Механика.Методика решения задач

ɇɚ ɪɢɫ. 5.11 ɢɡɨɛɪɚɠɟɧɵ ɬɚɤɠɟ ɢɧɬɟɪɜɚɥɵ ɜɪɟɦɟɧɢ ɦɟɠɞɭ ɫɨɛɵɬɢɹɦɢ, ɡɚɞɚɧɧɵɟ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ, – W1, W2 ɢ 'W. ɗɬɢ ɢɧɬɟɪɜɚɥɵ ɜɪɟɦɟɧɢ ɨɬɧɨɫɹɬɫɹ ɤ ɫɨɛɵɬɢɹɦ, ɩɪɨɢɫɯɨɞɹɳɢɦ ɜ ɨɞɧɨɣ ɬɨɱɤɟ ɩɪɨɫɬɪɚɧɫɬɜɚ, – A ɢ B ɜ ɫɢɫɬɟɦɟ S (ɢɧɬɟɪɜɚɥ W1), A1 ɢ B1 ɜ ɫɢɫɬɟɦɟ S' (ɢɧɬɟɪɜɚɥ W2), A1 ɢ C1 ɜ ɫɢɫɬɟɦɟ S' (ɢɧɬɟɪɜɚɥ 'W). ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫɨ ɫɥɟɞɫɬɜɢɟɦ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ Ʌɨɪɟɧɰɚ – "ɡɚɦɟɞɥɟɧɢɟɦ ɜɪɟɦɟɧɢ" (ɫɦ. Ɍɟɨɪɟɬɢɱɟɫɤɢɣ ɦɚɬɟɪɢɚɥ, ɮɨɪɦɭɥɭ (5.6)) – ɷɬɢ ɢɧɬɟɪɜɚɥɵ ɜɪɟɦɟɧɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɬɟɦ ɠɟ ɩɚɪɚɦ ɫɨɛɵɬɢɣ, ɢɡɦɟɪɟɧɧɵɟ ɩɨ ɱɚɫɚɦ ɞɪɭɝɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ, ɭɜɟɥɢɱɢɜɚɸɬɫɹ ɜ J ɪɚɡ (ɫɦ. ɪɢɫ. 5.11), ɝɞɟ

J1 .

1 U / c 2

II. ɉɭɫɬɶ ɜ ɦɨɦɟɧɬ ɜ ɦɨɦɟɧɬ ɜɫɩɵɲɤɢ ɫɜɟɬɚ ɧɚ ɧɨɫɭ ɩɟɪɜɨɝɨ ɡɜɟɡɞɨɥɟɬɚ (ɫɨɛɵɬɢɟ A) ɜɬɨɪɨɣ ɡɜɟɡɞɨɥɟɬ ɧɚɯɨɞɢɥɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ

LA ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ S. Ɍɨɝɞɚ ɢɧɬɟɪɜɚɥ ɜɪɟɦɟɧɢ 'tA ɦɟɠɞɭ ɫɨɛɵɬɢɹɦɢ A ɢ A1 ɜ ɷɬɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ ɫ ɭɱɟɬɨɦ ɫɤɨɪɨɫɬɢ ɫɛɥɢɠɟɧɢɹ ɡɜɟɡɞɨɥɟɬɨɜ ɪɚɜɟɧ:

ȼɫɩɵɲɤɚ ɫɜɟɬɚ ɧɚ ɤɨɪɦɟ ɩɟɪɜɨɝɨ ɡɜɟɡɞɨɥɟɬɚ (ɫɨɛɵɬɢɟ ɋ), ɩɪɨɢɡɨɲɟɞɲɚɹ ɨɞɧɨɜɪɟɦɟɧɧɨ ɫ ɩɟɪɜɨɣ ɜɫɩɵɲɤɨɣ ɧɚ ɟɝɨ ɧɨɫɭ (ɫɨɛɵɬɢɟ A) ɛɭɞɟɬ ɡɚɪɟɝɢɫɬɪɢɪɨɜɚɧɚ ɧɚ ɜɬɨɪɨɦ ɡɜɟɡɞɨɥɟɬɟ ɱɟɪɟɡ ɜɪɟɦɹ ǻtC ɩɨ ɱɚɫɚɦ ɩɟɪɜɨɝɨ ɡɜɟɡɞɨɥɟɬɚ:

ɂɧɬɟɪɜɚɥ ɜɪɟɦɟɧɢ 'tB ɦɟɠɞɭ ɫɨɛɵɬɢɹɦɢ B ɢ B1 ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ S ɫ ɭɱɟɬɨɦ ɭɦɟɧɶɲɟɧɢɹ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɡɜɟɡɞɨɥɟɬɚɦɢ ɡɚ

ɉɨɞɫɬɚɜɢɜ ɜ (5.71) ɢ (5.72) ɡɚɞɚɧɧɵɟ ɱɢɫɥɟɧɧɵɟ ɡɧɚɱɟɧɢɹ W1, W2 ɢ 'W, ɨɩɪɟɞɟɥɢɦ ɫɨɛɫɬɜɟɧɧɭɸ ɞɥɢɧɭ ɩɟɪɜɨɝɨ ɡɜɟɡɞɨɥɟɬɚ l0 ɢ ɫɤɨɪɨɫɬɶ ɨɬɧɨɫɢɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɡɜɟɡɞɨɥɟɬɨɜ U:

Ɂɚɞɚɱɚ 5.9

(ɂɧɜɚɪɢɚɧɬɧɨɫɬɶ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨ-ɜɪɟɦɟɧɧɵɯ ɢɧɬɟɪɜɚɥɨɜ)

ȼ ɧɟɤɨɬɨɪɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ ɩɪɨɢɫɯɨɞɹɬ ɞɜɚ ɫɨɛɵɬɢɹ ɫɨ ɫɥɟɞɭɸɳɢɦɢ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨ-ɜɪɟɦɟɧɧɵɦɢ ɤɨɨɪɞɢɧɚɬɚɦɢ: x1 = 0; t1 = 0 (ɫɨɛɵɬɢɟ Ⱥ) ɢ x2 = 5 ɦ; t2 = 10 8 c (ɫɨɛɵɬɢɟ ȼ). Ɉɩɪɟɞɟɥɢɬɶ:

1) ɜ ɤɚɤɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ ɷɬɢ ɫɨɛɵɬɢɹ ɩɪɨɢɫɯɨɞɹɬ ɧɚ ɦɢɧɢɦɚɥɶɧɨɦ ɪɚɫɫɬɨɹɧɢɢ ɞɪɭɝ ɨɬ ɞɪɭɝɚ ǻxc min , ɧɚɣɬɢ ɷɬɨ ɪɚɫɫɬɨɹɧɢɟ ɢ

ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ V;

2) ɜ ɤɚɤɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ ɷɬɢ ɫɨɛɵɬɢɹ ɩɪɨɢɫɯɨɞɹɬ ɫ ɦɢɧɢɦɚɥɶɧɵɦ ɜɪɟɦɟɧɧɵɦ ɢɧɬɟɪɜɚɥɨɦ ǻtc min , ɧɚɣɬɢ ɷɬɨɬ ɢɧɬɟɪɜɚɥ ɢ

ɫɤɨɪɨɫɬɶ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ V;

Ɂɚɞɚɱɚ 5.10

(ɉɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫɤɨɪɨɫɬɟɣ)

Ⱦɜɚ ɫɬɟɪɠɧɹ ɨɞɢɧɚɤɨɜɨɣ ɫɨɛɫɬɜɟɧɧɨɣ ɞɥɢɧɨɣ l0 ɞɜɢɠɭɬɫɹ ɜ ɩɪɨɞɨɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɧɚɜɫɬɪɟɱɭ ɞɪɭɝ ɞɪɭɝɭ ɩɚɪɚɥɥɟɥɶɧɨ ɨɛɳɟɣ ɨɫɢ ɫ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɩɨ ɜɟɥɢɱɢɧɟ ɫɤɨɪɨɫɬɶɸ V ɨɬɧɨɫɢɬɟɥɶɧɨ ɥɚɛɨɪɚɬɨɪɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ S (ɪɢɫ. 5.12). ɑɟɦɭ ɪɚɜɧɚ ɞɥɢɧɚ ɤɚɠɞɨɝɨ ɫɬɟɪɠɧɹ ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ, ɫɜɹɡɚɧɧɨɣ ɫ ɞɪɭɝɢɦ ɫɬɟɪɠɧɟɦ.

ɪɢɫ. 5.12). ɋɤɨɪɨɫɬɶ ɷɬɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɥɚɛɨɪɚɬɨɪɧɨɣ ɫɢɫɬɟɦɵ S ɫɨɜɩɚɞɚɟɬ ɫɨ ɫɤɨɪɨɫɬɶɸ ɩɟɪɜɨɝɨ ɫɬɟɪɠɧɹ X1 ɢ ɪɚɜɧɚ V. ɋɤɨɪɨɫɬɶ ɜɬɨɪɨɝɨ ɫɬɟɪɠɧɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɬɨɣ ɠɟ ɫɢɫɬɟɦɵ S ɪɚɜɧɚ X2 V .

Ɉɩɪɟɞɟɥɢɦ ɞɥɢɧɭ ɜɬɨɪɨɝɨ ɫɬɟɪɠɧɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ S', ɫɜɹɡɚɧɧɨɣ ɫ ɩɟɪɜɵɦ ɫɬɟɪɠɧɟɦ. Ⱦɥɹ ɷɬɨɝɨ ɧɟɨɛɯɨɞɢɦɨ ɩɪɨɜɟɫɬɢ ɢɡɦɟɪɟɧɢɟ ɤɨɨɪɞɢɧɚɬ ɤɨɧɰɨɜ ɜɬɨɪɨɝɨ ɫɬɟɪɠɧɹ ɜ ɫɢɫɬɟɦɟ S' ɨɞɧɨɜɪɟɦɟɧɧɨ. ɉɭɫɬɶ ɫɨɛɵɬɢɹ Ⱥ ɢ ȼ ɫɨɫɬɨɹɬ ɜ ɬɨɦ ɜ ɫɢɫɬɟɦɟ S' ɨɞɧɨɜɪɟɦɟɧɧɨ ɮɢɤɫɢɪɭɸɬɫɹ ɩɨɥɨɠɟɧɢɹ ɞɜɭɯ ɤɨɧɰɨɜ ɜɬɨɪɨɝɨ ɫɬɟɪɠɧɹ.

II. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫɨ ɫɥɟɞɫɬɜɢɟɦ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ Ʌɨɪɟɧɰɚ – "ɫɨɤɪɚɳɟɧɢɟɦ ɞɥɢɧɵ" – ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ S', ɞɥɹ ɤɨɬɨɪɨɣ ɫɨɛɵɬɢɹ Ⱥ ɢ ȼ ɩɪɨɢɫɯɨɞɹɬ ɨɞɧɨɜɪɟɦɟɧɧɨ, ɧɚɛɥɸɞɚɟɬɫɹ ɫɨɤɪɚɳɟɧɢɟ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɨɝɨ ɢɧɬɟɪɜɚɥɚ – ɞɥɢɧɵ ɜɬɨɪɨɝɨ ɫɬɟɪɠɧɹ:

ɝɞɟ X2c – ɫɤɨɪɨɫɬɶ ɜɬɨɪɨɝɨ ɫɬɟɪɠɧɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ

S'. Ɉɩɪɟɞɟɥɢɦ ɷɬɭ ɫɤɨɪɨɫɬɶ, ɢɫɩɨɥɶɡɭɹ ɮɨɪɦɭɥɭ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫɤɨɪɨɫɬɟɣ (5.21):

ɋɜɹɡɚɜ ɫɢɫɬɟɦɭ ɨɬɫɱɟɬɚ S' ɫɨ ɜɬɨɪɵɦ ɫɬɟɪɠɧɟɦ, ɚɧɚɥɨɝɢɱɧɵɦ ɨɛɪɚɡɨɦ ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɞɥɢɧɭ ɩɟɪɜɨɝɨ ɫɬɟɪɠɧɹ ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ,

Ɂɚɞɚɱɚ 5.11

(ɉɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫɤɨɪɨɫɬɟɣ)

Ⱦɜɚ ɧɟɩɨɞɜɢɠɧɵɯ ɩɪɨɠɟɤɬɨɪɚ ɢɡɥɭɱɚɸɬ ɭɡɤɢɟ ɩɭɱɤɢ ɫɜɟɬɚ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ Y ɥɚɛɨɪɚɬɨɪɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ (ɫɦ. ɪɢɫ. 5.13). ɋ ɤɚɤɨɣ ɫɤɨɪɨɫɬɶɸ U ɷɬɢ ɩɪɨɠɟɤɬɨɪɵ ɞɨɥɠɧɵ ɞɜɢɝɚɬɶɫɹ ɜ ɧɚɩɪɚɜɥɟɧɢɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɦ ɨɫɢ Y, ɱɬɨɛɵ ɩɭɱɤɢ ɫɜɟɬɚ ɪɚɫɩɪɨɫɬɪɚɧɹɥɢɫɶ ɩɨɞ ɭɝɥɨɦ D = 90q ɞɪɭɝ ɤ ɞɪɭɝɭ?

Y Y

U

X U X

Ɋɢɫ. 5.13

Ɋɟɲɟɧɢɟ

I. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɭɫɥɨɜɢɟɦ ɡɚɞɚɱɢ ɧɚɩɪɚɜɢɦ ɨɫɶ Y ɥɚɛɨɪɚɬɨɪɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ S ɜɞɨɥɶ ɩɭɱɤɚ ɫɜɟɬɚ, ɢɡɥɭɱɚɟɦɨɝɨ ɨɞɧɢɦ ɢɡ ɩɪɨɠɟɤɬɨɪɨɜ (ɪɢɫ. 5.13), ɚ ɨɫɶ X ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɢɯ ɞɜɢɠɟɧɢɹ. ɋɜɹɠɟɦ ɫɢɫɬɟɦɭ ɨɬɫɱɟɬɚ Sc ɫ ɩɪɨɠɟɤɬɨɪɚɦɢ, ɞɜɢɠɭɳɢɦɢɫɹ ɫɨ ɫɤɨ-

176 ɆȿɏȺɇɂɄȺ. ɆȿɌɈȾɂɄȺ Ɋȿɒȿɇɂə ɁȺȾȺɑ

ɪɨɫɬɶɸ U ɨɬɧɨɫɢɬɟɥɶɧɨ ɥɚɛɨɪɚɬɨɪɧɨɣ ɫɢɫɬɟɦɵ S, ɢ ɧɚɩɪɚɜɢɦ ɟɟ ɨɫɢ X' ɢ Y' ɜɞɨɥɶ ɨɫɟɣ X ɢ Yɫɨɨɬɜɟɬɫɬɜɟɧɧɨ.

II. ɉɨɫɤɨɥɶɤɭ ɩɪɨɠɟɤɬɨɪɚ ɩɨɤɨɹɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɢɫɬɟɦɵ S', ɬɨ ɩɪɨɟɤɰɢɢ ɫɤɨɪɨɫɬɟɣ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɞɜɭɯ ɩɭɱɤɨɜ ɫɜɟɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɷɬɨɣ ɫɢɫɬɟɦɵ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɭɫɥɨɜɢɟɦ ɡɚɞɚɱɢ ɪɚɜɧɵ:

Ɂɚɩɢɲɟɦ ɮɨɪɦɭɥɵ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɫɥɨɠɟɧɢɹ) ɫɤɨɪɨɫɬɟɣ (5.22) ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɩɪɨɟɤɰɢɣ ɫɤɨɪɨɫɬɟɣ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɩɭɱɤɨɜ ɫɜɟɬɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɥɚɛɨɪɚɬɨɪɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ S:

D 90q ɜ ɥɚɛɨɪɚɬɨɪɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ, ɧɟɨɛɯɨɞɢɦɨ ɜɵɩɨɥɧɟɧɢɟ ɫɥɟɞɭɸɳɢɯ ɭɫɥɨɜɢɣ:

III. Ɉɩɪɟɞɟɥɢɦ ɩɪɨɟɤɰɢɢ ɫɤɨɪɨɫɬɟɣ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɩɭɱɤɨɜ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ S (5.83) ɢ (5.84) ɫ ɭɱɟɬɨɦ ɫɨɨɬɧɨɲɟ-

ɉɨɞɫɬɚɜɢɜ ɩɨɥɭɱɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɩɪɨɟɤɰɢɣ ɫɤɨɪɨɫɬɟɣ ɜ (5.85), ɨɩɪɟɞɟɥɢɦ, ɫ ɤɚɤɨɣ ɫɤɨɪɨɫɬɶɸ U ɞɨɥɠɧɵ ɞɜɢɝɚɬɶɫɹ ɩɪɨɠɟɤɬɨɪɵ ɜ ɧɚɩɪɚɜɥɟɧɢɢ, ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɦ ɥɭɱɚɦ, ɞɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɩɭɱɤɢ ɫɜɟɬɚ ɪɚɫɩɪɨɫɬɪɚɧɹɥɢɫɶ ɩɨɞ ɭɝɥɨɦ 90q ɞɪɭɝ ɤ ɞɪɭɝɭ:

Ɂɚɞɚɱɚ 5.12

(ɉɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫɤɨɪɨɫɬɟɣ)

ɋɬɟɪɠɟɧɶ Ⱥȼ ɨɪɢɟɧɬɢɪɨɜɚɧ ɩɚɪɚɥɥɟɥɶɧɨ ɨɫɢ X' ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ S' ɢ ɞɜɢɠɟɬɫɹ ɜ ɷɬɨɣ ɫɢɫɬɟɦɟ ɫɨ ɫɤɨɪɨɫɬɶɸ U c 0,7c , ɧɚɩɪɚɜɥɟɧɧɨɣ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɨɫɢ Y' (ɫɦ. ɪɢɫ. 5.14). ɋɢɫɬɟɦɚ S' ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɞɜɢɠɟɬɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ V 0,6c ɨɬɧɨɫɢɬɟɥɶɧɨ ɥɚɛɨɪɚɬɨɪɧɨɣ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ S ɜ ɧɚɩɪɚɜɥɟɧɢɢ ɟɟ ɨɫɢ ɏ, ɫɨɜɩɚɞɚɸɳɟɣ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɫ ɨɫɶɸ X'. ɇɚɣɬɢ ɭɝɨɥ ɦɟɠɞɭ ɫɬɟɪɠɧɟɦ ɢ ɨɫɶɸ ɏ ɜ ɫɢɫɬɟɦɟ S.

Y S Y' S' V

AB

U'

X X'

Ɋɢɫ. 5.14

Ɋɟɲɟɧɢɟ

I. ɉɭɫɬɶ ɢɧɬɟɪɟɫɭɸɳɢɦɢ ɧɚɫ ɫɨɛɵɬɢɹɦɢ ɛɭɞɭɬ ɫɨɛɵɬɢɹ C ɢ D, ɫɨɫɬɨɹɳɢɟ ɜ ɬɨɦ, ɱɬɨ ɜ ɧɟɤɨɬɨɪɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɤɨɧɰɵ ɫɬɟɪɠɧɹ ɫɨɜɩɚɥɢ ɫ ɨɫɶɸ X' ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ S'. ɉɪɨɫɬɪɚɧɫɬɜɟɧɧɨɜɪɟɦɟɧɧɵɟ ɤɨɨɪɞɢɧɚɬɵ ɫɨɛɵɬɢɣ C ɢ D ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ S ɪɚɜɧɵ

( x1 , y1 , t1 ) ɢ ( x2 , y2 t2 ), ɚ ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ S' – ( x1c , y1c, t1c ) ɢ ( xc2 , yc2 , t2c ) (ɫɦ. ɪɢɫ. 5.15).

Y S Y' S' V

x1c x2c

U' X X'

Ɋɢɫ. 5.15

II. ɋɨɛɵɬɢɹ C ɢ D ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ S' ɩɪɨɢɫɯɨɞɹɬ ɨɞɧɨɜɪɟɦɟɧɧɨ, ɬɨ ɟɫɬɶ

ȼ ɨɬɥɢɱɢɟ ɨɬ ɫɢɫɬɟɦɵ S' ɜ ɫɢɫɬɟɦɟ S ɫɨɛɵɬɢɹ C ɢ D ɩɪɨɢɫɯɨɞɹɬ ɧɟ ɨɞɧɨɜɪɟɦɟɧɧɨ. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɦɢ Ʌɨɪɟɧɰɚ ɢɧɬɟɪɜɚɥ ɜɪɟɦɟɧɢ ǻt ɦɟɠɞɭ ɫɨɛɵɬɢɹɦɢ C ɢ D ɜ ɫɢɫɬɟɦɟ S ɫ ɭɱɟɬɨɦ

(5.89) ɪɚɜɟɧ:

ɱɬɨ ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ S ɤɨɧɰɵ ɫɬɟɪɠɧɹ A ɢ B ɩɟɪɟɫɟɤɭɬ ɧɟɤɨɬɨɪɭɸ ɩɪɨɢɡɜɨɥɶɧɭɸ ɩɪɹɦɭɸ y = y0 ɜ ɪɚɡɧɵɟ ɦɨɦɟɧɬɵ ɜɪɟɦɟɧɢ, ɫɧɚɱɚɥɚ Ⱥ, ɩɨɬɨɦ ɱɟɪɟɡ ɢɧɬɟɪɜɚɥ ɜɪɟɦɟɧɢ ǻt – B (ɫɦ. ɪɢɫ. 5.16).

S

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ S ɫɬɟɪɠɟɧɶ ɨɤɚɡɵɜɚɟɬɫɹ ɧɚɤɥɨɧɟɧɧɵɦ ɤ ɨɫɢ ɏ ɩɨɞ ɭɝɥɨɦ M. ȼ ɬɨɬ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ, ɤɨɝɞɚ ɤɨɧɟɰ Ⱥ ɞɨɫɬɢɝ ɩɪɹɦɨɣ y = y0, ɤɨɧɟɰ ȼ ɨɤɚɡɚɥɫɹ ɜɵɲɟ ɷɬɨɣ ɩɪɹɦɨɣ ɧɚ ɪɚɫɫɬɨɹɧɢɢ

ɝɞɟ U y – ɫɤɨɪɨɫɬɶ, ɫ ɤɨɬɨɪɨɣ ɫɬɟɪɠɟɧɶ ɞɜɢɠɟɬɫɹ ɜɞɨɥɶ ɨɫɢ Y ɜ

ɫɢɫɬɟɦɟ S. ɉɪɢ ɷɬɨɦ ɫɨɝɥɚɫɧɨ (5.7), ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ S ɩɪɨɢɡɨɣɞɟɬ ɫɨɤɪɚɳɟɧɢɟ ɢɧɬɟɪɜɚɥɚ ǻx x2 x1 :

ɉɪɨɚɧɚɥɢɡɢɪɭɟɦ ɡɚɜɢɫɢɦɨɫɬɶ ɭɝɥɚ M (5.96) ɨɬ ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ V ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ S' ɩɪɢ ɪɚɡɥɢɱɧɵɯ ɫɤɨɪɨɫɬɹɯ ɞɜɢɠɟɧɢɹ ɫɬɟɪɠɧɹ U'. ɇɚ ɪɢɫ. 5.17 ɢɡɨɛɪɚɠɟɧɵ ɝɪɚɮɢɤɢ ɡɚɜɢɫɢɦɨɫɬɢ M V / c ɩɪɢ ɬɪɟɯ ɡɧɚɱɟɧɢɹɯ ɩɚɪɚɦɟɬɪɚ U c/ c . Ƚɪɚɮɢɤ 1 ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɡɧɚɱɟɧɢɸ U c/ c 0,999 , ɝɪɚɮɢɤ 2 ɡɚɞɚɧɧɨɦɭ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ ɡɧɚɱɟ-

ɧɢɸ U c/ c 0,7 , ɚ ɝɪɚɮɢɤ 3 U c/ c 0,3 .

Ʉɚɤ ɜɢɞɢɦ, ɩɪɢ ɡɚɞɚɧɧɨɣ ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ S' ɜ ɥɚɛɨɪɚɬɨɪɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ S ɭɝɨɥ ɦɟɠɞɭ ɞɜɢɠɭɳɢɦɫɹ ɫɬɟɪɠɧɟɦ ɢ ɨɫɶɸ X ɢɦɟɟɬ ɩɪɟɞɟɥɶɧɨɟ ɡɧɚɱɟɧɢɟ Mɩɪɟɞ , ɨɩɪɟɞɟɥɹɟɦɨɟ

ɝɪɚɮɢɤɨɦ 1 ɧɚ ɪɢɫ. 5.17.

5.4. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ

Ɂɚɞɚɱɚ 1

ɇɚɣɬɢ ɫɨɛɫɬɜɟɧɧɭɸ ɞɥɢɧɭ ɫɬɟɪɠɧɹ, ɟɫɥɢ ɜ ɥɚɛɨɪɚɬɨɪɧɨɣ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ ɟɝɨ ɫɤɨɪɨɫɬɶ V = c/2, ɞɥɢɧɚ l = 1 ɦ ɢ ɭɝɨɥ ɦɟɠɞɭ ɧɢɦ ɢ ɧɚɩɪɚɜɥɟɧɢɟɦ ɞɜɢɠɟɧɢɹ - = 45q.

l 1 V / c 2 sin2 - 1 V / c 2 1,08 ɦ .

Ɂɚɞɚɱɚ 2

Ⱦɜɚ ɫɬɟɪɠɧɹ ɨɞɢɧɚɤɨɜɨɣ ɫɨɛɫɬɜɟɧɧɨɣ ɞɥɢɧɨɣ l0 ɞɜɢɠɭɬɫɹ ɧɚɜɫɬɪɟɱɭ ɞɪɭɝ ɞɪɭɝɭ ɩɚɪɚɥɥɟɥɶɧɨ ɨɛɳɟɣ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɨɫɢ. ȼ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ, ɫɜɹɡɚɧɧɨɣ ɫ ɨɞɧɢɦ ɢɡ ɫɬɟɪɠɧɟɣ, ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ ɦɟɠɞɭ ɦɨɦɟɧɬɚɦɢ ɫɨɜɩɚɞɟɧɢɹ ɥɟɜɵɯ ɢ ɩɪɚɜɵɯ ɤɨɧɰɨɜ ɫɬɟɪɠɧɟɣ ɨɤɚɡɚɥɫɹ ɪɚɜɧɵɦ 't. Ʉɚɤɨɜɚ ɫɤɨɪɨɫɬɶ ɨɞɧɨɝɨ ɫɬɟɪɠɧɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɪɭɝɨɝɨ?

Ɂɚɞɚɱɚ 3

ɋɬɟɪɠɟɧɶ, ɞɥɢɧɚ ɤɨɬɨɪɨɝɨ ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ S ɪɚɜɧɚ L, ɪɚɫɩɨɥɨɠɟɧ ɜ ɧɟɣ ɬɚɤ, ɱɬɨ ɫɨɫɬɚɜɥɹɟɬ ɫ ɨɫɶɸ X ɭɝɨɥ -. ɋɢɫɬɟɦɚ ɨɬɫɱɟɬɚ S' ɞɜɢɠɟɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɢɫɬɟɦɵ S ɫɨ ɫɤɨɪɨɫɬɶɸ V = c/2 ɜ ɫɬɨɪɨɧɭ, ɩɪɨɬɢɜɨɩɨɥɨɠɧɭɸ ɨɫɢ Y. Ɉɩɪɟɞɟɥɢɬɶ ɤɚɤɨɣ ɭɝɨɥ -' ɫɨɫɬɚɜɥɹɟɬ ɫɬɟɪɠɟɧɶ ɫ ɨɫɶɸ X' ɫɢɫɬɟɦɵ ɨɬɫɱɟɬɚ S' ɢ ɱɟɦɭ ɪɚɜɧɚ ɞɥɢɧɚ L' ɫɬɟɪɠɧɹ ɜ ɷɬɨɣ ɫɢɫɬɟɦɟ.