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Файл:Физика электричество и магнетизм. Ч. 2. Лабораторный практикум
.pdf
ɤɨɧɬɭɪɚ ɫ ɬɨɤɨɦ (ɜ ɬɨɦ ɱɢɫɥɟ ɢ ɷɥɟɤɬɪɨɧɚ, ɜɪɚɳɚɸɳɟɝɨɫɹ ɜɨɤɪɭɝ ɹɞ-
p
ɪ
p
@
p
M
M
ȼ
ȼ
F
ɪɚ ɚɬɨɦɚ) ɹɜɥɹɟɬɫɹ
,
dq
– ɫɢɥɚ ɬɨɤɚ;
ɝɞɟ
I
ɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ
GG
ISn
m
G
:
m
(3.2)
dt
S – ɩɥɨɳɚɞɶ, ɨɝɪɚɧɢɱɟɧɧɚɹ ɤɨɧɬɭɪɨɦ (ɪɢɫ. 3.1).
Ɋɢɫ. 3.1
G
G
p
ɇɚɩɪɚɜɥɟɧɢɟ ɜɟɤɬɨɪɚ
nnn
m
ɨɩɪɟɞɟɥɹɟɬɫɹ ɩɪɚɜɢɥɨɦ ɛɭɪɚɜɱɢɤɚ:
ɟɫɥɢ ɪɭɤɨɹɬɤɭ ɛɭɪɚɜɱɢɤɚ ɜɪɚɳɚɬɶ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɨɛɬɟɤɚɧɢɹ ɤɨɧɬɭɪɚ ɬɨɤɨɦ, ɬɨ ɩɨɫɬɭɩɚɬɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ ɛɭɪɚɜɱɢɤɚ ɫɨɜɩɚɞɟɬ ɫ ɧɚɩɪɚɜ-
ɥɟɧɢɟɦ ɧɨɪɦɚɥɢ ɢ ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ
ɦɨɦɟɧɬɚ:
>
= Ⱥɦ2.
m
G
. Ɋɚɡɦɟɪɧɨɫɬɶ ɦɚɝɧɢɬɧɨɝɨ
m
Ɍɚɤɨɣ ɩɪɨɛɧɵɣ ɤɨɧɬɭɪ, ɩɨɦɟɳɟɧɧɵɣ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɜɟɞɟɬ ɫɟɛɹ
ɩɨɞɨɛɧɨ ɦɚɝɧɢɬɧɨɣ ɫɬɪɟɥɤɟ: ɨɧ ɪɚɡɜɨɪɚɱɢɜɚɟɬɫɹ ɜ ɩɨɥɟ, ɩɪɢɱɟɦ ɜ
ɪɚɜɧɨɜɟɫɧɨɦ ɩɨɥɨɠɟɧɢɢ ɪɚɦɤɢ, ɤɨɝɞɚ ɦɟɯɚɧɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɫɢɥ
G
, ɞɟɣɫɬɜɭɸɳɢɣ ɧɚ ɪɚɦɤɭ ɫ ɬɨɤɨɦ, ɫɬɚɧɨɜɢɬɫɹ ɪɚɜɧɵɦ ɧɭɥɸ
G
(
= 0), ɧɨɪɦɚɥɶ ɤ ɟɟ ɩɨɜɟɪɯɧɨɫɬɢ
GG
nnnn
ɨɤɚɡɵɜɚɟɬɫɹ ɧɚɩɪɚɜɥɟɧ-
0
ɧɨɣ ɜ ɬɭ ɠɟ ɫɬɨɪɨɧɭ, ɱɬɨ ɢ ɩɪɨɞɨɥɶɧɚɹ ɨɫɶ ɦɚɝɧɢɬɧɨɣ ɫɬɪɟɥɤɢ. ɗɬɨ
ɧɚɩɪɚɜɥɟɧɢɟ ɩɪɢɧɢɦɚɟɬɫɹ ɡɚ ɧɚɩɪɚɜɥɟɧɢɟ ɜɟɤɬɨɪɚ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤ-
G
ɰɢɢ
, ɤɨɬɨɪɚɹ ɹɜɥɹɟɬɫɹ ɨɫɧɨɜɧɨɣ ɫɢɥɨɜɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɦɚɝ-
ɧɢɬɧɨɝɨ ɩɨɥɹ. ȼɟɥɢɱɢɧɭ ɜɟɤɬɨɪɚ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ ɨɩɪɟɞɟɥɹɸɬ
ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ.
ɉɪɢ ɩɨɦɟɳɟɧɢɢ ɩɪɨɛɧɨɝɨ ɤɨɧɬɭɪɚ ɫ ɬɨɤɨɦ ɜ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ
(ɪɢɫ. 3.1) ɧɚ ɧɟɝɨ ɞɟɣɫɬɜɭɟɬ ɪɟɡɭɥɶɬɢɪɭɸɳɚɹ ɫɢɥɚ
G
(ɫɦ. 3.1), ɫɨɡɞɚɸ-
G
41
Ɇ
GG
Ɇ
p
B
p
p
p
ȼ
X
ȼ
F
X
B
G
ɳɚɹ ɜɪɚɳɚɬɟɥɶɧɵɣ ɦɟɯɚɧɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɜɟɥɢɱɢɧɨɣ:
ªº
rF
¬¼
ɂɫɩɨɥɶɡɭɹ ɡɚɤɨɧ Ⱥɦɩɟɪɚ (3.1), ɥɟɝɤɨ ɩɨɥɭɱɢɬɶ, ɱɬɨ
Ɉɛɨɡɧɚɱɢɦ
ɟɫɥɢ
ɝɭ), ɬɨ
ɟɫɥɢ
sin 0D
0Ɇ G;
sin 1D
GG
ªº
ɪ BpBpB
mmm
¬¼
G
G
sin( ) sin
pB
D
m
. Ɉɱɟɜɢɞɧɨ,
(ɩɪɢ ɷɬɨɦ ɜɟɤɬɨɪɵ
(ɩɪɢ ɷɬɨɦ
G
m
G
BA
), ɬɨ
sin( ).
G
G
ɢ
ɩɚɪɚɥɥɟɥɶɧɵ ɞɪɭɝ ɞɪɭ-
m
G
Ɇ M
max
.
GG G
Ɉɤɚɡɵɜɚɟɬɫɹ, ɱɬɨ ɞɥɹ ɥɸɛɨɝɨ ɩɪɨɛɧɨɝɨ ɤɨɧɬɭɪɚ (ɫ ɪɚɡɧɵɦɢ I ɢ S),
ɩɨɦɟɳɟɧɧɨɝɨ ɜ ɨɞɧɭ ɢ ɬɭ ɠɟ ɬɨɱɤɭ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɨɬɧɨɲɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɦɟɯɚɧɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɤ ɦɚɝɧɢɬɧɨɦɭ ɦɨɦɟɧɬɭ ɤɨɧɬɭɪɚ
M
max
– ɩɨɫɬɨɹɧɧɚɹ ɜɟɥɢɱɢɧɚ. ɗɬɨ ɨɬɧɨɲɟɧɢɟ ɫɥɭɠɢɬ ɤɨɥɢɱɟɫɬɜɟɧ-
m
ɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɢ ɹɜɥɹɟɬɫɹ
ɦɚɝɧɢɬɧɨɣ ɢɧ-
ɞɭɤɰɢɟɣ
G
M
G
ȼ n
max
0
. (3.3)
m
.
ȼɟɥɢɱɢɧɚ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ ɱɢɫɥɟɧɧɨ ɪɚɜɧɚ ɦɚɤɫɢɦɚɥɶɧɨɦɭ
ɦɟɯɚɧɢɱɟɫɤɨɦɭ ɦɨɦɟɧɬɭ, ɞɟɣɫɬɜɭɸɳɟɦɭ ɧɚ ɩɪɨɛɧɵɣ ɤɨɧɬɭɪ ɫ ɬɨɤɨɦ
ɫɢɥɨɣ
ɜɟɤɬɨɪɚ
I = 1 Ⱥ, ɩɥɨɳɚɞɶ ɤɨɬɨɪɨɝɨ S = 1 ɦ
G
ɫɨɜɩɚɞɚɟɬ ɫ ɧɨɪɦɚɥɶɸ
G
n
2
. ɉɪɢ ɷɬɨɦ ɧɚɩɪɚɜɥɟɧɢɟ
ɤ ɩɥɨɫɤɨɫɬɢ ɤɨɧɬɭɪɚ ɩɪɢ ɟɝɨ
0
ɪɚɜɧɨɜɟɫɧɨɦ ɩɨɥɨɠɟɧɢɢ ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ.
Ɇɚɝɧɢɬɧɨɟ ɩɨɥɟ ɩɪɨɹɜɥɹɟɬ ɫɟɛɹ ɬɚɤɠɟ ɜ ɬɨɦ, ɱɬɨ ɧɚ ɥɸɛɨɣ ɡɚɪɹɞ
q , ɞɜɢɠɭɳɢɣɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ
G
ɜ ɦɚɝɧɢɬɧɨɦ ɩɨɥɟ ɫ ɢɧɞɭɤɰɢɟɣ
G
,
ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ Ʌɨɪɟɧɰɚ:
GG
G
ªº
qB
, (3.4)
¬¼
G
ɝɞɟ
ɤɚ»
42
– ɦɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ; ɤɜɚɞɪɚɬɧɵɟ ɫɤɨɛɤɢ ɨɛɨɡɧɚɱɚɸɬ ɜɟɤ-
ɬɨɪɧɨɟ ɩɪɨɢɡɜɟɞɟɧɢɟ.
ɇɚɩɪɚɜɥɟɧɢɟ ɫɢɥɵ Ʌɨɪɟɧɰɚ ɨɩɪɟɞɟɥɹɸɬ ɩɪɚɜɢɥɨɦ «ɛɭɪɚɜɱɢ-
>5@. Ⱥɛɫɨɥɸɬɧɚɹ ɜɟɥɢɱɢɧɚ (ɦɨɞɭɥɶ) ɫɢɥɵ Ʌɨɪɟɧɰɚ ɪɚɜɧɚ
sin( )
F
ȼ
X
F
X
r
r
GG
qB B
XX
G
. (3.5)
ɂɡ ɪɚɜɟɧɫɬɜɚ (3.5) ɫɥɟɞɭɟɬ, ɱɬɨ ɦɨɞɭɥɶ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ
G
G
ɱɢɫɥɟɧɧɨ ɪɚɜɟɧ ɦɚɤɫɢɦɚɥɶɧɨɣ (ɩɪɢ sin( ) 1B
ɧɚ ɟɞɢɧɢɱɧɵɣ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɡɚɪɹɞ (
ɧɢɱɧɨɣ ɫɤɨɪɨɫɬɶɸ (
=1 ɦ/ɫ) ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ:
X
) ɫɢɥɟ, ɞɟɣɫɬɜɭɸɳɟɣ
q=+1 Ʉɥ), ɞɜɢɠɭɳɢɣɫɹ ɫ ɟɞɢ-
G
max
B
. (3.6)
q
ȿɞɢɧɢɰɚ ɢɡɦɟɪɟɧɢɹ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ – ɬɟɫɥɚ; ɟɟ ɪɚɡɦɟɪɧɨɫɬɶ
[
ȼ] = H/(A ɦ) = ɤɝ/(ɫ2 Ⱥ) = Ɍɥ.
Ɂɚɤɨɧ Ȼɢɨ – ɋɚɜɚɪɚ – Ʌɚɩɥɚɫɚ. ɉɪɢɧɰɢɩ ɫɭɩɟɪɩɨɡɢɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
G
ɂɧɞɭɤɰɢɹ dB
ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɫɨɡɞɚɜɚɟɦɨɝɨ ɬɨɤɨɦ ɫɢɥɨɣ
ɬɨɪɵɣ ɬɟɱɟɬ ɱɟɪɟɡ ɛɟɫɤɨɧɟɱɧɨ ɦɚɥɵɣ ɭɱɚɫɬɨɤ
G
dl
ɩɪɨɜɨɞɧɢɤɚ, ɦɨɠɟɬ
I, ɤɨ-
ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɚ ɫ ɩɨɦɨɳɶɸ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨ ɩɨɥɭɱɟɧɧɨɝɨ ɡɚɤɨɧɚ
– ɋɚɜɚɪɚ – Ʌɚɩɥɚɫɚ:
Ȼɢɨ
G
dB
P
4
7
410
P S
ɝɞɟ
0
ɤɜɚɞɪɚɬɧɵɟ ɫɤɨɛɤɢ – ɜɟɤɬɨɪɧɨɟ ɩɪɨɢɡɜɟɞɟɧɢɟ;
ɧɚɩɪɚɜɥɟɧɢɟ ɜɟɤɬɨɪɚ
G
– ɜɟɤɬɨɪ, ɩɪɨɜɟɞɟɧɧɵɣ ɨɬ ɷɥɟɦɟɧɬɚ ɬɨɤɚ ( IdlG) ɜ ɬɨɱɤɭ, ɜ ɤɨɬɨ-
ɪɨɣ ɜɵɱɢɫɥɹɸɬ
Ƚɧ/ɦ – ɦɚɝɧɢɬɧɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜ ɋɂ;
G
ld
ɫɨɜɩɚɞɚɟɬ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɬɨɤɚ I;
G
Bd
.
ªº
Idlr
¬¼
0
S
G
G
, (3.7)
3
r
Ɇɨɞɭɥɶ
ɝɞɟ D – ɭɝɨɥ ɦɟɠɞɭ ɜɟɤɬɨɪɚɦɢ ld
dB
ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ
P
Idl
dB
0
S
4
G
ɢ
sin
D
, (3.8)
2
r
G
.
G
ɇɚɩɪɚɜɥɟɧɢɟ
Ⱦɥɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɤɚɤ ɢ ɞɥɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ, ɫɩɪɚɜɟɞɥɢɜ ɩɪɢɧ-
ɰɢɩ ɫɭɩɟɪɩɨɡɢɰɢɢ: ɦɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ ɩɨɥɹ, ɫɨɡɞɚɧɧɚɹ ɧɟɫɤɨɥɶɤɢ-
Bd
ɨɩɪɟɞɟɥɹɸɬ ɩɪɚɜɢɥɨɦ «ɛɭɪɚɜɱɢɤɚ» >5@.
43
ɦɢ ɬɨɤɚɦɢ, ɪɚɜɧɚ ɜɟɤɬɨɪɧɨɣ ɫɭɦɦɟ ɢɧɞɭɤɰɢɣ ɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ ɤɚɠ-
B
x
ȼ
x
y
x
B
ȼ
ȼ
ȼ
ȼ
ɞɨɝɨ ɬɨɤɚ ɜ ɨɬɞɟɥɶɧɨɫɬɢ:
GG
B
(3.9)
¦
i
i
ɢɥɢ
G
GG
ɝɞɟ
dB ,
dB
dB
,
idB jdB kdB
³³³
, – ɩɪɨɟɤɰɢɢ ɧɚ ɨɫɢ ɤɨɨɪɞɢɧɚɬ ɜɟɤɬɨɪɚ dBG, ɫɨɡ-
z
ɞɚɧɧɨɝɨ ɛɟɫɤɨɧɟɱɧɨ ɦɚɥɵɦ ɷɥɟɦɟɧɬɨɦ ɬɨɤɚ (
G
yz
, (3.10)
G
Idl
).
Ⱦɥɹ ɫɥɭɱɚɹ (3.10) ɜɟɥɢɱɢɧɚ ɪɟɡɭɥɶɬɢɪɭɸɳɟɝɨ ɜɟɤɬɨɪɚ ɪɚɜɧɚ
G
222
BBB
.
yz
ɋ ɩɨɦɨɳɶɸ ɡɚɤɨɧɚ Ȼɢɨ – ɋɚɜɚɪɚ – Ʌɚɩɥɚɫɚ ɢ ɩɪɢɧɰɢɩɚ ɫɭɩɟɪɩɨɡɢɰɢɢ ɦɨɠɧɨ ɨɩɪɟɞɟɥɹɬɶ ɧɚɩɪɚɜɥɟɧɢɟ ɢ ɜɟɥɢɱɢɧɭ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ ɩɨɥɟɣ, ɫɨɡɞɚɧɧɵɯ ɬɨɤɚɦɢ ɪɚɡɥɢɱɧɨɣ ɤɨɧɮɢɝɭɪɚɰɢɢ
>5@.
ɋɢɥɨɜɵɟ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
G
Ɇɚɝɧɢɬɧɨɟ ɩɨɥɟ
ɥɨɜɵɯ ɥɢɧɢɣ, ɤɨɬɨɪɵɟ ɩɪɨɜɨɞɹɬɫɹ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɤɚɫɚɬɟɥɶɧɚɹ
ɤ ɧɢɦ ɜ ɤɚɠɞɨɣ ɬɨɱɤɟ ɫɨɜɩɚɞɚɥɚ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɜɟɤɬɨɪɚ
ɫɢɥɨɜɵɯ ɥɢɧɢɣ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɜɟɥɢɱɢɧɟ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ
ɩɨɥɹ ɜ ɞɚɧɧɨɣ ɨɛɥɚɫɬɢ. Ɂɚɦɟɬɢɦ, ɱɬɨ ɧɚɩɪɚɜɥɟɧɢɟ ɜɟɤɬɨɪɚ
ɦɨɠɧɨ ɝɪɚɮɢɱɟɫɤɢ ɢɡɨɛɪɚɠɚɬɶ ɫ ɩɨɦɨɳɶɸ ɫɢ-
G
. Ƚɭɫɬɨɬɚ
G
.ɜɨɤɪɭɝ
ɩɪɨɜɨɞɧɢɤɨɜ ɫ ɬɨɤɚɦɢ ɜ ɥɸɛɨɣ ɬɨɱɤɟ ɩɪɨɫɬɪɚɧɫɬɜɚ ɦɨɠɧɨ ɧɚɣɬɢ
ɫ ɩɨɦɨɳɶɸ ɡɚɤɨɧɚ Ȼɢɨ – ɋɚɜɚɪɚ – Ʌɚɩɥɚɫɚ.
ɋɢɥɨɜɵɟ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ – ɡɚɦɤɧɭɬɵɟ ɤɪɢɜɵɟ, ɬɚɤɨɟ ɩɨɥɟ
ɹɜɥɹɟɬɫɹ ɜɢɯɪɟɜɵɦ. ɇɚɩɪɢɦɟɪ, ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɤɪɭɝɨɜɨɝɨ ɜɢɬɤɚ ɪɚɞɢɭɫɨɦ
ȼ ɰɟɧɬɪɟ ɜɢɬɤɚ (ɬɨɱɤɚ
R ɫ ɬɨɤɨɦ ɫɢɥɨɣ I ɢɡɨɛɪɚɠɟɧɵ ɧɚ ɪɢɫ. 3.2.
Ɉ) ɜɟɤɬɨɪ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ
G
ɧɚɩɪɚɜɥɟɧ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɤ ɩɥɨɫɤɨɫɬɢ ɜɢɬɤɚ ɢ ɟɝɨ ɧɚɩɪɚɜɥɟɧɢɟ ɨɩɪɟɞɟɥɹɸɬ ɫ ɩɨɦɨɳɶɸ ɩɪɚɜɢɥɚ ɛɭɪɚɜɱɢɤɚ, ɜɪɚɳɚɹ ɪɭɤɨɹɬɤɭ ɜɞɨɥɶ ɧɚɩɪɚɜɥɟɧɢɹ ɬɨɤɚ. Ⱦɥɹ ɧɚɯɨɠɞɟɧɢɹ ɜɟɥɢɱɢɧɵ
ɩɨɥɶɡɨɜɚɬɶɫɹ ɡɚɤɨɧɚɦɢ (3.7) ɢ (3.10)
ȼ ɜ ɰɟɧɬɪɟ ɜɢɬɤɚ ɧɚɞɨ ɜɨɫ-
>5].
44
R
Ɋɢɫ. 3.2
Ɉɤɚɡɵɜɚɟɬɫɹ, ɱɬɨ
P
I
0
ȼ
ɰ
(3.11)
.
2
ɋɢɥɨɜɵɟ ɥɢɧɢɢ ɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɦɚɝɧɢɬɚ (ɡɚɦɵɤɚɸɬɫɹ ɜɧɭɬɪɢ ɜɟɳɟɫɬɜɚ ɮɟɪɪɨɦɚɝɧɟɬɢɤɚ) ɢ ɩɪɹɦɨɥɢɧɟɣɧɨɝɨ ɛɟɫɤɨɧɟɱɧɨɝɨ ɬɨɤɚ ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 3.3,
ɚ, ɛ.
ɚ ɛ
Ɋɢɫ. 3.3
ȼɨɤɪɭɝ Ɂɟɦɥɢ ɫɭɳɟɫɬɜɭɟɬ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ, ɨɫɶ ɤɨɬɨɪɨɝɨ ɫɨɫɬɚɜɥɹɟɬ
ɧɟɛɨɥɶɲɨɣ ɭɝɨɥ (ɨɤɨɥɨ 12°) ɫ ɟɟ ɨɫɶɸ ɜɪɚɳɟɧɢɹ. ɋɢɥɨɜɵɟ ɥɢɧɢɢ ɜɵɯɨɞɹɬ ɢɡ ɫɟɜɟɪɧɨɝɨ ɩɨɥɸɫɚ, ɜɯɨɞɹɬ ɜ ɸɠɧɵɣ ɢ ɡɚɦɵɤɚɸɬɫɹ ɜɧɭɬɪɢ Ɂɟɦɥɢ.
ɋɭɳɟɫɬɜɨɜɚɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ Ɂɟɦɥɢ ɩɪɟɞɩɨɥɨɠɢɬɟɥɶɧɨ ɫɜɹɡɚɧɨ ɫ ɪɚɫɩɥɚɜɥɟɧɧɨɣ ɱɚɫɬɶɸ ɹɞɪɚ ɧɚɲɟɣ ɩɥɚɧɟɬɵ, ɫɨɫɬɨɹɳɟɝɨ ɜ ɨɫɧɨɜɧɨɦ ɢɡ ɠɢɞɤɢɯ ɠɟɥɟɡɚ, ɧɢɤɟɥɹ, ɤɪɟɦɧɢɹ. ɀɢɞɤɨɟ ɹɞɪɨ ɢɦɟɟɬ ɬɟɦ-
45
ɩɟɪɚɬɭɪɭ t ~ 5000 °ɋ ɢ ɞɚɜɥɟɧɢɟ ɜ 2 ɦɥɧ ɪɚɡ ɛɨɥɶɲɟɟ, ɱɟɦ ɧɚ ɩɨɜɟɪɯ-
B
ɧɨɫɬɢ Ɂɟɦɥɢ; ɩɪɢ ɬɚɤɢɯ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɯ ɭɫɥɨɜɢɹɯ ɦɧɨɝɢɟ ɷɥɟɤɬɪɨɧɵ ɧɟ ɫɜɹɡɚɧɵ ɜ ɚɬɨɦɚɯ. ɉɪɢ ɰɢɪɤɭɥɹɰɢɢ ɜɟɳɟɫɬɜɚ ɹɞɪɚ ɜɧɭɬɪɢ
Ɂɟɦɥɢ (ɢɡ-ɡɚ ɟɟ ɜɪɚɳɟɧɢɹ) ɨɛɪɚɡɭɸɬɫɹ ɤɪɭɝɨɜɵɟ ɬɨɤɢ (ɜ ɨɫɧɨɜɧɨɦ
ɩɨɬɨɤɢ ɷɥɟɤɬɪɨɧɨɜ), ɫɨɡɞɚɸɳɢɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɧɚɲɟɣ ɩɥɚɧɟɬɵ.
I ɢ II ɭɪɚɜɧɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ ɞɥɹ ɦɚɝɧɢɬɨɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ ɜ ɜɚɤɭɭɦɟ
ɉɨɫɤɨɥɶɤɭ ɩɪɢ ɢɧɬɟɪɩɪɟɬɚɰɢɢ ɩɨɬɨɤɚ ɜɟɤɬɨɪɧɨɝɨ ɩɨɥɹ ɫ ɩɨɦɨɳɶɸ
ɫɢɥɨɜɵɯ ɥɢɧɢɣ, ɩɨɥɧɵɣ ɩɨɬɨɤ ɪɚɜɟɧ ɫɭɦɦɚɪɧɨɦɭ ɱɢɫɥɭ ɫɢɥɨɜɵɯ ɥɢɧɢɣ, ɜɯɨɞɹɳɢɯ ɜ ɡɚɦɤɧɭɬɭɸ ɩɨɜɟɪɯɧɨɫɬɶ (ɫɨ ɡɧɚɤɨɦ ɦɢɧɭɫ) ɢ ɜɵɯɨɞɹɳɢɯ ɢɡ ɧɟɟ (ɫɨ ɡɧɚɤɨɦ ɩɥɸɫ), ɬɨ, ɨɱɟɜɢɞɧɨ, ɱɬɨ ɜɫɥɟɞɫɬɜɢɟ ɜɢɯɪɟɜɨɝɨ ɯɚɪɚɤɬɟɪɚ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɩɨɬɨɤ ɜɟɤɬɨɪɚ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ
K
ȼ
ɱɟɪɟɡ ɥɸɛɭɸ ɡɚɦɤɧɭɬɭɸ ɩɨɜɟɪɯɧɨɫɬɶ
G
ɗɬɨ I ɭɪɚɜɧɟɧɢɟ Ɇɚɤɫɜɟɥɥɚ ɞɥɹ ɩɨɫɬɨɹɧɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ. ȿɝɨ
ɮɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɜ ɩɪɢɪɨɞɟ ɧɟ ɫɭɳɟɫɬɜɭɟɬ ɦɚɝɧɢɬɧɵɯ ɡɚɪɹɞɨɜ (ɦɚɝɧɢɬɧɵɯ ɦɨɧɨɩɨɥɟɣ), ɩɨɞɨɛɧɵɯ ɢɫɬɨɱɧɢɤɚɦ
ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ, ɚ ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɹɜɥɹɸɬɫɹ
ɡɚɦɤɧɭɬɵɦɢ ɤɪɢɜɵɦɢ.
II ɭɪɚɜɧɟɧɢɟ Ɇɚɤɫɜɟɥɥɚ ɞɥɹ ɩɨɫɬɨɹɧɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ ɜɚɤɭɭɦɟ ɧɚɡɵɜɚɸɬ ɬɟɨɪɟɦɨɣ ɨ ɰɢɪɤɭɥɹɰɢɢ
ɞɭɤɰɢɢ. Ɍɟɨɪɟɦɚ ɝɥɚɫɢɬ: ɰɢɪɤɭɥɹɰɢɹ ɜɟɤɬɨɪɚ ɦɚɝɧɢɬɧɨɣ ɢɧɞɭɤɰɢɢ ɩɨ
ɡɚɦɤɧɭɬɨɦɭ ɤɨɧɬɭɪɭ
ɬɭɪ
, ɭɦɧɨɠɟɧɧɨɣ ɧɚ ɦɚɝɧɢɬɧɭɸ ɩɨɫɬɨɹɧɧɭɸ 0P :
L ɪɚɜɧɚ ɫɭɦɦɟ ɬɨɤɨɜ, ɩɪɨɧɢɡɵɜɚɸɳɢɯ ɷɬɨɬ ɤɨɧ-
G
()0.
BdS
³
v
S
S ɪɚɜɟɧ ɧɭɥɸ:
(3.12)
>5@ ɜɟɤɬɨɪɚ ɦɚɝɧɢɬɧɨɣ ɢɧ-
P
n
ɢɥɢ
¦
0
i
1
i
G
G
dl
v
³
L
.
dl I
dl
ɝɞɟ
(3.13) ɧɟɨɛɯɨɞɢɦɨ ɡɚɩɢɫɵɜɚɬɶ ɬɨɤɢ, ɬɟɤɭɳɢɟ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɯ
ɧɚɩɪɚɜɥɟɧɢɹɯ ɫ ɪɚɡɧɵɦɢ ɡɧɚɤɚɦɢ.
ɤɪɭɝ ɤɚɠɞɨɝɨ ɬɨɤɚ (ɞɜɢɠɭɳɟɝɨɫɹ ɡɚɪɹɞɚ) ɫɭɳɟɫɬɜɭɟɬ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ
46
– ɛɟɫɤɨɧɟɱɧɨ ɦɚɥɵɣ ɷɥɟɦɟɧɬ ɞɥɢɧɵ ɤɨɧɬɭɪɚ L, ɚ ɜɟɤɬɨɪ
G
ld
ɧɚɩɪɚɜɥɟɧ ɩɨ ɤɚɫɚɬɟɥɶɧɨɣ ɤ ɤɨɧɬɭɪɭ ɜ ɬɨɦ ɦɟɫɬɟ, ɝɞɟ ɜɵɛɪɚɧ
ɷɥɟɦɟɧɬ
ɇɚɞɨ ɩɨɦɧɢɬɶ, ɱɬɨ ɩɪɢ ɜɵɱɢɫɥɟɧɢɢ ɚɥɝɟɛɪɚɢɱɟɫɤɨɣ ɫɭɦɦɵ ɬɨɤɨɜ
Ɏɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ II ɭɪɚɜɧɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɱɬɨ ɜɨ-
G
G
Bdl jdS P
v
³³
LS
G
G
,
0
(3.13)
ɢ ɩɨɫɤɨɥɶɤɭ ɰɢɪɤɭɥɹɰɢɹ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɨɬɥɢɱɧɚ ɨɬ ɧɭɥɹ, ɬɨ ɯɚɪɚɤ-
G
ɬɟɪ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ – ɜɢɯɪɟɜɨɣ.
3.3. Ɉɩɢɫɚɧɢɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɭɫɬɚɧɨɜɤɢ
Ɇɚɝɧɢɬɧɨɟ ɩɨɥɟ Ɂɟɦɥɢ ɹɜɥɹɟɬɫɹ ɫɬɚɰɢɨɧɚɪɧɵɦ. ɉɪɢ ɨɪɢɟɧɬɢɪɨɜɚɧɢɢ
ɧɚ ɦɟɫɬɧɨɫɬɢ ɫ ɩɨɦɨɳɶɸ ɤɨɦɩɚɫɚ ɩɪɚɤɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ ɢɦɟɟɬ ɝɨɪɢɡɨɧɬɚɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɢɧɞɭɤɰɢɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ, ɤɨɬɨɪɚɹ ɦɚɤɫɢɦɚɥɶɧɚ
ɜɛɥɢɡɢ ɷɤɜɚɬɨɪɚ ɢ ɭɛɵɜɚɟɬ ɩɪɢ ɩɪɢɛɥɢɠɟɧɢɢ ɤ ɦɚɝɧɢɬɧɵɦ ɩɨɥɸɫɚɦ,
ɚ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɟɟ ɜɟɥɢɱɢɧɵ (
ɝɟɧɫ-ɝɚɥɶɜɚɧɨɦɟɬɪ
, ɩɪɟɞɫɬɚɜɥɟɧɧɵɣ ɫɥɟɜɚ ɧɚ ɪɢɫ. 3.4.
ȼ
) ɜ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɢɫɩɨɥɶɡɭɸɬ ɬɚɧ-
ɝ
Ɋɢɫ. 3.4
Ɍɚɧɝɟɧɫ-ɝɚɥɶɜɚɧɨɦɟɬɪ ɫɨɫɬɨɢɬ ɢɡ ɤɪɭɝɨɜɨɣ (ɪɚɞɢɭɫɨɦ R) ɬɨɧɤɨɣ
ɤɚɬɭɲɤɢ
ɧɢɤɭ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ
1, ɧɚ ɤɨɬɨɪɭɸ ɧɚɦɨɬɚɧ ɩɪɨɜɨɞ, ɩɨɞɤɥɸɱɟɧɧɵɣ ɤ ɢɫɬɨɱ-
2. ɉɥɨɫɤɨɫɬɶ ɤɚɬɭɲɤɢ ɪɚɫɩɨɥɨɠɟɧɚ ɜɟɪɬɢ-
ɤɚɥɶɧɨ ɬɚɤ, ɱɬɨ ɟɟ ɰɟɧɬɪ ɫɨɜɦɟɳɟɧ ɫ ɰɟɧɬɪɨɦ ɦɚɝɧɢɬɧɨɣ ɫɬɪɟɥɤɢ
4 ɤɨɦɩɚɫɚ 5.
ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɰɟɩɶ (ɩɪɚɜɚɹ ɱɚɫɬɶ ɪɢɫ. 3.4) ɬɚɧɝɟɧɫ-ɝɚɥɶɜɚɧɨɦɟɬɪɚ
ɫɨɫɬɨɢɬ ɢɡ ɢɫɬɨɱɧɢɤɚ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ
2, ɚɦɩɟɪɦɟɬɪɚ 6, ɩɟɪɟɦɟɧɧɨɝɨ
ɫɨɩɪɨɬɢɜɥɟɧɢɹ (ɪɟɡɢɫɬɨɪɚ) 7, ɤɨɬɨɪɵɣ ɢɫɩɨɥɶɡɭɟɬɫɹ ɞɥɹ ɢɡɦɟɧɟɧɢɹ
ɫɢɥɵ ɬɨɤɚ ɜ ɤɚɬɭɲɤɟ, ɢ ɩɟɪɟɤɥɸɱɚɬɟɥɹ ɧɚɩɪɚɜɥɟɧɢɹ ɬɨɤɚ (ɤɨɦɦɭɬɚɬɨɪɚ)
8. Ʉɨɦɦɭɬɚɰɢɹ ɬɨɤɚ ɜ ɩɪɨɰɟɫɫɟ ɢɡɦɟɪɟɧɢɣ ɩɪɨɢɡɜɨɞɢɬɫɹ ɞɥɹ
ɭɜɟɥɢɱɟɧɢɹ ɬɨɱɧɨɫɬɢ ɨɩɵɬɚ
Ɉɱɟɜɢɞɧɨ, ɱɬɨ ɜ ɨɬɫɭɬɫɬɜɢɢ ɜ ɜɢɬɤɚɯ ɤɚɬɭɲɤɢ
ɫɬɪɟɥɤɚ
ȼ
ɝ
4 ɨɪɢɟɧɬɢɪɨɜɚɧɚ ɜɞɨɥɶ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ
ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ Ɂɟɦɥɢ. ɉɪɢ ɷɬɨɦ ɤɚɬɭɲɤɭ ɧɚɞɨ ɩɨɜɟɪɧɭɬɶ ɜɨɤɪɭɝ
.
1 ɬɨɤɚ ɦɚɝɧɢɬɧɚɹ
47
ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɢ 3 ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɧɚɩɪɚɜɥɟɧɢɟ ɫɬɪɟɥɤɢ ɤɨɦ-
ȼ
G
ȼ
ȼ
ȼ
R
ɩɚɫɚ (ɚ ɡɧɚɱɢɬ, ɢ ɜɟɤɬɨɪɚ
G
) ɫɨɜɩɚɥɨ ɫ ɟɟ ɩɥɨɫɤɨɫɬɶɸ (ɪɢɫ. 3.5).
ɝ
Ɋɢɫ. 3.5
ȿɫɥɢ ɩɨ ɜɢɬɤɚɦ ɤɚɬɭɲɤɢ ɬɟɱɟɬ ɬɨɤ ɫɢɥɨɣ I, ɧɚɩɪɢɦɟɪ ɜ ɧɚɩɪɚɜɥɟɧɢɢ, ɭɤɚɡɚɧɧɨɦ ɧɚ ɪɢɫ. 3.5, ɬɨ ɜɨɤɪɭɝ ɤɚɬɭɲɤɢ ɜɨɡɧɢɤɚɟɬ ɦɚɝɧɢɬɧɨɟ
ɩɨɥɟ, ɫɢɥɨɜɵɟ ɥɢɧɢɢ ɤɨɬɨɪɨɝɨ ɢɡɨɛɪɚɠɟɧɵ ɧɚ ɪɢɫ. 3.2. ɉɪɢ ɷɬɨɦ ɜ
ȼ
ɰɟɧɬɪɟ ɤɚɬɭɲɤɢ ɦɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ
ɧɚɩɪɚɜɥɟɧɚ ɬɚɤ, ɤɚɤ ɩɨɤɚɡɚ-
ɤ
ɧɨ ɧɚ ɪɢɫ. 3.5. ɉɪɢ ɷɬɨɦ ɦɚɝɧɢɬɧɚɹ ɫɬɪɟɥɤɚ (ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɢɧɰɢɩɨɦ ɫɭɩɟɪɩɨɡɢɰɢɢ (3.9)) ɩɨɜɟɪɧɟɬɫɹ ɜ ɧɚɩɪɚɜɥɟɧɢɢ
ɫɭɦɦɵ
GG G
ȼȼ
ɤɝ
Ɉɩɪɟɞɟɥɢɜ ɭɝɨɥ
(ɫɦ. ɪɢɫ. 3.5).
D (ɫɦ. ɪɢɫ. 3.5) ɩɨ ɲɤɚɥɟ ɤɨɦɩɚɫɚ, ɦɨɠɧɨ ɧɚɣɬɢ
ɜɟɤɬɨɪɧɨɣ
ɤ
ȼ
ɝ
Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɪɚɫɫɱɢɬɚɬɶ ɦɚɝɧɢɬɧɭɸ ɢɧɞɭɤɰɢɸ
ɬɨɧɤɨɣ ɤɚɬɭɲɤɢ ɫ ɱɢɫɥɨɦ ɜɢɬɤɨɜ
ɜɢɬɤɨɦ (3.11), ɩɨ ɤɨɬɨɪɨɦɭ ɬɟɱɟɬ ɬɨɤ ɫɢɥɨɣ (
B
ɤ
. (3.14)
D
tg
ɜ ɰɟɧɬɪɟ
ɤ
N, ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɟɟ ɨɞɢɧɚɪɧɵɦ
INI
ɤ
NI
P
0
(3.15)
.
), ɬ.ɟ.
2
ɂɡ (3.14) ɢ (3.15) ɩɨɥɭɱɚɟɦ ɪɚɫɱɟɬɧɭɸ ɮɨɪɦɭɥɭ ɞɥɹ
NI
P
48
B
ɝ
2tg
0
(3.16)
.
D
R
3.4. ɉɨɪɹɞɨɤ ɜɵɩɨɥɧɟɧɢɹ ɪɚɛɨɬɵ
ȼ
ȼ
ȼ
ȼ
ȼ
I
R
ɢ ɨɛɪɚɛɨɬɤɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɞɚɧɧɵɯ
1. ȼ ɨɬɫɭɬɫɬɜɢɟ ɬɨɤɚ ɜ ɤɚɬɭɲɤɟ 1 ɩɨɜɟɪɧɭɬɶ ɟɟ ɬɚɤ, ɱɬɨɛɵ ɦɚɝɧɢɬɧɚɹ ɫɬɪɟɥɤɚ
ɤɨɦɩɚɫɚ ɩɪɢ ɷɬɨɦ
2. ȼɤɥɸɱɢɬɶ ɢɫɬɨɱɧɢɤ ɷɥɟɤɬɪɨɩɢɬɚɧɢɹ, ɜɵɠɞɚɬɶ ɦɢɧɭɬ ɩɹɬɶ ɞɥɹ
ɩɪɨɝɪɟɜɚ.
3. ɂɫɩɨɥɶɡɭɹ ɪɟɡɢɫɬɨɪ
ɡɧɚɱɟɧɢɟ ɬɨɤɚ
4. Ɉɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɟ ɭɝɥɚ
ɧɢɬɶ ɧɚɩɪɚɜɥɟɧɢɟ ɬɨɤɚ ɢ ɨɩɪɟɞɟɥɢɬɶ ɭɝɨɥ
ɩɨɜɟɪɧɟɬɫɹ ɧɚ 180°. ɇɚɣɬɢ ɫɪɟɞɧɟɚɪɢɮɦɟɬɢɱɟɫɤɨɟ ɡɧɚɱɟɧɢɟ
DD
D
5. ɉɨɜɬɨɪɢɬɶ ɢɡɦɟɪɟɧɢɹ ɩɩ. 3, 4 ɞɥɹ ɪɚɡɧɵɯ ɡɧɚɱɟɧɢɣ ɫɢɥɵ ɬɨɤɚ
ɧɟ ɦɟɧɟɟ 10 ɪɚɡ, ɡɚɧɨɫɹ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɟ ɞɚɧɧɵɟ ɜ ɬɚɛɥ. 3.1.
6. ɉɨ ɮɨɪɦɭɥɟ (3.16) ɜɵɱɢɫɥɢɬɶ ɞɥɹ ɤɚɠɞɨɝɨ ɡɧɚɱɟɧɢɹ ɫɢɥɵ ɬɨɤɚ
I ɜɟɥɢɱɢɧɭ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ
i
ɡɧɚɱɟɧɢɟ
7. ɇɚɣɬɢ ɫɥɭɱɚɣɧɭɸ ɚɛɫɨɥɸɬɧɭɸ ɨɲɢɛɤɭ ɤɚɠɞɨɝɨ ɢɡɦɟɪɟɧɢɹ
ɝɝɝi
ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɨɱɧɨɫɬɶɸ ɷɤɫɩɟɪɢɦɟɧɬɚ. Ɉɰɟɧɢɬɶ ɫɥɭɱɚɣɧɭɸ ɨɬɧɨ-
ɫɢɬɟɥɶɧɭɸ ɩɨɝɪɟɲɧɨɫɬɶ ɢɡɦɟɪɟɧɢɣ
ɜ ɬɚɛɥ. 3.1.
8. ɉɨɫɬɪɨɢɬɶ ɧɚ ɦɢɥɥɢɦɟɬɪɨɜɤɟ ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ
ɢ ɭɛɟɞɢɬɶɫɹ ɜ ɬɨɦ, ɱɬɨ ɬɨɱɤɢ ɧɚɯɨɞɹɬɫɹ ɜɛɥɢɡɢ ɩɪɹɦɨɣ ɥɢɧɢɢ. Ɉɩɪɟ-
ɞɟɥɢɬɶ ɩɨ ɝɪɚɮɢɤɭ ɤɨɷɮɮɢɰɢɟɧɬ
4 ɤɨɦɩɚɫɚ 5 ɨɤɚɡɚɥɚɫɶ ɜ ɟɟ ɩɥɨɫɤɨɫɬɢ. Ɉɬɫɱɟɬ ɩɨ ɲɤɚɥɟ
0D °.
0
7, ɭɫɬɚɧɨɜɢɬɶ ɩɨ ɩɨɤɚɡɚɧɢɹɦ ɚɦɩɟɪɦɟɬɪɚ 6
I
.
1
D
. ɋ ɩɨɦɨɳɶɸ ɤɨɦɦɭɬɚɬɨɪɚ 8 ɢɡɦɟ-
1
c
D
. ɉɪɢ ɷɬɨɦ ɜɟɤɬɨɪ
1
c
11
. ȼɫɟ ɞɚɧɧɵɟ ɡɚɧɟɫɬɢ ɜ ɬɚɛɥ. 3.1.
2
ɢ ɧɚɣɬɢ ɟɟ ɫɪɟɞɧɟɟ
ɝi
.
ɝ
ȼȼ'
ɢ ɟɟ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ
'
. Ɂɚɩɢɫɚɬɶ ɪɟɡɭɥɶɬɚɬ
ɝ
ȼ
'
ɝ
ȼ
G . Ɂɚɧɟɫɬɢ ɟɟ
ɝ
100 %
ȼ
ɝ
tg
tg
D
ɤ
ɷɤɫɩɟɪ
– ɷɬɨ ɡɧɚɱɟɧɢɟ ɞɥɹ
D ɨɬ
i
G
ɤ
I
I
i
i
ɤɚɠɞɨɝɨ ɬɚɧɝɟɧɫ-ɝɚɥɶɜɚɧɨɦɟɬɪɚ ɹɜɥɹɟɬɫɹ ɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɨɣ ɤɨɧɫɬɚɧɬɨɣ ɩɪɢɛɨɪɚ. ɋɪɚɜɧɢɬɶ ɜɟɥɢɱɢɧɵ
N
P
0
ɤ
ɬɟɨɪ
2
.
B
ɝ
ɤ ɢ
ɷɤɫɩɟɪ
ɤ , ɝɞɟ
ɬɟɨɪ
49
Ɍɚɛɥɢɰɚ 3.1
ɉɚɪɚɦɟɬɪɵ ɤɚɬɭɲɤɢ ɬɚɧɝɟɧɫ-ɝɚɥɶɜɚɧɨɦɟɬɪɚ
ɑɢɫɥɨ ɜɢɬɤɨɜ N = 100; ɪɚɞɢɭɫ R = 0,17 ɦ
ɇɨɦɟɪ
ɨɩɵɬɚ
1
2
…
…
10
,iI
A
ȼȼr'
D
i
ɝɝ
c
D
i
D
tgD
,B
Ɍɥ
ɝ
ȼG
ɝ
B'
Ʉɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ
1. Ɇɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɤɨɧɬɭɪɚ ɫ ɬɨɤɨɦ. ɋɢɥɨɜɨɟ ɞɟɣɫɬɜɢɟ ɦɚɝɧɢɬ-
ɧɨɝɨ ɩɨɥɹ ɧɚ ɤɨɧɬɭɪ ɫ ɬɨɤɨɦ. Ɇɚɝɧɢɬɧɚɹ ɢɧɞɭɤɰɢɹ. ɋɢɥɚ Ʌɨɪɟɧɰɚ.
2. Ɂɚɤɨɧ Ȼɢɨ – ɋɚɜɚɪɚ – Ʌɚɩɥɚɫɚ. ɉɪɢɧɰɢɩ ɫɭɩɟɪɩɨɡɢɰɢɢ ɞɥɹ ɦɚɝ-
ɧɢɬɧɵɯ ɩɨɥɟɣ.
3. Ⱦɟɣɫɬɜɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɧɚ ɬɨɤ. Ɂɚɤɨɧ Ⱥɦɩɟɪɚ.
4. ȼɵɱɢɫɥɢɬɶ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ ɜ ɰɟɧɬɪɟ ɤɨɪɨɬɤɨɣ ɤɪɭɝɨɜɨɣ ɤɚɬɭɲ-
ɤɢ ɫ ɬɨɤɨɦ.
5. ȼɵɱɢɫɥɢɬɶ ɫ
ɞɭɤɰɢɸ, ɫɨɡɞɚɧɧɭɸ ɞɥɢɧɧɵɦ ɩɪɹɦɨɥɢɧɟɣɧɵɦ ɬɨɤɨɦ.
6. Ⱦɜɚ ɭɪɚɜɧɟɧɢɹ Ɇɚɤɫɜɟɥɥɚ ɞɥɹ ɩɨɫɬɨɹɧɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɜ
ɜɚɤɭɭɦɟ. ɂɯ ɮɢɡɢɱɟɫɤɢɣ ɫɦɵɫɥ.
7. ȼɵɱɢɫɥɢɬɶ ɫ ɩɨɦɨɳɶɸ ɬɟɨɪɟɦɵ ɨ ɰɢɪɤɭɥɹɰɢɢ ɦɚɝɧɢɬɧɭɸ ɢɧ-
ɞɭɤɰɢɸ, ɫɨɡɞɚɧɧɭɸ ɞɥɢɧɧɵɦ ɩɪɹɦɨɥɢɧɟɣɧɵɦ ɬɨɤɨɦ.
ɩɨɦɨɳɶɸ ɩɪɢɧɰɢɩɚ ɫɭɩɟɪɩɨɡɢɰɢɢ ɦɚɝɧɢɬɧɭɸ ɢɧ-
ɝ
50
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