Механика.Методика решения задач
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Ƚɥɚɜɚ 7. Ɂɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ |
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Ɋɟɲɟɧɢɟ
I. ȼɵɛɟɪɟɦ ɨɫɢ ɞɟɤɚɪɬɨɜɨɣ ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ ɬɚɤ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɧɚ ɪɢɫ. 7.18. Ʉɚɬɨɤ ɭɱɚɫɬɜɭɟɬ ɜ ɞɜɭɯ ɞɜɢɠɟɧɢɹɯ – ɜɪɚɳɟɧɢɢ ɜɨɤɪɭɝ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɢ Z ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ Z ɢ ɜɨɤɪɭɝ ɫɨɛɫɬɜɟɧɧɨɣ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɨɫɢ AA' ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ Z1. ɇɚɩɪɚɜɥɟɧɢɹ ɭɝɥɨɜɵɯ ɫɤɨɪɨɫɬɟɣ ɩɨɤɚɡɚɧɵ ɧɚ ɪɢɫ. 7.18. ɇɟɩɨɞɜɢɠɧɨɣ ɨɫɬɚɟɬɫɹ ɬɨɱɤɚ ɤɪɟɩɥɟɧɢɹ ɤɚɬɤɚ ɤ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɢ – ɬɨɱɤɚ C.
Z
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C |
R |
A' |
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mg |
Z1 |
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Y |
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Ɋɢɫ. 7.18 |
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ɇɚ ɤɚɬɨɤ ɞɟɣɫɬɜɭɸɬ ɫɢɥɚ ɬɹɠɟɫɬɢ mg, ɫɢɥɚ ɪɟɚɤɰɢɢ ɨɩɨɪɵ N ɢ ɫɢɥɚ ɪɟɚɤɰɢɢ ɫɨ ɫɬɨɪɨɧɵ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɢ, ɩɪɢɥɨɠɟɧɧɚɹ ɜ ɬɨɱɤɟ ɋ (ɧɟ ɢɡɨɛɪɚɠɟɧɧɚɹ ɧɚ ɪɢɫ. 7.18). Ȼɭɞɟɦ ɫɱɢɬɚɬɶ ɫɬɟɪɠɟɧɶ, ɫ ɩɨɦɨɳɶɸ ɤɨɬɨɪɨɝɨ ɤɚɬɨɤ ɤɪɟɩɢɬɫɹ ɤ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɢ, ɧɟɜɟɫɨɦɵɦ. ɉɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ ɰɢɥɢɧɞɪɢɱɟɫɤɢɣ ɤɚɬɨɤ ɞɜɢɠɟɬɫɹ ɛɟɡ ɩɪɨɫɤɚɥɶɡɵɜɚɧɢɹ, ɷɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɬɨɥɳɢɧɚ ɤɚɬɤɚ ɫɭɳɟɫɬɜɟɧɧɨ ɦɟɧɶɲɟ ɪɚɫɫɬɨɹɧɢɹ R ɨɬ ɤɚɬɤɚ ɞɨ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɢ ɜɪɚɳɟɧɢɹ. Ɍɪɟɧɢɟɦ ɤɚɱɟɧɢɹ, ɜɨɡɧɢɤɚɸɳɢɦ ɩɪɢ ɧɟɭɩɪɭɝɢɯ ɞɟɮɨɪɦɚɰɢɹɯ, ɩɪɟɧɟɛɪɟɝɚɟɦ. ɉɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ ɬɪɟɛɭɟɬɫɹ ɧɚɣɬɢ ɩɨɥɧɭɸ ɫɢɥɭ ɞɚɜɥɟɧɢɹ ɤɚɬɤɚ ɧɚ ɨɩɨɪɧɭɸ ɩɥɢɬɭ, ɤɨɬɨɪɚɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɪɟɬɶɢɦ ɡɚɤɨɧɨɦ ɇɶɸɬɨɧɚ ɪɚɜɧɚ ɩɨ ɦɨɞɭɥɸ ɫɢɥɟ ɧɨɪɦɚɥɶɧɨɣ ɪɟɚɤɰɢɢ ɨɩɨɪɧɨɣ ɩɥɢɬɵ N, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɤɚɬɨɤ.
II. Ɉɬɥɢɱɧɵɟ ɨɬ ɧɭɥɹ ɦɨɦɟɧɬɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɱɤɢ C ɢɦɟɸɬ ɞɜɟ ɫɢɥɵ – ɫɢɥɚ ɬɹɠɟɫɬɢ Mmg ɢ ɫɢɥɚ ɧɨɪɦɚɥɶɧɨɣ ɪɟɚɤɰɢɢ ɫɨ ɫɬɨ-
ɪɨɧɵ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ M N . Ɂɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɟ ɦɨ-
ɦɟɧɬɨɜ ɞɥɹ ɤɚɬɤɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɱɤɢ C ɤɪɟɩɥɟɧɢɹ ɤɚɬɤɚ ɤ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɢ:
dL |
M N Mmg . |
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dt |
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262 ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ
ɉɪɢ ɤɚɱɟɧɢɢ ɤɚɬɤɚ ɩɨ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɩɪɨɢɫɯɨɞɢɬ ɩɨɫɬɨɹɧɧɨɟ ɢɡɦɟɧɟɧɢɟ ɧɚɩɪɚɜɥɟɧɢɹ ɟɝɨ ɨɫɢ, ɱɬɨ ɨɩɪɟɞɟɥɹɟɬ
ɢɡɦɟɧɟɧɢɟ ɧɚɩɪɚɜɥɟɧɢɹ ɜɟɤɬɨɪɚ ɦɨɦɟɧɬɚ ɢɦ- |
Z1 |
Lxy |
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ɩɭɥɶɫɚ. Ƚɨɪɢɡɨɧɬɚɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ ɦɨ- |
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ɦɟɧɬɚ ɢɦɩɭɥɶɫɚ LXY (ɫɦ. ɪɢɫ. 7.19) ɩɨɜɨɪɚ- |
Z |
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ɱɢɜɚɟɬɫɹ ɜɨɤɪɭɝ ɨɫɢ Z (ɫɦ. ɪɢɫ. 7.20), ɚ ɜɟɪ- |
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ɬɢɤɚɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɚɹ LZ ɨɫɬɚɟɬɫɹ ɧɟɢɡ- |
Lz |
L |
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ɦɟɧɧɨɣ: |
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Ɋɢɫ. 7.19 |
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dL |
dLXY dLZ dLXY . |
(7.106) |
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Lxy(t) |
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Z |
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Lxy(t) |
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dD |
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Lxy(t+dt) |
dLxy |
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Lxy(t+dt) |
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Ɋɢɫ. 7.20 |
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Ɇɨɦɟɧɬɵ ɫɢɥɵ ɬɹɠɟɫɬɢ |
Mmg ɢ ɫɢɥɵ ɧɨɪɦɚɥɶɧɨɣ ɪɟɚɤɰɢɢ |
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ɨɩɨɪɧɨɣ ɩɥɢɬɵ M N ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɱɤɢ C ɧɚɩɪɚɜɥɟɧɵ ɜ ɩɪɨɬɢɜɨ-
ɩɨɥɨɠɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ ɜɞɨɥɶ ɨɫɢ Y (ɫɦ. ɪɢɫ. 7.18). ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɥɹ ɜɟɥɢɱɢɧɵ ɫɤɨɪɨɫɬɢ ɢɡɦɟɧɟɧɢɹ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɫɨɫɬɚɜɥɹɸɳɟɣ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ LXY ɫ ɭɱɟɬɨɦ (7.105) ɢ (7.106) ɦɨɠɧɨ ɡɚɩɢ-
ɫɚɬɶ:
dLXY |
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M N Mmg |
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RN Rmg . |
(7.107) |
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dt |
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ɉɨɫɤɨɥɶɤɭ ɫɨɫɬɚɜɥɹɸɳɚɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ LXY ɧɚɩɪɚɜɥɟɧɚ ɜɞɨɥɶ ɫɨɛɫɬɜɟɧɧɨɣ ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɨɫɢ ɤɚɬɤɚ AA', ɬɨ ɜ ɫɨɨɬɜɟɬɫɬ-
ɜɢɢ ɫ ɮɨɪɦɭɥɨɣ (6.30) Ƚɥɚɜɵ 6: |
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LXY J0Z1 . |
(7.108) |
ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɭɫɥɨɜɢɟɦ ɡɚɞɚɱɢ ɤɚɱɟɧɢɟ ɩɪɨɢɫɯɨɞɢɬ ɛɟɡ ɩɪɨɫɤɚɥɶɡɵɜɚɧɢɹ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɫɤɨɪɨɫɬɢ ɬɨɱɟɤ ɤɚɬɤɚ, ɫɨɩɪɢɤɚɫɚɸɳɢɯɫɹ ɫ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɨɜɟɪɯɧɨɫɬɶɸ, ɪɚɜɧɵ ɧɭɥɸ. ɋ ɞɪɭɝɨɣ
Ƚɥɚɜɚ 7. Ɂɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ |
263 |
ɫɬɨɪɨɧɵ, ɜ ɫɢɥɭ ɩɪɢɧɰɢɩɚ ɫɭɩɟɪɩɨɡɢɰɢɢ ɞɜɢɠɟɧɢɣ, ɫɤɨɪɨɫɬɶ ɷɬɢɯ ɬɨɱɟɤ ɫɤɥɚɞɵɜɚɟɬɫɹ ɢɡ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɜɨɤɪɭɝ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɢ ɢ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɜɨɤɪɭɝ ɫɨɛɫɬɜɟɧɧɨɣ ɨɫɢ ɤɚɬɤɚ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ ɭɝɥɨɜɵɟ ɫɤɨɪɨɫɬɢ Z ɢ Z1 ɫɜɹɡɚɧɵ ɫɨɨɬɧɨɲɟɧɢɟɦ:
ZR Z1r |
0 . |
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(7.109) |
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ɇɚɣɞɟɦ ɜɟɥɢɱɢɧɭ ɫɤɨɪɨɫɬɢ ɢɡɦɟɧɟɧɢɹ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɫɨ- |
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ɫɬɚɜɥɹɸɳɟɣ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ |
LXY . ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɪɢɫ. 7.20. |
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ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ: |
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dLXY |
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LXYdD |
LXYZ . |
(7.110) |
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dt |
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ȼ ɪɟɡɭɥɶɬɚɬɟ ɩɨɥɭɱɟɧɚ ɩɨɥɧɚɹ ɫɢɫɬɟɦɚ ɭɪɚɜɧɟɧɢɣ (7.107) – (7.110) ɞɥɹ ɧɚɯɨɠɞɟɧɢɹ N.
III. Ɋɟɲɚɹ ɫɢɫɬɟɦɭ ɭɪɚɜɧɟɧɢɣ (7.107) – (7.110) ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɟɥɢɱɢɧɵ ɫɢɥɵ ɧɨɪɦɚɥɶɧɨɣ ɪɟɚɤɰɢɢ ɨɩɨɪɧɨɣ ɩɥɢɬɵ, ɩɨɥɭɱɚɟɦ:
dLXY |
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J0 |
R |
Z2 |
R N mg , |
(7.111) |
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r |
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N |
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J0 |
Z2 mg . |
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(7.112) |
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r |
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ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɬɪɟɬɶɢɦ ɡɚɤɨɧɨɦ ɇɶɸɬɨɧɚ ɢɫɤɨɦɚɹ ɩɨɥɧɚɹ ɫɢɥɚ ɞɚɜɥɟɧɢɹ ɤɚɬɤɚ ɧɚ ɨɩɨɪɧɭɸ ɩɥɢɬɭ ɪɚɜɧɚ ɩɨ ɦɨɞɭɥɸ ɫɢɥɟ ɧɨɪɦɚɥɶɧɨɣ ɪɟɚɤɰɢɢ ɨɩɨɪɧɨɣ ɩɥɢɬɵ N, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɤɚɬɨɤ (7.112).
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Ɂɚɞɚɱɚ 7.9 |
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Ƚɢɪɨɫɤɨɩ ɩɪɟɞɫɬɚɜɥɹɟɬ ɫɨ- |
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ɛɨɣ |
ɨɞɧɨɪɨɞɧɵɣ ɞɢɫɤ |
ɪɚɞɢɭɫɨɦ |
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R = 5 ɫɦ ɢ ɦɚɫɫɨɣ m0, |
ɡɚɤɪɟɩɥɟɧ- |
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ɧɵɣ ɧɚ ɧɟɜɟɫɨɦɨɦ ɝɨɪɢɡɨɧɬɚɥɶ- |
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ɧɨɦ |
ɫɬɟɪɠɧɟ, |
ɨɪɢɟɧɬɢɪɨɜɚɧɧɨɦ |
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ɜɞɨɥɶ ɨɫɢ OO' (ɪɢɫ. 7.21). Ƚɢɪɨ- |
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ɫɤɨɩ |
ɦɨɠɟɬ |
ɜɪɚɳɚɬɶɫɹ |
ɜɨɤɪɭɝ |
m0 |
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ɨɫɟɣ OO' ɢ CD. Ⱦɢɫɤ ɝɢɪɨɫɤɨɩɚ |
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ɭɪɚɜɧɨɜɟɲɟɧ ɧɚ ɞɪɭɝɨɦ ɤɨɧɰɟ ɨɫɢ |
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OO' ɬɟɥɨɦ ɫ ɬɨɣ ɠɟ ɦɚɫɫɨɣ m0. |
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Ƚɢɪɨɫɤɨɩ ɪɚɫɤɪɭɬɢɥɢ ɜɨɤɪɭɝ ɫɨɛ- |
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ɫɬɜɟɧɧɨɣ ɨɫɢ OO' ɬɚɤ, ɱɬɨ ɨɧ ɞɟ- |
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ɥɚɟɬ |
n = 50 ɨɛ./ɫ. Ɂɚɬɟɦ |
ɤ |
ɬɟɥɭ |
Ɋɢɫ. 7.21 |
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ɦɚɫɫɨɣ m0 ɩɨɞɜɟɫɢɥɢ |
ɟɳɟ |
ɨɞɧɨ |
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264 ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ
ɬɟɥɨ ɦɚɫɫɨɣ m m0 /10 . ɇɚɣɬɢ ɩɟɪɢɨɞ ɜɪɚɳɟɧɢɹ ɝɢɪɨɫɤɨɩɚ ɜɨɤɪɭɝ
ɨɫɢ CD, ɟɫɥɢ ɪɚɫɫɬɨɹɧɢɟ l ɨɬ ɨɫɢ CD ɞɨ ɬɨɱɤɢ ɩɨɞɜɟɫɚ ɬɟɥɚ ɦɚɫɫɨɣ m0 (ɫɦ. ɪɢɫ. 7.21) ɪɚɜɧɨ 10 ɫɦ.
Ɋɟɲɟɧɢɟ
I. Ⱦɨ ɩɨɞɜɟɲɢɜɚɧɢɹ ɬɟɥɚ ɦɚɫɫɨɣ m ɝɢɪɨɫɤɨɩ ɭɪɚɜɧɨɜɟɲɟɧ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫɭɦɦɚ ɦɨɦɟɧɬɨɜ ɫɢɥɵ ɬɹɠɟɫɬɢ, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɞɢɫɤ ɝɢɪɨɫɤɨɩɚ, ɢ ɫɢɥɵ ɧɚɬɹɠɟɧɢɹ ɧɢɬɢ ɩɨɞɜɟɫɚ ɬɟɥɚ ɦɚɫɫɨɣ m0 ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɱɤɢ ɩɟɪɟɫɟɱɟɧɢɹ ɨɫɟɣ ɜɪɚɳɟɧɢɹ OO' ɢ CD ɝɢɪɨɫɤɨɩɚ ɪɚɜɧɚ ɧɭɥɸ. ȼ ɭɫɥɨɜɢɢ ɪɚɜɧɨɜɟɫɢɹ ɝɢɪɨɫɤɨɩ ɧɟ ɫɨɜɟɪɲɚɟɬ ɩɪɟɰɟɫɫɢɢ. ɉɨɫɥɟ ɩɨɞɜɟɲɢɜɚɧɢɹ ɬɟɥɚ ɦɚɫɫɨɣ m ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɦɨɦɟɧɬ ɫɢɥɵ ɧɚɬɹɠɟɧɢɹ ɧɢɬɢ ɩɨɞɜɟɫɚ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɢɡɦɟɧɟɧɢɸ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɝɢɪɨɫɤɨɩɚ. ɉɨɫɤɨɥɶɤɭ ɦɨɦɟɧɬ ɢɦɩɭɥɶɫɚ ɝɢɪɨɫɤɨɩɚ ɡɧɚɱɢɬɟɥɶɧɨ ɛɨɥɶɲɟ ɢɡɦɟɧɟɧɢɹ ɦɨɦɟɧɬɚ ɫɢɥɵ ɧɚɬɹɠɟɧɢɹ ɧɢɬɢ ɩɨɞɜɟɫɚ, ɬɨ ɩɪɨɢɫɯɨɞɢɬ ɦɟɞɥɟɧɧɨɟ ɢɡɦɟɧɟɧɢɟ ɧɚɩɪɚɜɥɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɝɢɪɨɫɤɨɩɚ L – ɩɪɟɰɟɫɫɢɹ ɨɫɢ ɝɢɪɨɫɤɨɩɚ.
II. Ɂɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɟ ɩɪɟɰɟɫɫɢɢ ɝɢɪɨɫɤɨɩɚ (ɫɦ. (7.23)) ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɱɤɢ ɩɟɪɟɫɟɱɟɧɢɹ ɟɝɨ ɨɫɟɣ ɜɪɚɳɟɧɢɹ OO' ɢ CD (ɫɦ.
ɪɢɫ. 7.18): |
>ȍL@, |
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ɝɞɟ M ɫɭɦɦɚ ɦɨɦɟɧɬɨɜ ɜɧɟɲɧɢɯ ɫɢɥ, ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɝɢɪɨɫɤɨɩ, ȍ ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɩɪɟɰɟɫɫɢɢ.
Ⱦɨɩɨɥɧɢɦ ɷɬɨ ɭɪɚɜɧɟɧɢɟ ɜɵɪɚɠɟɧɢɟɦ (7.18) ɞɥɹ ɦɨɦɟɧɬɚ ɢɦ-
ɩɭɥɶɫɚ ɝɢɪɨɫɤɨɩɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɟɝɨ ɫɨɛɫɬɜɟɧɧɨɣ ɨɫɢ OO': |
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Ɂɞɟɫɶ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɝɢɪɨɫɤɨɩɚ, ɩɪɟɞɫɬɚɜɥɹɸɳɟɝɨ ɫɨɛɨɣ ɨɞɧɨɪɨɞɧɵɣ ɞɢɫɤ, ɡɚɤɪɟɩɥɟɧɧɵɣ ɧɚ ɧɟɜɟɫɨɦɨɦ ɫɬɟɪɠɧɟ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɮɨɪɦɭɥɨɣ (6.44) ɜ Ƚɥɚɜɟ 6 ɪɚɜɟɧ
J0 |
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ɚ ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɝɢɪɨɫɤɨɩɚ Z ɫɜɹɡɚɧɚ ɫ ɱɢɫɥɨɦ ɟɝɨ |
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ɨɛɨɪɨɬɨɜ n ɜɨɤɪɭɝ ɫɨɛɫɬɜɟɧɧɨɣ ɨɫɢ ɫɨɨɬɧɨɲɟɧɢɟɦ: |
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2Sn . |
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ɉɨɞɜɟɲɟɧɧɵɟ ɤ ɫɬɟɪɠɧɸ ɝɢɪɨɫɤɨɩɚ ɬɟɥɚ ɦɚɫɫɨɣ m0 ɢ m ɧɟ ɩɟɪɟɦɟɳɚɸɬɫɹ ɜɞɨɥɶ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɢ CD ɜ ɩɪɨɰɟɫɫɟ ɞɜɢɠɟɧɢɹ ɝɢɪɨɫɤɨɩɚ, ɩɨɷɬɨɦɭ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫɨ ɜɬɨɪɵɦ ɡɚɤɨɧɨɦ ɇɶɸɬɨɧɚ
ɫɢɥɚ ɧɚɬɹɠɟɧɢɹ ɧɢɬɢ ɩɨɞɜɟɫɚ ɬɟɥ F ɪɚɜɧɚ |
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m0 m g . |
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Ƚɥɚɜɚ 7. Ɂɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ |
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ɋɭɦɦɚ ɦɨɦɟɧɬɨɜ ɫɢɥɵ ɬɹɠɟɫɬɢ, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɞɢɫɤ ɝɢɪɨɫɤɨɩɚ ɦɚɫɫɨɣ m0, ɢ ɫɢɥɵ ɧɚɬɹɠɟɧɢɹ ɧɢɬɢ ɩɨɞɜɟɫɚ ɬɟɥ ɦɚɫɫɨɣ m0 ɢ m ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɱɤɢ ɩɟɪɟɫɟɱɟɧɢɹ ɨɫɟɣ ɜɪɚɳɟɧɢɹ OO' ɢ CD ɝɢɪɨɫɤɨ-
ɩɚ ɧɚɩɪɚɜɥɟɧɚ ɜɞɨɥɶ ɨɫɢ AB (ɫɦ. ɪɢɫ. 7.22) ɢ ɪɚɜɧɚ ɩɨ ɦɨɞɭɥɸ |
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M m0 gl m0 m gl mgl . |
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ȼɫɥɟɞɫɬɜɢɟ ɛɵɫɬɪɨɝɨ ɜɪɚɳɟɧɢɹ ɝɢɪɨɫɤɨɩɚ ɜɨɤɪɭɝ ɫɜɨɟɣ ɨɫɢ ɟɝɨ ɦɨɦɟɧɬ ɢɦɩɭɥɶɫɚ ɛɭɞɟɦ ɫɱɢɬɚɬɶ ɧɚɩɪɚɜɥɟɧɧɵɦ ɜɞɨɥɶ ɨɫɢ ɜɪɚɳɟɧɢɹ OO' (ɪɢɫ. 7.22). ɉɪɢ ɷɬɨɦ ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɩɪɟɰɟɫɫɢɢ ȍ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (7.113) ɧɚɩɪɚɜɥɟɧɚ ɜɞɨɥɶ ɨɫɢ CD (ɪɢɫ. 7.22).
ɉɨɞɫɬɚɜɥɹɹ (7.114) – (7.118) ɜ (7.113) ɫ ɭɱɟɬɨɦ ɧɚɩɪɚɜɥɟɧɢɹ ɜɟɤɬɨɪɨɜ M , L ɢ ȍ , ɞɥɹ ɦɨɞɭɥɹ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ ɩɪɟɰɟɫɫɢɢ ɝɢɪɨɫɤɨɩɚ : ɩɨɥɭɱɚɟɦ:
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ɂɫɤɨɦɵɣ ɩɟɪɢɨɞ ɜɪɚɳɟɧɢɹ ɝɢɪɨɫɤɨɩɚ ɜɨɤɪɭɝ ɨɫɢ CD ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (7.118) ɪɚɜɟɧ:
T |
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ɉɨɞɫɬɚɜɥɹɹ ɱɢɫɥɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ, ɡɚɞɚɧɧɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ, ɩɨɥɭɱɢɦ
T12,5 c .
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ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ |
7.4. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ
Ɂɚɞɚɱɚ 1
Ⱦɢɫɤ, ɜɪɚɳɚɸɳɢɣɫɹ ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ Z1 ɜɨɤɪɭɝ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɢ, ɩɪɨɯɨɞɹɳɢɣ ɱɟɪɟɡ ɟɝɨ ɰɟɧɬɪ ɦɚɫɫ, ɩɚɞɚɟɬ ɧɚ ɞɪɭɝɨɣ ɞɢɫɤ, ɜɪɚɳɚɸɳɢɣɫɹ ɧɚ ɝɥɚɞɤɨɣ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɫ ɭɝ-
ɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ Z2 ɜɨɤɪɭɝ ɬɨɣ ɠɟ ɨɫɢ (ɫɦ. ɪɢɫ.). Ɇɨɦɟɧɬɵ ɢɧɟɪ- |
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ɰɢɢ ɞɢɫɤɨɜ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɜɪɚɳɟ- |
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ɧɢɹ ɪɚɜɧɵ |
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ɜɟɪɯɧɟɝɨ ɞɢɫɤɚ ɧɚ ɧɢɠɧɢɣ ɨɛɚ ɞɢɫɤɚ, |
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ɛɥɚɝɨɞɚɪɹ ɬɪɟɧɢɸ ɦɟɠɞɭ ɧɢɦɢ, ɱɟɪɟɡ |
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ɧɟɤɨɬɨɪɨɟ ɜɪɟɦɹ ɫɬɚɥɢ ɜɪɚɳɚɬɶɫɹ ɤɚɤ |
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ɟɞɢɧɨɟ ɰɟɥɨɟ. ɇɚɣɬɢ ɪɚɛɨɬɭ A, ɤɨɬɨ- |
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ɪɭɸ ɫɨɜɟɪɲɢɥɢ ɩɪɢ ɷɬɨɦ ɫɢɥɵ ɬɪɟɧɢɹ, |
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ɞɟɣɫɬɜɭɸɳɢɟ ɦɟɠɞɭ ɞɢɫɤɚɦɢ. |
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Ɉɬɜɟɬ: A |
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Ɂɚɞɚɱɚ 2 |
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ɉɨ ɜɧɭɬɪɟɧɧɟɣ ɩɨɜɟɪɯɧɨɫɬɢ ɤɨɧɢɱɟ- |
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ɫɤɨɣ ɜɨɪɨɧɤɢ, ɫɬɨɹɳɟɣ ɜɟɪɬɢɤɚɥɶɧɨ, ɛɟɡ ɬɪɟ- |
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ɧɢɹ ɫɤɨɥɶɡɢɬ ɦɚɥɟɧɶɤɢɣ ɲɚɪɢɤ (ɫɦ. ɪɢɫ.). ȼ |
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ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɲɚɪɢɤ ɧɚɯɨɞɢɬɫɹ |
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ɧɚ ɜɵɫɨɬɟ h0 ɢ ɢɦɟɟɬ ɫɤɨɪɨɫɬɶ X0, ɧɚɩɪɚɜɥɟɧ- |
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ɧɭɸ ɝɨɪɢɡɨɧɬɚɥɶɧɨ. ɇɚ ɤɚɤɭɸ ɦɚɤɫɢɦɚɥɶɧɭɸ |
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ɜɵɫɨɬɭ h ɩɨɞɧɢɦɟɬɫɹ ɲɚɪɢɤ ɜ ɩɪɨɰɟɫɫɟ ɞɜɢ- |
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ɠɟɧɢɹ? ɑɟɦɭ ɪɚɜɧɚ ɟɝɨ ɫɤɨɪɨɫɬɶ X |
ɧɚ ɷɬɨɣ |
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ɜɵɫɨɬɟ? |
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Ɉɬɜɟɬ: h |
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¸ ; ɫɤɨɪɨɫɬɶ ɲɚɪɢɤɚ ɧɚɩɪɚɜɥɟɧɚ ɝɨɪɢ- |
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ɡɨɧɬɚɥɶɧɨ ɢ ɟɟ ɦɨɞɭɥɶ ɪɚɜɟɧ: X |
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Ɂɚɞɚɱɚ 3
Ɍɨɧɤɚɹ ɩɚɥɨɱɤɚ ɞɥɢɧɨɣ l ɢ ɦɚɫɫɨɣ m ɥɟɠɢɬ ɧɚ ɝɥɚɞɤɨɣ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ. ɉɭɥɹ ɦɚɫɫɨɣ m0 m / 8 , ɥɟɬɟɜɲɚɹ ɩɟɪɩɟɧ-
Ƚɥɚɜɚ 7. Ɂɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ |
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ɞɢɤɭɥɹɪɧɨ ɩɚɥɨɱɤɟ ɢ ɩɚɪɚɥɥɟɥɶɧɨ ɩɨɜɟɪɯɧɨɫɬɢ ɫɨ ɫɤɨɪɨɫɬɶɸ X0, ɩɨɩɚɞɚɟɬ ɜ ɩɚɥɨɱɤɭ ɧɚ ɪɚɫɫɬɨɹɧɢɢ l0 l / 4 ɨɬ ɟɟ ɤɨɧɰɚ ɢ ɡɚɫɬɪɟɜɚɟɬ
ɜ ɧɟɣ. ɇɚɣɬɢ ɭɝɥɨɜɭɸ ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɫɢɫɬɟɦɵ ɬɟɥ ɩɨɫɥɟ ɫɨɭɞɚɪɟɧɢɹ.
Ɉɬɜɟɬ: Z |
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Ɂɚɞɚɱɚ 4
ɇɚ ɝɥɚɞɤɨɦ ɝɨɪɢɡɨɧɬɚɥɶɧɨɦ ɫɬɟɪɠɧɟ, ɜɪɚɳɚɸɳɟɦɫɹ ɜɨɤɪɭɝ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɢ ɫ ɩɨɫɬɨɹɧɧɨɣ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ Z, ɧɚ ɪɚɫɫɬɨɹɧɢɢ l0 ɨɬ ɨɫɢ ɧɚɯɨɞɢɬɫɹ ɦɭɮɬɚ ɦɚɫɫɨɣ m (ɫɦ. ɪɢɫ.). ȼ ɧɟɤɨɬɨɪɵɣ
ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɦɭɮɬɟ ɫɨɨɛɳɚɸɬ ɫɤɨ- |
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ɪɨɫɬɶ X0 |
l0Z ɜɞɨɥɶ ɫɬɟɪɠɧɹ, |
ɧɚɩɪɚɜ- |
Z |
l0 |
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ɥɟɧɧɭɸ |
ɨɬ ɨɫɢ ɜɪɚɳɟɧɢɹ. Ʉɚɤɨɣ ɦɨ- |
ȣ0 |
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ɦɟɧɬ ɫɢɥ M ɞɨɥɠɟɧ ɛɵɬɶ ɩɪɢɥɨɠɟɧ ɤ |
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ɫɬɟɪɠɧɸ ɞɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɨɧ ɩɪɨɞɨɥɠɚɥ |
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ɪɚɜɧɨɦɟɪɧɨɟ ɜɪɚɳɟɧɢɟ? Ʉɚɤ ɦɟɧɹɟɬɫɹ |
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ɪɚɫɫɬɨɹɧɢɟ ɦɭɮɬɵ ɨɬ ɨɫɢ ɜɪɚɳɟɧɢɹ ɜ |
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ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɪɟɦɟɧɢ? |
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Ɉɬɜɟɬ: M (t) 2ml 2Z2e2Zt , l(t) |
l |
eZt . |
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Ɂɚɞɚɱɚ 5
Ʉɨɪɚɛɥɶ ɞɜɢɠɟɬɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ X = 40 ɤɦ/ɱɚɫ ɩɨ ɞɭɝɟ ɨɤɪɭɠɧɨɫɬɢ ɪɚɞɢɭɫɚ R = 300 ɦ. ɇɚɣɬɢ ɦɨɦɟɧɬ ɝɢɪɨɫɤɨɩɢɱɟɫɤɢɯ ɫɢɥ MȽ, ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɩɨɞɲɢɩɧɢɤɢ ɞɜɢɝɚɬɟɥɹ ɤɨɪɚɛɥɹ ɫɨ ɫɬɨɪɨɧɵ ɪɨɬɨɪɚ, ɤɨɬɨɪɵɣ ɢɦɟɟɬ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɜɪɚɳɟɧɢɹ J0 = 3,6 103 ɤɝ ɦ2 ɢ ɞɟɥɚɟɬ n = 150 ɨɛ./ɦɢɧ. Ɉɫɶ ɜɪɚɳɟɧɢɹ ɪɚɫɩɨ-
ɥɨɠɟɧɚ ɜɞɨɥɶ ɤɨɪɚɛɥɹ. |
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Ɉɬɜɟɬ: M |
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2SnJ |
X |
2,1 103 ɇ ɦ . |
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0 R |
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Ɂɚɞɚɱɚ 6
Ƚɢɪɨɫɤɨɩ ɦɚɫɫɨɣ m = 0,5 ɤɝ ɜɪɚɳɚɟɬɫɹ ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ Z = 200 ɪɚɞ/ɫ. Ɇɨɦɟɧɬ ɢɧɟɪɰɢɢ ɝɢɪɨɫɤɨɩɚ J = 5 10-4 ɤɝ ɦ2. ɍɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɩɪɟɰɟɫɫɢɢ ɜ ɩɨɥɟ ɫɢɥ ɬɹɠɟɫɬɢ Ɂɟɦɥɢ : 0,5 ɪɚɞ/ɫ. ɍɝɨɥ
ɦɟɠɞɭ ɜɟɪɬɢɤɚɥɶɸ ɢ ɨɫɶɸ ɝɢɪɨɫɤɨɩɚ D 300 . Ɉɩɪɟɞɟɥɢɬɶ ɪɚɫɫɬɨɹ-
Z
Ƚɥɚɜɚ 7. Ɂɚɤɨɧɵ ɫɨɯɪɚɧɟɧɢɹ ɦɨɦɟɧɬɚ ɢɦɩɭɥɶɫɚ ɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ |
269 |
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ɫɬɟɪɠɟɧɶ ɩɨɫɥɟ ɭɞɚɪɚ ɨɫɬɚɧɨɜɢɬɫɹ? |
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Ɉɬɜɟɬ: |
M |
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l 2 |
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2 |
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Ɂɚɞɚɱɚ 10
ɑɚɫɬɢɰɚ ɦɚɫɫɨɣ m ɞɜɢɠɟɬɫɹ ɩɨ ɷɥɥɢɩɬɢɱɟɫɤɨɣ ɬɪɚɟɤɬɨɪɢɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɰɟɧɬɪɚɥɶɧɨɣ ɭɩɪɭɝɨɣ ɫɢɥɵ F kr . Ɇɢɧɢɦɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɱɚɫɬɢɰɵ ɞɨɫɬɢɝɚɟɬɫɹ ɩɪɢ ɡɧɚɱɟɧɢɢ ɟɟ ɪɚɞɢɭɫ-ɜɟɤɬɨɪɚ
rr0 ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɢɥɨɜɨɝɨ ɰɟɧɬɪɚ, ɫɨɜɩɚɞɚɸɳɟɝɨ ɫ ɨɞɧɢɦ ɢɡ
ɮɨɤɭɫɨɜ ɷɥɥɢɩɫɚ. ɇɚɣɬɢ ɦɨɞɭɥɶ ɦɚɤɫɢɦɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ
Xmax .
Ɉɬɜɟɬ: X |
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max |
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Ɂɚɞɚɱɚ 11
Ⱦɜɟ ɨɞɢɧɚɤɨɜɵɟ ɲɚɣɛɵ ɫɤɨɥɶɡɹɬ ɧɚɜɫɬɪɟɱɭ ɞɪɭɝ ɞɪɭɝɭ ɩɨ ɝɥɚɞɤɨɣ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɫɨ ɫɤɨɪɨɫɬɹɦɢ X1 ɢ X2 , ɜɪɚ-
ɳɚɹɫɶ ɫ ɭɝɥɨɜɵɦɢ ɫɤɨɪɨɫɬɹɦɢ Z1 ɢ Z2 (ɫɦ. ɪɢɫ.). ȼ ɧɟɤɨɬɨɪɵɣ ɦɨ-
ɦɟɧɬ ɜɪɟɦɟɧɢ ɩɪɨɢɫɯɨɞɢɬ ɢɯ ɰɟɧɬɪɚɥɶɧɨɟ ɚɛɫɨɥɸɬɧɨ ɧɟɭɩɪɭɝɨɟ ɫɨɭɞɚɪɟɧɢɟ, ɜ ɪɟɡɭɥɶɬɚɬɟ ɤɨɬɨɪɨɝɨ ɲɚɣɛɵ ɧɚɱɢɧɚɸɬ ɫɤɨɥɶɡɢɬɶ ɩɨ ɩɨɜɟɪɯɧɨɫɬɢ ɢ ɜɪɚɳɚɬɶɫɹ ɜɦɟɫɬɟ. ɋɱɢɬɚɹ ɢɡɜɟɫɬɧɵɦɢ ɦɚɫɫɭ m ɢ ɪɚɞɢɭɫ R ɤɚɠɞɨɣ ɢɡ ɲɚɣɛ, ɧɚɣɬɢ ɢɡɦɟɧɟɧɢɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ
ɲɚɣɛ ǻE k ɢ ɭɝɥɨɜɭɸ ɫɤɨɪɨɫɬɶ ɢɯ ɜɪɚɳɟɧɢɹ Z ɩɨɫɥɟ ɫɨɭɞɚɪɟɧɢɹ.
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Z1 |
X X |
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Ɉɬɜɟɬ: ǻE k |
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m |
>6(X1 X2 )2 |
6R2 |
(Z12 Z22 ) R2 (Z1 Z2 )2 @, |
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Z1 Z2 . |
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270 |
ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ |
ȽɅȺȼȺ 8 ɋȼɈȻɈȾɇɕȿ ɂ ȼɕɇɍɀȾȿɇɇɕȿ ɄɈɅȿȻȺɇɂə ɋɂɋɌȿɆ
ɋ ɈȾɇɈɃ ɋɌȿɉȿɇɖɘ ɋȼɈȻɈȾɕ. ɊȿɁɈɇȺɇɋ
8.1. Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ
Ɇɟɯɚɧɢɱɟɫɤɢɟ ɤɨɥɟɛɚɧɢɹ – ɷɬɨ ɩɨɜɬɨɪɹɸɳɟɟɫɹ ɨɝɪɚɧɢɱɟɧɧɨɟ ɞɜɢɠɟɧɢɟ ɬɟɥ ɦɟɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɤɨɬɨɪɨɝɨ ɫɜɨɟɝɨ ɩɨɥɨɠɟɧɢɹ. ɉɪɢ ɷɬɨɦ ɨɛɨɛɳɟɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ, ɨɩɪɟɞɟɥɹɸɳɢɟ ɩɨɥɨɠɟɧɢɹ ɬɟɥ ɫɢɫɬɟɦɵ ɜ ɩɪɨɫɬɪɚɧɫɬɜɟ (ɫɦ. ɩ. 6.1.1 ɜ Ƚɥɚɜɟ 6), ɨɝɪɚɧɢɱɟɧɨ ɢɡɦɟɧɹɸɬɫɹ ɨɤɨɥɨ ɧɟɤɨɬɨɪɨɝɨ ɫɜɨɟɝɨ ɡɧɚɱɟɧɢɹ
(ɫɦ. ɪɢɫ. 8.1).
[ (t)
t
Ɋɢɫ. 8.1. Ɂɚɜɢɫɢɦɨɫɬɶ ɨɛɨɛɳɟɧɧɨɣ ɤɨɨɪɞɢɧɚɬɵ [(t) ɨɬ ɜɪɟɦɟɧɢ ɜ ɫɥɭɱɚɟ ɤɨɥɟɛɚɧɢɣ
ɉɟɪɢɨɞɢɱɟɫɤɢɣ ɦɟɯɚɧɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ – ɞɜɢɠɟɧɢɟ ɬɟɥ ɦɟ-
ɯɚɧɢɱɟɫɤɨɣ ɫɢɫɬɟɦɵ, ɬɨɱɧɨ ɩɨɜɬɨɪɹɸɳɟɟɫɹ ɜɨ ɜɪɟɦɟɧɢ. Ⱦɥɹ ɫɢɫɬɟɦɵ ɫ ɨɞɧɨɣ ɫɬɟɩɟɧɶɸ ɫɜɨɛɨɞɵ, ɷɬɨɬ ɤɨɥɟɛɚɬɟɥɶɧɵɣ ɩɪɨɰɟɫɫ ɦɨɠɟɬ ɛɵɬɶ ɨɩɢɫɚɧ ɨɞɧɨɣ ɮɢɡɢɱɟɫɤɨɣ ɜɟɥɢɱɢɧɨɣ [(t) , ɩɟɪɢɨɞɢɱɟɫɤɢ ɡɚ-
ɜɢɫɹɳɟɣ ɨɬ ɜɪɟɦɟɧɢ (ɫɦ. ɪɢɫ. 8.2).
[ (t) |
T |
t
Ɋɢɫ. 8.2. Ɂɚɜɢɫɢɦɨɫɬɶ ɨɛɨɛɳɟɧɧɨɣ ɤɨɨɪɞɢɧɚɬɵ [(t) ɨɬ ɜɪɟɦɟɧɢ ɜ ɫɥɭɱɚɟ ɩɟɪɢɨɞɢɱɟɫɤɨɝɨ ɩɪɨɰɟɫɫɚ
ɉɟɪɢɨɞ T – ɦɢɧɢɦɚɥɶɧɵɣ ɢɧɬɟɪɜɚɥ ɜɪɟɦɟɧɢ, ɱɟɪɟɡ ɤɨɬɨɪɵɣ ɩɪɨɰɟɫɫ ɜ ɬɨɱɧɨɫɬɢ ɩɨɜɬɨɪɹɟɬɫɹ (ɪɢɫ. 8.2).