Второй закон Ньютона

§12 Âòîðîé çàêîí Íüþòîíà
12. Âòîðîé çàêîí Íüþòîíà
§02
1-04
ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɟɞɫɬɚɜɥɟɧɢɹɦɢ Ƚɚɥɢɥɟɹ, ɞɥɹ ɬɨɝɨ ɱɬɨɛɵ ɬɟɥɨ ɫɬɚɥɨ ɭɫɤɨɪɹɬɶɫɹ, ɧɚ ɧɟɝɨ
ɞɨɥɠɧɚ ɩɨɞɟɣɫɬɜɨɜɚɬɶ ɫɢɥɚ. ɉɪɢ ɤɚɤɢɯ ɭɫɥɨɜɢɹɯ ɬɟɥɨ ɛɭɞɟɬ ɞɜɢɝɚɬɶɫɹ ɪɚɜɧɨɭɫɤɨɪɟɧɧɨ? Ʉɚɤ
ɦɨɠɧɨ ɭɩɪɚɜɥɹɬɶ ɭɫɤɨɪɟɧɢɟɦ ɫ ɩɨɦɨɳɶɸ ɫɢɥɵ? Ʉɚɤ ɡɚɜɢɫɢɬ ɭɫɤɨɪɟɧɢɟ ɨɬ ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ
ɬɟɥɨ ɫɢɥɵ?
ɋɧɚɱɚɥɚ ɜɫɩɨɦɧɢɦ, ɤɚɤ ɞɜɢɠɟɬɫɹ ɢɡɨɥɢɪɨɜɚɧɧɚɹ ɱɚɫɬɢɰɚ. ȿɫɥɢ ɱɚɫɬɢɰɚ ɧɚɯɨɞɢɬɫɹ ɜɞɚɥɢ ɨɬ
ɞɪɭɝɢɯ ɱɚɫɬɢɰ-ɢɫɬɨɱɧɢɤɨɜ ɩɨɥɟɣ, ɦɨɠɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ ɧɚ ɧɟɟ ɧɟ ɞɟɣɫɬɜɭɸɬ ɫɢɥɵ. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ
ɫ ɡɚɤɨɧɨɦ ɢɧɟɪɰɢɢ Ƚɚɥɢɥɟɹ (ɢɧɨɝɞɚ ɟɝɨ ɧɚɡɵɜɚɸɬ ɩɟɪɜɵɦ ɡɚɤɨɧɨɦ ɇɶɸɬɨɧɚ) ɬɚɤɚɹ ɱɚɫɬɢɰɚ
ɞɜɢɠɟɬɫɹ ɪɚɜɧɨɦɟɪɧɨ ɢ ɩɪɹɦɨɥɢɧɟɣɧɨ ɢɥɢ ɩɨɤɨɢɬɫɹ. ȼ ɤɚɱɟɫɬɜɟ ɩɪɢɦɟɪɚ ɦɨɠɧɨ ɭɤɚɡɚɬɶ
ɧɚ ɦɨɥɟɤɭɥɭ ɪɚɡɪɟɠɟɧɧɨɝɨ ɝɚɡɚ, ɤɨɬɨɪɚɹ ɧɚɯɨɞɢɬɫɹ ɞɨɫɬɚɬɨɱɧɨ ɞɚɥɟɤɨ ɨɬ ɞɪɭɝɢɯ ɦɨɥɟɤɭɥ
(ɫɢɥɭ ɬɹɠɟɫɬɢ, ɞɟɣɫɬɜɭɸɳɭɸ ɧɚ ɦɨɥɟɤɭɥɭ, ɧɟ ɭɱɢɬɵɜɚɟɦ, ɚ ɬɚɤɠɟ ɩɪɟɧɟɛɪɟɝɚɟɦ ɞɟɣɫɬɜɢɟɦ
ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɢ ɦɚɝɧɢɬɧɵɯ ɩɨɥɟɣ). Ɍɚɤɚɹ ɱɚɫɬɢɰɚ ɛɭɞɟɬ ɞɜɢɝɚɬɶɫɹ ɪɚɜɧɨɦɟɪɧɨ ɢ ɩɪɹɦɨɥɢɧɟɣɧɨ
ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɧɟ ɨɤɚɠɟɬɫɹ ɜɛɥɢɡɢ ɞɪɭɝɨɣ ɱɚɫɬɢɰɵ. Ɋɚɜɧɨɦɟɪɧɨ ɢ ɩɪɹɦɨɥɢɧɟɣɧɨ ɞɜɢɠɟɬɫɹ
ɤɨɫɦɢɱɟɫɤɢɣ ɤɨɪɚɛɥɶ, ɤɨɬɨɪɵɣ ɜɞɚɥɢ ɨɬ ɦɚɫɫɢɜɧɵɯ ɬɟɥ ɧɟɫɟɬɫɹ ɜ ɩɭɫɬɨɬɟ ɫ ɜɵɤɥɸɱɟɧɧɵɦɢ
ɞɜɢɝɚɬɟɥɹɦɢ.
Ⱦɥɹ ɪɟɲɟɧɢɹ ɫɥɟɞɭɸɳɟɣ ɡɚɞɚɱɢ ɩɪɢɦɟɦ ɛɟɡ ɞɨɤɚɡɚɬɟɥɶɫɬɜɚ ɞɨɫɬɚɬɨɱɧɨ ɩɪɚɜɞɨɩɨɞɨɛɧɨɟ
ɭɬɜɟɪɠɞɟɧɢɟ: ɱɚɫɬɢɰɚ, ɧɚ ɤɨɬɨɪɭɸ ɞɟɣɫɬɜɭɟɬ ɩɨɫɬɨɹɧɧɚɹ ɫɢɥɚ, ɞɜɢɠɟɬɫɹ ɫ ɩɨɫɬɨɹɧɧɵɦ
ɭɫɤɨɪɟɧɢɟɦ.
Ɂɚɞɚɱɚ. ɂɡɨɥɢɪɨɜɚɧɧɚɹ
ɱɚɫɬɢɰɚ
ɦɚɫɫɨɣ
m
ɞɜɢɠɟɬɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ
υ1. ȼ ɧɟɤɨɬɨɪɵɣ ɦɨɦɟɧɬ
ɜɪɟɦɟɧɢ t1 ɨɧɚ ɩɨɩɚɞɚɟɬ
ɜ ɨɞɧɨɪɨɞɧɨɟ ɩɨɥɟ, ɝɞɟ
ɧɚ ɧɟɟ ɧɚɱɢɧɚɟɬ ɞɟɣɫɬɜɨɜɚɬɶ ɫɢɥɚ F, ɫɨɧɚɩɪɚɜɥɟɧɧɚɹ ɫɤɨɪɨɫɬɢ ɱɚɫɬɢɰɵ (ɫɦ. ɪɢɫ.). ɇɚɣɬɢ:
ɚ) ɫɤɨɪɨɫɬɶ υ2, ɫ ɤɨɬɨɪɨɣ ɛɭɞɟɬ ɞɜɢɝɚɬɶɫɹ ɱɚɫɬɢɰɚ ɜ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t2 > t1; ɛ) ɩɭɬɶ S, ɤɨɬɨɪɵɣ
ɩɪɨɣɞɟɬ ɱɚɫɬɢɰɚ ɡɚ ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ Δt = t2 − t1; ɜ) ɭɫɤɨɪɟɧɢɟ ɱɚɫɬɢɰɵ.
Ɋɟɲɟɧɢɟ. ɍ ɧɚɫ ɧɟɬ ɝɨɬɨɜɨɝɨ ɫɩɨɫɨɛɚ ɪɟɲɟɧɢɹ ɷɬɨɣ ɡɚɞɚɱɢ, ɩɨɷɬɨɦɭ ɫɧɚɱɚɥɚ ɡɚɩɢɲɟɦ ɜɫɟ
ɮɨɪɦɭɥɵ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɧɚɦ ɩɪɢɝɨɞɢɬɶɫɹ:
§26
1. Ɉɩɪɟɞɟɥɟɧɢɟ ɪɚɛɨɬɵ ɩɨɫɬɨɹɧɧɨɣ ɫɢɥɵ F ɧɚ ɩɭɬɢ S:
§05
2. Ɍɟɨɪɟɦɚ ɨɛ ɢɡɦɟɧɟɧɢɢ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ:
§11
3. ɋɪɟɞɧɹɹ ɫɤɨɪɨɫɬɶ ɩɪɢ ɪɚɜɧɨɭɫɤɨɪɟɧɧɨɦ ɞɜɢɠɟɧɢɢ:
4. ɉɪɨɣɞɟɧɧɵɣ ɩɭɬɶ ɫɨ ɫɪɟɞɧɟɣ ɫɤɨɪɨɫɬɶɸ υɫɪ ɜɪɟɦɹ Δt:
§22
A = F · S (1)
(2)
(3)
S = υɫɪ · Δt (4)
5. Ɉɩɪɟɞɟɥɟɧɢɟ ɭɫɤɨɪɟɧɢɹ ɩɪɢ ɪɚɜɧɨɭɫɤɨɪɟɧɧɨɦ ɞɜɢɠɟɧɢɢ:
ȼɨɫɩɨɥɶɡɭɣɬɟɫɶ ɩɪɟɞɥɨɠɟɧɧɨɣ ɫɯɟɦɨɣ ɢ ɩɨɥɭɱɢɬɟ ɧɨɜɵɟ ɮɨɪɦɭɥɵ:
38
(5)
Âòîðîé çàêîí Íüþòîíà §12
ɂɡ (9) ɜɵɪɚɡɢɦ ɢɫɤɨɦɭɸ ɫɤɨɪɨɫɬɶ:
(10)
ɉɪɟɨɛɪɚɡɭɟɦ ɮɨɪɦɭɥɭ (5) ɤ ɩɨɯɨɠɟɦɭ ɜɢɞɭ: υ2 = υ1 + a · (t2 – t1) ɢ ɫɪɚɜɧɢɦ ɫ (10).
ɂɬɚɤ, ɦɵ ɜɢɞɢɦ, ɱɬɨ ɭɫɤɨɪɟɧɢɟ ɱɚɫɬɢɰɵ ɪɚɜɧɨ:
(11)
ȼɨɫɩɨɥɶɡɭɣɬɟɫɶ ɮɨɪɦɭɥɚɦɢ (3), (4) ɢ (10) ɢ ɩɨɥɭɱɢɬɟ:
ɂɫɩɨɥɶɡɭɹ ɩɨɥɭɱɟɧɧɵɟ ɮɨɪɦɭɥɵ, ɪɟɲɢɬɟ ɡɚɞɚɱɭ.
Ɂɚɞɚɱɚ. ɉɥɚɫɬɢɥɢɧɨɜɵɣ ɲɚɪɢɤ ɛɟɡ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɩɚɞɚɟɬ ɫ
ɜɵɫɨɬɵ 20 ɦ. ɋɱɢɬɚɹ, ɱɬɨ ɧɚ ɧɟɝɨ ɞɟɣɫɬɜɭɟɬ ɬɨɥɶɤɨ ɫɢɥɚ ɬɹɠɟɫɬɢ F = mg
(g ≈ 10 ɇ/ɤɝ), ɧɚɣɬɢ: ɚ) ɭɫɤɨɪɟɧɢɟ ɲɚɪɢɤɚ; ɛ) ɫɤɨɪɨɫɬɶ ɲɚɪɢɤɚ ɱɟɪɟɡ 1 ɫ, 2 ɫ,
3 ɫ; ɜ) ɩɭɬɶ, ɩɪɨɣɞɟɧɧɵɣ ɲɚɪɢɤɨɦ ɡɚ ɩɟɪɜɭɸ ɫɟɤɭɧɞɭ, ɡɚ ɜɬɨɪɭɸ ɫɟɤɭɧɞɭ,
ɡɚ ɬɪɟɬɶɸ ɫɟɤɭɧɞɭ, ɡɚ ɞɜɟ ɫɟɤɭɧɞɵ (ɡɚ ɩɟɪɜɭɸ ɢ ɜɬɨɪɭɸ ɜɦɟɫɬɟ), ɡɚ ɬɪɢ
ɫɟɤɭɧɞɵ; ɝ) ɫɪɟɞɧɸɸ ɫɤɨɪɨɫɬɶ ɡɚ ɩɟɪɜɭɸ ɫɟɤɭɧɞɭ, ɡɚ ɜɬɨɪɭɸ ɫɟɤɭɧɞɭ,
ɡɚ ɬɪɟɬɶɸ ɫɟɤɭɧɞɭ, ɧɚ ɜɫɟɦ ɩɭɬɢ. ɉɨɫɬɪɨɢɬɶ ɝɪɚɮɢɤɢ ɡɚɜɢɫɢɦɨɫɬɢ:
ɚ) ɭɫɤɨɪɟɧɢɹ ɨɬ ɜɪɟɦɟɧɢ; ɛ) ɫɤɨɪɨɫɬɢ ɨɬ ɜɪɟɦɟɧɢ; ɜ) ɩɭɬɢ ɨɬ ɜɪɟɦɟɧɢ.
ɂ. ɇɶɸɬɨɧ
(1642–1727)
Ɏɨɪɦɭɥɵ (9) ɢ (11) ɢɝɪɚɸɬ ɜ ɮɢɡɢɤɟ ɧɚɫɬɨɥɶɤɨ ɜɚɠɧɭɸ ɪɨɥɶ, ɱɬɨ
ɩɨɥɭɱɢɥɢ ɫɬɚɬɭɫ ɡɚɤɨɧɚ. ɗɬɨɬ ɡɚɤɨɧ, ɩɨɥɭɱɢɜɲɢɣ ɧɚɡɜɚɧɢɟ ɜɬɨɪɨɝɨ ɡɚɤɨɧɚ
ɇɶɸɬɨɧɚ, ɩɪɢɧɹɬɨ ɡɚɩɢɫɵɜɚɬɶ ɞɜɭɦɹ ɫɩɨɫɨɛɚɦɢ:
ɂɦɩɭɥɶɫ ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɬɟɥɨ ɫɢɥɵ
ɪɚɜɟɧ ɢɡɦɟɧɟɧɢɸ ɢɦɩɭɥɶɫɚ ɬɟɥɚ.
ɍɫɤɨɪɟɧɢɟ ɬɟɥɚ ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ
ɩɪɢɥɨɠɟɧɧɨɣ ɤ ɬɟɥɭ ɫɢɥɟ ɢ ɨɛɪɚɬɧɨ
ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨ ɦɚɫɫɟ ɬɟɥɚ.
ȼ ɦɟɠɞɭɧɚɪɨɞɧɨɣ ɫɢɫɬɟɦɟ ɟɞɢɧɢɰ (ɋɂ) ɫɢɥɚ ɢɡɦɟɪɹɟɬɫɹ ɜ ɧɶɸɬɨɧɚɯ:
ɉɪɨɱɢɬɚɣɬɟ ɜɵɞɟɪɠɤɢ ɢɡ ɤɧɢɝɢ ɂ. ɇɶɸɬɨɧɚ «Ɇɚɬɟɦɚɬɢɱɟɫɤɢɟ ɧɚɱɚɥɚ ɧɚɬɭɪɚɥɶɧɨɣ
ɮɢɥɨɫɨɮɢɢ». Ʉɚɤɚɹ ɢɡ ɩɪɢɜɟɞɟɧɧɵɯ ɜɵɲɟ ɮɨɪɦɭɥɢɪɨɜɨɤ ɛɥɢɠɟ ɤ ɧɶɸɬɨɧɨɜɫɤɨɣ? Ʉɚɤ ɦɵ
ɫɟɣɱɚɫ ɧɚɡɵɜɚɟɦ ɮɢɡɢɱɟɫɤɭɸ ɜɟɥɢɱɢɧɭ, ɤɨɬɨɪɚɹ ɩɪɟɠɞɟ ɧɚɡɵɜɚɥɚɫɶ ɤɨɥɢɱɟɫɬɜɨɦ ɞɜɢɠɟɧɢɹ?
ɑɬɨ ɧɚɡɵɜɚɟɬɫɹ ɢɦɩɭɥɶɫɨɦ ɫɢɥɵ?
1-04
39