§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