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ȼɚɪɢɚɧɬɵ ɤ ɡɚɞɚɧɢɸ 4
x
ω
29
2
M
3
30
2
1
M
3
x
ɉɪɢɦɟɪ ʋ 3
Ƚɪɭɡ Ɋ (ɪɢɫ. 29) ɩɨɞɜɟɲɟɧ ɧɚ ɧɟɪɚɫɬɹɠɢɦɨɦ ɬɪɨɫɟ, ɧɚɦɨɬɚɧɧɨɦ ɧɚ
ɛɚɪɚɛɚɧ. Ȼɚɪɚɛɚɧ ɪɚɞɢɭɫɨɦ
ɥɟɫɨɦ
2 ɪɚɞɢɭɫɨɦ R2 = 0,3 ɦ ɢ ɢɦɟɟɬ ɨɛɳɭɸ ɫ ɧɢɦ ɧɟɩɨɞɜɢɠɧɭɸ ɨɫɶ
ɜɪɚɳɟɧɢɹ
ɪɚɞɢɭɫɨɦ r
Ɉ1. Ɂɭɛɱɚɬɨɟ ɤɨɥɟɫɨ 2 ɧɚɯɨɞɢɬɫɹ ɜ ɡɚɰɟɩɥɟɧɢɢ ɫ ɲɟɫɬɟɪɧɟɣ 3
= 0,15 ɦ.
3
ε
2
A
x
υ
1
a
1
ɇɚɣɬɢ ɫɤɨɪɨɫɬɶ ɢ ɭɫɤɨɪɟɧɢɟ ɬɨɱɤɢ
ɦɟɧɬ
t = 1,5 ɫ, ɟɫɥɢ ɝɪɭɡ ɞɜɢɠɟɬɫɹ ɩɨ ɡɚɤɨɧɭ: ɏ = 1 + 0,4t2, (x – ɜ ɦɟɬ-
ɪɚɯ,
t – ɜ ɫɟɤɭɧɞɚɯ).
r2 = 0,2 ɦ ɠɟɫɬɤɨ ɫɤɪɟɩɥɟɧ ɫ ɡɭɛɱɚɬɵɦ ɤɨ-
2
R
2
O
r
2
2
a
K
υ
K
1
K
ε
3
r
3
ω
O
2
a
n
M
a
a
τ
3
υ
M
1
Ɋɢɫ. 29.
Ɇ; ɭɝɥɨɜɨɟ ɭɫɤɨɪɟɧɢɟ
3
ε
ɜ ɦɨ-
3
71
Ɋȿɒȿɇɂȿ
υ
υ
υ
υ
ɉɨ ɡɚɤɨɧɭ ɞɜɢɠɟɧɢɹ ɝɪɭɡɚ ɧɚɣɞɟɦ ɟɝɨ ɫɤɨɪɨɫɬɶ ɢ ɭɫɤɨɪɟɧɢɟ:
)1(
=⋅===
,
ɫ/ɦ2,15,18,0t8,0x
υ
)1(
2
,
ɫ/ɦ8,0xa ===
a,
ɜɟɤɬɨɪɵ
ɧɚɩɪɚɜɥɟɧɵ ɜɧɢɡ.
Ɍɚɤ ɤɚɤ ɬɪɨɫ ɧɟɪɚɫɬɹɠɢɦ, ɬɨ ɜɫɟ ɟɝɨ ɬɨɱɤɢ ɢɦɟɸɬ ɫɤɨɪɨɫɬɢ ɢ
ɭɫɤɨɪɟɧɢɹ, ɪɚɜɧɵɟ ɫɤɨɪɨɫɬɢ ɢ ɭɫɤɨɪɟɧɢɸ ɝɪɭɡɚ
1.
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɢ ɬɨɱɤɢ ɨɛɨɞɚ ɛɚɪɚɛɚɧɚ ɢɦɟɸɬ ɬɭ ɠɟ ɫɤɨɪɨɫɬɶ ɢ
ɭɫɤɨɪɟɧɢɟ:
=
A
,
a =
υ
A
)1(
.
a
)1(
ɉɪɢ ɨɩɭɫɤɚɧɢɢ ɝɪɭɡɚ
ɤɪɭɝ ɨɫɢ
Ɉ
ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ
1
1 ɛɚɪɚɛɚɧ ɢ ɡɭɛɱɚɬɨɟ ɤɨɥɟɫɨ 2 ɜɪɚɳɚɟɬɫɹ ɜɨ-
ω
ɢ ɫ ɭɝɥɨɜɵɦ ɭɫɤɨɪɟɧɢɟɦ
2
ε
.
2
ɋɤɨɪɨɫɬɶ ɬɨɱɟɤ ɨɛɨɞɚ ɛɚɪɚɛɚɧɚ ɪɚɜɧɚ:
=
ω
⋅ r
A
,
2
2
ɨɬɤɭɞɚ:
υ
ω
2
2,1
A
2,0
r
2
1
−
c6
===
.
ɍɫɤɨɪɟɧɢɟ ɬɨɱɟɤ ɨɛɨɞɚ ɛɚɪɚɛɚɧɚ ɪɚɜɧɨ:
ɚA =
ε
⋅ r,
1
ɨɬɤɭɞɚ:
a
ε
2
8,0
A
2,0
r
2
2
−
c4
===
.
ȿɫɥɢ ɞɜɚ ɬɟɥɚ ɜ ɩɪɨɰɟɫɫɟ ɞɜɢɠɟɧɢɹ ɤɚɫɚɸɬɫɹ ɞɪɭɝ ɞɪɭɝɚ ɢ ɜ ɬɨɱɤɟ
ɢɯ ɤɨɧɬɚɤɬɚ ɨɬɫɭɬɫɬɜɭɟɬ ɩɪɨɫɤɚɥɶɡɵɜɚɧɢɟ, ɬɨ ɬɨɱɤɢ ɤɨɧɬɚɤɬɚ ɢɦɟɸɬ
ɨɞɢɧɚɤɨɜɵɟ ɫɤɨɪɨɫɬɢ ɢ ɭɫɤɨɪɟɧɢɹ.
72
ɉɨɷɬɨɦɭ ɫɤɨɪɨɫɬɢ ɢ ɭɫɤɨɪɟɧɢɹ ɬɨɱɤɢ
υ
υ
ɤɢ
Ʉ ɲɟɫɬɟɪɧɢ 3 ɪɚɜɧɵ. ɉɪɢ ɜɪɚɳɟɧɢɢ ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ 2 ɫ ɭɝɥɨɜɨɣ
ɫɤɨɪɨɫɬɶɸ
ɧɭ ɜɨɤɪɭɝ ɨɫɢ
ɉɪɢ ɷɬɨɦ ɫɤɨɪɨɫɬɶ ɬɨɱɤɢ
ω
ɲɟɫɬɟɪɧɹ 3 ɛɭɞɟɬ ɜɪɚɳɚɬɶɫɹ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɭɸ ɫɬɨɪɨ-
2
Ɉ
ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ
2
K ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ:
K ɡɭɛɱɚɬɨɝɨ ɤɨɥɟɫɚ 2 ɢ ɬɨɱ-
ω
ɢ ɫ ɭɝɥɨɜɵɦ ɭɫɤɨɪɟɧɢɟɦ
3
=
ω
⋅ R2 =
ω
⋅ r
K
2
,
3
3
ɨɬɤɭɞɚ:
R
2
ωω
23
r
3
3,0
6
15,0
1
−
c12
==⋅=
.
ɍɫɤɨɪɟɧɢɟ ɬɨɱɤɢ
Ʉ:
ɚ
=
ε
⋅ R2 =
ε
⋅ r
ɤ
2
,
3
3
ɨɬɤɭɞɚ:
ε
R
ε
⋅
=
3
r
3
⋅
22
3,04
=
15,0
2
−
c8
=
.
Ɉɩɪɟɞɟɥɢɦ ɭɝɥɨɜɭɸ ɫɤɨɪɨɫɬɶ
ɇɚɣɞɟɦ ɫɤɨɪɨɫɬɶ ɬɨɱɤɢ
Ɇ:
ɢ ɭɝɥɨɜɨɟ ɭɫɤɨɪɟɧɢɟ
3
ε
.
3
ω
=
ω
⋅ r3 = 12 × 0,15 = 1,8 ɦ/ɫ.
M
3
τ
Ʉɚɫɚɬɟɥɶɧɨɟ ɭɫɤɨɪɟɧɢɟ
a :
M
τ
ε
M
33
=×=⋅=
2
.
ɫ/ɦ2,115,08ra
ɇɨɪɦɚɥɶɧɨɟ ɭɫɤɨɪɟɧɢɟ ɬɨɱɤɢ
Ɇ ɜɫɟɝɞɚ ɧɚɩɪɚɜɥɟɧɨ ɤ ɨɫɢ ɜɪɚɳɟ-
ɧɢɹ, ɚ ɟɝɨ ɦɨɞɭɥɶ ɪɚɜɟɧ:
τ
ω
M
323
=×=⋅=
22
ɫ/ɦ6,2115,012ra
.
Ɇɨɞɭɥɶ ɩɨɥɧɨɝɨ ɭɫɤɨɪɟɧɢɹ ɬɨɱɤɢ
Ɇ ɧɚɯɨɞɢɬɫɹ ɩɨ ɫɨɫɬɚɜɥɹɸɳɢɦ
ɭɫɤɨɪɟɧɢɹ:
ε
.
3
73
τ
υ
()()
M
aaa
22
n
MM
=+=+=
222
ɫ/ɦ6,216,212,1
.
Ɉɬɜɟɬ:
= 1,8 ɦ/ɫ; ɚɆ = 21,6 ɦ/ɫ2;
M
ε
= 8 ɫ
3
-2
.
2. ɄɈɇɌɊɈɅɖɇɕȿ ȼɈɉɊɈɋɕ
1.
ɑɬɨ ɧɚɡɵɜɚɟɬɫɹ ɩɨɫɬɭɩɚɬɟɥɶɧɵɦ ɞɜɢɠɟɧɢɟɦ?
2.
ɑɬɨ ɦɨɠɧɨ ɫɤɚɡɚɬɶ ɨ ɬɪɚɟɤɬɨɪɢɹɯ ɪɚɡɥɢɱɧɵɯ ɬɨɱɟɤ ɩɪɢ ɩɨɫɬɭ-
ɩɚɬɟɥɶɧɨɦ ɞɜɢɠɟɧɢɢ, ɫɤɨɪɨɫɬɹɯ ɢ ɭɫɤɨɪɟɧɢɹɯ ɪɚɡɥɢɱɧɵɯ ɬɨɱɟɤ?
3.
Ʉɚɤ ɨɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ ɢ ɭɫɤɨɪɟɧɢɟ ɬɟɥɚ ɩɪɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨɦ
ɞɜɢɠɟɧɢɢ?
4.
Ʉɚɤɨɟ ɞɜɢɠɟɧɢɟ ɬɟɥɚ ɧɚɡɵɜɚɟɬɫɹ ɜɪɚɳɚɬɟɥɶɧɵɦ?
5.
ɑɬɨ ɬɚɤɨɟ ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɢ ɭɝɥɨɜɨɟ ɭɫɤɨɪɟɧɢɟ? ȿɞɢɧɢɰɚ ɢɡ-
ɦɟɪɟɧɢɹ.
6.
Ɏɨɪɦɭɥɵ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɤɨɪɨɫɬɢ ɢ ɭɫɤɨɪɟɧɢɣ ɬɨɱɤɢ ɜɪɚɳɚ-
ɸɳɟɝɨɫɹ ɬɟɥɚ. ɇɚɩɪɚɜɥɟɧɢɟ ɫɤɨɪɨɫɬɢ ɢ ɭɫɤɨɪɟɧɢɣ. ȿɞɢɧɢɰɵ ɢɡɦɟɪɟɧɢɹ.
74
ɉɊȺɄɌɂɑȿɋɄɈȿ ɁȺɇəɌɂȿ ʋ 6
Ɍɟɦɚ: Ɉɩɪɟɞɟɥɟɧɢɟ ɤɢɧɟɦɚɬɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɪɢ ɩɥɨɫɤɨ-
ɩɚɪɚɥɥɟɥɶɧɨɦ ɞɜɢɠɟɧɢɢ.
ɐɟɥɶ: Ɉɫɜɨɢɬɶ ɨɩɪɟɞɟɥɟɧɢɟ ɫɤɨɪɨɫɬɟɣ ɬɨɱɟɤ ɩɪɢ ɩɥɨɫɤɨɦ ɞɜɢɠɟ-
ɧɢɢ ɬɟɥɚ.
ȼɪɟɦɹ ɩɪɨɜɟɞɟɧɢɹ: 2 ɱɚɫɚ.
1. ɈɋɇɈȼɇɕȿ ɉɈɅɈɀȿɇɂə ɌȿɈɊɂɂ
ɉɥɨɫɤɢɦ (ɩɥɨɫɤɨɩɚɪɚɥɥɟɥɶɧɵɦ) ɞɜɢɠɟɧɢɟɦ ɧɚɡɵɜɚɟɬɫɹ ɞɜɢɠɟɧɢɟ
ɬɜɟɪɞɨɝɨ ɬɟɥɚ, ɩɪɢ ɤɨɬɨɪɨɦ ɜɫɟ ɟɝɨ ɬɨɱɤɢ ɞɜɢɠɭɬɫɹ ɜ ɩɥɨɫɤɨɫɬɹɯ, ɩɚɪɚɥɥɟɥɶɧɵɯ ɧɟɤɨɬɨɪɨɣ ɧɟɩɨɞɜɢɠɧɨɣ ɩɥɨɫɤɨɫɬɢ.
ɉɪɢ ɢɡɭɱɟɧɢɢ ɩɥɨɫɤɨɝɨ ɞɜɢɠɟɧɢɹ ɬɜɟɪɞɨɝɨ ɬɟɥɚ ɞɨɫɬɚɬɨɱɧɨ ɢɫɫɥɟɞɨɜɚɬɶ ɞɜɢɠɟɧɢɟ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ, ɹɜɥɹɸɳɟɣɫɹ ɫɟɱɟɧɢɟɦ ɬɜɟɪɞɨɝɨ
ɬɟɥɚ ɩɥɨɫɤɨɫɬɶɸ, ɩɚɪɚɥɥɟɥɶɧɨɣ ɧɟɩɨɞɜɢɠɧɨɣ.
Ɉɞɧɢɦ ɢɡ ɦɟɬɨɞɨɜ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɧɚ ɷɬɨ ɞɜɢɠɟɧɢɟ ɹɜɥɹɟɬɫɹ
ɨɩɪɟɞɟɥɟɧɢɟ
ɝɨ ɰɟɧɬɪɚ ɫɤɨɪɨɫɬɟɣ (Ɇɐɋ). ɉɪɢ ɧɟɩɨɫɬɭɩɚɬɟɥɶɧɨɦ ɞɜɢɠɟɧɢɢ ɩɥɨɫɤɨɣ
ɮɢɝɭɪɵ (
ɤɨɬɨɪɨɣ ɪɚɜɧɚ ɧɭɥɸ – ɷɬɨ Ɇɐɋ. Ɍɨɝɞɚ ɩɥɨɫɤɨɟ ɞɜɢɠɟɧɢɟ ɮɢɝɭɪɵ
ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɫɨɜɨɤɭɩɧɨɫɬɶ ɦɝɧɨɜɟɧɧɵɯ ɜɪɚɳɚɬɟɥɶɧɵɯ
ɞɜɢɠɟɧɢɣ ɜɨɤɪɭɝ Ɇɐɋ.
ɋɨɨɬɜɟɬɫɬɜɟɧɧɨ ɫɤɨɪɨɫɬɢ ɬɨɱɟɤ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ ɛɭɞɭɬ ɩɪɹɦɨ
ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ ɪɚɫɫɬɨɹɧɢɹɦ ɨɬ ɬɨɱɟɤ ɞɨ Ɇɐɋ.
ɫɤɨɪɨɫɬɟɣ ɬɨɱɟɤ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ ɩɪɢ ɩɨɦɨɳɢ ɦɝɧɨɜɟɧɧɨ-
ω ≠ 0) ɜ ɤɚɠɞɵɣ ɞɚɧɧɵɣ ɦɨɦɟɧɬ ɫɭɳɟɫɬɜɭɟɬ ɬɨɱɤɚ, ɫɤɨɪɨɫɬɶ
υ
A
B
υ
B
.
.
A
Ɋɢɫ. 30.
ɉɪɢ ɢɡɜɟɫɬɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ ɫɤɨɪɨɫɬɟɣ ɞɜɭɯ ɬɨɱɟɤ ɩɥɨɫɤɨɣ ɮɢɝɭɪɵ ɦɝɧɨɜɟɧɧɵɣ ɰɟɧɬɪ ɫɤɨɪɨɫɬɟɣ ɧɚɯɨɞɢɬɫɹ ɜ ɬɨɱɤɟ
ɩɟɪɩɟɧɞɢɤɭɥɹɪɨɜ, ɜɨɫɫɬɚɧɨɜɥɟɧɧɵɯ ɜ ɷɬɢɯ ɬɨɱɤɚɯ ɤ ɜɟɤɬɨɪɚɦ ɫɤɨɪɨɫɬɟɣ (ɪɢɫ. 30).
75
ω
P
Ɋ ɩɟɪɟɫɟɱɟɧɢɹ
υ
A
ω
β
7
B
AP
A
=
,
BP
υ
B
υυ
BA
P
BP
ω
=== !
.
Ⱦɪɭɝɢɟ ɫɥɭɱɚɢ ɧɚɯɨɠɞɟɧɢɹ Ɇɐɋ ɫɦɨɬɪɟɬɶ ɜ ɤɨɧɫɩɟɤɬɟ ɥɟɤɰɢɣ
ɢɥɢ ɪɟɤɨɦɟɧɞɭɟɦɨɦ ɭɱɟɛɧɢɤɟ.
Ɂɚɞɚɧɢɟ 4. ɒɚɪɧɢɪɧɵɣ ɱɟɬɵɪɟɯɡɜɟɧɧɢɤ ɫɨɫɬɨɢɬ ɢɡ ɧɟɩɨɞɜɢɠɧɨɝɨ
ɡɜɟɧɚ
Ɉ1Ɉ2 = l, ɤɪɢɜɨɲɢɩɨɜ Ɉ1Ⱥ = r1, Ɉ2B = r
ɲɢɩ
Ɉ1Ⱥ ɜɪɚɳɚɟɬɫɹ ɫ ɩɨɫɬɨɹɧɧɨɣ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ
ɢ ɫɬɟɪɠɧɹ Ⱥȼ. Ʉɪɢɜɨ-
2
ω
ɢ ɜ ɞɚɧɧɵɣ
1
ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɡɚɧɢɦɚɟɬ ɩɨɥɨɠɟɧɢɟ, ɨɩɪɟɞɟɥɹɟɦɨɟ ɭɝɥɨɦ
ɭɝɨɥ, ɤɚɤ ɢ ɭɝɨɥ
β
ɞɥɹ ɜɬɨɪɨɝɨ ɤɪɢɜɨɲɢɩɚ Ɉ
B, ɨɬɤɥɚɞɵɜɚɟɬɫɹ ɩɪɨɬɢɜ
2
ɱɚɫɨɜɨɣ ɫɬɪɟɥɤɢ (ɪɢɫ. 31).
A
ω
1
α
. ɗɬɨɬ
O
1
α
O
β
2
Ɋɢɫ. 31.
Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ ɬɨɱɤɢ
ɫɬɟɪɠɧɹ
Ⱥȼ ɢ ɭɝɥɨɜɭɸ ɫɤɨɪɨɫɬɶ ɤɪɢɜɨɲɢɩɚ Ɉ2B. Ⱦɚɧɧɵɟ ɞɥɹ ɪɟɲɟɧɢɹ
ȼ, ɦɝɧɨɜɟɧɧɭɸ ɭɝɥɨɜɭɸ ɫɤɨɪɨɫɬɶ
ɩɪɢɜɟɞɟɧɵ ɜ ɬɚɛɥ. 12.
Ɍɚɛɥɢɰɚ 12
ʋ
-1
, ɫ
1
l, ɦ r
, ɦ r
1
2
, ɦ
d°
°
1 2 3 4 5 6 7
1 3 0,5 0,2 0,
0 60
2 4 0,3 0,1 0,5 30 270
3 2 0,8 0,3 0,2 30 120
4 5 0,4 0,2 0,8 30 300
5 8 2,2 0,5 0,6 60 150
6 10 1,2 0,4 1,0 60 330
7 6 1,0 0,6 1,2 60 270
8 2 0,6 0,3 0,1 90 30
9 5 1,5 0,8 0,5 90 45
76
Ɉɤɨɧɱɚɧɢɟ ɬɚɛɥɢɰɵ 12
ω
β
7
7
7
7
7
7
υ
ʋ
-1
, ɫ
1
l, ɦ r
, ɦ r
1
2
, ɦ
d°
°
10 3 0,8 1,0 0,6 90 60
11 4 1,4 1,2 0,9 90 120
12 8 0,9 0,2 0,4 90 135
13 10 1,6 0,
0,8 90 150
14 9 1,1 0,4 0,2 90 0
15
1,8 1,5 0,7 90 210
16 1 2,0 2,5 0,3 90 225
17 6 1,2 1,1 1,0 90 240
18 12 1,9 0,5 1,4 90 300
19 15 0,
0,1 1,2 90 315
20 14 1,0 0,6 0,5 90 330
21 8 1,5 0,2 0,8 120 30
22 2 0,8 0,
0,2 120 210
23 5 1,4 1,0 0,3 120 270
24 4 0,9 0,3 0,4 45 135
25 3 1,2 0,4 0,6 45 315
26 10 1,6 0,8 1,0 45 270
27 6 1,0 0,5 0,8 135 45
28 8 1,3 0,2 0,5 135 225
29 5 1,
30
0,6 0,3 0,2 150 240
1,2 0,1 150 60
ɉɪɢɦɟɪ ʋ 4
ɍɫɥɨɜɢɟ ɩɪɢɦɟɪɚ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɡɚɞɚɧɢɸ ɧɚ ɫɚɦɨɫɬɨɹɬɟɥɶɧɭɸ ɪɚɛɨɬɭ.
Ⱦɚɧɨ:
ω
(ɪɢɫ. 32).
Ɉɩɪɟɞɟɥɢɬɶ:
= 2 ɫ
1
-1
, l = 1 ɦ, r
,
ω
,
ω
AB
B
= 0,5 ɦ, r2 = 0,6 ɦ, α = 30°, β = 45°
1
.
2
77
υ
A
B
ω
Ɋ
υ
υ
A
B
A
.
ω
1
O
1
30
Ɉ
2
.
B
ω
2
45
Ⱦ
Ɋɢɫ. 32.
Ɋȿɒȿɇɂȿ
1. ɉɨ ɡɚɞɚɧɧɵɦ ɭɝɥɚɦ
2. Ɉɩɪɟɞɟɥɹɟɦ ɫɤɨɪɨɫɬɶ ɬɨɱɤɢ
α
ɢ
β
ɫɬɪɨɢɦ ɲɚɪɧɢɪɧɵɣ ɱɟɬɵɪɟɯɡɜɟɧɧɢɤ.
Ⱥ:
=
ω
⋅ r1 = 2 ⋅ 0,5 = 1 ɦ/ɫ.
1
A
ɋɬɪɨɢɦ ɜɟɤɬɨɪ ɫɤɨɪɨɫɬɢ
v ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɤɪɢɜɨɲɢɩɭ Ɉ
A
Ⱥ ɜ
1
ɫɬɨɪɨɧɭ ɜɪɚɳɟɧɢɹ. ɉɨɤɚɠɟɦ ɚɧɚɥɨɝɢɱɧɨ ɧɚɩɪɚɜɥɟɧɢɟ ɜɟɤɬɨɪɚ ɫɤɨɪɨɫɬɢ ɬɨɱɤɢ
V
ɢ
ɫɬɨɹɧɢɹ ɨɬ ɬɨɱɤɢ
ȼ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɤɪɢɜɨɲɢɩɭ Ɉ2ȼ.
3. ɇɚ ɩɟɪɟɫɟɱɟɧɢɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɨɜ ɤ ɧɚɩɪɚɜɥɟɧɢɹɦ ɜɟɤɬɨɪɨɜ
ɧɚɯɨɞɢɦ Ɇɐɋ – ɬɨɱɤɭ Ɋ.
B
4. ɂɡ ɩɪɹɦɨɭɝɨɥɶɧɵɯ ɬɪɟɭɝɨɥɶɧɢɤɨɜ
Ɉ1ɊȾ ɢ Ɉ2ɊȾ ɧɚɯɨɞɢɦ ɪɚɫ-
Ⱥ ɢ ɬɨɱɤɢ ȼ ɞɨ Ɇɐɋ (ɬɨɱɤɚ Ɋ):
V
(r
+ AP)⋅ sin30° = (r2 + BP)⋅ sin45°;
1
A
+ AP)⋅ cos 30° = l + (r2 + BP)⋅ cos45°;
(r
1
(0,5 + AP)⋅ 0,5 = (0,6 + BP)⋅ 0,7;
(0,5 + AP)
⋅
0,9 = 1 + (0,6 + BP)⋅ 0,7.
Ɋɟɲɚɹ ɫɢɫɬɟɦɭ 2-ɯ ɭɪɚɜɧɟɧɢɣ, ɧɚɯɨɞɢɦ:
AP = 2 ɦ, ȼɊ = 1,18 ɦ.
78
5. Ɉɩɪɟɞɟɥɹɟɦ ɭɝɥɨɜɭɸ ɫɤɨɪɨɫɬɶ ɫɬɟɪɠɧɹ
A
υ
υ
Ⱥȼ:
υ
1
ω
AB
A
===
P
2
1
−
c5,0
.
6. ɇɚɯɨɞɢɦ ɫɤɨɪɨɫɬɶ ɬɨɱɤɢ
ȼ:
=
ω
⋅ BP = 0,5 ⋅ 1,18 = 0,59 ɦ/ɫ.
AB
B
7. Ɉɩɪɟɞɟɥɹɟɦ ɭɝɥɨɜɭɸ ɫɤɨɪɨɫɬɶ ɜɬɨɪɨɝɨ ɤɪɢɜɨɲɢɩɚ Ɉ
υ
ω
2
59,0
B
r
6,0
2
1
−
c1
≈==
.
Ɉɬɜɟɬ:
= 0,59 ɦ/ɫ;
B
ω
= 0,5 ɫ-1; ω = 1 ɫ
AB
-1
.
2. ɄɈɇɌɊɈɅɖɇɕȿ ȼɈɉɊɈɋɕ
1.
ɑɬɨ ɬɚɤɨɟ ɩɥɨɫɤɨɩɚɪɚɥɥɟɥɶɧɨɟ ɞɜɢɠɟɧɢɟ?
2.
Ʉɚɤɢɟ ɭɩɪɨɳɟɧɢɹ ɢɫɩɨɥɶɡɭɸɬ ɩɪɢ ɢɡɭɱɟɧɢɢ ɩɥɨɫɤɨɝɨ ɞɜɢɠɟ-
ɧɢɹ?
3.
Ʉɚɤɢɟ ɫɭɳɟɫɬɜɭɸɬ ɦɟɬɨɞɵ ɨɩɪɟɞɟɥɟɧɢɹ ɫɤɨɪɨɫɬɟɣ ɬɨɱɟɤ ɩɪɢ
ɩɥɨɫɤɨɦ ɞɜɢɠɟɧɢɢ?
4.
ɑɬɨ ɬɚɤɨɟ ɦɝɧɨɜɟɧɧɵɣ ɰɟɧɬɪ ɫɤɨɪɨɫɬɟɣ?
ȼ:
2
79
ɊȺɁȾȿɅ III
«ȾɂɇȺɆɂɄȺ»
ɉɊȺɄɌɂɑȿɋɄɈȿ ɁȺɇəɌɂȿ ʋ 7
Ɍɟɦɚ: Ⱦɜɟ ɨɫɧɨɜɧɵɟ ɡɚɞɚɱɢ ɞɢɧɚɦɢɤɢ.
ɐɟɥɶ: Ɉɫɜɨɢɬɶ ɪɟɲɟɧɢɟ ɩɟɪɜɨɣ ɢ ɜɬɨɪɨɣ ɡɚɞɚɱɢ ɞɢɧɚɦɢɤɢ ɞɥɹ ɦɚ-
ɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ, ɢɫɩɨɥɶɡɭɹ ɨɫɧɨɜɧɵɟ ɭɪɚɜɧɟɧɢɹ ɞɢɧɚɦɢɤɢ ɢ ɦɟɬɨɞ
ɤɢɧɟɬɨɫɬɚɬɢɤɢ.
ȼɪɟɦɹ ɩɪɨɜɟɞɟɧɢɹ: 2 ɱɚɫɚ.
ɉɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɜɵɩɨɥɧɟɧɢɹ:
– ɢɡɭɱɢɬɶ ɬɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ;
– ɨɬɜɟɬɢɬɶ ɧɚ ɤɨɧɬɪɨɥɶɧɵɟ ɜɨɩɪɨɫɵ;
– ɪɚɡɨɛɪɚɬɶ ɩɪɟɞɥɨɠɟɧɧɵɟ ɩɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ;
– ɪɟɲɢɬɶ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɡɚɞɚɱɢ ɩɨ ɞɚɧɧɨɣ ɬɟɦɟ ɫɨɝɥɚɫɧɨ ɫɜɨɟɦɭ
ɜɚɪɢɚɧɬɭ.
1. ɈɋɇɈȼɇɕȿ ɉɈɅɈɀȿɇɂə ɌȿɈɊɂɂ
1.1. Ɉɫɧɨɜɧɨɣ ɡɚɤɨɧ ɞɢɧɚɦɢɤɢ. Ⱦɜɟ ɨɫɧɨɜɧɵɟ ɡɚɞɚɱɢ ɞɢɧɚɦɢɤɢ
ɂɡ ɨɫɧɨɜɧɨɝɨ ɡɚɤɨɧɚ ɞɢɧɚɦɢɤɢ
ɰɢɚɥɶɧɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ:
ɚ) ɜ ɞɟɤɚɪɬɨɜɵɯ ɤɨɨɪɞɢɧɚɬɚɯ:
ɝɞɟ m – ɦɚɫɫɚ ɬɨɱɤɢ; z,y,x
ɤɨɨɪɞɢɧɚɬ;
ɛ) ɜ ɟɫɬɟɫɬɜɟɧɧɵɯ ɨɫɹɯ:
– ɩɪɨɟɤɰɢɢ ɭɫɤɨɪɟɧɢɹ ɧɚ ɨɫɢ ɞɟɤɚɪɬɨɜɵɯ
=ɤFam
ɩɨɥɭɱɚɟɦ ɞɢɮɮɟɪɟɧ-
¦
=
=
=
,Fxm
¦
ɤɯ
(4)
,Fym
¦
ɤy
,Fzm
¦
ɤz
=
2
s
m
ρ
=
¦
,Fsm
¦
ɤ
τ
=
,F
¦
ɤɜ
(5)
KN
,F0
80
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