Механика.Методика решения задач

Ɂɚɞɚɱɚ 4

Ⱦɜɚ ɬɪɚɤɬɨɪɚ, ɞɜɢɠɭɳɢɟɫɹ ɫɨ ɫɤɨɪɨɫɬɹɦɢ X1 ɢ X2 , ɛɭɤɫɢɪɭɸɬ ɫ ɩɨɦɨɳɶɸ ɬɪɨɫɨɜ ɚɜɬɨɦɨɛɢɥɶ (ɫɦ. ɪɢɫ.).

ȣ1

D

ȣ2

Ɉɩɪɟɞɟɥɢɬɶ ɦɨɞɭɥɶ ɢ ɧɚɩɪɚɜɥɟɧɢɟ ɫɤɨɪɨɫɬɢ ȣ ɚɜɬɨɦɨɛɢɥɹ ɜ ɬɨɬ ɦɨɦɟɧɬ, ɤɨɝɞɚ ɬɪɨɫɵ ɩɚɪɚɥɥɟɥɶɧɵ ɜɟɤɬɨɪɚɦ ȣ1 ɢ ȣ2 , ɚ ɭɝɨɥ ɦɟɠɞɭ ɧɢɦɢ ɪɚɜɟɧ D.

ɬɨɪɚɦɢ ȣ ɢ ȣ1 .

Ɂɚɞɚɱɚ 5

Ɍɟɥɨ Ⱥ ɩɨɞɜɟɲɟɧɨ ɧɚ ɧɢɬɹɯ, ɩɟɪɟɤɢɧɭɬɵɯ ɱɟɪɟɡ ɛɥɨɤɢ ȼ ɢ ɋ ɦɚɥɨɝɨ ɞɢɚɦɟɬɪɚ ɬɚɤ, ɱɬɨ Ⱥȼ = ȼɋ (ɫɦ. ɪɢɫ.).

B L C

H

X A X

Ʉɨɧɰɵ ɧɢɬɟɣ ɬɹɧɭɬ ɫ ɨɞɢɧɚɤɨɜɵɦɢ ɫɤɨɪɨɫɬɹɦɢ X . Ɋɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɛɥɨɤɚɦɢ ȼ ɢ ɋ ɪɚɜɧɨ L. ɇɚɣɬɢ ɦɨɞɭɥɶ ɫɤɨɪɨɫɬɢ XA ɬɟɥɚ

ȽɅȺȼȺ 2 ȾɂɇȺɆɂɄȺ ɆȺɌȿɊɂȺɅɖɇɈɃ ɌɈɑɄɂ ɂ

ɉɊɈɋɌȿɃɒɂɏ ɋɂɋɌȿɆ

2.1.Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ

2.1.1.Ɂɚɤɨɧɵ ɇɶɸɬɨɧɚ

ɉɟɪɜɵɣ ɡɚɤɨɧ ɇɶɸɬɨɧɚ. ɋɭɳɟɫɬɜɭɸɬ ɬɚɤɢɟ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɤɨɬɨɪɵɯ ɢɡɨɥɢɪɨɜɚɧɧɚɹ ɦɚɬɟɪɢɚɥɶɧɚɹ ɬɨɱɤɚ (ɧɚ ɤɨɬɨɪɭɸ ɧɟ ɞɟɣɫɬɜɭɸɬ ɫɢɥɵ) ɞɜɢɠɟɬɫɹ ɪɚɜɧɨɦɟɪɧɨ ɢ ɩɪɹɦɨɥɢɧɟɣɧɨ ɢɥɢ ɩɨɤɨɢɬɫɹ. Ɍɚɤɢɟ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ ɧɚɡɵɜɚɸɬɫɹ ɢɧɟɪɰɢɚɥɶ-

ɧɵɦɢ.

ȼɬɨɪɨɣ ɡɚɤɨɧ ɇɶɸɬɨɧɚ. ȼ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ ɩɪɨɢɡɜɟɞɟɧɢɟ ɦɚɫɫɵ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ ɧɚ ɟɟ ɭɫɤɨɪɟɧɢɟ ɪɚɜɧɨ ɫɭɦɦɟ ɜɫɟɯ ɫɢɥ, ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɷɬɭ ɦɚɬɟɪɢɚɥɶɧɭɸ ɬɨɱɤɭ ɫɨ ɫɬɨ-

i

Ɍɪɟɬɢɣ ɡɚɤɨɧ ɇɶɸɬɨɧɚ. ɋɢɥɵ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɞɜɭɯ ɦɚɬɟɪɢɚɥɶɧɵɯ ɬɨɱɟɤ:

1)ɩɚɪɧɵɟ ɢ ɩɪɢɥɨɠɟɧɵ ɤ ɪɚɡɧɵɦ ɦɚɬɟɪɢɚɥɶɧɵɦ ɬɨɱɤɚɦ,

2)ɨɞɧɨɣ ɩɪɢɪɨɞɵ,

3)ɪɚɜɧɵ ɩɨ ɦɨɞɭɥɸ,

4)ɩɪɨɬɢɜɨɩɨɥɨɠɧɵ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ,

5)ɧɚɩɪɚɜɥɟɧɵ ɜɞɨɥɶ ɩɪɹɦɨɣ, ɫɨɟɞɢɧɹɸɳɟɣ ɦɚɬɟɪɢɚɥɶɧɵɟ ɬɨɱɤɢ.

ɍɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ – ɜɬɨɪɨɣ ɡɚɤɨɧ ɇɶɸɬɨɧɚ, ɡɚɩɢɫɚɧɧɵɣ ɜ ɜɟɤɬɨɪɧɨɣ ɮɨɪɦɟ ɢɥɢ ɜ ɩɪɨɟɤɰɢɹɯ ɧɚ ɨɫɢ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ:

Ɂɚɦɟɬɢɦ, ɱɬɨ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɩɪɨɟɤɰɢɹɯ ɧɚ ɥɸɛɭɸ, ɜ ɬɨɦ ɱɢɫɥɟ ɢ ɩɪɨɢɡɜɨɥɶɧɨ ɞɜɢɠɭɳɭɸɫɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɧɟɪɰɢɚɥɶɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ, ɨɫɶ. Ⱦɥɹ ɷɬɨɝɨ ɞɨɫɬɚɬɨɱɧɨ

ɭɦɧɨɠɢɬɶ ɫɤɚɥɹɪɧɨ ɥɟɜɭɸ ɢ ɩɪɚɜɭɸ ɱɚɫɬɢ ɜɟɤɬɨɪɧɨɝɨ ɭɪɚɜɧɟɧɢɹ ɞɜɢɠɟɧɢɹ (2) ɧɚ ɟɞɢɧɢɱɧɵɣ ɜɟɤɬɨɪ (ɨɪɬ), ɡɚɞɚɸɳɢɣ ɧɚɩɪɚɜɥɟɧɢɟ ɷɬɨɣ ɨɫɢ. ɇɚɩɪɢɦɟɪ, ɧɚ ɧɚɩɪɚɜɥɟɧɢɟ ɫɤɨɪɨɫɬɢ IJ ɢ ɧɚ ɧɚɩɪɚɜɥɟɧɢɟ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɟ ɫɤɨɪɨɫɬɢ n :

ɚɥɶɧɚɹ ɫɨɫɬɚɜɥɹɸɳɢɟ ɭɫɤɨɪɟɧɢɹ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ.

Ɂɚɤɨɧɵ ɞɢɧɚɦɢɤɢ – ɷɬɨ ɡɚɤɨɧɵ ɇɶɸɬɨɧɚ ɢ ɡɚɤɨɧɵ, ɨɩɢɫɵɜɚɸɳɢɟ ɢɧɞɢɜɢɞɭɚɥɶɧɵɟ ɫɜɨɣɫɬɜɚ ɫɢɥ.

2.1.2. Ɂɚɤɨɧɵ, ɨɩɢɫɵɜɚɸɳɢɟ ɢɧɞɢɜɢɞɭɚɥɶɧɵɟ ɫɜɨɣɫɬɜɚ ɫɢɥ

Ⱥ. Ƚɪɚɜɢɬɚɰɢɨɧɧɵɟ ɫɢɥɵ Ɂɚɤɨɧ ɜɫɟɦɢɪɧɨɝɨ ɬɹɝɨɬɟɧɢɹ. Ɇɚɬɟɪɢɚɥɶɧɵɟ ɬɨɱɤɢ ɩɪɢɬɹ-

ɝɢɜɚɸɬɫɹ ɞɪɭɝ ɤ ɞɪɭɝɭ ɫ ɫɢɥɚɦɢ F21 ɢ F12 (ɫɦ. ɪɢɫ. 2.1), ɦɨɞɭɥɢ

ɤɨɬɨɪɵɯ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ ɩɪɨɢɡɜɟɞɟɧɢɸ ɢɯ ɦɚɫɫ ɢ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ ɤɜɚɞɪɚɬɭ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɧɢɦɢ:

Ɋɢɫ. 2.1. Ɉɪɢɟɧɬɚɰɢɹ ɫɢɥ ɝɪɚɜɢɬɚɰɢɨɧɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɞɜɭɯ ɦɚɬɟɪɢɚɥɶɧɵɯ ɬɨɱɟɤ

ɋɢɥɵ ɝɪɚɜɢɬɚɰɢɨɧɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫɮɟɪɢɱɟɫɤɢ ɫɢɦɦɟɬɪɢɱɧɵɯ ɬɟɥ, ɤɚɤ ɧɟɬɪɭɞɧɨ ɩɨɤɚɡɚɬɶ, ɨɩɪɟɞɟɥɹɸɬɫɹ ɜɵɪɚɠɟɧɢɟɦ

(2.4), ɜ ɤɨɬɨɪɨɦ r12 – ɪɚɞɢɭɫ-ɜɟɤɬɨɪ ɰɟɧɬɪɚ ɜɬɨɪɨɝɨ ɬɟɥɚ ɨɬɧɨɫɢ-

ɬɟɥɶɧɨ ɰɟɧɬɪɚ ɩɟɪɜɨɝɨ ɬɟɥɚ.

ɋɢɥɚ ɬɹɠɟɫɬɢ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɦɚɬɟɪɢɚɥɶɧɭɸ ɬɨɱɤɭ, –

ɫɭɦɦɚ ɫɢɥɵ ɝɪɚɜɢɬɚɰɢɨɧɧɨɝɨ ɩɪɢɬɹɠɟɧɢɹ Ɂɟɦɥɢ (ɢɥɢ ɥɸɛɨɝɨ ɞɪɭɝɨɝɨ ɤɨɫɦɢɱɟɫɤɨɝɨ ɨɛɴɟɤɬɚ) ɢ ɰɟɧɬɪɨɛɟɠɧɨɣ ɫɢɥɵ ɢɧɟɪɰɢɢ (ɫɦ. Ƚɥɚɜɭ 4), ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɦɚɬɟɪɢɚɥɶɧɭɸ ɬɨɱɤɭ ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ, ɫɜɹɡɚɧɧɨɣ ɫ Ɂɟɦɥɟɣ.

ɋɢɥɚ ɬɹɠɟɫɬɢ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɬɟɥɨ, – ɫɭɦɦɚ ɫɢɥ ɬɹɠɟɫɬɢ,

ɞɟɣɫɬɜɭɸɳɢɯ ɧɚ ɦɚɬɟɪɢɚɥɶɧɵɟ ɬɨɱɤɢ ɷɬɨɝɨ ɬɟɥɚ.

ȼ ɨɞɧɨɪɨɞɧɨɦ ɩɨɥɟ ɫɢɥɵ ɬɹɠɟɫɬɢ ɜɛɥɢɡɢ ɩɨɜɟɪɯɧɨɫɬɢ Ɂɟɦɥɢ ɫɢɥɚ ɬɹɠɟɫɬɢ Fɬ ɪɚɜɧɚ ɩɪɨɢɡɜɟɞɟɧɢɸ ɦɚɫɫɵ ɬɟɥɚ m ɧɚ ɭɫɤɨɪɟɧɢɟ ɰɟɧɬɪɚ ɦɚɫɫ ɬɟɥɚ ɩɪɢ ɫɜɨɛɨɞɧɨɦ ɩɚɞɟɧɢɢ (ɭɫɤɨɪɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ) g ɨɬɧɨɫɢɬɟɥɶɧɨ Ɂɟɦɥɢ: Fɬ mg .

ȼɟɫ ɬɟɥɚ – ɫɢɥɚ, ɫ ɤɨɬɨɪɨɣ ɬɟɥɨ, ɧɚɯɨɞɹɳɟɟɫɹ ɜ ɩɨɥɟ ɫɢɥ ɬɹɠɟɫɬɢ, ɞɟɣɫɬɜɭɟɬ ɧɚ ɧɟɩɨɞɜɢɠɧɭɸ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɝɨ ɨɩɨɪɭ ɢɥɢ ɩɨɞɜɟɫ, ɩɪɟɩɹɬɫɬɜɭɸɳɢɟ ɫɜɨɛɨɞɧɨɦɭ ɩɚɞɟɧɢɸ ɬɟɥɚ.

Ȼ. ɍɩɪɭɝɢɟ ɫɢɥɵ

ȿɫɥɢ ɩɨɫɥɟ ɩɪɟɤɪɚɳɟɧɢɹ ɜɧɟɲɧɟɝɨ ɜɨɡɞɟɣɫɬɜɢɹ ɞɟɮɨɪɦɢɪɨɜɚɧɧɨɟ ɬɟɥɨ ɜɨɫɫɬɚɧɚɜɥɢɜɚɟɬ ɫɜɨɸ ɮɨɪɦɭ ɢ ɪɚɡɦɟɪɵ, ɬɨ ɞɟɮɨɪɦɚɰɢɹ ɧɚɡɵɜɚɟɬɫɹ ɭɩɪɭɝɨɣ.

Ɂɚɤɨɧ Ƚɭɤɚ. ɉɪɢ ɦɚɥɵɯ ɭɩɪɭɝɢɯ ɞɟɮɨɪɦɚɰɢɹɯ ɜɟɥɢɱɢɧɚ ɞɟɮɨɪɦɚɰɢɢ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɜɟɥɢɱɢɧɟ ɜɵɡɵɜɚɸɳɟɣ ɟɟ ɫɢɥɵ.

ȼ ɱɚɫɬɧɨɫɬɢ, ɩɪɢ ɞɟɮɨɪɦɚɰɢɢ ɪɚɫɬɹɠɟɧɢɹ (ɫɠɚɬɢɹ) ɭɩɪɭɝɨɝɨ ɫɬɟɪɠɧɹ (ɩɪɭɠɢɧɵ, ɪɟɡɢɧɨɜɨɝɨ ɲɧɭɪɚ) ɞɟɮɨɪɦɚɰɢɹ ɫɬɟɪɠɧɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɜɟɥɢɱɢɧɟ ɜɵɡɵɜɚɸɳɟɣ ɟɟ ɫɢɥɵ, ɞɟɣɫɬɜɭɸɳɟɣ ɜɞɨɥɶ ɫɬɟɪɠɧɹ:

– ɭɞɥɢɧɟɧɢɟ ɫɬɟɪɠɧɹ, l ɢ l0 – ɞɥɢɧɚ ɫɬɟɪɠɧɹ ɜ ɞɟɮɨɪɦɢɪɨɜɚɧɧɨɦ ɢ ɧɟɞɟɮɨɪɦɢɪɨɜɚɧɧɨɦ ɫɨɫɬɨɹɧɢɹɯ (ɫɦ. ɪɢɫ. 2.2).

ȿɫɥɢ ɫɢɥɚ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɫɬɟɪɠɟɧɶ, ɧɚɩɪɚɜɥɟɧɚ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɭɤɚɡɚɧɧɨɦɭ ɧɚ ɪɢɫ. 2 ɧɚɩɪɚɜɥɟɧɢɸ, ɬɨ ɭɩɪɭɝɢɣ ɫɬɟɪɠɟɧɶ ɢɫɩɵɬɵɜɚɟɬ ɫɠɚɬɢɟ. ɉɪɢ ɷɬɨɦ ǻl 0 ɢ F ɜ ɮɨɪɦɭɥɟ (2.5) ɫɥɟɞɭɟɬ ɫɱɢɬɚɬɶ ɩɪɨɟɤɰɢɟɣ ɫɢɥɵ F ɧɚ ɨɫɶ X ɫɢɫɬɟɦɵ ɤɨɨɪɞɢɧɚɬ, ɢɡɨɛɪɚɠɟɧɧɨɣ ɧɚ ɪɢɫ. 2.2.

X l

Ɋɢɫ. 2.2. ɍɞɥɢɧɟɧɢɟ ɫɬɟɪɠɧɹ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɩɪɨɞɨɥɶɧɨɣ ɫɢɥɵ

ɉɪɢ ɞɟɮɨɪɦɚɰɢɢ ɪɚɫɬɹɠɟɧɢɹ (ɫɠɚɬɢɹ) ɨɞɧɨɪɨɞɧɨɝɨ ɭɩɪɭɝɨɝɨ ɫɬɟɪɠɧɹ ɫ ɩɨɫɬɨɹɧɧɵɦ ɜɞɨɥɶ ɫɬɟɪɠɧɹ ɫɟɱɟɧɢɟɦ ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɭɞɥɢɧɟɧɢɟ ɫɬɟɪɠɧɹ H ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɧɨɪɦɚɥɶɧɨɦɭ ɧɚɩɪɹɠɟɧɢɸ V:

Ɂɞɟɫɶ E – ɦɨɞɭɥɶ ɘɧɝɚ ɦɚɬɟɪɢɚɥɚ, ɢɡ ɤɨɬɨɪɨɝɨ ɫɞɟɥɚɧ ɫɬɟɪɠɟɧɶ,

ɧɚɩɪɹɠɟɧɢɟ, S – ɩɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɫɬɟɪɠɧɹ.

Ɂɚɦɟɬɢɦ, ɱɬɨ ɞɥɹ ɨɞɧɨɪɨɞɧɨɝɨ ɭɩɪɭɝɨɝɨ ɫɬɟɪɠɧɹ ɫ ɩɨɫɬɨɹɧɧɵɦ ɜɞɨɥɶ ɫɬɟɪɠɧɹ ɫɟɱɟɧɢɟɦ ɤɨɷɮɮɢɰɢɟɧɬ ɠɟɫɬɤɨɫɬɢ (ɭɩɪɭɝɨɫɬɢ) ɷɬɨɝɨ ɫɬɟɪɠɧɹ ɫɜɹɡɚɧ ɫ ɦɨɞɭɥɟɦ ɘɧɝɚ ɫɨɨɬɧɨɲɟɧɢɟɦ:

ȼ ɫɥɭɱɚɟ ɪɚɫɬɹɠɟɧɢɹ (ɫɠɚɬɢɹ) ɫɬɟɪɠɧɹ ɭɦɟɧɶɲɚɸɬɫɹ (ɭɜɟɥɢɱɢɜɚɸɬɫɹ) ɟɝɨ ɩɨɩɟɪɟɱɧɵɟ ɪɚɡɦɟɪɵ. ɉɪɢ ɷɬɨɦ ɨɬɧɨɲɟɧɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɩɨɩɟɪɟɱɧɨɝɨ ɫɠɚɬɢɹ ɫɬɟɪɠɧɹ ɤ ɟɝɨ ɨɬɧɨɫɢɬɟɥɶɧɨɦɭ ɭɞɥɢɧɟɧɢɸ ɡɚɜɢɫɢɬ ɬɨɥɶɤɨ ɨɬ ɦɚɬɟɪɢɚɥɚ ɫɬɟɪɠɧɹ ɢ ɧɚɡɵɜɚɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɉɭɚɫɫɨɧɚ:

ɧɨɟ ɢɡɦɟɧɟɧɢɟ ɩɨɩɟɪɟɱɧɵɯ ɪɚɡɦɟɪɨɜ ɫɬɟɪɠɧɹ, d ɢ d0 – ɩɨɩɟɪɟɱɧɵɣ ɥɢɧɟɣɧɵɣ ɪɚɡɦɟɪ ɫɬɟɪɠɧɹ ɜ ɞɟɮɨɪɦɢɪɨɜɚɧɧɨɦ ɢ ɧɟɞɟɮɨɪɦɢɪɨɜɚɧɧɨɦ ɫɨɫɬɨɹɧɢɹɯ (ɫɦ. ɪɢɫ. 2.2).

ɉɪɢ ɞɟɮɨɪɦɚɰɢɢ ɫɬɟɪɠɧɹ ɜɨɡɧɢɤɚɸɬ ɜɧɭɬɪɟɧɧɢɟ ɭɩɪɭɝɢɟ ɫɢɥɵ Fɭɩɪ , ɞɟɣɫɬɜɭɸɳɢɟ ɦɟɠɞɭ ɟɝɨ ɱɚɫɬɹɦɢ, ɤɨɬɨɪɵɟ ɫɬɪɟɦɹɬɫɹ ɜɟɪ-

ɧɭɬɶ ɫɬɟɪɠɟɧɶ ɜ ɧɟɞɟɮɨɪɦɢɪɨɜɚɧɧɨɟ ɫɨɫɬɨɹɧɢɟ. ɇɚɩɪɹɠɟɧɢɟ ɭɩɪɭɝɢɯ ɫɢɥ ɪɚɜɧɨ

Ɋɚɫɫɦɨɬɪɢɦ ɫɥɨɣ ɫɬɟɪɠɧɹ ɫ ɤɨɨɪɞɢɧɚɬɚɦɢ ɝɪɚɧɢɰ x ɢ x dx ɜɞɨɥɶ ɫɬɟɪɠɧɹ (ɫɦ. ɪɢɫ. 2.3).

Ɋɢɫ. 2.3. ɋɦɟɳɟɧɢɟ ɝɪɚɧɢɰ ɜɵɞɟɥɟɧɧɨɝɨ ɫɥɨɹ ɫɬɟɪɠɧɹ

ȼ ɪɟɡɭɥɶɬɚɬɟ ɞɟɣɫɬɜɢɹ ɜɧɭɬɪɟɧɧɢɯ ɭɩɪɭɝɢɯ ɫɢɥ ɜɨɡɧɢɤɚɟɬ ɫɦɟɳɟɧɢɟ ɥɟɜɨɣ [(x) ɢ ɩɪɚɜɨɣ [(x+dx) ɝɪɚɧɢɰ ɜɵɞɟɥɟɧɧɨɝɨ ɫɥɨɹ.

Ɍɨɝɞɚ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɩɪɨɞɨɥɶɧɚɹ ɞɟɮɨɪɦɚɰɢɹ H ɷɬɨɝɨ ɫɥɨɹ ɪɚɜɧɚ

ȼ ɫɥɭɱɚɟ ɞɟɮɨɪɦɚɰɢɢ ɫɥɨɹ ɢɡɦɟɧɹɸɬɫɹ ɟɝɨ ɩɨɩɟɪɟɱɧɵɟ ɪɚɡɦɟɪɵ. ɉɪɢ ɷɬɨɦ ɨɬɧɨɲɟɧɢɟ ɩɨɩɟɪɟɱɧɨɣ ɤ ɩɪɨɞɨɥɶɧɨɣ ɞɟɮɨɪɦɚɰɢɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɉɭɚɫɫɨɧɚ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (2.8).

ɉɪɢ ɭɫɤɨɪɟɧɧɨɦ ɞɜɢɠɟɧɢɢ ɫɬɟɪɠɧɹ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɟɣ ɫɢɥɵ, ɜɵɡɵɜɚɸɳɟɣ ɟɝɨ ɞɟɮɨɪɦɚɰɢɸ, ɜɨɡɧɢɤɚɸɬ ɧɟɨɞɧɨɪɨɞɧɵɟ ɜɞɨɥɶ ɫɬɟɪɠɧɹ ɧɚɩɪɹɠɟɧɢɹ ɭɩɪɭɝɢɯ ɫɢɥ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɜɨɡɧɢɤɚɸɳɢɟ ɧɟɨɞɧɨɪɨɞɧɵɟ ɞɟɮɨɪɦɚɰɢɢ ɩɨ-ɩɪɟɠɧɟɦɭ ɨɩɪɟɞɟɥɹɸɬɫɹ ɜɵɪɚ-

ɠɟɧɢɹɦɢ (2.11), (2.8).

ȼ. ɋɢɥɵ ɬɪɟɧɢɹ ɋɢɥɚ ɬɪɟɧɢɹ – ɫɨɫɬɚɜɥɹɸɳɚɹ ɫɢɥɵ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨɝɨ ɜɡɚɢ-

ɦɨɞɟɣɫɬɜɢɹ ɬɟɥ ɩɪɢ ɫɨɩɪɢɤɨɫɧɨɜɟɧɢɢ ɜɞɨɥɶ ɩɥɨɫɤɨɫɬɢ ɫɨɩɪɢɤɨɫɧɨɜɟɧɢɹ.

ɋɢɥɚ ɧɨɪɦɚɥɶɧɨɝɨ ɞɚɜɥɟɧɢɹ (ɪɟɚɤɰɢɢ ɨɩɨɪɵ) – ɫɨɫɬɚɜ-

ɥɹɸɳɚɹ ɫɢɥɵ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɬɟɥ ɩɪɢ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨɦ ɫɨɩɪɢɤɨɫɧɨɜɟɧɢɢ ɜɞɨɥɶ ɧɚɩɪɚɜɥɟɧɢɹ ɧɨɪɦɚɥɢ ɤ ɩɥɨɫɤɨɫɬɢ ɫɨɩɪɢɤɨɫɧɨɜɟɧɢɹ.

ɋɢɥɵ ɜɹɡɤɨɝɨ (ɜɧɭɬɪɟɧɧɟɝɨ) ɬɪɟɧɢɹ Fɜ – ɫɢɥɵ ɬɪɟɧɢɹ, ɜɨɡ-

ɧɢɤɚɸɳɢɟ ɩɪɢ ɞɜɢɠɟɧɢɢ ɬɟɥɚ ɜ ɜɹɡɤɨɣ (ɠɢɞɤɨɣ ɢɥɢ ɝɚɡɨɨɛɪɚɡɧɨɣ) ɫɪɟɞɟ.

ɉɪɢ ɦɚɥɨɣ ɜɟɥɢɱɢɧɟ ɫɤɨɪɨɫɬɢ ȣ ɞɜɢɠɟɧɢɹ ɬɟɥɚ ɨɬɧɨɫɢɬɟɥɶɧɨ

ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨɦ ɫɨɩɪɢɤɨɫɧɨɜɟɧɢɢ ɬɜɟɪɞɵɯ ɬɟɥ.

ɋɢɥɵ ɬɪɟɧɢɹ ɩɨɤɨɹ Fɩ – ɫɢɥɵ ɫɭɯɨɝɨ ɬɪɟɧɢɹ, ɜɨɡɧɢɤɚɸɳɢɟ ɜ ɨɬɫɭɬɫɬɜɢɟ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɬɟɥ.

ɋɢɥɚ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ Fcɤ – ɫɢɥɚ ɫɭɯɨɝɨ ɬɪɟɧɢɹ, ɜɨɡɧɢ-

ɤɚɸɳɚɹ ɩɪɢ ɨɬɧɨɫɢɬɟɥɶɧɨɦ ɞɜɢɠɟɧɢɢ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɬɟɥ. Ɂɚɤɨɧ Ⱥɦɨɧɬɨɧɚ – Ʉɭɥɨɧɚ – ɷɦɩɢɪɢɱɟɫɤɢɣ ɡɚɤɨɧ, ɨɩɢɫɵ-

ɜɚɸɳɢɣ ɫɜɨɣɫɬɜɚ ɫɢɥ ɫɭɯɨɝɨ ɬɪɟɧɢɹ:

1) ɦɨɞɭɥɶ ɫɢɥɵ ɫɭɯɨɝɨ ɬɪɟɧɢɹ ɩɨɤɨɹ ɦɨɠɟɬ ɩɪɢɧɢɦɚɬɶ ɡɧɚɱɟɧɢɹ ɨɬ ɧɭɥɹ ɞɨ ɧɟɤɨɬɨɪɨɝɨ ɫɜɨɟɝɨ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɡɧɚɱɟɧɢɹ:

0d Fɩ d Fmax ;

2)ɦɨɞɭɥɶ ɫɢɥɵ ɫɭɯɨɝɨ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ ɪɚɜɟɧ ɦɚɤɫɢɦɚɥɶ-

ɧɨɦɭ ɡɧɚɱɟɧɢɸ ɦɨɞɭɥɹ ɫɢɥɵ ɫɭɯɨɝɨ ɬɪɟɧɢɹ ɩɨɤɨɹ: Fcɤ Fmax ;

3) ɦɨɞɭɥɶ ɫɢɥɵ ɫɭɯɨɝɨ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɦɨɞɭɥɸ ɫɢɥɵ ɧɨɪɦɚɥɶɧɨɝɨ ɞɚɜɥɟɧɢɹ:

ɝɞɟ P – ɤɨɷɮɮɢɰɢɟɧɬ (ɫɢɥɵ ɫɭɯɨɝɨ) ɬɪɟɧɢɹ, ɧɟ ɡɚɜɢɫɹɳɢɣ ɨɬ ɫɢɥɵ ɧɨɪɦɚɥɶɧɨɝɨ ɞɚɜɥɟɧɢɹ, ɚ ɬɨɥɶɤɨ ɨɬ ɜɟɳɟɫɬɜɚ ɢ ɫɨɫɬɨɹɧɢɹ ɩɨɜɟɪɯɧɨɫɬɟɣ ɬɪɭɳɢɯɫɹ ɬɟɥ;