010 - 7 m = 2310 3 nm<br />
458
3 <br />
31<br />
<br />
m in = c =<br />
ma x<br />
ch<br />
E - E 1<br />
= 91410 - 8 m = 914 nm<br />
<br />
m ax = c =<br />
m in<br />
ch<br />
=<br />
E 2 - E 1<br />
= 12210 - 7 m = 122 nm<br />
=<br />
310 8 66310 - 34<br />
0 - ( - 1361610 - 1 9 )<br />
310 8 66310 - 3 4<br />
( 1/ 4 - 1)( - 1361610 - 19 )<br />
32= 5 <br />
? ?<br />
p , <br />
<br />
<br />
p 2<br />
2m H<br />
+ h = E 5 - E 1<br />
p =<br />
h / c<br />
h h <br />
2m H c 2 + 1 = E 5 - E 1<br />
h©¦E 1©¦= 13. 6eV , mH c 2 = 939MeV , m H c 2 h ,<br />
h = E 5- E 1<br />
= c = ch<br />
E 5 - E 1<br />
= 095210 - 7 m = 95. 2 nm<br />
=<br />
310 8 66310 - 34<br />
( 1/ 25 - 1)( - 1361610 - 1 9 )<br />
459
v =<br />
=<br />
p mH<br />
=<br />
h<br />
mH <br />
66310 - 3 4<br />
16710 - 27 095210 - 7 = 4. 17 m/ s<br />
33: <br />
<br />
E = -<br />
E = -<br />
h 2<br />
2m ea 2 0<br />
1<br />
2<br />
e 2<br />
1<br />
8 0a 0 2<br />
a 0= 4 0 h 2 / ( mee 2 ) , <br />
<br />
E = -<br />
E = -<br />
= -<br />
m ee 4<br />
1<br />
= -<br />
2( 4 0) 2 h 2 2<br />
h 2<br />
- 2m ea 2 0<br />
1<br />
2<br />
mee 4<br />
1<br />
= -<br />
2( 4 0 ) 2 h 2 2<br />
h 2<br />
1<br />
2m e( 4 0 h 2 / ( mee 2 ) ) 2 2<br />
e 2<br />
8 0 [ 4 0 h 2 / ( m e e 2 ) ]<br />
1<br />
2 = -<br />
e 2<br />
1<br />
8 0 a 0 2<br />
34 = 1 , ( 34) <br />
a 0<br />
<br />
a 0<br />
E k=<br />
e 2<br />
E = E k + E p =<br />
E p= -<br />
8 0a 0<br />
e 2<br />
-<br />
8 0a 0<br />
e 2<br />
e 2<br />
<br />
<br />
4 0a 0<br />
= -<br />
4 0a 0<br />
e 2<br />
= -<br />
8 0a 0<br />
mee 4<br />
2( 4 0) 2 h 2<br />
351884 <br />
<br />
( 1/ ) , <br />
<br />
460
1 = R<br />
4 - 1<br />
2<br />
, = 3, 4, 5, <br />
R , <br />
( R =<br />
1097373177( 83)10 7 m - 1 ) <br />
<br />
E = -<br />
m ee 4<br />
1<br />
2( 4 0) 2 h 2 2<br />
3 = 2 <br />
, <br />
<br />
1 =<br />
=<br />
<br />
c =<br />
, <br />
R =<br />
=<br />
m ee 4<br />
2 ( 4 0) 2 h 3 c<br />
E<br />
ch = m ee 4<br />
2 ( 4 0) 2 h 3 c<br />
1<br />
2 2 -<br />
9. 1110 - 31 ( 16010 - 19 ) 4<br />
2 ( 488510 - 12 ) 2 ( 1. 0510 - 34 ) 3 30010 8<br />
= 1. 1110 7 m - 1<br />
36 <br />
, <br />
L = h<br />
? = 2 = 1 , <br />
?<br />
r , <br />
<br />
<br />
e 2<br />
= m<br />
4 0( 2r ) 2 e<br />
v 2 <br />
r <br />
L = 2mev r = h<br />
1<br />
2<br />
461
, m in<br />
r = 4 0 h 2<br />
2<br />
me e 2<br />
= 4 0 h 2<br />
1 2<br />
me e 2<br />
=<br />
<br />
( 10510 - 34 ) 2<br />
910 9 9. 1110 - 31 ( 1610 - 19 ) 2<br />
= 5310 - 1 1 m<br />
E = E k, +<br />
E p , <br />
= 2 1 2 m ev2 + -<br />
= -<br />
mee 4<br />
1<br />
4( 4 0) 2 h 2 2<br />
e 2<br />
4 0 ¡¤2r <br />
= 2 = 1 , <br />
= E 2 - E 1<br />
2h<br />
=<br />
m ee 4<br />
1<br />
-<br />
8 ( 4 0) 2 h 3 1 2<br />
= 9. 1110 - 3 1 ( 1610 - 19 ) 4 ( 910 9 ) 2<br />
3 8( 10510 - 34 ) 3 4<br />
= 12510 15 Hz<br />
37, : , <br />
, , <br />
, L = h, <br />
( 1) ;<br />
( 2) 15010 11 m<br />
?<br />
( 3) <br />
?<br />
( 1) , , <br />
462<br />
1<br />
2 2
G Mm<br />
R 2 <br />
mvR =<br />
R =<br />
= mv 2 <br />
R <br />
h<br />
h 2<br />
GMm 2 2<br />
( 2) =<br />
GMm 2 R <br />
h<br />
= 5981024 66710 - 11 19910 30 15010 11<br />
1. 0510 - 34<br />
= 2. 5410 74<br />
( 3) R = R + 1- R <br />
=<br />
=<br />
h 2<br />
[ ( + 1) 2 - 2 h 2<br />
] = 2<br />
GMm 2 GMm 2<br />
( 1. 0510 - 34 ) 225410 2 74<br />
66710 - 1 19910 1 3 ( 0 59810 24 ) 2<br />
= 1. 1810 - 63 m<br />
38, <br />
<br />
4117nm 4357nm <br />
( 1) <br />
, ? <br />
?<br />
( 2) , ?<br />
( 1) , <br />
= 411. 7nm, = 435. 7nm <br />
, <br />
463
=<br />
=<br />
1<br />
4 + ch<br />
E 1<br />
= c = ch<br />
E =<br />
- 1/ 2<br />
ch<br />
E 1( 1/ 2 - 1/ 4)<br />
1<br />
4 + 310 8 66310 - 34<br />
411710 - 9 ( - 1361610 - 1 9 )<br />
= 599 6<br />
<br />
<br />
0 =<br />
=<br />
ch<br />
E 1( 1/ 6 2 - 1/ 4)<br />
310 8 66310 - 34<br />
1361. 610 - 19 ( 1/ 4 - 1/ 36)<br />
= 4. 11310 - 7 m = 411. 3 nm<br />
m =<br />
/ 0 = 411. 7/ 411. 3 = 1. 00097<br />
<br />
> , < , = 5 = 2 <br />
<br />
- 1/ 2<br />
ch<br />
0 =<br />
E 1( 1/ 5 2 - 1/ 4) = 310 8 66310 - 34<br />
1361. 610 - 1 9 ( 1/ 4 - 1/ 25)<br />
= 435. 3 nm<br />
<br />
m = / 0 = 435. 7/ 435. 3 = 1. 00092 m<br />
( 2) , <br />
<br />
<br />
464<br />
1 - u / c<br />
= 0<br />
1 + u / c 0( 1 - u/ c)<br />
u = ( 1 -<br />
/ 0) c = ( 1 - 0/ ) c
= ( 1 - 411. 3/ 411. 7)310 8 = 2. 910 5 m / s<br />
39 <br />
t <br />
[ ( 134) ] , E <br />
E <br />
<br />
t 110 -<br />
<br />
8<br />
s<br />
, <br />
, E 1= 0 <br />
<br />
= E 2 - E 1<br />
h<br />
=<br />
= E 2 - E 1<br />
h<br />
= E 2<br />
= 1 h h<br />
1<br />
= 810 6 H z = 8 MH z<br />
4110 - 8<br />
h<br />
2 t = 1<br />
4 t<br />
310 , <br />
( ) , , <br />
300K, H <br />
( 45610 14 Hz) ?<br />
<br />
c v<br />
= 0<br />
c v<br />
vc, <br />
= 0 1 v c<br />
T = 300K , <br />
v =<br />
kT<br />
m H<br />
=<br />
RT<br />
M H<br />
465
, H <br />
2v<br />
= 0<br />
c =<br />
2 0 RT<br />
c M H<br />
=<br />
24. 5610<br />
14<br />
310 8<br />
8. 31300<br />
110 - 3 = 4. 810 9 Hz<br />
311: , [ <br />
( 312) ] r 0 1<br />
?<br />
<br />
P 1, 0, 0dr = 4<br />
0<br />
a 3 0<br />
<br />
0<br />
r 2 e -<br />
2r / a 0 dr<br />
= [ 1 - e - 2r / a 0 ( 1 + 2r / a 0 + 2r 2 / a 2 0) ]<br />
<br />
0 = 1<br />
1 <br />
<br />
<br />
312, r <br />
r = <br />
<br />
0 rP 1, 0, 0dr = 4 a 3 0<br />
<br />
0 r 3 e - 2r / a 0 dr<br />
= 3 2 a0[ 1 - e- 2r/ a 0<br />
( 1 + 2r/ a0 + 2r 2 / a 2 0 + 4r 3 / a 3 0) ]<br />
<br />
0<br />
= 3 2 a 0<br />
313 , , <br />
, <br />
?<br />
<br />
<br />
E<br />
- e<br />
p1<br />
2<br />
- e2 4r<br />
= P 1 , 0, 0dr = e - 2r/ a 0<br />
dr = -<br />
0 4 0r 40<br />
= -<br />
466<br />
0 <br />
a 3 0<br />
e 2<br />
4 0a0<br />
m ee 4<br />
= 2E<br />
( 4 0) 2 h 2 1 = 2( - 136) = - 272 eV
E<br />
<br />
k = E 1 - E <br />
p 1 = - 13. 6 - ( - 272) = 136 eV<br />
<br />
v 2 = 2E k/ m e<br />
= 21361610 - 19 / ( 091110 - 30 )<br />
= 21810 6 m/ s<br />
314 = 2, l = 1 m= 0, + 1, - 1 <br />
<br />
2, 1, 0( r , , ) = 1/ ( 4 2 ) ( a - 0 3 / 2<br />
) ( r/ a0) e - r / ( 2a 0 ) cos<br />
2, 1, 1( r , , ) = 1/ ( 8 ) ( a - 0 3/ 2<br />
) ( r / a 0) e - r/ ( 2a 0 ) sin e i<br />
2 , 1, - 1( r , , ) = 1/ ( 8 ) ( a - 0 3/ 2<br />
) ( r / a 0) e - r/ ( 2a 0 ) sin e -<br />
( 1) P 2, 1 , 0, P 2, 1, 1P 2, 1 , -<br />
36( b ) ( c) <br />
( 2) <br />
( 3) P 2, 1 , 01, <br />
P =P 2 , 1, 0 = 2<br />
<br />
( 1) P 2, 1, 0= ©¦<br />
0 <br />
0<br />
2<br />
2, 1 , 0©¦<br />
2<br />
P 2, 1, 1= ©¦ 2, 1 , 1©¦<br />
P 2, 1, -<br />
0 ©¦<br />
=<br />
2<br />
2 , 1, 0©¦<br />
1 r 2<br />
32 a 5 0<br />
e -<br />
r 2 sin drd d = 1<br />
r / a 0<br />
cos 2 <br />
= 1/ ( 8 ) ( a - 3/ 2 ) ( r / a 0) e - r / ( 2 a 0 ) sin 2<br />
e e i -<br />
i <br />
= 1 r 2<br />
e - r / a 0<br />
sin 2 <br />
64 a 5 0<br />
1= ©¦ 2 , 1, - 1©¦<br />
2 = 1 r 2<br />
64<br />
e -<br />
a 5 0<br />
r/ a 0<br />
sin 2 <br />
i<br />
1<br />
467
36( b ) ( c) <br />
( 2) P 2, 1, 0+ P 2, 1 , 1+ P 2, 1 , - 1= 1 r 2<br />
e r/ a 0<br />
( cos 2 + sin 2 )<br />
32 a 5 0<br />
= 1 r 2<br />
e r/ a<br />
32 a 5 0<br />
0<br />
, , <br />
2<br />
0<br />
<br />
0 0<br />
<br />
( 3) P = P 2, 1, 0 = <br />
1<br />
r 2 e - r / a 0<br />
cos 2 r 2 sin drd d<br />
32 a 5 0<br />
1<br />
=<br />
32<br />
2<br />
3 24 = 1<br />
= 2, l = 1, m = 0 , <br />
<br />
315l= 1 , <br />
<br />
31 , , j 1= l + 1/ 2= 3/ 2, j 2 =<br />
l - 1/ 2= 1/ 2<br />
31315 <br />
j 1= 3 2<br />
468<br />
, S=<br />
3<br />
4 h, L= 2 h, J 1= 15<br />
4<br />
h,
15/ 4 = 3/ 4 + 2 - 2 3 2 cos 1, 1 = 65. 9<br />
4<br />
j 2= 1 2 , S=<br />
3<br />
4 h , L= 2 h, J 2=<br />
3<br />
4 h , <br />
3<br />
4 = 3 4 + 2 + 2 3 2 cos 2, <br />
4 2 = 1447<br />
316 , 2P 3 / 2 2P 1/ 2 <br />
4510 -<br />
<br />
?<br />
5 eV <br />
( 1) <br />
( 2) = 2, l = 1 , <br />
( 1) h = E 2p- E 1s<br />
E 2 p - E 1 s<br />
=<br />
h<br />
=<br />
E 2p - 0<br />
h<br />
= 4510- 5 1610 - 19<br />
66310 - 3 4 = 1. 110 10 Hz<br />
©¦ ©¦= c = c = <br />
2<br />
<br />
2 c <br />
= ( 12210- 7 ) 2<br />
310 8 1. 110 10<br />
= 5410 - 13 m = 0. 54 pm<br />
( 2) E 2p= 2 BB, <br />
B =<br />
E 2p<br />
= 4510 - 5 1610 - 19<br />
= 039 T<br />
2 B 292710 - 24<br />
317 , <br />
B= 12T <br />
<br />
32 S 1 = S 2<br />
469
= 3 h/ 2, S z = h/ 2, <br />
cos = 1/ 3 , 1 = 547 , 2 = 125. 3<br />
32<br />
<br />
E = BB = 92710 - 24 12 = 1110 - 2 3 J<br />
1 <br />
<br />
318, 40cm, <br />
15 T / mm2500K <br />
( 1) <br />
( 2) <br />
dB<br />
( 1) F = B<br />
dz = 92710 - 2 1510 4 3<br />
= 1410 - 2 0 N<br />
( 2) z = Bd 2<br />
dB<br />
24<br />
3kT dz = 92710- 0. 041510 2 3<br />
313810 - 2 2500<br />
3<br />
= 2. 110 - 4 m= 0. 21 mm<br />
<br />
319160T <br />
<br />
14110 -<br />
470<br />
26 J/ T
, <br />
? ?<br />
2 z B, <br />
h = 2 z B<br />
= 2 zB/ h = 21. 4110 - 26 1. 60/ ( 6. 6310 - 34 )<br />
= 0. 68110 8 H z = 68. 1 MH z<br />
= c/ = 310 8 / ( 0. 68110 8 ) = 4. 41 m<br />
<br />
320: <br />
( 1) , l 2( 2l+ 1) <br />
( 2) 2 2 <br />
( 1) , l , m l 0, 1, 2, , l, <br />
( 2l+ 1) m l 1/ 2 m s , <br />
2( 2l+ 1) , , 2( 2l+ 1) <br />
<br />
( 2) , l 0, 1, 2, , - 1 , <br />
<br />
- 1<br />
2( 2l + 1) =<br />
l = 0<br />
2 + 2( 2- 2 + 1)<br />
= 2 2<br />
2<br />
321 ( B, Z= 5) , ( A r, Z = 18) , ( Cu , Z = 29) , <br />
( Br , Z= 35) <br />
<br />
B: 1s 2 2s 2 2p 1 ;<br />
A r: 1s 2 2s 2 2p 6 3s 2 3p 6 ;<br />
Cu: 1s 2 2s 2 2p 6 3s 2 3p 6 3d 1 0 4s 1 ;<br />
Br: 1s 2 2s 2 2p 6 3s 2 3p 6 3d 1 0 4s 2 4p 5 <br />
322 30k eV X <br />
0041nm<br />
471
E k= eV= h = hc/ cu t<br />
h = cu teV/ c<br />
= 004110 - 9 1. 610 - 19 3010 3 / ( 310 8 )<br />
= 6610 - 34 J ¡¤s<br />
3230100nm X , X <br />
?<br />
V m in= hc e = 66310 - 34 310 8<br />
= 1. 2410 4 V<br />
010010 - 1610 9 - 19<br />
32440k eV 4 <br />
3 , X <br />
?<br />
4 <br />
, 20keV, 10keV , 5keV 5k eV = ch/ E <br />
X 0062nm, 0124nm , 0248n m<br />
0248nm<br />
Z =<br />
325X K 316nm<br />
( 1) L K ?<br />
( 2) ?<br />
( 1) E = h = hc/ <br />
= 66310 - 34 310 8 / ( 3. 1610 - 9 )<br />
= 6. 2910 - 17 J= 393 eV<br />
( 2) = 4. 9610 7 ( Z- 1) <br />
c/ <br />
4. 9610 7 + 1 =<br />
Z 7, ( N ) <br />
310 8 / ( 31610 - 9 )<br />
4. 9610 7 + 1 = 7. 21<br />
326 K L 8979keV <br />
0951keV X N aCl <br />
741 <br />
472
?<br />
d =<br />
2dsin = m , = ch/ E L K m= 1 <br />
=<br />
ch<br />
2sin E LK<br />
310 8 66310 - 34<br />
2sin741( 8979 - 0951)10 3 1610 - 19<br />
= 0. 8010 - 1 0 m<br />
327CO 2<br />
106 m<br />
( 1) CO 2 ?<br />
( 2) 300K , CO 2 <br />
?<br />
( 3) CO 2 <br />
1% , <br />
?<br />
( 1) E = h = ch / = 310 66310 8 - 3 4 / 10. 610 - 6<br />
= 18810 - 20 J= 0117 eV<br />
( 2) N 2/ N 1 = exp ( - E/ ( kT ) )<br />
( 3) T = -<br />
= -<br />
= exp [ - 1. 8810 - 20 / ( 1. 3810 - 2 3 300) ]<br />
= 1. 07%<br />
hc<br />
k ln N 2<br />
N 1<br />
66310 - 34 310 8<br />
ln<br />
10. 610 - 13810 6 - 23<br />
= - 1. 310 5 K<br />
1. 01<br />
1<br />
328 <br />
10fs( 1fs= 10 -<br />
500nm<br />
1 5 s) ? <br />
N = ct/ = 31010 8 - 1 10/ 5 ( 50010 - 9 ) = 6<br />
329 6944nm , <br />
473
12ps, 0150J: ( 1) ; ( 2) <br />
; ( 3) <br />
( 1) l = ct= 310 8 1210 - 12<br />
= 3610 - 3 m = 036 mm<br />
( 2) P = W/ t= 0150/ ( 1210 - 1 2 ) = 1. 2510 10 W<br />
= 12. 5 GW<br />
( 3) N = W/ ( h ) = W / ( hc)<br />
= 0150694410 - 9 / ( 66310 - 34 310 8 )<br />
= 5210 1 7<br />
330 GaA lA s 200 m 3 ( = 2<br />
10 - 7 mm 3 ) 50mW 080 m <br />
?<br />
N = P / ( h ) = P / ( hc)<br />
= 5010 - 3 08010 - 6 / ( 66310 - 3 4 310 8 )<br />
= 2. 010 16 / s<br />
331 300mm,<br />
500W, 515nm <br />
350cm , <br />
( 1) ? ( 2) <br />
? ( 3) 84% , <br />
?<br />
( 1) <br />
I 0 = P =<br />
r 2<br />
( 2) <br />
<br />
474<br />
500<br />
= 70710 5 W / m 2<br />
( 1510 - 3 ) 2<br />
= sin=<br />
1. 22<br />
d
R = f =<br />
1. 22 f = 1. 2251510 - 9 35010 - 2<br />
d<br />
3. 0010 - 3<br />
= 7. 3310 - 6 m = 733 m<br />
( 3) <br />
I F = P84% =<br />
R 2<br />
500084<br />
= 24910 1 0 W / m 2<br />
( 73310 - 6 ) 2<br />
3328610 1 0<br />
H z266<br />
10 - 2 6 kg<br />
= h<br />
2 I = h<br />
mr 2 0<br />
r 0 =<br />
h<br />
m = 1. 0510 - 34<br />
26610 - 2 6 8610 10<br />
= 1210 - 1 0 m = 012 nm<br />
333 , <br />
<br />
?<br />
I = 2 5 ma 2 02= 4 5 ma2 0<br />
( j = 1) <br />
E 1 = h 2<br />
I<br />
=<br />
5 h<br />
4ma 2 0<br />
= 5410 - 1 8 J = 34 eV<br />
<br />
=<br />
5( 10510 - 34 ) 2<br />
4091110 - 3 0 ( 05310 - 10 ) 2<br />
T = E 1/ k = 5410 - 1 8 / ( 1. 3810 - 23 ) = 3910 5 K<br />
, <br />
, <br />
<br />
<br />
334CO 64210 13 Hz<br />
475
= 1 K<br />
2m m= m1m 2/ ( m1+ m 2) <br />
m 1m<br />
K = ( 2 ) 2 2<br />
m 1 +<br />
m2<br />
, m <br />
= ( 64210 13 ) 2 1216<br />
27<br />
16610-<br />
12 + 16<br />
= 1. 8510 3 N / m<br />
476
4 <br />
41 193g/ cm 3 , <br />
?<br />
,<br />
h 2<br />
E F = ( 3<br />
2 ) 2/ 3 2/ 3<br />
2m e<br />
( 10510 - 34 ) 2<br />
19310 3 60210 23 2/ 3<br />
= ( 3<br />
2 ) 2/ 3 291110 - 31 19710 - 3<br />
= 8. 8010 - 19 J = 5. 50 eV<br />
v F = 2E F / m e = 28. 8010 - 19 / ( 9. 1110 - 31 )<br />
= 1. 3910 6 m/ s<br />
T F = E F/ k = 8. 8010 - 19 / ( 1. 3810 - 23 )<br />
= 6. 3810 4 K<br />
=<br />
h<br />
2m e E F<br />
=<br />
= 52410 - 10 = 0524 nm<br />
6. 6310 - 34<br />
29. 1110 - 31 8. 8010 - 19<br />
42 0K <br />
<br />
E t ot al = E F<br />
E g ( E ) dE = E F<br />
0<br />
= 1 5 ( 2me ) E 5/ 2<br />
3/ 2 F<br />
= 3 <br />
2 h 3 5 E F<br />
<br />
E<br />
= E t ot al / = 3E F / 5<br />
0<br />
E ( 2m e ) 3/ 2<br />
E 1 / 2 dE<br />
2<br />
2 h 3<br />
477
430K <br />
, vF <br />
<br />
v = 1 E F<br />
0<br />
vg ( E ) dE<br />
= 1 E F<br />
0<br />
2E<br />
me<br />
1<br />
2<br />
( 2me ) 3/ 2<br />
E 1/ 2 dE<br />
2<br />
2 h 3<br />
= 2m e 1<br />
<br />
2 h 3 2 E F 2 = 3 4 vF<br />
v 2 =<br />
1<br />
E F<br />
0<br />
v 2 g ( E ) dE<br />
1/ 2<br />
=<br />
1<br />
E F<br />
0<br />
2E<br />
me<br />
( 2me ) 3/ 2<br />
E 1/ 2 dE<br />
2<br />
2 h 3<br />
1 / 2<br />
=<br />
3<br />
5 2 E F<br />
me<br />
1/ 2<br />
=<br />
3<br />
5 v F<br />
44 5<br />
10 16 kg/ m 3 <br />
E F<br />
h 2<br />
= ( 3<br />
2 ) 2/ 3 3<br />
2m n 2/<br />
( 1. 0510 - 34 ) 2<br />
2 / 3<br />
= ( 3<br />
2 ) 2/ 3 51016<br />
216710 - 27 16710 - 27<br />
= 30. 510 - 1 3 J= 19 Mev<br />
v F = 2E F/ mn = 230. 510 - 13 / ( 16710 - 27 )<br />
= 6010 7 m/ s<br />
45 , <br />
10% ? 5eV <br />
<br />
<br />
478<br />
<br />
2 kT R<br />
2E F<br />
= 0. 1 3 2 R
T =<br />
0. 3E F<br />
=<br />
<br />
2 k<br />
1 9<br />
0. 351610-<br />
= 1810 3 K<br />
2 1. 3810 - 2 3<br />
46 , <br />
T 3<br />
T , ,<br />
, <br />
Cm = ( 20810 - 3 T + 25710 - 3 T 3 ) J/ ( mol ¡¤K )<br />
( 1) <br />
<br />
( 2) ?<br />
( 1) <br />
E F<br />
<br />
2 Rk<br />
2E F<br />
= 20810 - 3<br />
= 2 83113810 - 2 3<br />
220810 - 3<br />
= 27210 - 19 J = 1. 70 eV<br />
<br />
20810 - 3 T = 25710 - 3 T 3<br />
T =<br />
20810 - 3<br />
25710 - 3 = 0900 K<br />
47 10510 3 k g/ m 3 , 1610 - 8<br />
m( ) <br />
( 1) <br />
( 2) <br />
( 3) <br />
( 4) ( 2) ( 3) <br />
( 1) = m e/ ( e 2 ) , =<br />
D N A / MA g= 10510 3 602310 2 3 / ( 10810 - 3 ) = 5. 8610 2 8<br />
m -<br />
1 , <br />
479
=<br />
m e<br />
e 2 =<br />
= 3810 - 14 s<br />
9. 1110 - 3 1<br />
1610 - 8 58610 28 ( 1610 - 19 ) 2<br />
( 2) <br />
<br />
c la = v =<br />
8kT<br />
<br />
me<br />
813810 - 2 300<br />
3<br />
=<br />
3810 - 1 4<br />
91110 - 3 1<br />
= 40910 - 9 m= 4. 09 nm<br />
( 3) <br />
<br />
F er= v F = 139103810 6 - 14<br />
= 5310 - 8 m= 53 nm<br />
( 4) a = 3 1/ = ( 58610 2 8 ) - 1/ 3 = 2610 - 1 0 m= 026 nm<br />
<br />
481000K , 01eV <br />
? 010eV <br />
?<br />
+ =<br />
E -<br />
- =<br />
E + = E F + 010eV <br />
1<br />
e ( E + - E F ) / ( kT ) + 1 = 1<br />
e 011 610 - 19 / ( 13 81 0 - 23 10 00)<br />
= E F - 010eV <br />
e ( E -<br />
1<br />
- E F<br />
) / ( kT )<br />
+ 1 = 1<br />
e - 0 1161 0- 19 / ( 13810 - 23 1 000 )<br />
4955eV <br />
+ 1 = 024<br />
+ 1 = 076<br />
( 1) ? <br />
300K<br />
?<br />
( 2) <br />
( 1) N u p<br />
= e - E / ( kT ) = e - 5 5161 0- 19 / ( 13810 - 23 300 )<br />
N be<br />
480<br />
= 4. 910 - 93
, <br />
( 2) m a x=<br />
ch<br />
E = 3108 66310 - 34<br />
551610 - 19<br />
= 22610 - 7 m= 226 nm<br />
410 0 10 1 6 m - 3 <br />
10 6 , ( 1) <br />
? 233g/ cm 3 <br />
( 2) 10g ?<br />
( 1) <br />
= 10 6 0 - 0 = 10 6 0 = 10 22 m - 3<br />
10 2 2 , 10 22 1m 3<br />
<br />
S i =<br />
D S i<br />
MS i<br />
N A =<br />
<br />
( 2) mp<br />
2. 3310 3<br />
28110 - 3 60210 23 = 50010 28 m - 3<br />
<br />
=<br />
Si<br />
= m S i<br />
Mp =<br />
D S iN A<br />
10 2 2<br />
50010 28 =<br />
1<br />
510 6<br />
10 - 3 10 2 2 3110 - 3<br />
23310 - 3 602310 23<br />
= 2210 - 1 0 kg= 0. 22 g<br />
<br />
41112eV, <br />
E D = 0045eV <br />
<br />
m ax =<br />
ch = 310 66310 8 - 34<br />
E D 00451610 - 19<br />
= 27610 - 5 m= 276 m<br />
412 CdS P bS 242eV <br />
030eV ? ?<br />
CdS,<br />
481
ma x = ch = 3108 66310 - 34<br />
E g 2421610 - 19<br />
PbS,<br />
<br />
= 51310 - 7 m = 513 nm<br />
ma x = ch = 3108 66310 - 34<br />
E g 0301610 - 19<br />
= 414 m<br />
413Ga A sP 19eV <br />
?<br />
m ax =<br />
ch = 310 66310 8 - 34<br />
E g 191610 - 1 9<br />
= 65410 - 7 m= 654 nm<br />
414KCl 76eV <br />
140nm , ?<br />
140nm <br />
E = hc = 66310 - 3 4 310 8<br />
14010 - 9<br />
= 14210 - 1 9 J = 8. 9 eV<br />
K Cl , <br />
482
5 <br />
51 6MeV ( 1 97 Au ) <br />
, ? ( 14 N ) ? <br />
? <br />
?<br />
6MeV ( 410 3 MeV ) , <br />
6MeV E k M , <br />
<br />
2Ze 2<br />
E k= E k + E kM + = 1 4 0r mi n 2<br />
<br />
E k =<br />
mv =<br />
m <br />
( m + M) v<br />
2 +<br />
( m + M) v<br />
m + M E k + 2Ze 2<br />
4 0r m in<br />
r m in = m + M 2Ze2<br />
ME k 4 0<br />
, M= 197m , , <br />
r min =<br />
2Ze 2<br />
4 0r m in<br />
2Ze 2<br />
= 2791610- 19 910 9<br />
E k 4 0<br />
610 6<br />
= 3810 - 14 m<br />
, M= 14, , <br />
r mi n = 4 + 14 2Ze2 = 1871610 - 1 9 910 9<br />
14E k 4 0<br />
7610 6<br />
= 43210 - 15 m<br />
r N = 12A 1/ 3 10 - 15 = 28910 - 15 m<br />
483
6MeV <br />
52 1 6 N , 1 6 O 1 6 F 16006099u,<br />
15994915u 16011465u<br />
<br />
BE = Mc 2 = [ Zm p + N m n - ( M - Zm e) ] c 2<br />
<br />
16<br />
N : BE = 1180 MeV<br />
16<br />
O: BE = 1277 MeV<br />
16<br />
F : BE = 1115 MeV<br />
53 , Z <br />
A <br />
56<br />
Fe 238 U ( MeV ) <br />
<br />
h 2<br />
h 2<br />
E F = ( 3<br />
2 ) 2/ 3 2/ 3<br />
p = ( 3<br />
2 ) 2/ 3<br />
2mp<br />
2mp<br />
=<br />
=<br />
2/<br />
9<br />
3 h 2<br />
4 2m p R 2 0<br />
Z<br />
A<br />
2/ 3<br />
Z3<br />
4 R 3 0A<br />
2/ 3<br />
9<br />
10510 - 34<br />
<br />
4 216710 - 27 ( 1210 - 15 ) 2 1. 610 - 13<br />
2/ 3<br />
Z = 53 Z A A<br />
<br />
2/ 3<br />
MeV<br />
2/ 3<br />
E F , 1 = 3 5 E F = 32 Z A<br />
2 / 3<br />
MeV<br />
25 Fe , Z= 26, A= 56, E F = 32MeV , E F , 1= 19MeV<br />
238 U , Z= 92, A = 238, E F = 28MeV , E F , 1= 17MeV<br />
54<br />
1 1<br />
C 11 B, 15 O 15 N , 21 N a 2 1 N e<br />
279MeV, 348MeV <br />
484
430MeV A 1 / 3 ? <br />
?<br />
, , <br />
1, <br />
E p =<br />
3e 2<br />
54 0r [ Z2 - ( Z - 1) 2 ] =<br />
r = 3e2 ( 2Z - 1)<br />
54 0 E p<br />
11 C 1 1 B, Z= Z C= 6, r 11= 341fm<br />
15 O 15 B, Z= Z O = 8, r 15= 372fm<br />
21 Na 21 N e, Z= Z N a = 11, r 2 1= 422fm<br />
r = R0A 1 / 3 ,<br />
R 0, 1 1 = r 1 1/ 11 1/ 3 = 153 fm<br />
R 0, 1 5 = r 1 5/ 15 1/ 3 = 151 fm<br />
R 0, 2 1 = r 2 1/ 21 1/ 3 = 153 fm<br />
3e 2<br />
[ 2Z - 1]<br />
54 0r<br />
, r A 1/ 3 , R0= 15fm<br />
55 <br />
, 12 C <br />
, 16 O <br />
12 C 16 O <br />
, 242MeV<br />
<br />
, <br />
BE O = ( 81007825 + 81008665 -<br />
= 127. 7 MeV<br />
15994915)9315<br />
BE C = ( 61007825 + 61008665 - 12000000)9315<br />
= 9216 MeV<br />
BE = ( 21007825 + 21008665 - 4002603)93149<br />
485
= 28. 3 MeV<br />
<br />
BE O = 4BE + E C 2 4 = 4283 + 2426<br />
= 1277 MeV<br />
BE C = 3BE + E C 2 3 = 3283 + 2423<br />
= 922 MeV<br />
<br />
56 23 2 T h <br />
<br />
Z = 90, A = 232<br />
E = 2BE A / 2, Z/ 2- BE A , Z<br />
= - 4. 6A 2/ 3 + 026 Z 2<br />
A 1 / 3<br />
= 169 MeV<br />
57Z, A 2Z, 2A <br />
<br />
12<br />
C <br />
E = BE 2A , 2Z- 2BE A , Z<br />
= 15. 7532A - 17804( 2A ) 2/ 3 - 07103 ( 2Z) 2<br />
2<br />
( 2A- 4Z)<br />
- 2369<br />
2A<br />
( 2A) 1/ 3<br />
- 215. 753A - 217804A 2/ 3 - 207103 Z 2<br />
2<br />
( A- 2Z)<br />
- 22369<br />
A<br />
= - 08345 Z 2<br />
+ 73458A 2 / 3<br />
A 1 / 3 MeV<br />
12 C, Z= 6, A = 12 <br />
486<br />
E =<br />
254MeV<br />
A 1 / 3
58 <br />
? ?<br />
©¦ dN ©¦= N 0e -<br />
t / dt/ , <br />
1<br />
t 2 = N t 2 ©¦ dN ©¦= N 0<br />
0<br />
N 0<br />
t = , <br />
t<br />
2 <br />
e- t / dt = 2<br />
2<br />
( t - ) 2 = t 2 - 2t+ <br />
2 = 2<br />
2 - 2<br />
2 + <br />
2 = <br />
, <br />
0<br />
59 40 K 1210 -<br />
4 <br />
1310 9 a , <br />
037% <br />
70kg , <br />
A = N =<br />
=<br />
0. 693<br />
t 1/ 2<br />
mN A<br />
M<br />
0. 693<br />
700. 0037<br />
<br />
1. 310 9 3. 1510 7 39. 110 - 3<br />
1210 - 4 60210 2 3<br />
= 8. 1 k Bq<br />
51010kg ( U 3O 8) 226 Ra 2 31 Pa <br />
2 38 U 9927% , 2 35 U 072% ; 226 Ra <br />
1600a, 231 Pa 32710 4 a<br />
226 Ra 23 1 Pa , 22 6 Ra 238 U , 231 Pa <br />
235<br />
U 226 Ra 2 38 U ( 44610 9 a) , 23 1 P a<br />
23 5 U ( 70410 8 a ) <br />
N A A = N B B N A / t 1/ 2 , A = N B / t 1/ 2, B <br />
226 Ra <br />
487
N 238 U =<br />
N 226 Ra<br />
m 226 Ra =<br />
10 4<br />
816 + 3238 36023102 3 09927<br />
= 21310 25<br />
= 21310 25 t 1/ 2, 226 R a<br />
t 1/ 2, 238 U<br />
= 76410 18<br />
= 2. 1310 25 1600<br />
4. 4610 9<br />
76410<br />
18<br />
60210 23 226 = 2. 8710 - 3 g = 2. 87 mg<br />
231 Pa <br />
N 235 U =<br />
10 4<br />
816 + 3235 360210 23 00072<br />
= 15210 23<br />
N 231 P a<br />
= 15210 23 t 1/ 2, 231 P a<br />
t 1/ 2, 235 U<br />
= 70610 18<br />
4<br />
3. 2710<br />
= 1. 5210 23 <br />
7. 0410 8<br />
m 231 P a =<br />
70610<br />
18<br />
60210 23 231 = 2. 7110 - 3 g = 271 mg<br />
511 30 Ci 12 3 I 24 , <br />
4 Ci 12 3 I 131h<br />
24 12 3 I ( <br />
15% 40% ) <br />
A 0 = 30 Ci, A 0, t h =<br />
A 0p 24 , <br />
4= A t h = A 0, t he - t = A 0p e - t =<br />
<br />
p = 0. 48 = 48%<br />
30 p e -<br />
0. 6 9324<br />
1 31<br />
512 24 N a 300k Bq <br />
10 30Bq<br />
24 Na 1497h <br />
488
V = A 0<br />
e -<br />
A 1<br />
<br />
t = 30010 3<br />
30<br />
A 1V = A 0e -<br />
e -<br />
t<br />
0. 6 9310<br />
1 49 7<br />
= 62910 3 cm 3 = 629 L<br />
513 <br />
03mol CO 2 14 C <br />
9 <br />
<br />
t =<br />
N 0= 031310 - 12 60210 23 = 2. 3510 1 1<br />
A = 9/ 60 s - 1 , = 82703. 1510 7 s<br />
A = A 0e - t/ = 1 N 0e - t / <br />
ln N 0<br />
A = 8270ln 2. 3510 11 60<br />
827031510 7 9 =<br />
15104 a<br />
51403g 238 U 012g 206 Pb<br />
238 U , <br />
2 38 U 2 06 Pb 2 38 U<br />
, 20 6 Pb , <br />
2 38 U 20 6 P b 2 38 U <br />
<br />
N U , 0 = N U + N P b =<br />
0. 36. 0210<br />
23<br />
238<br />
= 75910 20 + 35110 2 0 = 11110 2 1<br />
N U = N U , 0e -<br />
<br />
t =<br />
t<br />
1 <br />
ln N U , 0<br />
N U<br />
=<br />
9<br />
4. 4610<br />
ln<br />
0693<br />
+ 012602102 3<br />
206<br />
1. 11102<br />
1<br />
75910 2 0 = 24510 9 a<br />
515 2 26 Ra 47825MeV <br />
489
?<br />
47825MeV ( 410 3 MeV ) <br />
, mM d <br />
, <br />
<br />
m v = M dvd<br />
E kd = 1 2 Mdv 2 d = 1 2<br />
<br />
m<br />
v 2 =<br />
M d<br />
m <br />
E k <br />
Md<br />
= 4 47825 = 00862 MeV<br />
222<br />
E = E k + E kd = 4. 7825 + 0. 0862 = 4. 8707 MeV<br />
516 <br />
64<br />
Cu 64 Zn, <br />
+ 64 Ni<br />
Q 057MeV 066MeV 64 Zn <br />
64 Ni , u <br />
64 Cu <br />
64 6<br />
Cu<br />
4 Zn + <br />
- + <br />
<br />
e<br />
64<br />
Cu <br />
+ <br />
Q<br />
- = [ M Cu - ( M Zn + me ) ] c 2<br />
64<br />
Cu<br />
64<br />
N i + <br />
+ + e<br />
Q <br />
+ = [ M Cu - ( M N i + m e) ] c 2<br />
Q <br />
+ - Q <br />
- = ( MZn - MN i) c 2<br />
E = M Zn - MN i = Q + - Q<br />
-<br />
=<br />
c 2<br />
=<br />
066 - 057<br />
9315<br />
= 9710 - 5 u<br />
0. 66 - 0. 57<br />
c 2<br />
MeV<br />
517 60 Co ( 527a) <br />
490
, 60 Co <br />
6 0 Co <br />
59 Co <br />
59<br />
Co+ n<br />
60<br />
Co+ <br />
120b2cm ( <br />
59<br />
Co 100% ) 210 1 2 cm - 2 s - 1 <br />
6h 8858g/ cm 3 <br />
59 Co <br />
N 59 = 8885860210 23 / 59 = 7. 2310 23<br />
, , <br />
60 Co <br />
R = N 59I = 12010 - 2 4 72310 23 210 1 2<br />
= 1. 7410 1 4 s - 1<br />
6h527a, 6h 6 0 Co <br />
, 60 Co Rt, 60 Co <br />
<br />
A =<br />
N 60 = Rt = 0. 6931. 741014 63600<br />
5. 273. 1510 7 3. 710 1 0<br />
= 042 Ci<br />
518Cd 8 , <br />
Cd 4000b, <br />
95% , Cd Cd 1124g/ mol, <br />
864g / cm 3 <br />
S d Cd , <br />
Cd , <br />
R = 0. 95I S =<br />
d =<br />
=<br />
0. 95<br />
=<br />
N I =<br />
0. 95M<br />
DN A<br />
Sd I<br />
0. 95112. 4<br />
400010 - 28 8. 6410 3 6. 0210 23 491
= 5. 110 - 5 m = 51 m<br />
519Q , :<br />
13<br />
C( p , ) 10 B, 13 C( p , d ) 1 2 C, 13 C( p , ) 14 N<br />
13 C( p , ) 10 B <br />
Q = ( 13003355 + 1007825 - 4002603 - 10012937)9315<br />
= - 406 MeV<br />
<br />
13 C( p , d ) 12 C <br />
Q = ( 13003355 + 1007825 - 2014102 - 120000)9315<br />
= - 272 MeV<br />
<br />
13 C( p , ) 14 N <br />
Q = ( 13003355 + 1007825 -<br />
= 755 MeV<br />
<br />
14003074)9315<br />
520 13 C( p , ) 10 B , , <br />
13 C <br />
, <br />
E 1 = Q 1 + m p<br />
mC<br />
= 4. 06 1 + 1<br />
13<br />
= 437 MeV<br />
13 C , <br />
r = r c + r p = r 0A 1/ 3<br />
C + r 0<br />
= 1210 - 15 ( 13 1/ 3 + 1) = 4010 - 15 m<br />
<br />
E 2 = 6e2 1 + m p<br />
4 0r mC<br />
492<br />
= 61. 610- 19 910 9<br />
4010 - 15 10 6 1 + 1 13<br />
= 23 MeV
E t h = E 1 + E 2 = 4. 37 + 2. 3 = 6. 7 MeV<br />
521 1510 3 0 kg , <br />
3910 26 W , <br />
?<br />
<br />
4 1 H<br />
4<br />
H e+ 2e + + 2 e+ 24. 67 MeV<br />
N = 1510 30 / ( 16710 - 27 ) = 0. 9010 5 7<br />
<br />
t = 0901057 246710 6 1610 - 19<br />
43910 26<br />
= 2. 2810 18 s = 7. 210 1 0 a<br />
522<br />
, :<br />
1<br />
H +<br />
12 C<br />
13<br />
N<br />
1<br />
H + 13 C<br />
1 3<br />
N + ( 1)<br />
1 3<br />
C + e + + e ( 2)<br />
1 4 N + ( 3)<br />
1<br />
H + 14 N<br />
1 5 O + ( 4)<br />
1<br />
H +<br />
1 5 O<br />
15<br />
N<br />
1 5 N + e + + e ( 5)<br />
1 2<br />
C + 4 H e ( 6)<br />
( 1) , <br />
( 2) ( 3) <br />
?<br />
( 1) , <br />
, <br />
4 1 H<br />
<br />
4<br />
H e + 2e + + 3+ 2 e<br />
( 2) <br />
493
E 1 = ( 1007825 + 12000000 - 13005738)9315<br />
= 1944 MeV<br />
E 2 = ( 13005738 - 13003355)9315 - 20511<br />
= 1198 MeV<br />
E 3 = ( 1007825 + 13003355 - 14003074)9315<br />
= 7551 MeV<br />
E 4 = ( 1007825 + 14003074 - 15003065)9315<br />
= 7297 MeV<br />
E 5 = ( 15003065 - 15000109)9315 - 20511<br />
= 1732 MeV<br />
E 6 = ( 1007825 + 15000109 - 12000000 - 4002603)<br />
9315 =<br />
4966 MeV<br />
( 3) <br />
E =<br />
6<br />
E = 2469 MeV<br />
= 1<br />
494