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ȼɚɪɢɚɧɬɵ ɤ ɡɚɞɚɧɢɸ 2
4
7
1
m
q
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2
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a ɜɫ
a ɜɫa
F
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3
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1
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m
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a ɫaɜ
5
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m
1
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α
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a
ɜ
ɫa
1
C
m
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ɜ
a
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a
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F
m
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2
a ɜ
1
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m
q
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A
F
2
ɫ
a
ɜ
ɫ
F
1
α
B
a
21
9
11
13
A
15
ȼɚɪɢɚɧɬɵ ɤ ɡɚɞɚɧɢɸ 2
10
F
m
A
2
α
q
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m
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α
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1
a
ɜ
a
ɫ
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12
F
m
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1
ɜɫɚa
2
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m
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a
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1
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a
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1
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m
m
α
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a
ɜɫɜ
A
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a
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F
m
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q
B
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1
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ɜ
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ɜ
F
1
ɜ
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22
17
2
19
ȼɚɪɢɚɧɬɵ ɤ ɡɚɞɚɧɢɸ 2
18
F
F
m
A
2
B
α
a
ɜ
q
F
1
ɋ
ɜ
m
ȼ
A
q
ɜ
a
2
α
C
F
1
ɫɜ
20
F
1
α
q
A
m
B
m
q
B
A
α
23
A
F
2
a
ɜ
1
m
A
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2
ɚɜ
ɫ
a
22
F
F
1
ɋ
α
B
A
2
α
q
F
1
ɜ
a
F
ɜ
ɫ
m
q
B
ɜ
ɫ
24
F
1
q
m
B
A
m
q
α
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2
ɜ
a
ɫ
a
F
1
B
α
F
2
ɜ
ɫ
23
ȼɚɪɢɚɧɬɵ ɤ ɡɚɞɚɧɢɸ 2
2
0
α
25
27
B
F
2
A
α
F
a
m
1
ɜ
F
2
m
q
C
c
a
q
A
α
F
1
a
ɜ
ɫ
9
F
2
q
A
α
ȼ
F
1
ɫ
a
ɜ
26
m
A
F
2
α
B
q
F
1
ɫɜa ɜ
28
F
m
B
q
A
F
1
B
α
2
ɫɜa ɚ
3
m
C
m
q
F
2
α
A
ȼ
F
1
C
a ɜɫɚ
Ɍɚɛɥɢɰɚ 2
ʋ ɩ/ɩ 1 2 3 4 5 6 7 8 9 10
F1, ɤɇ 5 4 3 2 6 4 2 5 8 4
q, ɤɇ/ɦ 0,2 0,4 0,5 0,6 0,2 0,8 0,4 0,8 0,5 0,2
m, ɤɇ ⋅ ɦ
, ɝɪɚɞ
F2, ɤɇ 2 3 5 1 2 6 4 3 2 1
ɚ, ɦ 4 2 3 5 3 4 2 7 3 6
ɜ, ɦ 2 3 5 3 7 2 5 3 6 2
ɫ, ɦ 5 6 2 7 1 5 3 2 4 3
4 1 2 3 4 2 5 3 6 7
60 50 40 55 35 30 60 40 70 30
24
Ɂɚɞɚɧɢɟ 3. Ɉɩɪɟɞɟɥɢɬɶ ɪɟɚɤɰɢɢ ɠɟɫɬɤɨɣ ɡɚɞɟɥɤɢ, ɞɚɧɧɵɟ ɜɡɹɬɶ ɢɡ
2
4
6
ɬɚɛɥ. 2.
ȼɚɪɢɚɧɬɵ ɤ ɡɚɞɚɧɢɸ 3
1
F
m
1
m
q
30
A
F
2
3
m
q
F
2
F
1
50
5
F
1
m
60
F
2
A
F
2
aa
m
A
q
ɜa
F
2
q
A
F
60
1
q
ɜa
50
F
1
ɜa
q
A
50
F
1
ɚa
m
A
F
2
ɜa
25
ȼɚɪɢɚɧɬɵ ɤ ɡɚɞɚɧɢɸ 3
7
8
9
11
F
2
q
60
F
ɜa ɫ
A
60
F
a ɜ
m
A
a ɜ
m
F
2
50
m
A
A
q
1
10
m
q
F
1
ɜa
F
2
q
m
A
60
1
F
2
30
F
2
12
F
1
F
1
a
ɜ
F
1
c
m
F
2
30
A
q
a ɜ c
q
13
A
F
2
a ɜ
m
F
1
50
q
14
m
A
a ɜ
q
60
F
2
F
1
26
15
ȼɚɪɢɚɧɬɵ ɤ ɡɚɞɚɧɢɸ 3
16
19
17
q
A
50
a ɜ
F
q
q
50
a
m
F
1
2
m
60
F
1
A
ɜac
m
A
F
F
1
2
ɜ
F
1
F
2
A
a ɜ c
18
m
F
50
F
m
2
30
q
1
F
2
A
q
ɜa ɜ
20
F
2
m
q
50
F
1
A
a
21
F
60
22
F
1
q
a
m
2
A
ɜ
F
m
2
q
30
A
F
1
ɜa
27
23
F
ȼɚɪɢɚɧɬɵ ɤ ɡɚɞɚɧɢɸ 3
24
m
q
2
50
F
A
1
ɜa
m
q
A
F
a ɜɫ
2
50
F
1
25
29
27
F
2
A
30
F
a
1
ɜ
m
A
q
a ɜɫ
F
q
1
30
A
F
a ɜ
2
26
m
q
q
m
A
50
F
1
ɫ
28
F
2
ɜɚ ɫ a
m
F
2
q
A
60
F
1
30
m
a ɜ
F
50
F
1
F
2
1
m
30
A
q
F
a ɜ c
2
28
ɉɪɢɦɟɪ ʋ 2
y
Ɉɩɪɟɞɟɥɢɬɶ ɪɟɚɤɰɢɢ ɫɜɹɡɟɣ ɞɜɭɯɨɩɨɪɧɨɣ ɛɚɥɤɢ.
V
A
F
R
2
q
m
q
H
A
Ⱥ
60
F
R
ȼ
R
F
1x
F
1y
1
By
ȼ
R
Bx
x
30
1ɦ
2ɦ 1ɦ
1ɦ
Ɋɢɫ. 14.
Ɋȿɒȿɇɂȿ
Ɋɟɲɚɟɦ ɡɚɞɚɱɭ ɜ ɫɥɟɞɭɸɳɟɦ ɩɨɪɹɞɤɟ:
1.
Ɋɚɫɫɦɨɬɪɢɦ ɪɚɜɧɨɜɟɫɢɟ ɛɚɥɤɢ Ⱥȼ.
2.
ɂɡɨɛɪɚɡɢɦ ɜɫɟ ɡɚɞɚɧɧɵɟ ɫɢɥɵ, ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɛɚɥɤɭ.
Ɉɫɜɨɛɨɞɢɦ ɛɚɥɤɭ ɨɬ ɫɜɹɡɟɣ ɢ ɡɚɦɟɧɢɦ ɢɯ ɪɟɚɤɰɢɹɦɢ.
3.
Ɋɟɚɤɰɢɹ ɧɟɩɨɞɜɢɠɧɨɣ ɲɚɪɧɢɪɧɨɣ ɨɩɨɪɵ
ɜɡɚɢɦɧɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ
ɞɜɭɯ
Ⱥ ɩɪɟɞɫɬɚɜɥɟɧɚ ɜ ɜɢɞɟ
V ɢ AH (ɪɢɫ. 14).
A
Ɋɟɚɤɰɢɹ ɲɚɪɧɢɪɧɨ-ɩɨɞɜɢɠɧɨɣ ɨɩɨɪɵ ɜ ɬɨɱɤɟ ȼ – ɷɬɨ ɜɟɤɬɨɪ BR ,
ɧɚɩɪɚɜɥɟɧɧɵɣ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɨɩɨɪɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ.
4.
ȼɵɛɢɪɚɟɦ ɨɞɧɭ ɢɡ ɬɪɟɯ ɮɨɪɦ ɭɪɚɜɧɟɧɢɣ ɪɚɜɧɨɜɟɫɢɹ, ɤɨɬɨɪɚɹ
ɹɜɥɹɟɬɫɹ ɧɚɢɛɨɥɟɟ ɪɚɰɢɨɧɚɥɶɧɨɣ ɞɥɹ ɞɚɧɧɨɣ ɤɨɧɫɬɪɭɤɰɢɢ. Ɋɚɰɢɨɧɚɥɶɧɨɫɬɶ ɜɵɛɨɪɚ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɬɨɦ, ɱɬɨɛɵ ɜ ɤɚɠɞɨɦ ɭɪɚɜɧɟɧɢɢ ɪɚɜɧɨɜɟɫɢɹ ɫɨɞɟɪɠɚɥɨɫɶ ɨɞɧɨ ɧɟɢɡɜɟɫɬɧɨɟ. Ⱦɥɹ ɞɜɭɯɨɩɨɪɧɨɣ ɛɚɥɤɢ
Ⱥȼ ɜɵɛɢ-
ɪɚɟɦ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ:
0m
=
¦
A
°
¦
®
°
¦
¯
,
0m
=
B
0F
=
kx
ɝɞɟ ɝɨɪɢɡɨɧɬɚɥɶɧɚɹ ɨɫɶ
ɯ ɧɟ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚ ɩɪɹɦɨɣ Ⱥȼ.
29
5.
ɉɪɟɨɛɪɚɡɭɟɦ ɫɢɥɵ, ɞɟɣɫɬɜɭɸɳɢɟ ɧɚ ɛɚɥɤɭ Ⱥȼ, ɢ ɫɨɫɬɚɜɢɦ
ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ. Ɋɚɜɧɨɦɟɪɧɨ ɪɚɫɩɪɟɞɟɥɟɧɧɭɸ ɧɚɝɪɭɡɤɭ ɢɧɬɟɧɫɢɜɧɨɫɬɶɸ
q ɩɪɟɞɫɬɚɜɢɦ ɜ ɜɢɞɟ ɫɨɫɪɟɞɨɬɨɱɟɧɧɨɣ ɫɢɥɵ Rq = q ⋅ 2, ɩɪɢ-
ɥɨɠɟɧɧɨɣ ɜ ɫɟɪɟɞɢɧɟ ɨɬɪɟɡɤɚ ɞɥɢɧɨɣ 2 ɦ, ɧɚ ɤɨɬɨɪɨɦ ɞɟɣɫɬɜɭɟɬ
ɧɚɝɪɭɡɤɚ, ɢ ɧɚɩɪɚɜɥɟɧɧɨɣ ɜɟɪɬɢɤɚɥɶɧɨ ɜɧɢɡ.
ɇɚɤɥɨɧɧɵɟ ɫɢɥɵ
F ɢ BR ɩɪɟɞɫɬɚɜɢɦ ɜ ɜɢɞɟ ɞɜɭɯ ɜɡɚɢɦɧɨ ɩɟɪ-
1
ɩɟɧɞɢɤɭɥɹɪɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ, ɦɨɞɭɥɢ ɤɨɬɨɪɵɯ ɪɚɜɧɵ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ:
– ɩɨ ɝɨɪɢɡɨɧɬɚɥɢ: F1 ⋅ cos60° ɢ R
–
ɩɨ ɜɟɪɬɢɤɚɥɢ: F
6.
ɋɨɫɬɚɜɥɹɟɦ ɭɪɚɜɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ, ɩɨɥɶɡɭɹɫɶ ɬɟɨɪɟɬɢɱɟɫɤɢɦɢ
⋅ cos30° ɢ RB ⋅ cos30°.
1
⋅
cos60°;
B
ɩɪɢɥɨɠɟɧɢɹɦɢ:
⋅
(Fk) = 0; F2 ⋅ 1 + q ⋅ 2 ⋅ 2 + m + F1cos 30° ⋅ 4 – R
m
A
⋅
cos30° ⋅ 5 = 0.
B
ɉɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɱɢɫɥɨɜɵɯ ɡɧɚɱɟɧɢɣ ɡɚɞɚɧɧɵɯ ɫɢɥ ɨɩɪɟɞɟɥɹɟɦ
ɜɟɥɢɱɢɧɭ
R
:
B
6⋅ 1 + 6 ⋅ 2 ⋅ 2 + 4 + 5 ⋅ 0,9 ⋅ 4 – RB ⋅ 0,9 ⋅ 5 = 0,
= 3,56 ɤɇ,
R
B
m
) = 0; VA ⋅ 5 – F
ȼ(Fk
= 0; HA + F1 ⋅ cos60° – RB ⋅ cos60°⋅ S = 0,
F
KX
⋅
4 – q ⋅ 2 ⋅ 3 + m + F
2
= 10,3 ɤɇ,
y
A
⋅
cos30° ⋅ 1 = 0,
1
HA = 0,72 ɤɇ.
Ɉɬɪɢɰɚɬɟɥɶɧɨɟ ɡɧɚɱɟɧɢɟ
ɰɢɢ ɨɩɨɪɵ ɜ ɬɨɱɤɟ
Ⱥ ɧɚɩɪɚɜɥɟɧɚ ɜ ɫɬɨɪɨɧɭ, ɩɪɨɬɢɜɨɩɨɥɨɠɧɭɸ ɭɤɚɡɚɧ-
ɇ
ɨɡɧɚɱɚɟɬ, ɱɬɨ ɷɬɚ ɫɨɫɬɚɜɥɹɸɳɚɹ ɪɟɚɤ-
Ⱥ
ɧɨɣ ɧɚ ɱɟɪɬɟɠɟ.
Ⱦɥɹ ɩɪɨɜɟɪɤɢ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɱɢɫɥɢɦ ɚɥɝɟɛɪɚɢɱɟɫɤɭɸ ɫɭɦɦɭ
ɩɪɨɟɤɰɢɣ ɧɚ ɨɫɶ
ɭ ɜɫɟɯ ɫɢɥ, ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɛɚɥɤɭ:
FKy = VA – F2 – q ⋅ 2 +F
⋅
= 10,3 – 6 – 6
2 + 5 ⋅ 0,9 + 3,56 ⋅ 0,9 = –18 + 18 = 0.
⋅
cos30° + R
1
⋅
cos30° =
B
Ɉɬɜɟɬ: ɭ
= 10,3 ɤɇ; ɇȺ = –0,72 ɤɇ; Rȼ = 3,56 ɤɇ.
Ⱥ
30
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