ɎȿȾȿɊȺɅɖɇɈȿ ȺȽȿɇɌɋɌȼɈ ɉɈ ɈȻɊȺɁɈȼȺɇɂɘ ȽɈɋɍȾȺɊɋɌȼȿɇɇɈȿ ɈȻɊȺɁɈȼȺɌȿɅɖɇɈȿ ɍɑɊȿɀȾȿɇɂȿ ȼɕɋɒȿȽɈ ɉɊɈɎȿɋɋɂɈɇȺɅɖɇɈȽɈ ɈȻɊȺɁɈȼȺɇɂə «ȼɈɊɈɇȿɀɋɄɂɃ ȽɈɋɍȾȺɊɋɌȼȿɇɇɕɃ ɍɇɂȼȿɊɋɂɌȿɌ»
ɄɍɊɋ ɈȻɓȿɃ ɎɂɁɂɄɂ
ɆȿɏȺɇɂɄȺ ɂ ɆɈɅȿɄɍɅəɊɇȺə ɎɂɁɂɄȺ ɑɚɫɬɶ 1
ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɞɥɹ ɜɭɡɨɜ
ɂɡɞɚɬɟɥɶɫɤɨ-ɩɨɥɢɝɪɚɮɢɱɟɫɤɢɣ ɰɟɧɬɪ ȼɨɪɨɧɟɠɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ 2007
ɍɬɜɟɪɠɞɟɧɨ ɧɚɭɱɧɨ-ɦɟɬɨɞɢɱɟɫɤɢɦ ɫɨɜɟɬɨɦ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɮɚɤɭɥɶɬɟɬɚ 2 ɢɸɥɹ 2007 ɝ., ɩɪɨɬɨɤɨɥ ʋ 6
ɋɨɫɬɚɜɢɬɟɥɢ: Ɉ.ȼ. Ɋɨɝɚɡɢɧɫɤɚɹ, Ⱥ.Ȼ. ɉɥɚɤɫɢɰɤɢɣ, ɋ.Ⱦ. Ɇɢɥɨɜɢɞɨɜɚ, Ⱥ.Ⱥ. ɋɢɞɨɪɤɢɧ
ɉɪɚɤɬɢɱɟɫɤɨɟ ɩɨɫɨɛɢɟ ɩɨɞɝɨɬɨɜɥɟɧɨ ɧɚ ɤɚɮɟɞɪɟ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɮɢɡɢɤɢ ɮɢɡɢɱɟɫɤɨɝɨ ɮɚɤɭɥɶɬɟɬɚ ȼɨɪɨɧɟɠɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ. Ɋɟɤɨɦɟɧɞɭɟɬɫɹ ɜ ɤɚɱɟɫɬɜɟ ɭɱɟɛɧɨɝɨ ɩɨɫɨɛɢɹ ɤ ɤɨɧɬɪɨɥɶɧɵɦ ɪɚɛɨɬɚɦ ɞɥɹ ɫɬɭɞɟɧɬɨɜ 1 ɤɭɪɫɚ ɡɚɨɱɧɨɝɨ ɨɬɞɟɥɟɧɢɹ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɮɚɤɭɥɶɬɟɬɚ. Ɋɚɛɨɬɚ ɜɵɩɨɥɧɟɧɚ ɩɪɢ ɩɨɞɞɟɪɠɤɟ ɝɪɚɧɬɚ VZ-010 Ⱥɦɟɪɢɤɚɧɫɤɨɝɨ ɮɨɧɞɚ ɝɪɚɠɞɚɧɫɤɢɯ ɢɫɫɥɟɞɨɜɚɧɢɣ ɢ ɪɚɡɜɢɬɢɹ (CRDF) ɢ ɩɨ ɩɪɨɝɪɚɦɦɟ «Ɏɭɧɞɚɦɟɧɬɚɥɶɧɵɟ ɢɫɫɥɟɞɨɜɚɧɢɹ ɢ ɜɵɫɲɟɟ ɨɛɪɚɡɨɜɚɧɢɟ».
Ⱦɥɹ ɫɩɟɰɢɚɥɶɧɨɫɬɢ: 130301 – Ƚɟɨɥɨɝɢɱɟɫɤɚɹ ɫɴɟɦɤɚ, ɩɨɢɫɤ ɢ ɪɚɡɜɟɞɤɚ ɦɟɫɬɨɪɨɠɞɟɧɢɣ ɩɨɥɟɡɧɵɯ ɢɫɤɨɩɚɟɦɵɯ 2
ɋɈȾȿɊɀȺɇɂȿ 1. Ɇɟɬɨɞɢɱɟɫɤɢɟ ɭɤɚɡɚɧɢɹ ɤ ɜɵɩɨɥɧɟɧɢɸ ɢ ɨɮɨɪɦɥɟɧɢɸ ɤɨɧɬɪɨɥɶɧɵɯ ɪɚɛɨɬ…….……………………………...…………………….3 2. ɉɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɡɚɞɚɱ.………………………………………………..….7 3. Ɂɚɞɚɱɢ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ..….…..………………………….17 4. ȼɚɪɢɚɧɬɵ ɤɨɧɬɪɨɥɶɧɨɣ ɪɚɛɨɬɵ ʋ 1……..………………………...……..19 ɆȿɌɈȾɂɑȿɋɄɂȿ ɍɄȺɁȺɇɂə Ʉ ȼɕɉɈɅɇȿɇɂɘ ɂ ɈɎɈɊɆɅȿɇɂɘ ɄɈɇɌɊɈɅɖɇɕɏ ɊȺȻɈɌ 1. ȼ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɭɱɟɛɧɵɦ ɩɥɚɧɨɦ ɜ 1-ɨɦ ɫɟɦɟɫɬɪɟ 1 ɤɭɪɫɚ ɫɬɭɞɟɧɬɵ ɜɵɩɨɥɧɹɸɬ ɤɨɧɬɪɨɥɶɧɭɸ ɪɚɛɨɬɭ ɩɨ ɦɟɯɚɧɢɤɟ ɢ ɦɨɥɟɤɭɥɹɪɧɨɣ ɮɢɡɢɤɟ, ɤɨɬɨɪɭɸ ɧɟɨɛɯɨɞɢɦɨ ɜɵɫɥɚɬɶ ɜ ɞɟɤɚɧɚɬ ɝɟɨɥɨɝɢɱɟɫɤɨɝɨ ɮɚɤɭɥɶɬɟɬɚ ɞɨ 1 ɞɟɤɚɛɪɹ. 2. ȼɵɩɨɥɧɹɬɶ ɤɨɧɬɪɨɥɶɧɭɸ ɪɚɛɨɬɭ ɧɭɠɧɨ ɬɨɥɶɤɨ ɩɨɫɥɟ ɢɡɭɱɟɧɢɹ ɫɥɟɞɭɸɳɢɯ ɪɚɡɞɟɥɨɜ ɮɢɡɢɤɢ: 1) «Ɏɢɡɢɱɟɫɤɢɟ ɨɫɧɨɜɵ ɦɟɯɚɧɢɤɢ», ɜɤɥɸɱɚɹ «Ʉɨɥɟɛɚɧɢɹ ɢ ɜɨɥɧɵ»; 2) «Ɇɨɥɟɤɭɥɹɪɧɚɹ ɮɢɡɢɤɚ ɢ ɬɟɪɦɨɞɢɧɚɦɢɤɚ». 3. ɉɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɪɚɡɥɢɱɧɵɯ ɪɚɡɞɟɥɨɜ ɮɢɡɢɤɢ ɜɫɬɪɟɱɚɟɬɫɹ ɦɧɨɠɟɫɬɜɨ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ: ɞɥɢɧɚ, ɜɪɟɦɹ, ɫɢɥɚ, ɢɦɩɭɥɶɫ ɢ ɬ. ɞ. ɗɬɢ ɩɨɧɹɬɢɹ ɢɦɟɸɬ ɧɟ ɬɨɥɶɤɨ ɱɢɫɥɟɧɧɵɟ ɡɧɚɱɟɧɢɹ, ɨɧɢ ɨɛɥɚɞɚɸɬ ɪɚɡɦɟɪɧɨɫɬɹɦɢ, ɚ ɤɪɨɦɟ ɬɨɝɨ, ɟɞɢɧɢɰɟɣ, ɜ ɤɨɬɨɪɨɣ ɮɢɡɢɱɟɫɤɚɹ ɜɟɥɢɱɢɧɚ ɢɦɟɟɬ ɞɚɧɧɨɟ ɡɧɚɱɟɧɢɟ. ɇɟɬ ɧɢɤɚɤɨɝɨ ɫɦɵɫɥɚ ɜ ɭɬɜɟɪɠɞɟɧɢɢ, ɱɬɨ ɫɚɦɵɟ ɛɨɥɶɲɢɟ ɪɚɫɬɟɧɢɹ – ɝɢɝɚɧɬɫɤɢɟ ɫɟɤɜɨɣɢ – ɢɦɟɸɬ ɜɵɫɨɬɭ, ɪɚɜɧɭɸ 100. ȼɟɫɶɦɚ ɫɭɳɟɫɬɜɟɧɧɨ, ɱɬɨ ɷɬɚ ɜɵɫɨɬɚ – 100 ɦɟɬɪɨɜ. Ɇɟɥɶɱɚɣɲɢɟ ɤɥɟɬɤɢ ɢɦɟɸɬ ɪɚɡɦɟɪɵ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ 10-6 ɦ (ɚ ɧɟ ɩɪɨɫɬɨ 10-6), ɬ. ɟ. ɦɚɤɫɢɦɚɥɶɧɵɟ ɨɬɧɨɲɟɧɢɹ ɪɚɡɦɟɪɨɜ ɠɢɜɵɯ ɨɛɴɟɤɬɨɜ ɫɨɫɬɚɜɥɹɸɬ 108 ɢɥɢ 100 ɦɥɧ. 4. ɉɪɢɫɬɭɩɚɹ ɤ ɪɟɲɟɧɢɸ ɡɚɞɚɱ, ɧɟɨɛɯɨɞɢɦɨ: ɚ) ɩɨɥɧɨɫɬɶɸ ɧɚɩɢɫɚɬɶ ɭɫɥɨɜɢɟ ɡɚɞɚɱɢ ɜ ɬɟɬɪɚɞɢ; ɛ) ɜɵɩɢɫɚɬɶ ɡɚɞɚɧɧɵɟ ɜɟɥɢɱɢɧɵ ɜ ɛɭɤɜɟɧɧɵɯ ɜɵɪɚɠɟɧɢɹɯ ɫ ɢɯ ɱɢɫɥɟɧɧɵɦɢ ɡɧɚɱɟɧɢɹɦɢ ɢ ɪɚɡɦɟɪɧɨɫɬɹɦɢ, ɚ ɢɫɤɨɦɵɟ ɜɟɥɢɱɢɧɵ – ɫ ɜɨɩɪɨɫɢɬɟɥɶɧɵɦɢ ɡɧɚɤɚɦɢ; ɩɪɢ ɪɟɲɟɧɢɢ ɡɚɞɚɱ ɩɨɥɶɡɨɜɚɬɶɫɹ ɫɢɫɬɟɦɨɣ ɋɂ; ɜ) ɟɫɥɢ ɷɬɨ ɧɟɨɛɯɨɞɢɦɨ ɩɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ, ɫɞɟɥɚɬɶ ɱɟɪɬɟɠ (ɫ ɩɨɦɨɳɶɸ ɱɟɪɬɟɠɧɵɯ ɩɪɢɧɚɞɥɟɠɧɨɫɬɟɣ), ɧɚ ɧɟɦ ɭɤɚɡɚɬɶ ɧɚɩɪɚɜɥɟɧɢɟ ɡɚɞɚɧɧɵɯ ɢ ɢɫɤɨɦɵɯ ɜɟɥɢɱɢɧ, ɫɚɦɢ ɷɬɢ ɜɟɥɢɱɢɧɵ ɨɛɨɡɧɚɱɢɬɶ ɛɭɤɜɚɦɢ. 5. Ɋɟɲɟɧɢɹ ɡɚɞɚɱ ɫɨɩɪɨɜɨɠɞɚɬɶ ɨɛɴɹɫɧɟɧɢɹɦɢ. 6. ȼɫɟ ɮɢɡɢɱɟɫɤɢɟ ɜɟɥɢɱɢɧɵ ɜɵɪɚɠɚɸɬɫɹ ɜ ɫɜɨɢɯ ɟɞɢɧɢɰɚɯ. ȼɫɟ ɮɢɡɢɱɟɫɤɢɟ ɜɟɥɢɱɢɧɵ, ɤɚɤ ɱɢɫɥɚ, ɬɚɤ ɢ ɢɯ ɟɞɢɧɢɰɵ, ɜ ɨɛɟɢɯ ɱɚɫɬɹɯ ɭɪɚɜɧɟɧɢɣ ɞɨɥɠɧɵ ɛɵɬɶ ɨɞɢɧɚɤɨɜɵɦɢ. 7. ɉɪɨɫɬɵɟ ɡɚɞɚɱɢ ɥɭɱɲɟ ɪɟɲɚɬɶ ɜ ɨɛɳɟɦ ɜɢɞɟ ɢ ɬɨɥɶɤɨ ɜ ɤɨɧɟɱɧɵɯ ɜɵɪɚɠɟɧɢɹɯ ɩɪɨɢɡɜɨɞɢɬɶ ɜɵɱɢɫɥɟɧɢɹ. ȿɫɥɢ ɡɚɞɚɱɚ ɬɪɟɛɭɟɬ ɝɪɨɦɨɡɞɤɢɯ ɜɵɱɢɫɥɟɧɢɣ, ɬɨ ɦɨɠɧɨ ɩɪɨɢɡɜɨɞɢɬɶ ɢɯ ɧɟ ɜ ɤɨɧɟɱɧɵɯ, ɚ ɜ ɩɪɨɦɟɠɭɬɨɱɧɵɯ ɮɨɪɦɭɥɚɯ. 3
8. ȼ ɤɨɧɟɱɧɵɯ ɮɨɪɦɭɥɚɯ ɨɛɹɡɚɬɟɥɶɧɨ ɭɤɚɡɵɜɚɬɶ ɪɚɡɦɟɪɧɨɫɬɶ ɜɟɥɢɱɢɧ, ɩɨɥɭɱɟɧɧɵɯ ɜ ɪɟɡɭɥɶɬɚɬɟ ɜɵɱɢɫɥɟɧɢɣ. 9. Ɉɛɹɡɚɬɟɥɶɧɨ ɜɵɩɢɫɚɬɶ ɨɬɜɟɬ ɡɚɞɚɱɢ. ɉɨɪɹɞɨɤ ɜɵɩɨɥɧɟɧɢɹ ɢ ɨɮɨɪɦɥɟɧɢɹ ɪɚɛɨɬ 1. ɇɚ ɨɛɥɨɠɤɟ ɬɟɬɪɚɞɢ ɧɭɠɧɨ ɭɤɚɡɚɬɶ ɧɨɦɟɪ ɤɨɧɬɪɨɥɶɧɨɣ ɪɚɛɨɬɵ, ɧɨɦɟɪ ɡɚɱɟɬɧɨɣ ɤɧɢɠɤɢ, ɜɚɪɢɚɧɬ, ɮɚɤɭɥɶɬɟɬ, ɤɭɪɫ, ɮɚɦɢɥɢɸ ɢ ɢɧɢɰɢɚɥɵ ɫɬɭɞɟɧɬɚ. 2. ɍɫɥɨɜɢɹ ɡɚɞɚɱ ɧɭɠɧɨ ɩɟɪɟɩɢɫɵɜɚɬɶ ɩɨɥɧɨɫɬɶɸ, ɚ ɪɟɲɟɧɢɹ ɢɯ ɢɡɥɚɝɚɬɶ ɩɨ ɩɪɚɜɢɥɚɦ, ɩɪɢɜɟɞɟɧɧɵɦ ɜɵɲɟ. 3. Ɍɟɤɫɬ ɤɨɧɬɪɨɥɶɧɨɣ ɪɚɛɨɬɵ ɞɨɥɠɟɧ ɛɵɬɶ ɧɚɩɢɫɚɧ ɝɪɚɦɨɬɧɨ, ɪɚɡɛɨɪɱɢɜɨ ɢ ɚɤɤɭɪɚɬɧɨ. ɇɟɛɪɟɠɧɨ ɨɮɨɪɦɥɟɧɧɵɟ ɪɚɛɨɬɵ ɛɭɞɭɬ ɜɨɡɜɪɚɳɟɧɵ ɛɟɡ ɩɪɨɜɟɪɤɢ. 4. ɉɢɫɚɬɶ ɤɨɧɬɪɨɥɶɧɭɸ ɪɚɛɨɬɭ ɧɭɠɧɨ ɫ ɨɫɬɚɜɥɟɧɢɟɦ ɩɨɥɟɣ (3–4 ɫɦ) ɞɥɹ ɡɚɦɟɱɚɧɢɣ ɪɟɰɟɧɡɟɧɬɚ. 5. ȼ ɤɨɧɰɟ ɤɨɧɬɪɨɥɶɧɨɣ ɪɚɛɨɬɵ ɞɨɥɠɟɧ ɛɵɬɶ ɭɤɚɡɚɧ ɩɟɪɟɱɟɧɶ ɥɢɬɟɪɚɬɭɪɵ, ɢɫɩɨɥɶɡɨɜɚɧɧɨɣ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɪɚɛɨɬɵ. 6. Ɂɚɤɨɧɱɢɜ ɪɚɛɨɬɭ, ɧɭɠɧɨ ɜɧɢɦɚɬɟɥɶɧɨ ɩɪɨɱɢɬɚɬɶ ɟɟ, ɢɫɩɪɚɜɢɬɶ ɨɲɢɛɤɢ, ɩɨɞɩɢɫɚɬɶɫɹ ɢ ɩɨɫɬɚɜɢɬɶ ɞɚɬɭ. 7. ȿɫɥɢ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɤɨɧɬɪɨɥɶɧɨɣ ɪɚɛɨɬɵ ɜ ɩɪɨɰɟɫɫɟ ɪɟɲɟɧɢɹ ɡɚɞɚɱ ɢ ɫɜɹɡɚɧɧɨɝɨ ɫ ɷɬɢɦ ɢɡɭɱɟɧɢɟɦ ɬɟɨɪɟɬɢɱɟɫɤɨɝɨ ɦɚɬɟɪɢɚɥɚ ɜɫɬɪɟɱɚɸɬɫɹ ɨɬɞɟɥɶɧɵɟ ɡɚɬɪɭɞɧɟɧɢɹ, ɤɨɬɨɪɵɟ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɩɪɟɨɞɨɥɟɬɶ ɧɟ ɭɞɚɟɬɫɹ, ɧɭɠɧɨ ɩɪɢɣɬɢ ɧɚ ɤɨɧɫɭɥɶɬɚɰɢɸ ɤ ɩɪɟɩɨɞɚɜɚɬɟɥɸ, ɱɢɬɚɸɳɟɦɭ ɤɭɪɫ ɮɢɡɢɤɢ ɧɚ ɮɚɤɭɥɶɬɟɬɟ, ɢɥɢ (ɞɥɹ ɢɧɨɝɨɪɨɞɧɢɯ) ɩɨɫɥɚɬɶ ɩɨ ɩɨɱɬɟ ɡɚɩɪɨɫ ɜ ɭɧɢɜɟɪɫɢɬɟɬ ɞɥɹ ɩɨɥɭɱɟɧɢɹ ɧɟɨɛɯɨɞɢɦɵɯ ɭɤɚɡɚɧɢɣ. 8. ɉɪɨɜɟɪɟɧɧɵɟ ɤɨɧɬɪɨɥɶɧɵɟ ɪɚɛɨɬɵ ɫɥɟɞɭɟɬ ɫɨɯɪɚɧɹɬɶ ɢ ɩɪɟɞɴɹɜɥɹɬɶ ɢɯ ɧɚ ɷɤɡɚɦɟɧɟ ɤɚɤ ɞɨɤɭɦɟɧɬ ɨ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨ ɩɪɨɞɟɥɚɧɧɨɣ ɪɚɛɨɬɟ. Ȼɟɡ ɩɪɟɞɴɹɜɥɟɧɢɹ ɤɨɧɬɪɨɥɶɧɵɯ ɪɚɛɨɬ ɫɬɭɞɟɧɬ ɤ ɫɞɚɱɟ ɷɤɡɚɦɟɧɚ ɩɨ ɮɢɡɢɤɟ ɧɟ ɞɨɩɭɫɤɚɟɬɫɹ. ɍɦɟɧɢɟ ɪɟɲɚɬɶ ɡɚɞɚɱɢ ɩɪɢɨɛɪɟɬɚɟɬɫɹ ɫɢɫɬɟɦɚɬɢɱɟɫɤɢɦɢ ɭɩɪɚɠɧɟɧɢɹɦɢ. ɑɬɨɛɵ ɧɚɭɱɢɬɶɫɹ ɪɟɲɚɬɶ ɡɚɞɚɱɢ ɢ ɩɨɞɝɨɬɨɜɢɬɶɫɹ ɤ ɜɵɩɨɥɧɟɧɢɸ ɤɨɧɬɪɨɥɶɧɵɯ ɪɚɛɨɬ, ɧɭɠɧɨ ɩɨɫɥɟ ɢɡɭɱɟɧɢɹ ɨɱɟɪɟɞɧɨɝɨ ɪɚɡɞɟɥɚ ɭɱɟɛɧɢɤɚ ɜɧɢɦɚɬɟɥɶɧɨ ɪɚɡɨɛɪɚɬɶ ɩɨɦɟɳɟɧɧɵɟ ɜ ɷɬɨɦ ɭɤɚɡɚɧɢɢ ɩɪɢɦɟɪɵ ɪɟɲɟɧɢɹ ɬɢɩɨɜɵɯ ɡɚɞɚɱ, ɪɟɲɢɬɶ ɡɚɞɚɱɢ, ɩɪɟɞɥɚɝɚɟɦɵɟ ɞɥɹ ɫɚɦɨɫɬɨɹɬɟɥɶɧɨɝɨ ɪɟɲɟɧɢɹ, ɢ ɩɨɫɥɟ ɷɬɨɝɨ ɩɪɢɫɬɭɩɚɬɶ ɤ ɜɵɩɨɥɧɟɧɢɸ ɤɨɧɬɪɨɥɶɧɨɣ ɪɚɛɨɬɵ.
4
ɈɋɇɈȼɇɕȿ ȿȾɂɇɂɐɕ ɎɂɁɂɑȿɋɄɂɏ ȼȿɅɂɑɂɇ ɆȿɀȾɍɇȺɊɈȾɇɈɃ ɋɂɋɌȿɆɕ ɋɂ ȿɞɢɧɢɰɵ ɜɫɟɯ ɦɟɯɚɧɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ ɦɨɠɧɨ ɜɵɪɚɡɢɬɶ ɱɟɪɟɡ ɬɪɢ ɨɫɧɨɜɧɵɟ – ɟɞɢɧɢɰɵ ɞɥɢɧɵ, ɦɚɫɫɵ ɢ ɜɪɟɦɟɧɢ. Ʉɨɝɞɚ ɜɜɨɞɹɬɫɹ ɬɚɤɢɟ ɜɟɥɢɱɢɧɵ, ɤɚɤ ɫɢɥɚ ɢɥɢ ɷɧɟɪɝɢɹ, ɞɥɹ ɭɞɨɛɫɬɜɚ ɟɞɢɧɢɰɚɦ ɞɚɸɬɫɹ ɫɩɟɰɢɚɥɶɧɵɟ ɧɚɡɜɚɧɢɹ (ɧɶɸɬɨɧ ɢɥɢ ɞɠɨɭɥɶ), ɧɨ ɨɧɢ ɨɩɪɟɞɟɥɟɧɵ ɤɚɤ ɤɨɦɛɢɧɚɰɢɢ ɟɞɢɧɢɰ ɞɥɢɧɵ, ɦɚɫɫɵ ɢ ɜɪɟɦɟɧɢ. ɗɬɢ ɬɪɢ ɟɞɢɧɢɰɵ: ɦɟɬɪ, ɤɢɥɨɝɪɚɦɦ, ɫɟɤɭɧɞɚ – ɜɫɟ, ɱɬɨ ɧɚɦ ɧɟɨɛɯɨɞɢɦɨ, ɬɚɤ ɤɚɤ ɥɸɛɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɜɟɥɢɱɢɧɚ ɦɨɠɟɬ ɛɵɬɶ ɜɵɪɚɠɟɧɚ ɱɟɪɟɡ ɷɬɢ ɟɞɢɧɢɰɵ (ɬɚɛɥ. 2). Ɉɫɧɨɜɧɚɹ ɟɞɢɧɢɰɚ ɞɥɢɧɵ – ɦɟɬɪ. ɋɬɚɧɞɚɪɬ ɞɥɢɧɵ – ɷɬɨ ɞɥɢɧɚ ɜɨɥɧɵ ɠɟɥɬɨɣ ɥɢɧɢɢ ɜ ɫɩɟɤɬɪɟ ɢɡɥɭɱɟɧɢɹ ɢɡɨɬɨɩɚ ɤɪɢɩɬɨɧɚ. Ɍɚɛɥɢɰɚ 1 ɇɚɡɜɚɧɢɟ ɟɞɢɧɢɰɵ ɇɚɢɦɟɧɨɜɚɧɢɟ Ɉɛɨɡɧɚɱɟɧɢɟ Ⱦɥɢɧɚ ɦɟɬɪ ɦ Ɇɚɫɫɚ ɤɢɥɨɝɪɚɦɦ ɤɝ ȼɪɟɦɹ ɫɟɤɭɧɞɚ ɫ ɋɢɥɚ ɷɥɟɤɬɪ. ɬɨɤɚ ɚɦɩɟɪ Ⱥ Ɍɟɪɦɨɞɢɧɚɦɢɱɟɫɤɚɹ ɤɟɥɶɜɢɧ Ʉ ɬɟɦɩɟɪɚɬɭɪɚ Ʉɨɥɢɱɟɫɬɜɨ ɜɟɳɟɫɬɜɚ ɦɨɥɶ ɦɨɥɶ ɋɢɥɚ ɫɜɟɬɚ ɤɚɧɞɟɥɚ Ʉɞ Ⱦɨɩɨɥɧɢɬɟɥɶɧɵɟ ɟɞɢɧɢɰɵ ɫɢɫɬɟɦɵ ɋɂ ɉɥɨɫɤɢɣ ɭɝɨɥ ɪɚɞɢɚɧ Ɋɚɞ Ɍɟɥɟɫɧɵɣ ɭɝɨɥ ɫɬɟɪɚɞɢɚɧ ɋɪ Ɉɫɧɨɜɧɨɣ ɟɞɢɧɢɰɟɣ ɜɪɟɦɟɧɢ ɫɥɭɠɢɬ ɫɟɤɭɧɞɚ. ɉɟɪɢɨɞ ɤɨɥɟɛɚɧɢɹ ɚɬɨɦɨɜ ɰɟɡɢɹ ɩɪɢɧɹɬ ɡɚ ɫɬɚɧɞɚɪɬ ɜɪɟɦɟɧɢ. Ɉɫɧɨɜɧɚɹ ɟɞɢɧɢɰɚ ɦɚɫɫɵ – ɤɢɥɨɝɪɚɦɦ. ɉɨɤɚ ɟɳɟ ɧɟɬ ɜɵɫɨɤɨɬɨɱɧɨɝɨ ɫɬɚɧɞɚɪɬɚ ɦɚɫɫɵ ɜ ɚɬɨɦɧɵɯ ɬɟɪɦɢɧɚɯ, ɩɨɷɬɨɦɭ ɢɫɩɨɥɶɡɭɟɦɵɣ ɷɬɚɥɨɧ – ɷɬɨ ɨɩɪɟɞɟɥɟɧɧɵɣ ɛɪɭɫ ɦɟɬɚɥɥɚ, ɧɚɯɨɞɹɳɢɣɫɹ ɜ ɦɟɠɞɭɧɚɪɨɞɧɨɦ ɯɪɚɧɢɥɢɳɟ ɫɬɚɧɞɚɪɬɨɜ. ɇȿɄɈɌɈɊɕȿ ɎɂɁɂɑȿɋɄɂȿ ɉɈɋɌɈəɇɇɕȿ ɋɤɨɪɨɫɬɶ ɫɜɟɬɚ ɜ ɜɚɤɭɭɦɟ
c
2,999108 ɦ/ɫ
Ƚɪɚɜɢɬɚɰɢɨɧɧɚɹ ɩɨɫɬɨɹɧɧɚɹ
J
6,6710-11 ɇ ɦ2/ɤɝ2
NA
6,022 1023 ɦɨɥɶ-1
R
8,314 Ⱦɠ/(ɦɨɥɶ Ʉ)
ɑɢɫɥɨ Ⱥɜɨɝɚɞɪɨ ɍɧɢɜɟɪɫɚɥɶɧɚɹ ɩɨɫɬɨɹɧɧɚɹ
ɝɚɡɨɜɚɹ
5
Ɍɚɛɥɢɰɚ 2 ȼɵɪɚɠɟɧɢɟ ɱɟɪɟɡ ɨɫɧɨɜɧɵɟ ɢ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɟɞɢɧɢɰɵ
ɇɚɢɦɟɧɨɜɚɧɢɟ
ɇɚɡɜɚɧɢɟ ɟɞɢɧɢɰɵ
ɋɨɤɪɚɳɟɧɧɨɟ ɨɛɨɡɧɚɱɟɧɢɟ
ɋɢɥɚ
ɇɶɸɬɨɧ
ɇ
ɇ = ɤɝ ɦ ɫ-2
Ⱦɚɜɥɟɧɢɟ, ɦɟɯɚɧɢɱɟɫɤɨɟ ɧɚɩɪɹɠɟɧɢɟ, ɦɨɞɭɥɶ ɭɩɪɭɝɨɫɬɢ
ɉɚɫɤɚɥɶ
ɉɚ
ɉɚ = ɇ/ɦ2 = ɦ-1 · ɤɝ ɫ-2
ɗɧɟɪɝɢɹ, ɪɚɛɨɬɚ, ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ
Ⱦɠɨɭɥɶ
Ⱦɠ
Ⱦɠ = ɇ ɦ = = ɦ2 ɤɝ ɫ2
Ɇɨɳɧɨɫɬɶ Ɇɨɦɟɧɬ ɫɢɥɵ
ȼɚɬɬ ɇɶɸɬɨɧ-ɦɟɬɪ
ȼɬ ɇɦ
ȼɬ = Ⱦɠ/ɫ = = ɦ2 ɤɝ ɫ-3 ɇ ɦ = ɦ2 ɤɝ ɫ-2
ɂɦɩɭɥɶɫ (ɤɨɥɢɱɟɫɬɜɨ ɞɜɢɠɟɧɢɹ)
Ʉɢɥɨɝɪɚɦɦɦɟɬɪ ɜ ɫɟɤɭɧɞɭ
ɦ ɤɝ ɫ-1
ɂɦɩɭɥɶɫ ɫɢɥɵ ɑɚɫɬɨɬɚ
ɇɶɸɬɨɧɫɟɤɭɧɞɚ Ƚɟɪɰ
ɇ ɫ = ɦ ɤɝ ɫ-1 Ƚɰ = ɫ-1
Ɍɟɩɥɨɟɦɤɨɫɬɶ
Ⱦɠɨɭɥɶ ɧɚ ɤɟɥɶɜɢɧ
Ƚɰ Ⱦɠ/Ʉ
Ⱦɠ/Ʉ = ɦ2 ɤɝ ɫ-2 Ʉ-1
ɉɊɂɋɌȺȼɄɂ Ʉ ɈȻɈɁɇȺɑȿɇɂəɆ ȿȾɂɇɂɐ ɉɪɢɫɬɚɜɤɚ
Ɉɛɨɡɧɚɱɟɧɢɟ
Ɇɧɨɠɢɬɟɥɶ
Ɇɟɝɚ
Ɇ
106
Ʉɢɥɨ
ɤ
103
Ⱦɟɰɢ
ɞ
10-1
ɋɚɧɬɢ
ɫ
10-2
Ɇɢɥɥɢ
ɦ
10-3
Ɇɢɤɪɨ
ɦɤ
10-6
ɉɢɤɨ
ɩ
10-12
6
ɉɊɂɆȿɊɕ Ɋȿɒȿɇɂə ɁȺȾȺɑ Ɂɚɞɚɱɚ 1. Ɍɨɱɤɚ ɜɪɚɳɚɟɬɫɹ ɜɨɤɪɭɝ ɧɟɩɨɞɜɢɠɧɨɣ ɨɫɢ ɩɨ ɡɚɤɨɧɭ, ɜɵɪɚɠɚɟɦɨɦɭ ɮɨɪɦɭɥɨɣ M = Ⱥ + ȼt – ɋt2 , ɝɞɟ M – ɭɝɨɥ ɩɨɜɨɪɨɬɚ, t – ɜɪɟɦɹ ɜɪɚɳɟɧɢɹ, Ⱥ = 10, ȼ = 20 ɫ-1, ɋ = 2 ɫ-2. ɇɚɣɬɢ ɜɟɥɢɱɢɧɭ ɢ ɧɚɩɪɚɜɥɟɧɢɟ ɩɨɥɧɨɝɨ ɭɫɤɨɪɟɧɢɹ ɬɨɱɤɢ, ɧɚɯɨɞɹɳɟɣɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ 0,1 ɦ ɨɬ ɨɫɢ ɜɪɚɳɟɧɢɹ ɞɥɹ ɦɨɦɟɧɬɚ ɜɪɟɦɟɧɢ t = 4 ɫ. Ⱦɚɧɨ: 2 M = Ⱥ + ȼt – Ct , Ⱥ = 10, ȼ = 20 ɫ-1, ɋ = 2 ɫ-2, t = 4 ɫ, r = 0,1 ɦ. a = ?, D = ?, J = ? Ɋɟɲɟɧɢɟ. ɉɨɥɧɨɟ ɭɫɤɨɪɟɧɢɟ ɬɨɱɤɢ, ɞɜɢɠɭɳɟɣɫɹ ɩɨ ɤɪɢɜɨɣ ɥɢɧɢɢ, ɹɜɥɹɟɬɫɹ ɜɟɤɬɨɪɧɨɣ ɫɭɦɦɨɣ ɬɚɧɝɟɧɰɢɚɥɶɧɨɝɨ a t ɢ ɧɨɪɦɚɥɶɧɨɝɨ a n ɭɫɤɨɪɟɧɢɣ: G G G a a t a n .Ɍɚɧɝɟɧɰɢɚɥɶɧɨɟ ɭɫɤɨɪɟɧɢɟ ɧɚɩɪɚɜɥɟɧɨ ɩɨ ɤɚɫɚɬɟɥɶɧɨɣ ɤ ɬɪɚɟɤɬɨɪɢɢ ɞɜɢɠɟɧɢɹ, ɧɨɪɦɚɥɶɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɤ ɰɟɧɬɪɭ ɤɪɢɜɢɡɧɵ ɬɪɚɟɤɬɨɪɢɢ. ɋɨɝɥɚɫɧɨ ɪɢɫ. 1 a a t2 a n2 , (1) a t ɢ a n ɫɜɹɡɚɧɵ ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ ɢ ɭɫɤɨɪɟɧɢɟɦ ɫɥɟɞɭɸɳɢɦɢ ɫɨɨɬɧɨɲɟɧɢɹɦɢ: at E r , (2) (3) an Z 2 r , ɝɞɟ E – ɭɝɥɨɜɨɟ ɭɫɤɨɪɟɧɢɟ ɜɪɚɳɚɸɳɟɣɫɹ ɬɨɱɤɢ, Z – ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɪɚɳɚɸɳɟɣɫɹ ɬɨɱɤɢ, r – ɪɚɫɫɬɨɹɧɢɟ ɬɨɱɤɢ ɨɬ ɨɫɢ ɜɪɚɳɟɧɢɹ. Ɉɩɪɟɞɟɥɢɦ Z ɢ E. ɍɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ Z ɪɚɜɧɚ ɩɟɪɜɨɣ ɩɪɨɢɡɜɨɞɧɨɣ ɨɬ ɭɝɥɚ ɩɨɜɨɪɨɬɚ ɩɨ ɜɪɟɦɟɧɢ d ( Ⱥ ȼt ɋt 2 ) dt
dM dt
Z
ȼ 2 ɋ t.
(4)
ȼ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t = 4 c ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ -1 Z 20 ɫ 1 – 2 2 ɫ 2 4 ɫ = 4 ɫ . ɍɝɥɨɜɨɟ ɭɫɤɨɪɟɧɢɟ ɜɪɚɳɚɸɳɟɝɨɫɹ ɬɟɥɚ ɪɚɜɧɨ ɩɟɪɜɨɣ ɩɪɨɢɡɜɨɞɧɨɣ ɨɬ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɢ Z ɩɨ ɜɪɟɦɟɧɢ: E
dZ dt
d ( ȼ 2ɋt ) 2C , dt -2 -2 E = –2 2 c = –4 c .
ȼɵɱɢɫɥɢɦ ɬɟɩɟɪɶ ɩɨ ɮɨɪɦɭɥɚɦ (2) ɢ (3) a t ɢ a n : 7
(5)
2
4 0,1 0,4 ɦ/c ; ɚ n = 42 0,1 = 1,6 ɦ/c 2 .
at
ɉɨɞɫɬɚɜɢɜ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɚ t ɢ ɚ n ɜ ɮɨɪɦɭɥɭ (1), ɨɩɪɟɞɟɥɹɸɳɭɸ ɦɨɞɭɥɶ ɩɨɥɧɨɝɨ ɭɫɤɨɪɟɧɢɹ, ɢ ɜɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ ɮɨɪɦɭɥɚɦɢ (2) ɢ (3), ɩɨɥɭɱɢɦ: (6) ɚ r E 2 Z4 , a
0,1 ( 4) 2 4 4 ɦ/c 2 = 1,65 ɦ/c 2 .
ɇɚɩɪɚɜɥɟɧɢɟ ɩɨɥɧɨɝɨ ɭɫɤɨɪɟɧɢɹ ɨɩɪɟɞɟɥɢɦ, ɟɫɥɢ ɧɚɣɞɟɦ ɭɝɥɵ, ɤɨɬɨɪɵɟ ɜɟɤɬɨɪ ɭɫɤɨɪɟɧɢɹ, ɨɛɪɚɡɭɟɬ ɫ ɤɚɫɚɬɟɥɶɧɨɣ ɤ ɬɪɚɟɤɬɨɪɢɢ ɢɥɢ ɧɨɪɦɚɥɶɸ ɤ ɧɟɣ (ɫɦ. ɪɢɫ. 1): cos D =
ɚt , ɚ
cos J =
an , a
ɝɞɟ cos D = 0,4 /1,65 = 0,242, cos J = 1,6/1,65 = 0,97. ɉɨ ɬɪɢɝɨɧɨɦɟɬɪɢɱɟɫɤɢɦ ɬɚɛɥɢɰɚɦ ɧɚɯɨɞɢɦ D = 76º, J = 14º. Ɉɬɜɟɬ: a = 1,65 ɦ/ɫ 2 ; D = 76º; J = 14º. Ɂɚɞɚɱɚ 2. ɉɭɥɹ ɦɚɫɫɨɣ m = 0,01 ɤɝ, ɥɟɬɹɳɚɹ ɫɨ ɫɤɨɪɨɫɬɶɸ V = 800 ɦ/ɫ, ɩɨɩɚɞɚɟɬ ɜ ɞɟɪɟɜɨ ɢ ɭɝɥɭɛɥɹɟɬɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɟ s = 0,1 ɦ. ɇɚɣɬɢ ɫɢɥɭ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɟɪɟɜɚ ɢ ɜɪɟɦɹ ɞɜɢɠɟɧɢɹ ɩɭɥɢ ɜ ɞɟɪɟɜɟ, ɫɱɢɬɚɹ ɞɜɢɠɟɧɢɟ ɪɚɜɧɨɡɚɦɟɞɥɟɧɧɵɦ ɢ ɫɢɥɭ ɬɪɟɧɢɹ ɩɨɫɬɨɹɧɧɨɣ. ɉɟɪɜɵɣ ɜɚɪɢɚɧɬ ɪɟɲɟɧɢɹ. Ʉɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɩɭɥɢ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɩɪɟɨɞɨɥɟɧɢɟ ɫɢɥɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɞɟɪɟɜɚ F, ɬ. ɟ. ɩɨ ɡɚɤɨɧɭ ɫɨɯɪɚɧɟɧɢɹ ɷɧɟɪɝɢɢ ɢɦɟɟɦ mV 2 = F s, 2 mV 2 F= . 2s
ɨɬɤɭɞɚ
(1)
Ɉɩɪɟɞɟɥɢɬɶ ɜɪɟɦɹ ɞɜɢɠɟɧɢɹ ɩɭɥɢ ɜ ɞɟɪɟɜɟ ɦɨɠɧɨ ɩɨ ɮɨɪɦɭɥɟ ɩɭɬɢ ɪɚɜɧɨɡɚɦɟɞɥɟɧɧɨɝɨ ɞɜɢɠɟɧɢɹ: s=
at 2 , 2
ɝɞɟ ɭɫɤɨɪɟɧɢɟ a
Vn Vk t
Vn , t
ɚ V n , V k – ɧɚɱɚɥɶɧɵɟ ɢ ɤɨɧɟɱɧɵɟ ɫɤɨɪɨɫɬɢ ɞɜɢɠɟɧɢɹ ɩɭɥɢ, V k ɩɨ ɭɫɥɨɜɢɸ ɪɚɜɧɚ 0, ɬɨɝɞɚ V 2 t s t 2 2s . t V
ɨɬɤɭɞɚ
V t , 2
(2)
Ɉɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɚɟɦ F=
0,01 800 20,1
32 10 3 (ɇ),
8
t
2 0,1 800
25 10 5 ɫ.
ȼɬɨɪɨɣ ɜɚɪɢɚɧɬ ɪɟɲɟɧɢɹ. ɂɡɦɟɧɟɧɢɟ ɢɦɩɭɥɶɫɚ ɩɭɥɢ ɪɚɜɧɨ ɢɦɩɭɥɶɫɭ ɫɢɥɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ G 'p F 't . Ⱦɥɹ ɡɚɩɢɫɢ ɷɬɨɝɨ ɪɚɜɟɧɫɬɜɚ ɜ ɫɤɚɥɹɪɧɨɣ ɮɨɪɦɟ ɜɨɡɶɦɟɦ ɤɨɨɪɞɢɧɚɬɧɭɸ ɨɫɶ, ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɤɨɬɨɪɨɣ ɫɨɜɩɚɞɚɟɬ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɫɢɥɵ F. Ɍɨɝɞɚ ɷɬɨ ɠɟ ɭɪɚɜɧɟɧɢɟ ɡɚɩɢɲɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: 0 – ( – mv) = F ' t, ɢɥɢ m v = F ' t, ɨɬɤɭɞɚ F = mv/ ' t. Ɉɩɪɟɞɟɥɢɜ ɩɨ ɮɨɪɦɭɥɟ (2) ɜɪɟɦɹ t ɢ ɩɨɞɫɬɚɜɢɜ (3), ɩɨɥɭɱɢɦ: F=
mV 2S / V
(3)
mV 2 , 2S
ɬ. ɟ. ɩɨɥɭɱɢɥɢ ɮɨɪɦɭɥɭ (1). Ɂɚɞɚɱɚ 3. ɋɬɚɥɶɧɨɣ ɲɚɪɢɤ ɦɚɫɫɨɣ m = 0,02 ɤɝ, ɩɚɞɚɹ ɜɟɪɬɢɤɚɥɶɧɨ ɫ ɜɵɫɨɬɵ h 1 = 1 ɦ ɧɚ ɫɬɚɥɶɧɭɸ ɩɥɢɬɭ, ɨɬɫɤɚɤɢɜɚɟɬ ɨɬ ɧɟɟ ɧɚ ɜɵɫɨɬɭ h 2 = 0,81 ɦ. ɇɚɣɬɢ: 1) ɢɦɩɭɥɶɫ ɫɢɥɵ, ɩɨɥɭɱɟɧɧɵɣ ɩɥɢɬɨɣ ɡɚ ɜɪɟɦɹ ɭɞɚɪɚ, 2) ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɚ, ɜɵɞɟɥɢɜɲɟɝɨɫɹ ɩɪɢ ɭɞɚɪɟ. Ɋɟɲɟɧɢɟ. ɂɦɩɭɥɶɫ ɫɢɥɵ, ɩɨɥɭɱɟɧɧɵɣ ɲɚɪɢɤɨɦ ɨɬ ɩɥɢɬɵ, ɨɩɪɟɞɟɥɢɬɫɹ ɢɡ ɜɬɨɪɨɝɨ ɡɚɤɨɧɚ ɇɶɸɬɨɧɚ: G G Fɲ
G ma
'V , 't
ɢɥɢ
G Fɲ 't
'(mV ) , (1) G ɝɞɟ Fɲ 't – ɢɦɩɭɥɶɫ ɫɢɥɵ F, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɲɚɪɢɤ ɜ ɬɟɱɟɧɢɟ ɜɪɟɦɟɧɢ 't . m
Ɉɛɨɡɧɚɱɢɦ ɱɟɪɟɡ V1 ɢ V 2 ɫɤɨɪɨɫɬɢ ɲɚɪɢɤɚ ɜ ɦɨɦɟɧɬɵ ɧɟɩɨɫɪɟɞɫɬɜɟɧɧɨ ɞɨ ɢ ɩɨɫɥɟ ɫɨɭɞɚɪɟɧɢɹ ɫ ɩɥɢɬɨɣ. ɉɟɪɟɣɞɟɦ ɤ ɫɤɚɥɹɪɧɨɣ ɡɚɩɢɫɢ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ. ɇɚ ɪɢɫ. 3 ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ G ɤɨɨɪɞɢɧɚɬɧɨɣ ɨɫɢ h ɫɨɜɩɚɞɚɟɬ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɜɟɤɬɨɪɚ V2 , ɬɨɝɞɚ ɩɪɨɟɤɰɢɹ G G ɜɟɤɬɨɪɚ V2 ɧɚ ɨɫɶ h ɟɫɬɶ V 2 , ɚ ɩɪɨɟɤɰɢɹ ɜɟɤɬɨɪɚ V1 ɟɫɬɶ (– V1 ); ɡɚɩɢɲɟɦ ɬɟɩɟɪɶ ɪɚɜɟɧɫɬɜɨ (1) ɜ ɫɤɚɥɹɪɧɨɣ ɮɨɪɦɟ: Fɲ 't
m 'V
m[V2 (V1 )] m(V2 V1 ), G G ɝɞɟ V1 ɢ V 2 – ɦɨɞɭɥɢ ɫɤɨɪɨɫɬɟɣ V1 ɢ V2 . ɉɨɫɤɨɥɶɤɭ ɢɦɩɭɥɶɫ Fɲ 't ɩɨɥɭɱɢɥɫɹ ɜɟɥɢɱɢɧɨɣ ɩɨɥɨɠɢɬɟɥɶɧɨɣ, ɨɧ
ɧɚ ɪɢɫ. 3 ɧɚɩɪɚɜɥɟɧ ɜɜɟɪɯ. ɉɨ ɬɪɟɬɶɟɦɭ ɡɚɤɨɧɭ ɇɶɸɬɨɧɚ ɫɢɥɚ F, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɩɥɢɬɭ ɫɨ ɫɬɨɪɨɧɵ ɲɚɪɢɤɚ, ɩɨ ɦɨɞɭɥɸ ɪɚɜɧɚ Fɲ , ɧɨ ɧɚɩɪɚɜɥɟɧɚ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɭɸ ɫɬɨɪɨɧɭ. ɉɨɷɬɨɦɭ ɢɦɩɭɥɶɫ ɫɢɥɵ, ɩɨɥɭɱɟɧɧɵɣ ɩɥɢɬɨɣ, ɧɚɩɪɚɜɥɟɧ ɜɧɢɡ. Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɟɝɨ ɦɨɞɭɥɹ ɧɚɣɞɟɦ V1 ɢ V 2 . Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ V1 ɢɫɩɨɥɶɡɭɟɦ ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɷɧɟɪɝɢɢ. Ɍɚɤ ɤɚɤ ɧɚɱɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɩɪɢ ɩɚɞɟɧɢɢ ɲɚɪɢɤɚ ɫ ɜɵɫɨɬɵ h ɪɚɜɧɚ ɧɭɥɸ, ɢɦɟɟɦ 9
mV12 /2, ɨɬɤɭɞɚ V1
2gh1 . Ⱥɧɚɥɨɝɢɱɧɨ ɨɩɪɟɞɟɥɢɦ V 2 , ɭɱɢɬɵɜɚɹ, ɱɬɨ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɲɚɪɢɤɚ ( mV22 )/2, ɤɨɬɨɪɨɣ ɨɧ ɨɛɥɚɞɚɟɬ ɜ ɦɨɦɟɧɬ ɫɪɚɡɭ ɩɨɫɥɟ ɫɨɭɞɚɪɟɧɢɹ, ɩɟɪɟɯɨɞɢɬ ɜ ɩɨɬɟɧɰɢɚɥɶɧɭɸ ɷɧɟɪɝɢɸ ɩɨɞɴɟɦɚ ɧɚ ɜɵɫɨɬɭ h 2 : mV22 / 2 mgh2 , ɨɬɤɭɞɚ V 2 2gh 2 . Ɍɨɝɞɚ F ' t = 0,02 ɤɝ ( 2 9,8 1 2 9,8 0,81 ) ɦ/ɫ = 0,168 ɇ · ɫ.
mgh1
Ɉɩɪɟɞɟɥɢɦ ɬɟɩɟɪɶ ɤɨɥɢɱɟɫɬɜɨ ɜɵɞɟɥɢɜɲɟɝɨɫɹ ɩɪɢ ɭɞɚɪɟ ɬɟɩɥɚ. ɋɨɝɥɚɫɧɨ ɡɚɤɨɧɭ ɫɨɯɪɚɧɟɧɢɹ ɷɧɟɪɝɢɢ ɢɡɦɟɧɟɧɢɟ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɪɚɜɧɨ ɤɨɥɢɱɟɫɬɜɭ ɜɵɞɟɥɢɜɲɟɝɨɫɹ ɬɟɩɥɚ. ɋ ɭɱɟɬɨɦ ɬɨɝɨ, ɱɬɨ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ ɲɚɪɢɤɚ ɧɚ ɜɵɫɨɬɟ h1 ȿ n1 mgh1 , ɚ ɧɚ ɜɵɫɨɬɟ h 2 ȿ n 2 mgh2 , ɩɨɥɭɱɢɦ ȿ = ȿ n1 – ȿ n 2 = Q; Q = mg( h1 h2 ). ɂ ɨɤɨɧɱɚɬɟɥɶɧɨ ɩɨɥɭɱɚɟɦ: Q = 0,02 ɤɝ 9,8 ɦ/ɫ (1 – 0,81) ɦ = 3,710 2 Ⱦɠ. Ɂɚɞɚɱɚ 4. ɋ ɤɚɤɨɣ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ ɧɚɞɨ ɛɪɨɫɢɬɶ ɦɹɱ ɫ ɜɵɫɨɬɵ h, ɱɬɨɛɵ ɨɧ ɩɨɞɩɪɵɝɧɭɥ ɧɚ ɜɵɫɨɬɭ 2h? ɍɞɚɪ ɭɩɪɭɝɢɣ, ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɡɞɭɯɚ ɨɬɫɭɬɫɬɜɭɟɬ. Ɋɟɲɟɧɢɟ. Ɍɚɤ ɤɚɤ ɦɹɱ, ɧɚɯɨɞɹɳɢɣɫɹ ɧɚ ɜɵɫɨɬɟ h, ɛɪɨɫɚɸɬ ɫ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ, ɨɧ ɨɛɥɚɞɚɟɬ ɤɚɤ ɩɨɬɟɧɰɢɚɥɶɧɨɣ, ɬɚɤ ɢ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɟɣ, ɢ ɟɝɨ ɩɨɥɧɚɹ ɷɧɟɪɝɢɹ ɟɫɬɶ
mV 2 mgh . 2
ɉɨɫɥɟ ɭɩɪɭɝɨɝɨ ɭɞɚɪɚ ɨɛ ɩɨɥ ɦɹɱ, ɫɨɝɥɚɫɧɨ ɭɫɥɨɜɢɸ ɡɚɞɚɱɢ, ɩɨɞɧɹɥɫɹ ɧɚ ɜɵɫɨɬɭ 2h, ɢ ɟɝɨ ɩɨɥɧɚɹ ɷɧɟɪɝɢɹ ɫɨɜɩɚɞɚɟɬ ɫ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɟɣ mg 2h. ɋɨɝɥɚɫɧɨ ɡɚɤɨɧɭ ɫɨɯɪɚɧɟɧɢɹ ɷɧɟɪɝɢɢ mV 2 mgh 2
ɨɬɤɭɞɚ V
2mgh ,
2 gh .
Ɂɚɞɚɱɚ 5. Ⱦɢɫɤ ɪɚɞɢɭɫɨɦ R = 1,5 ɦ ɢ ɦɚɫɫɨɣ m 1 = 180 ɤɝ ɜɪɚɳɚɟɬɫɹ ɩɨ ɢɧɟɪɰɢɢ ɜɨɤɪɭɝ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɢ, ɞɟɥɚɹ n = 10 ɨɛ/ɦɢɧ. ȼ ɰɟɧɬɪɟ ɞɢɫɤɚ ɫɬɨɢɬ ɱɟɥɨɜɟɤ ɦɚɫɫɨɣ m 2 = 60 ɤɝ. Ʉɚɤɭɸ ɥɢɧɟɣɧɭɸ ɫɤɨɪɨɫɬɶ ɨɬɧɨɫɢɬɟɥɶɧɨ ɩɨɥɚ ɛɭɞɟɬ ɢɦɟɬɶ ɱɟɥɨɜɟɤ, ɟɫɥɢ ɨɧ ɩɟɪɟɣɞɟɬ ɧɚ ɤɪɚɣ ɞɢɫɤɚ? Ɋɟɲɟɧɢɟ. Ⱦɥɹ ɫɢɫɬɟɦɵ ɱɟɥɨɜɟɤ-ɞɢɫɤ ɛɭɞɟɬ ɜɵɩɨɥɧɹɬɶɫɹ ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɢɦɩɭɥɶɫɚ: (I 1 + I 2 ) Z = (I 1 + I' 2 ) Z ', (1) ɝɞɟ I 1 – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɞɢɫɤɚ, I 2 – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɱɟɥɨɜɟɤɚ, ɫɬɨɹɳɟɝɨ ɜ ɰɟɧɬɪɟ ɞɢɫɤɚ, Z – ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɞɢɫɤɚ ɫ ɱɟɥɨɜɟɤɨɦ, ɫɬɨɹɳɢɦ ɜ ɟɟ ɰɟɧɬɪɟ, I' 2 – ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɱɟɥɨɜɟɤɚ, ɫɬɨɹɳɟɝɨ ɧɚ ɤɪɚɸ ɞɢɫɤɚ, Z ' – ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɞɢɫɤɚ ɫ ɱɟɥɨɜɟɤɨɦ, ɫɬɨɹɳɢɦ ɧɚ ɤɪɚɸ. ȼɟɥɢɱɢɧɚ ɥɢɧɟɣɧɨɣ ɫɤɨɪɨɫɬɢ ɱɟɥɨɜɟɤɚ, ɫɬɨɹɳɟɝɨ ɧɚ ɤɪɚɸ ɞɢɫɤɚ, ɫɜɹɡɚɧɚ ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ Z ɫɨɨɬɧɨɲɟɧɢɟɦ V = Z ' · R. 10
ɂɫɩɨɥɶɡɭɹ ɫɤɨɪɨɫɬɢ
(1), ɩɨɥɭɱɢɦ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɜɟɥɢɱɢɧɵ ɥɢɧɟɣɧɨɣ
(2) V = (I 1 + I 2 ) Z .R/(I 1 + I' 2 ). Ɇɨɦɟɧɬ ɢɧɟɪɰɢɢ ɞɢɫɤɚ ɨɩɪɟɞɟɥɢɦ ɩɨ ɮɨɪɦɭɥɟ I 1 = (1/2)m 1 R2, ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɱɟɥɨɜɟɤɚ ɪɚɫɫɱɢɬɚɟɦ ɩɨ ɮɨɪɦɭɥɟ, ɨɩɪɟɞɟɥɹɸɳɟɣ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ ɦɚɫɫɵ m 2 . ɉɨɷɬɨɦɭ ɞɥɹ ɦɨɦɟɧɬɚ ɢɧɟɪɰɢɢ ɱɟɥɨɜɟɤɚ, ɧɚɯɨɞɹɳɟɝɨɫɹ ɜ ɰɟɧɬɪɟ ɞɢɫɤɚ, I 2 = 0, ɚ ɞɥɹ ɦɨɦɟɧɬɚ ɢɧɟɪɰɢɢ ɱɟɥɨɜɟɤɚ ɧɚ ɤɪɚɸ ɞɢɫɤɚ – I' 2 = m 2 R2. ɍɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɞɢɫɤɚ ɞɨ ɩɟɪɟɯɨɞɚ ɱɟɥɨɜɟɤɚ Z = 2 S n. Ɂɚɦɟɧɢɜ ɜ ɮɨɪɦɭɥɟ (2) ɜɟɥɢɱɢɧɵ I 1 , I 2 , I' 2 ɢ Z ɢɯ ɜɵɪɚɠɟɧɢɹɦɢ, ɩɨɥɭɱɢɦ V=
1 m1 R 2 2 1 m1 R 2 m 2 R 2 2
ɢɥɢ
2SnR
V=
m1 2S nR. m1 2m2
ɉɨɞɫɬɚɜɥɹɹ ɱɢɫɥɟɧɧɵɟ ɡɧɚɱɟɧɢɹ, ɩɨɥɭɱɢɦ: V=
180 ɤɝ 1 ɦ 2 3,14 1,5 = 1,18 ɦ/c. 180 2 60 ɤɝ 6 ɫ
Ɂɚɞɚɱɚ 6. ɋɤɨɥɶɤɨ ɦɨɥɟɤɭɥ ɫɨɞɟɪɠɢɬɫɹ ɜ 1 ɦ3 ɜɨɞɵ? Ʉɚɤɨɜɚ ɦɚɫɫɚ ɦɨɥɟɤɭɥɵ ɜɨɞɵ? ɋɱɢɬɚɹ, ɱɬɨ ɦɨɥɟɤɭɥɵ ɢɦɟɸɬ ɜɢɞ ɲɚɪɢɤɨɜ, ɫɨɩɪɢɤɚɫɚɸɳɢɯɫɹ ɞɪɭɝ ɫ ɞɪɭɝɨɦ, ɧɚɣɬɢ ɞɢɚɦɟɬɪ ɦɨɥɟɤɭɥɵ. Ɋɟɲɟɧɢɟ. ɂɡɜɟɫɬɧɨ, ɱɬɨ ɱɢɫɥɨ ɦɨɥɟɤɭɥ ɜ ɨɞɧɨɦ ɦɨɥɟ ɥɸɛɨɝɨ ɜɟɳɟɫɬɜɚ (ɬɜɟɪɞɨɝɨ, ɠɢɞɤɨɝɨ ɢɥɢ ɝɚɡɨɨɛɪɚɡɧɨɝɨ) ɨɩɪɟɞɟɥɹɟɬɫɹ ɱɢɫɥɨɦ Ⱥɜɨɝɚɞɪɨ NA. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɱɢɫɥɨ ɦɨɥɟɣ n, ɫɨɞɟɪɠɚɳɢɯɫɹ ɜ ɦɚɫɫɟ m, ɨɩɪɟɞɟɥɢɬɫɹ ɫɨɨɬɧɨɲɟɧɢɟɦ n = (m / P )NA, ɝɞɟ P – ɦɚɫɫɚ ɨɞɧɨɝɨ ɦɨɥɹ. Ɍɚɤ ɤɚɤ m = U V, ɝɞɟ U – ɩɥɨɬɧɨɫɬɶ ɜɨɞɵ ɢ V – ɨɛɴɟɦ, ɡɚɧɢɦɚɟɦɵɣ ɜɨɞɨɣ, ɬɨ n = ( U V/ P ) NA. ɉɨɞɫɬɚɜɢɜ ɜ ɮɨɪɦɭɥɭ ɱɢɫɥɨɜɵɟ ɡɧɚɱɟɧɢɹ 3 3 3 26 -1 U = 10 ɤɝ/ɦ , V = 1 ɦ , NA = 6,02210 ɤɦɨɥɶ , P = 18 ɤɝ/ɤɦɨɥɶ, ɩɨɥɭɱɢɦ n = (103/18) 6,022 1026 = 3,34 1028 (ɦɨɥɟɤɭɥ). Ɇɚɫɫɚ ɨɞɧɨɣ ɦɨɥɟɤɭɥɵ m1 = P / NA: m1 = 18 ɤɝ/ɤɦɨɥɶ : 6,022 1026 ɤɦɨɥɶ-1 = 2,99 10-26 ɤɝ. ȿɫɥɢ ɦɨɥɟɤɭɥɵ ɜɨɞɵ ɩɨɥɧɨɫɬɶɸ ɩɪɢɥɟɝɚɸɬ ɞɪɭɝ ɤ ɞɪɭɝɭ, ɬɨ ɦɨɠɧɨ ɫɱɢɬɚɬɶ, ɱɬɨ ɧɚ ɤɚɠɞɭɸ ɦɨɥɟɤɭɥɭ ɩɪɢɯɨɞɢɬɫɹ ɨɛɴɟɦ V1 = d3, ɝɞɟ d – ɞɢɚɦɟɬɪ ɦɨɥɟɤɭɥɵ. Ɉɬɫɸɞɚ d = 3 V1 . Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɨɛɴɟɦɚ V1 ɪɚɡɞɟɥɢɦ ɦɨɥɹɪɧɵɣ ɨɛɴɟɦ V0 ɧɚ ɱɢɫɥɨ ɦɨɥɟɤɭɥ ɜ ɦɨɥɟ V1 = V0 / NA, ɬɨɝɞɚ d = 3 V0 / N A . ȼɯɨɞɹɳɢɣ ɜ ɷɬɭ ɮɨɪɦɭɥɭ ɦɨɥɹɪɧɵɣ ɨɛɴɟɦ V0 = P / U , ɬɨɝɞɚ ɢɫɤɨɦɵɣ ɞɢɚɦɟɬɪ ɦɨɥɟɤɭɥɵ: d = 3 P /( U N A ) , 11
18
d =
3
ɤɝ ɤɦɨɥɶ
ɤɝ 1 10 3 6, 022 1026 ɦ ɤɦɨɥɶ
3,111010 ɦ.
3
Ɂɚɞɚɱɚ 7. Ȼɚɥɥɨɧ ɫɨɞɟɪɠɢɬ m1 = 0,08 ɤɝ ɤɢɫɥɨɪɨɞɚ ɢ m2 = 0,3 ɤɝ ɚɪɝɨɧɚ. Ⱦɚɜɥɟɧɢɟ ɫɦɟɫɢ Ɋ = 1, 01 Ɇɉɚ, ɬɟɦɩɟɪɚɬɭɪɚ Ɍ = 288 Ʉ. ɋɱɢɬɚɹ ɝɚɡɵ ɢɞɟɚɥɶɧɵɦɢ, ɨɩɪɟɞɟɥɢɬɶ ɨɛɴɟɦ ɛɚɥɥɨɧɚ. (Ɇɚɫɫɚ ɨɞɧɨɝɨ ɦɨɥɹ ɤɢɫɥɨɪɨɞɚ P 1 = 32 ɤɝ/ɤɦɨɥɶ, ɚɪɝɨɧɚ P 2 = 40 ɤɝ/ɤɦɨɥɶ.) Ɋɟɲɟɧɢɟ. ɉɨ ɡɚɤɨɧɭ Ⱦɚɥɶɬɨɧɚ ɞɚɜɥɟɧɢɟ ɫɦɟɫɢ ɪɚɜɧɨ ɫɭɦɦɟ ɩɚɪɰɢɚɥɶɧɵɯ ɞɚɜɥɟɧɢɣ ɝɚɡɨɜ, ɜɯɨɞɹɳɢɯ ɜ ɫɨɫɬɚɜ ɫɦɟɫɢ. ɉɚɪɰɢɚɥɶɧɵɦ ɞɚɜɥɟɧɢɟɦ ɝɚɡɚ ɧɚɡɵɜɚɟɬɫɹ ɞɚɜɥɟɧɢɟ, ɤɨɬɨɪɨɟ ɩɪɨɢɡɜɨɞɢɥ ɛɵ ɷɬɨɬ ɝɚɡ, ɟɫɥɢ ɛɵ ɬɨɥɶɤɨ ɨɧ ɧɚɯɨɞɢɥɫɹ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɦ ɫɨɫɭɞɟ. ɉɨ ɭɪɚɜɧɟɧɢɸ Ɇɟɧɞɟɥɟɟɜɚ – Ʉɥɚɣɩɟɪɨɧɚ ɩɚɪɰɢɚɥɶɧɵɟ ɞɚɜɥɟɧɢɹ Ɋ1 ɢ Ɋ2 ɤɢɫɥɨɪɨɞɚ ɢ ɚɪɝɨɧɚ ɪɚɜɧɵ Ɋ1 =
m1 RT , P1 V
Ɋ2 =
m 2 RT . P2 V
ȼ ɪɟɡɭɥɶɬɚɬɟ ɫɭɦɦɚɪɧɨɟ ɞɚɜɥɟɧɢɟ Ɋ ɜɵɪɚɡɢɬɫɹ § m1 m 2 · ¸¸ , ¨¨ © P1 P 2 ¹ §m m · RT V = ¨¨ 1 2 ¸¸ , © P1 P 2 ¹ P 0, 08 0,3 · 8,31103 288 ɤɝ Ⱦɠ Ʉ ɦ 2 | 0, 0237 ɦ3 . V = §¨ ¸ 6 ɤɝ Ʉ ɦɨɥɶ ɇ 40 ¹ 1, 0110 © 32 ɤɦɨɥɶ
Ɋ = Ɋ1 + Ɋ 2 =
ɨɬɤɭɞɚ
RT V
Ɂɚɞɚɱɚ 8. Ɋɚɫɫɱɢɬɚɬɶ ɫɪɟɞɧɸɸ ɞɥɢɧɭ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɦɨɥɟɤɭɥ ɜɨɡɞɭɯɚ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ 290 Ʉ, ɞɚɜɥɟɧɢɢ Ɋ = 0,101 Ɇɉɚ. ɗɮɮɟɤɬɢɜɧɵɣ ɞɢɚɦɟɬɪ d ɦɨɥɟɤɭɥɵ ɜɨɡɞɭɯɚ ɩɪɢɧɹɬɶ ɪɚɜɧɵɦ 3 10-10 ɦ. Ɋɟɲɟɧɢɟ. ɋɪɟɞɧɹɹ ɞɥɢɧɚ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ: O = 1/ 2 Sd 2 n 0 , ɝɞɟ n0 – ɤɨɧɰɟɧɬɪɚɰɢɹ ɦɨɥɟɤɭɥ (ɱɢɫɥɨ ɦɨɥɟɤɭɥ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ). Ʉɨɧɰɟɧɬɪɚɰɢɹ ɦɨɥɟɤɭɥ ɨɩɪɟɞɟɥɢɬɫɹ ɩɨ ɮɨɪɦɭɥɟ n0 = Ɋ/(kɌ), ɝɞɟ k – ɩɨɫɬɨɹɧɧɚɹ Ȼɨɥɶɰɦɚɧɚ, ɪɚɜɧɚɹ 1,38 · 10-23 Ⱦɠ/Ʉ, Ɍ – ɚɛɫɨɥɸɬɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ. ȼ ɪɟɡɭɥɶɬɚɬɟ O =
kT
1 P 2 Sd kT 2
12
2 Sd 2 p
,
1,38 1023
O = 2 3,14 (3 10
Ⱦɠ 290 Ʉ Ʉ
10
ɇ )ɦ 1, 01 10 2 ɦ 2
0, 01105 ɦ .
5
Ɂɚɞɚɱɚ 9. ȼɵɱɢɫɥɢɬɶ ɞɥɹ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɣ ɢ ɞɥɹ ɬɟɦɩɟɪɚɬɭɪɵ 373 Ʉ ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɤɜɚɞɪɚɬɢɱɧɨɣ ɫɤɨɪɨɫɬɢ ɢ ɷɧɟɪɝɢɸ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɦɨɥɟɤɭɥ ɭɝɥɟɤɢɫɥɨɝɨ ɝɚɡɚ. ɇɚɣɬɢ ɫɪɟɞɧɸɸ ɞɥɢɧɭ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɦɨɥɟɤɭɥ ɩɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ, ɟɫɥɢ ɱɢɫɥɨ ɫɬɨɥɤɧɨɜɟɧɢɣ (Z0) ɤɚɠɞɨɣ ɦɨɥɟɤɭɥɵ ɫ ɞɪɭɝɢɦɢ ɜ ɫɪɟɞɧɟɦ ɡɚ 1 ɫ ɪɚɜɧɨ 9,12 109 ɫ-1. (Ⱦɥɹ ɭɝɥɟɤɢɫɥɨɝɨ ɝɚɡɚ P = 44 ɤɝ/ɤɦɨɥɶ, U 0 = 1,98 ɤɝ/ɦ3.) Ɋɟɲɟɧɢɟ. ɋɪɟɞɧɹɹ ɤɜɚɞɪɚɬɢɱɧɚɹ ɫɤɨɪɨɫɬɶ ɦɨɥɟɤɭɥ ɝɚɡɚ ɩɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɨɩɪɟɞɟɥɢɬɫɹ ɩɨ ɮɨɪɦɭɥɟ 2
U0 = V = 3Ɋ0 / U 0, ɡɞɟɫɶ Ɋ0 – ɧɨɪɦɚɥɶɧɨɟ ɚɬɦɨɫɮɟɪɧɨɟ ɞɚɜɥɟɧɢɟ, ɪɚɜɧɨɟ 760 ɦɦ ɪɬ. ɫɬ. = 760 · 133 ɉɚ = 1,01105 ɉɚ, U 0 – ɩɥɨɬɧɨɫɬɶ ɝɚɡɚ ɩɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ (ɧɨɪɦɚɥɶɧɨɦ ɚɬɦɨɫɮɟɪɧɨɦ ɞɚɜɥɟɧɢɢ ɢ t = 0 ºɋ = 273 Ʉ). ɋɪɟɞɧɹɹ ɤɜɚɞɪɚɬɢɱɧɚɹ ɫɤɨɪɨɫɬɶ ɩɪɢ ɡɚɞɚɧɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ Ɍ: 2
3RT / P . U= V ɋɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɷɧɟɪɝɢɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɦɨɥɟɤɭɥ
ȿ=
3 kT , 2
ɝɞɟ k – ɩɨɫɬɨɹɧɧɚɹ Ȼɨɥɶɰɦɚɧɚ. ȼ ɧɚɲɟɦ ɫɥɭɱɚɟ ɧɭɠɧɨ ɜɵɱɢɫɥɢɬɶ ȿ0 – ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɷɧɟɪɝɢɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɦɨɥɟɤɭɥ ɭɝɥɟɤɢɫɥɨɝɨ ɝɚɡɚ ɞɥɹ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɣ ɢ ȿ – ɫɪɟɞɧɟɟ ɡɧɚɱɟɧɢɟ ɷɧɟɪɝɢɢ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɦɨɥɟɤɭɥ ɭɝɥɟɤɢɫɥɨɝɨ ɝɚɡɚ ɞɥɹ Ɍ = 373 Ʉ. ɋɪɟɞɧɹɹ ɞɥɢɧɚ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɦɨɥɟɤɭɥ ɩɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ O 0 = V/Z0, ɝɞɟ V – cɪɟɞɧɹɹ ɚɪɢɮɦɟɬɢɱɟɫɤɚɹ ɫɤɨɪɨɫɬɶ ɦɨɥɟɤɭɥ ɝɚɡɚ: V=
8RT
SP
| 0,92 U,
U=
U0 =
3 1, 01105 ɇ / ɦ 2 1,98 ɤɝ / ɦ3
3 8,31 103 373 Ⱦɠ Ʉ / Ʉ ɤɦɨɥɶ 44 ɤɝ/ɤɦɨɥɶ
460 ɦ/ɫ.
ȼɵɱɢɫɥɢɦ ȿ0, ȿ, O 0: 3 1,38 1023 Ⱦɠ / Ʉ 373 Ʉ 7, 72 1021 Ⱦɠ, 2 3 1,38 1023 ȿ0 = Ⱦɠ / Ʉ 273 Ʉ 5, 65 1021 Ⱦɠ, 2
ȿ=
13
392 ɦ/ɫ,
O0 =
0,92 392 ɦ / ɫ 1 9,12 109 ɫ 1
4, 0 108 ɦ.
Ɂɚɞɚɱɚ 10. ɇɚɣɬɢ ɫɪɟɞɧɸɸ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɢ ɩɨɥɧɭɸ ɫɪɟɞɧɸɸ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɦɨɥɟɤɭɥ ɝɟɥɢɹ ɢ ɚɡɨɬɚ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ Ɍ = 300 Ʉ, ɚ ɬɚɤɠɟ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɜɫɟɯ ɦɨɥɟɤɭɥ, ɫɨɞɟɪɠɚɳɢɯɫɹ ɜ m = 0,004 ɤɝ ɚɡɨɬɚ. Ɋɟɲɟɧɢɟ. ɇɚ ɤɚɠɞɭɸ ɫɬɟɩɟɧɶ ɫɜɨɛɨɞɵ ɦɨɥɟɤɭɥɵ ɝɚɡɚ ɩɪɢɯɨɞɢɬɫɹ ɨɞɢɧɚɤɨɜɚɹ ɷɧɟɪɝɢɹ, ɜɵɪɚɠɚɟɦɚɹ ɮɨɪɦɭɥɨɣ W=
1 kT, 2
ɝɞɟ k – ɩɨɫɬɨɹɧɧɚɹ Ȼɨɥɶɰɦɚɧɚ, T – ɚɛɫɨɥɸɬɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ. ɉɨɥɧɚɹ ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɦɨɥɟɤɭɥ ɡɚɜɢɫɢɬ ɧɟ ɬɨɥɶɤɨ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ, ɧɨ ɢ ɨɬ ɫɬɪɭɤɬɭɪɵ ɦɨɥɟɤɭɥɵ – ɨɬ ɱɢɫɥɚ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ. Ƚɟɥɢɣ – ɨɞɧɨɚɬɨɦɧɵɣ ɝɚɡ, ɱɢɫɥɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɫ ɭɱɟɬɨɦ ɬɨɥɶɤɨ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ i = 3, ɩɨɷɬɨɦɭ ɩɨɥɧɚɹ ɫɪɟɞɧɹɹ ɷɧɟɪɝɢɹ ɦɨɥɟɤɭɥɵ ɝɟɥɢɹ ɪɚɜɧɚ ɷɧɟɪɝɢɢ ɟɝɨ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ, ɬ. ɟ. W= WHe =
i 3 kT = kT, 2 2
3 1,38 1023 Ⱦɠ/Ʉ 300 Ʉ 2
6, 21 1021 Ⱦɠ.
Ⱥɡɨɬ – ɞɜɭɯɚɬɨɦɧɵɣ ɝɚɡ, ɞɥɹ ɧɟɝɨ i = 5, ɬɨɝɞɚ WN = (5/2) 1,38 10-23 Ⱦɠ/Ʉ 300 Ʉ = 10,35 10-21 Ⱦɠ. Ɍɚɤ ɤɚɤ ɩɨɥɧɨɟ ɱɢɫɥɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɞɜɭɯɚɬɨɦɧɨɣ ɦɨɥɟɤɭɥɵ ɚɡɨɬɚ i = 5, ɚ ɧɚ ɞɨɥɸ ɩɨɫɬɭɩɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɩɪɢɯɨɞɢɬɫɹ i = 3, ɬɨ ɧɚ ɞɨɥɸ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɞɜɭɯɚɬɨɦɧɨɣ ɦɨɥɟɤɭɥɵ ɩɪɢɯɨɞɢɬɫɹ ɞɜɟ ɫɬɟɩɟɧɢ ɫɜɨɛɨɞɵ. Ɍɨɝɞɚ ɷɧɟɪɝɢɹ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɨɞɧɨɣ ɦɨɥɟɤɭɥɵ ɚɡɨɬɚ ɨɩɪɟɞɟɥɢɬɫɹ ɮɨɪɦɭɥɨɣ Wɜɪɚɳ. = (2/2)kT; Wɜɪɚɳ. = 1,38 10-23 Ⱦɠ/Ʉ; 300 Ʉ = 4,14 10-21Ⱦɠ. Ʉɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɜɪɚɳɚɬɟɥɶɧɨɝɨ ɞɜɢɠɟɧɢɹ ɜɫɟɯ n ɦɨɥɟɤɭɥ ɚɡɨɬɚ Wɜɪɚɳ. = nWɜɪɚɳ., ɝɞɟ n = (m / P ) · NA (ɫɦ. ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ 6). Wɜɪɚɳ. = (m / P ) NA Wɜɪɚɳ. Ⱦɥɹ ɚɡɨɬɚ P = 28 ɤɝ/ɤɦɨɥɶ, Wɜɪɚɳ = (0,004 ɤɝ / 28 ɤɝ/ɤɦɨɥɶ) 6,022 10-26 ɤɦɨɥɶ-1 4,14 10-21 Ⱦɠ = = 3,56 102 Ⱦɠ. Ɂɚɞɚɱɚ 11. ȼɵɱɢɫɥɢɬɶ ɭɞɟɥɶɧɵɟ ɬɟɩɥɨɟɦɤɨɫɬɢ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɨɛɴɟɦɟ ɫv ɢ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ ɫp ɧɟɨɧɚ ɢ ɜɨɞɨɪɨɞɚ, ɫɱɢɬɚɹ ɷɬɢ ɝɚɡɵ ɢɞɟɚɥɶɧɵɦ. Ɋɟɲɟɧɢɟ. ɍɞɟɥɶɧɵɟ ɬɟɩɥɨɟɦɤɨɫɬɢ ɫɪ ɢ ɫV ɢɞɟɚɥɶɧɵɯ ɝɚɡɨɜ ɜɵɪɚɠɚɸɬɫɹ ɮɨɪɦɭɥɚɦɢ 14
ɫv =
i R , 2P
cɪ =
i2 R , 2 P
i – ɱɢɫɥɨ ɫɬɟɩɟɧɟɣ ɫɜɨɛɨɞɵ ɦɨɥɟɤɭɥɵ ɝɚɡɚ, P – ɦɚɫɫɚ ɤɢɥɨɦɨɥɹ, P Ne = 20 ɤɝ/ɤɦɨɥɶ, P H = 2 ɤɝ/ɤɦɨɥɶ. ɇɟɨɧ – ɨɞɧɨɚɬɨɦɧɵɣ ɝɚɡ, ɩɨɷɬɨɦɭ i = 3: 2
ɫv =
3 8,31103 Ⱦɠ/(Ʉ ɤɦɨɥɶ) 2 20 ɤɝ/ɤɦɨɥɶ
ɫɪ =
3 2 8,31 103 2 20
6, 23 102 Ⱦɠ/(Ʉ ɤɝ),
1, 04 103 Ⱦɠ/(Ʉ ɤɝ).
Ⱦɥɹ ɜɨɞɨɪɨɞɚ (ɞɜɭɯɚɬɨɦɧɵɣ ɝɚɡ) i = 5: ɫv = ɫɪ =
5 8,31 103 2 2
1, 04 104 Ⱦɠ/ɤɝɄ,
5 2 8,31 103 2 2
1, 45 104 Ⱦɠ/ɤɝɄ.
Ɂɚɞɚɱɚ 12. ȼɵɱɢɫɥɢɬɶ ɭɞɟɥɶɧɵɟ ɬɟɩɥɨɟɦɤɨɫɬɢ ɫv ɢ ɫɪ ɫɦɟɫɢ ɧɟɨɧɚ ɢ ɜɨɞɨɪɨɞɚ, ɟɫɥɢ ɦɚɫɫɚ ɧɟɨɧɚ m1 ɫɨɫɬɚɜɥɹɟɬ 80 % ɦɚɫɫɵ ɫɦɟɫɢ, ɦɚɫɫɚ ɜɨɞɨɪɨɞɚ m2 – 20 %. Ɋɟɲɟɧɢɟ. Ɍɟɩɥɨɬɭ, ɧɟɨɛɯɨɞɢɦɭɸ ɞɥɹ ɧɚɝɪɟɜɚɧɢɹ ɫɦɟɫɢ ɧɚ ' t ɝɪɚɞɭɫɨɜ, ɜɵɪɚɡɢɦ ɞɜɭɦɹ ɫɩɨɫɨɛɚɦɢ: Q = cv(m1 + m2) ' t , (1) Q = (cv1 m1 + cv2 m2) ' t , (2) ɝɞɟ ɫv – ɭɞɟɥɶɧɚɹ ɬɟɩɥɨɟɦɤɨɫɬɶ ɫɦɟɫɢ, ɫv1 – ɭɞɟɥɶɧɚɹ ɬɟɩɥɨɟɦɤɨɫɬɶ ɧɟɨɧɚ, ɫv – ɭɞɟɥɶɧɚɹ ɬɟɩɥɨɟɦɤɨɫɬɶ ɜɨɞɨɪɨɞɚ. ɉɪɢɪɚɜɧɢɜɚɹ (1) ɢ (2), ɩɨɥɭɱɢɦ ɫv(m1 + m2) ' t = (cv1 m1 + cv2 m2) ' t, ɨɬɤɭɞɚ ɫv
=
ɫv1 m1 cv 2 m2 m1 m2
cv1
m1 m2 cv 2 . m1 m2 m1 m2
(3)
ȼɟɥɢɱɢɧɵ q1 = m1 / (m1 + m2) ɢ q2 = m2 / (m1 + m2) ɩɨɤɚɡɵɜɚɸɬ, ɤɚɤɭɸ ɞɨɥɸ ɦɚɫɫɵ ɫɦɟɫɢ ɫɨɫɬɚɜɥɹɟɬ ɦɚɫɫɚ ɧɟɨɧɚ ɢ ɜɨɞɨɪɨɞɚ. ɉɟɪɟɩɢɲɟɦ (3): cv = cv1 q1 + cv2 q2. Ⱥɧɚɥɨɝɢɱɧɵɦɢ ɪɚɫɫɭɠɞɟɧɢɹɦɢ ɩɨɥɭɱɚɟɦ ɮɨɪɦɭɥɭ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɭɞɟɥɶɧɨɣ ɬɟɩɥɨɟɦɤɨɫɬɢ ɫɦɟɫɢ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ cp = cp1 q1 + cp2 q2. Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ ɫv ɢ ɫɪ ɫɦɟɫɢ ɜɨɫɩɨɥɶɡɭɟɦɫɹ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɡɧɚɱɟɧɢɹɦɢ ɫv ɢ ɫɪ ɞɥɹ ɧɟɨɧɚ ɢ ɜɨɞɨɪɨɞɚ ɢɡ ɩɪɟɞɵɞɭɳɟɣ ɡɚɞɚɱɢ: ɫv = (6,23102 0,8 + 1,04 104 0,2) Ⱦɠ/(ɤɝ Ʉ) = 2,58103 Ⱦɠ/(ɤɝ Ʉ), ɫɪ = (1,04 103 0,8 + 1,45 104 0,2) Ⱦɠ/(ɤɝ Ʉ) = 3,73103 Ⱦɠ/(ɤɝ Ʉ).
15
Ɂɚɞɚɱɚ 13. ɉɪɢ ɬɟɦɩɟɪɚɬɭɪɟ 399,9 Ʉ ɢ ɞɚɜɥɟɧɢɢ 600 ɦɦ ɪɬ. ɫɬ. ɧɚɯɨɞɢɬɫɹ 15 ɥ ɚɡɨɬɚ. Ɉɩɪɟɞɟɥɢɬɶ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɤɨɬɨɪɨɟ ɧɭɠɧɨ ɫɨɨɛɳɢɬɶ ɷɬɨɣ ɦɚɫɫɟ ɚɡɨɬɚ, ɱɬɨɛɵ ɩɪɢ ɧɟɢɡɦɟɧɧɨɦ ɨɛɴɟɦɟ ɩɨɜɵɫɢɬɶ ɟɟ ɬɟɦɩɟɪɚɬɭɪɭ ɧɚ 100 ºɋ. Ɋɟɲɟɧɢɟ. Ɍɚɤ ɤɚɤ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɧɟɨɛɯɨɞɢɦɨɟ ɞɥɹ ɩɨɜɵɲɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɨɞɧɨɝɨ ɦɨɥɹ ɝɚɡɚ ɧɚ 1 ɝɪɚɞɭɫ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɨɛɴɟɦɟ, ɪɚɜɧɨ ɦɨɥɹɪɧɨɣ ɬɟɩɥɨɟɦɤɨɫɬɢ ɫv, ɬɨ ɞɥɹ ɭɜɟɥɢɱɟɧɢɹ ɬɟɦɩɟɪɚɬɭɪɵ ɧɚ Ɍ ɧɟɤɨɬɨɪɨɣ ɦɚɫɫɵ ɝɚɡɚ m / P (m – ɦɚɫɫɚ ɝɚɡɚ, P – ɦɨɥɹɪɧɚɹ ɦɚɫɫɚ ɝɚɡɚ) ɧɟɨɛɯɨɞɢɦɨ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ: ' Q = (m/ P ) ɫv ' T, ɝɞɟ ɫv = (i/2) R (ɫɦ. ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ 11), ɬɨɝɞɚ ' Q = (m/ P ) (i/2) R ' T = (5/2) (m/ P ) R ' T. ɋɨɝɥɚɫɧɨ ɭɪɚɜɧɟɧɢɸ Ɇɟɧɞɟɥɟɟɜɚ – Ʉɥɚɣɩɟɪɨɧɚ PV = (m / P ) · RT, ɨɬɤɭɞɚ mR / P = PV/T, ɢ (1) ɩɟɪɟɩɢɲɟɬɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ: 'Q =
5 PV 'T . 2 T
Ⱦɥɹ ɜɵɱɢɫɥɟɧɢɹ Q ɜ ɫɢɫɬɟɦɟ ɋɂ ɭɱɬɟɦ, ɱɬɨ V = 15 ɥ = 15 10-2 ɦ3, ɢ ɜɵɪɚɡɢɦ ɞɚɜɥɟɧɢɟ ɜ ɉɚ, ɤɚɤ ɷɬɨ ɫɞɟɥɚɧɨ ɜ ɡɚɞɚɱɟ 9: 'Q =
5 60 13,33 ɉɚ 15 103 ɦ3 100 ɝɪɚɞ | 3 ɇ ɦ 3 Ⱦɠ. 2 2(126,9 100 273) ɝɪɚɞ
Ɂɚɞɚɱɚ 14. Ɍɟɩɥɨɜɚɹ ɦɚɲɢɧɚ ɪɚɛɨɬɚɟɬ ɩɨ ɨɛɪɚɬɧɨɦɭ ɰɢɤɥɭ Ʉɚɪɧɨ. Ɍɟɦɩɟɪɚɬɭɪɚ ɧɚɝɪɟɜɚɬɟɥɹ 500 Ʉ. Ɉɩɪɟɞɟɥɢɬɶ ɤ.ɩ.ɞ. ɰɢɤɥɚ Ș ɢ ɬɟɦɩɟɪɚɬɭɪɭ Ɍ2 ɬɟɩɥɨɜɨɣ ɦɚɲɢɧɵ, ɟɫɥɢ ɡɚ ɫɱɟɬ ɤɚɠɞɨɝɨ ɤɢɥɨɞɠɨɭɥɹ ɬɟɩɥɨɬɵ, ɩɨɥɭɱɟɧɧɨɣ ɨɬ ɧɚɝɪɟɜɚɬɟɥɹ, ɦɚɲɢɧɚ ɫɨɜɟɪɲɚɟɬ ɪɚɛɨɬɭ 350 Ⱦɠ. Ɋɟɲɟɧɢɟ. Ʉ.ɩ.ɞ. ɬɟɩɥɨɜɨɣ ɦɚɲɢɧɵ ɪɚɜɟɧ ɨɬɧɨɲɟɧɢɸ ɩɨɥɟɡɧɨɣ ɪɚɛɨɬɵ ɤ ɡɚɬɪɚɱɟɧɧɨɣ: Ș = Ⱥ/Ⱥ1 = Ⱥ/Q, ɝɞɟ Ⱥ – ɪɚɛɨɬɚ, ɫɨɜɟɪɲɟɧɧɚɹ ɪɚɛɨɱɢɦ ɬɟɥɨɦ ɬɟɩɥɨɜɨɣ ɦɚɲɢɧɵ; Q – ɬɟɩɥɨɬɚ, ɩɨɥɭɱɟɧɧɚɹ ɨɬ ɧɚɝɪɟɜɚɬɟɥɹ: Ș = 350/1000 = 0,35 = 35 %. Ɂɧɚɹ ɤ.ɩ.ɞ. ɰɢɤɥɚ, ɦɨɠɧɨ ɩɨ ɮɨɪɦɭɥɟ Ș = (Ɍ1 – Ɍ2) / Ɍ1 ɨɩɪɟɞɟɥɢɬɶ ɬɟɦɩɟɪɚɬɭɪɭ Ɍ2 ɯɨɥɨɞɢɥɶɧɢɤɚ (Ɍ1 – ɬɟɦɩɟɪɚɬɭɪɚ ɧɚɝɪɟɜɚɬɟɥɹ): Ɍ2 = Ɍ1(1– Ș), Ɍ2 = 500 (1–0,35) = 500 0,65 = 325 Ʉ. Ɂɚɞɚɱɚ 15. Ɇɚɬɟɪɢɚɥɶɧɚɹ ɬɨɱɤɚ ɫ ɦɚɫɫɨɣ m = 0,02 ɤɝ ɫɨɜɟɪɲɚɟɬ ɝɚɪɦɨɧɢɱɟɫɤɢɟ ɤɨɥɟɛɚɧɢɹ ɩɨ ɡɚɤɨɧɭ ɫɢɧɭɫɚ ɫ ɩɟɪɢɨɞɨɦ Ɍ = 2 ɫ ɢ ɧɚɱɚɥɶɧɨɣ ɮɚɡɨɣ, ɪɚɜɧɨɣ ɧɭɥɸ. ɉɨɥɧɚɹ ɷɧɟɪɝɢɹ ɤɨɥɟɛɥɸɳɟɣɫɹ ɬɨɱɤɢ W = 110-3 Ⱦɠ. ɇɚɣɬɢ: ɚ) ɚɦɩɥɢɬɭɞɭ ɤɨɥɟɛɚɧɢɣ Ⱥ; ɛ) ɧɚɩɢɫɚɬɶ ɭɪɚɜɧɟɧɢɟ ɞɚɧɧɵɯ ɤɨɥɟɛɚɧɢɣ; ɜ) ɧɚɣɬɢ ɧɚɢɛɨɥɶɲɟɟ ɡɧɚɱɟɧɢɟ ɫɢɥɵ Fɦɚɯ, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɬɨɱɤɭ. Ɋɟɲɟɧɢɟ. ɍɪɚɜɧɟɧɢɟ ɝɚɪɦɨɧɢɱɟɫɤɢɯ ɤɨɥɟɛɚɧɢɣ ɛɟɡ ɧɚɱɚɥɶɧɨɣ ɮɚɡɵ 16
ɢɦɟɟɬ ɜɢɞ x = A sinȦt, ɨɬɤɭɞɚ ɫɤɨɪɨɫɬɶ ɤɨɥɟɛɥɸɳɟɣɫɹ ɬɨɱɤɢ ɪɚɜɧɚ x =
(1)
dx = A Ȧ cosȦt. dt
Ʉɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɤɨɥɟɛɥɸɳɟɣɫɹ ɬɨɱɤɢ Wɤ =
1 1 1 mV2 = m(AȦ cosȦt)2 = mA2 Ȧ2 cos2Ȧt. 2 2 2
ɉɨɥɧɚɹ ɷɧɟɪɝɢɹ ɤɨɥɟɛɥɸɳɟɣɫɹ ɬɨɱɤɢ ɨɩɪɟɞɟɥɢɬɫɹ ɢɡ ɭɪɚɜɧɟɧɢɹ A=
1 mA2 Ȧ2, 2
ɨɬɫɸɞɚ ɚɦɩɥɢɬɭɞɚ ɤɨɥɟɛɚɧɢɣ Ⱥ=
1
Z
2W . m
Ʉɪɭɝɨɜɚɹ (ɰɢɤɥɢɱɟɫɤɚɹ) ɱɚɫɬɨɬɚ ɫɜɹɡɚɧɚ ɫ ɩɟɪɢɨɞɨɦ ɤɨɥɟɛɚɧɢɣ Ɍ: Ȧ = ɬɨɝɞɚ
Ⱥ=
Ⱥ=
1 2S T
2 2 10 4 2 3,14 2 10 2
2W m
T 2S
1 1 3,14 10 2
2S , T
2W , m
1 | 0,03 (ɦ). 10 3,14
ɇɚɣɞɟɦ Ȧ: Ȧ = 2ʌ/2 = ʌ (c-1). Ɂɧɚɹ Ⱥ ɢ Ȧ, ɫɨɝɥɚɫɧɨ (1) ɭɪɚɜɧɟɧɢɟ ɤɨɥɟɛɥɸɳɟɣɫɹ ɬɨɱɤɢ ɛɭɞɟɬ: x = 0,03 sin ʌt. Fɦɚɯ ɨɩɪɟɞɟɥɢɦ ɢɡ ɜɬɨɪɨɝɨ ɡɚɤɨɧɚ ɇɶɸɬɨɧɚ: Fmɚɯ = m ɚmɚɯ, ɚ =
dV = – Ⱥ Ȧ2 sin Ȧt, dt
ɚmɚɯ = ȺȦ2,
Fmax = – mȺȦ2.
Fmax = – 0,02 · 0,03(ʌ)2 (ɤɝ ɦ)/ɫ2 = –5,9 · 10-3 ɇ. Ɂɧɚɤ ɦɢɧɭɫ ɭɤɚɡɵɜɚɟɬ ɧɚ ɬɨ, ɱɬɨ ɧɚɩɪɚɜɥɟɧɢɟ ɫɢɥɵ ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɧɚɩɪɚɜɥɟɧɢɸ ɫɦɟɳɟɧɢɹ. ɁȺȾȺɑɂ ȾɅə ɋȺɆɈɋɌɈəɌȿɅɖɇɈȽɈ Ɋȿɒȿɇɂə 1. Ɍɨɱɤɚ ɞɜɢɠɟɬɫɹ ɩɨ ɨɤɪɭɠɧɨɫɬɢ ɪɚɞɢɭɫɚ 8 ɦ. Ɂɚɤɨɧ ɟɟ ɞɜɢɠɟɧɢɹ ɜɵɪɚɠɚɟɬɫɹ ɭɪɚɜɧɟɧɢɟɦ s = a + bt2, ɝɞɟ ɚ = 20 ɦ, b = 2 ɦ ɫ-2. ɇɚɣɬɢ, ɜ ɤɚɤɨɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ ɧɨɪɦɚɥɶɧɨɟ ɭɫɤɨɪɟɧɢɟ ɬɨɱɤɢ an ɛɭɞɟɬ ɪɚɜɧɨ 3 ɦ ɫ-2. Ɉɬɜɟɬ: 1,21 ɫ. 2. ɋ ɤɚɤɨɣ ɫɪɟɞɧɟɣ ɫɢɥɨɣ F ɞɚɜɢɬ ɩɪɢ ɫɬɪɟɥɶɛɟ ɪɭɱɧɨɣ ɩɭɥɟɦɟɬ, ɟɫɥɢ ɦɚɫɫɚ ɩɭɥɢ m = 0,01 ɤɝ, ɟɟ ɫɤɨɪɨɫɬɶ ɩɪɢ ɜɵɥɟɬɟ v = 800 ɦ/ɫ ɢ ɫɤɨɪɨɫɬɪɟɥɶɧɨɫɬɶ ɩɭɥɟɦɟɬɚ n = 600 ɜɵɥɟɬɨɜ ɜ ɦɢɧɭɬɭ? Ɉɬɜɟɬ: 80 ɇ. 17
3. ɋɬɚɥɶɧɨɣ ɲɚɪɢɤ, ɭɩɚɜɲɢɣ ɫ ɜɵɫɨɬɵ 1 ɦ ɧɚ ɫɬɚɥɶɧɭɸ ɞɨɫɤɭ, ɨɬɫɤɚɤɢɜɚɟɬ ɨɬ ɧɟɟ ɫɨ ɫɤɨɪɨɫɬɶɸ V2 = 0,75V1, ɝɞɟ V1 – ɫɤɨɪɨɫɬɶ, ɫ ɤɨɬɨɪɨɣ ɨɧ ɩɨɞɥɟɬɟɥ ɤ ɞɨɫɤɟ. 1) ɇɚ ɤɚɤɭɸ ɜɵɫɨɬɭ ɨɧ ɩɨɞɧɢɦɟɬɫɹ? 2) ɋɤɨɥɶɤɨ ɜɪɟɦɟɧɢ ɩɪɨɣɞɟɬ ɨɬ ɧɚɱɚɥɚ ɞɜɢɠɟɧɢɹ ɲɚɪɢɤɚ ɞɨ ɜɬɨɪɢɱɧɨɝɨ ɟɝɨ ɩɚɞɟɧɢɹ ɧɚ ɞɨɫɤɭ? Ɉɬɜɟɬ: h = 0,84 ɦ, t = 1,4 ɫ. 4. ɇɚ ɫɤɚɦɶɟ ɀɭɤɨɜɫɤɨɝɨ ɫɢɞɢɬ ɱɟɥɨɜɟɤ ɢ ɞɟɪɠɢɬ ɧɚ ɜɵɬɹɧɭɬɵɯ ɪɭɤɚɯ ɝɢɪɢ ɩɨ 10 ɤɝ ɤɚɠɞɚɹ. Ɋɚɫɫɬɨɹɧɢɟ ɨɬ ɤɚɠɞɨɣ ɝɢɪɢ ɞɨ ɨɫɢ ɜɪɚɳɟɧɢɹ ɫɤɚɦɶɢ l1 = 0,75 ɦ. ɋɤɚɦɶɹ ɜɪɚɳɚɟɬɫɹ, ɞɟɥɚɹ n = 1 ɨɛ/ɫ. Ʉɚɤ ɢɡɦɟɧɢɬɫɹ ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɫɤɚɦɶɢ ɢ ɤɚɤɭɸ ɪɚɛɨɬɭ ɩɪɨɢɡɜɟɞɟɬ ɱɟɥɨɜɟɤ, ɟɫɥɢ ɨɧ ɫɨɠɦɟɬ ɪɭɤɢ ɬɚɤ, ɱɬɨ ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɤɚɠɞɨɣ ɝɢɪɢ ɞɨ ɨɫɢ ɭɦɟɧɶɲɢɬɫɹ ɞɨ l2 = 0,2 ɦ? ɋɭɦɦɚɪɧɵɣ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɱɟɥɨɜɟɤɚ ɢ ɫɤɚɦɶɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɜɪɚɳɟɧɢɹ I0 = 2,5 ɤɝ ɦ2. Ɉɬɜɟɬ: Ȧ = 4,2 ɨɛ/ɫ, Ⱥ = 870 Ⱦɠ. 5. Ʉɚɤɨɟ ɤɨɥɢɱɟɫɬɜɨ ɦɨɥɟɤɭɥ ɧɚɯɨɞɢɬɫɹ ɜ ɤɨɦɧɚɬɟ ɨɛɴɟɦɨɦ 80 ɦ3 ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ 17 ºɋ ɢ ɞɚɜɥɟɧɢɢ 750 ɦɦ ɪɬ. ɫɬ.? Ɉɬɜɟɬ: 21027. 6. ɇɚɣɬɢ ɫɪɟɞɧɸɸ ɞɥɢɧɭ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɚɬɨɦɨɜ ɝɟɥɢɹ ɜ ɭɫɥɨɜɢɹɯ, ɤɨɝɞɚ ɩɥɨɬɧɨɫɬɶ ɝɟɥɢɹ ȡ = 2,110-2 ɤɝ/ɦ3. Ɉɬɜɟɬ: 1,8 10-6 ɦ. 7. Ɋɚɫɫɱɢɬɚɬɶ ɩɨɥɧɭɸ ɷɧɟɪɝɢɸ ɜɫɟɯ ɦɨɥɟɤɭɥ ɤɢɫɥɨɪɨɞɚ, ɡɚɧɢɦɚɸɳɟɝɨ ɩɪɢ ɞɚɜɥɟɧɢɢ Ɋ = 0,2 Ɇɉɚ, ɨɛɴɟɦ V = 30 ɥ. Ɉɬɜɟɬ: 1,5 104 Ⱦɠ. 8. 160 ɝ ɤɢɫɥɨɪɨɞɚ ɧɚɝɪɟɜɚɸɬɫɹ ɨɬ 50 ɞɨ 60 ºɋ. ɇɚɣɬɢ ɤɨɥɢɱɟɫɬɜɨ ɩɨɝɥɨɳɟɧɧɨɣ ɬɟɩɥɨɬɵ ɢ ɢɡɦɟɧɟɧɢɟ ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ ɜ ɫɥɭɱɚɹɯ, ɟɫɥɢ 1) ɩɪɨɰɟɫɫ ɩɪɨɢɫɯɨɞɢɬ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɨɛɴɟɦɟ; 2) ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ. Ɉɬɜɟɬ: 1) Q1 = U1 = 1040 Ⱦɠ; 2) U2 = 1040 Ⱦɠ, Q2 = 1400 Ⱦɠ. 9. Ɋɚɛɨɬɚ ɢɡɨɬɟɪɦɢɱɟɫɤɨɝɨ ɪɚɫɲɢɪɟɧɢɹ 10 ɝ ɧɟɤɨɬɨɪɨɝɨ ɝɚɡɚ ɨɬ ɨɛɴɟɦɚ V1 ɞɨ ɨɛɴɟɦɚ V2 = 2V1 ɪɚɜɧɚ 575 Ⱦɠ. ɇɚɣɬɢ ɫɪɟɞɧɸɸ ɤɜɚɞɪɚɬɢɱɧɭɸ ɫɤɨɪɨɫɬɶ ɦɨɥɟɤɭɥ ɝɚɡɚ ɩɪɢ ɷɬɨɣ ɬɟɦɩɟɪɚɬɭɪɟ. Ɉɬɜɟɬ: 500 ɦ/ɫ. 10. Ƚɚɡ ɫɨɜɟɪɲɚɟɬ ɰɢɤɥ Ʉɚɪɧɨ. Ⱥɛɫɨɥɸɬɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɧɚɝɪɟɜɚɬɟɥɹ ɜ ɬɪɢ ɪɚɡɚ ɜɵɲɟ, ɱɟɦ ɬɟɦɩɟɪɚɬɭɪɚ ɨɯɥɚɞɢɬɟɥɹ. ɇɚɝɪɟɜɚɬɟɥɶ ɩɟɪɟɞɚɥ ɝɚɡɭ Q1 = 10 ɤɤɚɥ ɬɟɩɥɨɬɵ. Ʉɚɤɭɸ ɪɚɛɨɬɭ ɫɨɜɟɪɲɢɥ ɝɚɡ? Ɉɬɜɟɬ: 2,81104 Ⱦɠ.
18
ȼȺɊɂȺɇɌɕ ɄɈɇɌɊɈɅɖɇɈɃ ɊȺȻɈɌɕ ʋ 1 (Ɇɟɯɚɧɢɤɚ ɢ ɦɨɥɟɤɭɥɹɪɧɚɹ ɮɢɡɢɤɚ) ȿɫɥɢ ɧɟɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɭɤɚɡɚɧɢɣ ɩɪɟɩɨɞɚɜɚɬɟɥɹ, ɬɨ ɤɚɠɞɵɣ ɫɬɭɞɟɧɬ ɜɵɩɨɥɧɹɟɬ ɤɨɧɬɪɨɥɶɧɭɸ ɪɚɛɨɬɭ, ɧɨɦɟɪ ɜɚɪɢɚɧɬɚ ɤɨɬɨɪɨɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɩɨɫɥɟɞɧɟɣ ɰɢɮɪɟ ɧɨɦɟɪɚ ɡɚɱɟɬɧɨɣ ɤɧɢɠɤɢ ɫɬɭɞɟɧɬɚ. Ʉɨɧɬɪɨɥɶɧɚɹ ɪɚɛɨɬɚ ɧɚɱɢɧɚɟɬɫɹ ɫ ɭɤɚɡɚɧɢɹ ɧɨɦɟɪɚ ɜɚɪɢɚɧɬɚ ɢ ɧɨɦɟɪɚ ɡɚɱɟɬɧɨɣ ɤɧɢɠɤɢ. ɇɚɩɨɦɢɧɚɟɦ, ɱɬɨ ɭɫɥɨɜɢɟ ɡɚɞɚɱɢ ɩɟɪɟɩɢɫɵɜɚɟɬɫɹ ɩɨɥɧɨɫɬɶɸ. ȼɚɪɢɚɧɬ
ɇɨɦɟɪɚ ɡɚɞɚɱ
ʋ 1
101 111
121
131
141
151
161
171
181
191
2
102
112
122
132
142
152
162
172
182
192
3
103
113
123
133
143
153
163
173
183
193
4
104
114
124
134
144
154
164
174
184
194
5
105
115
125
135
145
155
165
175
185
195
6
106
116
126
136
146
156
166
176
186
196
7
107
117
127
137
147
157
167
177
187
197
8
108
118
128
138
148
158
168
178
188
198
9
109
119
129
139
149
159
169
179
189
199
10
110
120
130
140
150
160
170
180
190
200
19
101. Ʉɢɧɟɦɚɬɢɱɟɫɤɨɟ ɭɪɚɜɧɟɧɢɟ ɞɜɢɠɟɧɢɹ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ ɩɨ ɩɪɹɦɨɣ (ɨɫɶ ɯ) ɢɦɟɟɬ ɜɢɞ x = A + Bt + Ct3, ɝɞɟ Ⱥ = 4 ɦ, ȼ = 2 ɦ/ɫ, ɋ = 0,5 ɦ/ɫ2. Ⱦɥɹ ɦɨɦɟɧɬɚ ɜɪɟɦɟɧɢ t = 2 ɫ ɨɩɪɟɞɟɥɢɬɶ: 1) ɤɨɨɪɞɢɧɚɬɭ x1 ɬɨɱɤɢ; 2) ɦɝɧɨɜɟɧɧɭɸ ɫɤɨɪɨɫɬɶ v1; 3) ɦɝɧɨɜɟɧɧɨɟ ɭɫɤɨɪɟɧɢɟ ɚ1. 102. ɉɟɪɜɭɸ ɩɨɥɨɜɢɧɭ ɜɪɟɦɟɧɢ ɫɜɨɟɝɨ ɞɜɢɠɟɧɢɹ ɚɜɬɨɦɨɛɢɥɶ ɞɜɢɝɚɥɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ v1 = 80 ɤɦ/ɱ, ɚ ɜɬɨɪɭɸ ɩɨɥɨɜɢɧɭ ɜɪɟɦɟɧɢ – ɫɨ ɫɤɨɪɨɫɬɶɸ v2 = 40 ɤɦ/ɱ. Ʉɚɤɨɜɚ ɫɪɟɞɧɹɹ ɫɤɨɪɨɫɬɶ v ɞɜɢɠɟɧɢɹ ɚɜɬɨɦɨɛɢɥɹ? 103. Ⱦɢɫɤ ɜɪɚɳɚɟɬɫɹ ɫ ɭɝɥɨɜɵɦ ɭɫɤɨɪɟɧɢɟɦ İ = –2 ɪɚɞ/ɫ2. ɋɤɨɥɶɤɨ ɨɛɨɪɨɬɨɜ N ɫɞɟɥɚɟɬ ɞɢɫɤ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɨɬ Ȟ1 = 240 ɦɢɧ-1 ɞɨ Ȟ2 = 90 ɦɢɧ-1? ɇɚɣɬɢ ɜɪɟɦɹ ǻt, ɜ ɬɟɱɟɧɢɟ ɤɨɬɨɪɨɝɨ ɷɬɨ ɩɪɨɢɡɨɣɞɟɬ. 104. Ʉɚɛɢɧɚ ɥɢɮɬɚ, ɭ ɤɨɬɨɪɨɣ ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɩɨɥɚ ɞɨ ɩɨɬɨɥɤɚ 2,7 ɦ, ɧɚɱɚɥɚ ɩɨɞɧɢɦɚɬɶɫɹ ɫ ɭɫɤɨɪɟɧɢɟɦ 1,2 ɦ/ɫ2. ɑɟɪɟɡ 2,0 ɫ ɩɨɫɥɟ ɧɚɱɚɥɚ ɩɨɞɴɟɦɚ ɫ ɩɨɬɨɥɤɚ ɤɚɛɢɧɵ ɫɬɚɥ ɩɚɞɚɬɶ ɛɨɥɬ. ɇɚɣɬɢ: ɚ) ɜɪɟɦɹ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ ɛɨɥɬɚ; ɛ) ɩɟɪɟɦɟɳɟɧɢɟ ɢ ɩɭɬɶ ɛɨɥɬɚ ɡɚ ɜɪɟɦɹ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ ɜ ɫɢɫɬɟɦɟ ɨɬɫɱɟɬɚ, ɫɜɹɡɚɧɧɨɣ ɫ ɲɚɯɬɨɣ ɥɢɮɬɚ. 105. Ɇɚɬɟɪɢɚɥɶɧɚɹ ɬɨɱɤɚ ɞɜɢɠɟɬɫɹ ɩɨ ɨɤɪɭɠɧɨɫɬɢ ɪɚɞɢɭɫɨɦ R ɫɨ ɫɤɨɪɨɫɬɶɸ v = v0 · e-SR , ɝɞɟ S – ɩɪɨɣɞɟɧɧɵɣ ɩɭɬɶ; v0 – ɩɨɥɨɠɢɬɟɥɶɧɚɹ ɤɨɧɫɬɚɧɬɚ. ɇɚɣɬɢ: 1) ɡɚɜɢɫɢɦɨɫɬɶ ɩɭɬɢ ɨɬ ɜɪɟɦɟɧɢ; 2) ɭɝɨɥ ij ɦɟɠɞɭ ɜɟɤɬɨɪɚɦɢ ɫɤɨɪɨɫɬɢ ɢ ɭɫɤɨɪɟɧɢɹ ɜ ɩɪɨɢɡɜɨɥɶɧɵɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ; 3) ɭɫɤɨɪɟɧɢɟ ɤɚɤ ɮɭɧɤɰɢɸ ɫɤɨɪɨɫɬɢ. 106. ɇɚɣɬɢ ɭɝɥɨɜɨɟ ɭɫɤɨɪɟɧɢɟ ɤɨɥɟɫɚ, ɟɫɥɢ ɢɡɜɟɫɬɧɨ, ɱɬɨ ɱɟɪɟɡ 2 ɫ ɩɨɫɥɟ ɧɚɱɚɥɚ ɪɚɜɧɨɭɫɤɨɪɟɧɧɨɝɨ ɞɜɢɠɟɧɢɹ ɜɟɤɬɨɪ ɩɨɥɧɨɝɨ ɭɫɤɨɪɟɧɢɹ ɬɨɱɤɢ, ɥɟɠɚɳɟɣ ɧɚ ɨɛɨɞɟ, ɫɨɫɬɚɜɥɹɟɬ ɭɝɨɥ 60º ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɥɢɧɟɣɧɨɣ ɫɤɨɪɨɫɬɢ ɷɬɨɣ ɬɨɱɤɢ. 107. ɂɡ ɨɞɧɨɝɨ ɢ ɬɨɝɨ ɠɟ ɦɟɫɬɚ ɧɚɱɚɥɢ ɪɚɜɧɨɭɫɤɨɪɟɧɧɨ ɞɜɢɝɚɬɶɫɹ ɜ ɨɞɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɞɜɟ ɬɨɱɤɢ, ɩɪɢɱɟɦ ɜɬɨɪɚɹ ɧɚɱɚɥɚ ɫɜɨɟ ɞɜɢɠɟɧɢɟ ɱɟɪɟɡ 2 ɫ ɩɨɫɥɟ ɩɟɪɜɨɣ. ɉɟɪɜɚɹ ɬɨɱɤɚ ɞɜɢɝɚɥɚɫɶ ɫ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ V1 = l ɦ/ɫ ɢ ɭɫɤɨɪɟɧɢɟɦ a1 = 2 ɦ/ɫ2, ɜɬɨɪɚɹ – ɫ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ V2 = 10 ɦ/ɫ ɢ ɭɫɤɨɪɟɧɢɟɦ ɚ2 = 1 ɦ/ɫ2. ɑɟɪɟɡ ɤɚɤɨɟ ɜɪɟɦɹ ɢ ɧɚ ɤɚɤɨɦ ɪɚɫɫɬɨɹɧɢɢ ɨɬ ɢɫɯɨɞɧɨɝɨ ɩɨɥɨɠɟɧɢɹ ɜɬɨɪɚɹ ɬɨɱɤɚ ɞɨɝɨɧɢɬ ɩɟɪɜɭɸ? 108. Ⱦɜɢɠɟɧɢɹ ɞɜɭɯ ɦɚɬɟɪɢɚɥɶɧɵɯ ɬɨɱɟɤ ɜɵɪɚɠɚɸɬɫɹ ɭɪɚɜɧɟɧɢɹɦɢ: x1 = A1 + B1t + C1t2; x2 = A2 + B2t + C2t2, ɝɞɟ Ⱥ1 = 20 ɦ, Ⱥ2 = 2 ɦ, ȼ2 = ȼ1 = 2 ɦ/ɫ, ɋ1 = –4 ɦ/ɫ2, ɋ2 = –0,5 ɦ/ɫ2. ȼ ɤɚɤɨɣ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t ɫɤɨɪɨɫɬɢ ɷɬɢɯ ɬɨɱɟɤ ɛɭɞɭɬ ɨɞɢɧɚɤɨɜɵɦɢ? Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɢ v1 ɢ v2 ɢ ɭɫɤɨɪɟɧɢɹ. 109. Ʉɨɥɟɫɨ ɪɚɞɢɭɫɨɦ r = 0,1 ɦ ɜɪɚɳɚɟɬɫɹ ɫ ɩɨɫɬɨɹɧɧɵɦ ɭɝɥɨɜɵɦ ɭɫɤɨɪɟɧɢɟɦ H = 3,14 ɪɚɞ/ɫ2. ɇɚɣɬɢ ɞɥɹ ɬɨɱɟɤ ɧɚ ɨɛɨɞɟ ɤɨɥɟɫɚ ɤ ɤɨɧɰɭ ɩɟɪɜɨɣ ɫɟɤɭɧɞɵ ɩɨɫɥɟ ɧɚɱɚɥɚ ɞɜɢɠɟɧɢɹ: 1) ɭɝɥɨɜɭɸ ɫɤɨɪɨɫɬɶ, 2) ɥɢɧɟɣɧɭɸ ɫɤɨɪɨɫɬɶ, 3) ɬɚɧɝɟɧɰɢɚɥɶɧɨɟ ɭɫɤɨɪɟɧɢɟ, 4) ɧɨɪɦɚɥɶɧɨɟ ɭɫɤɨɪɟɧɢɟ, 5) ɩɨɥɧɨɟ ɭɫɤɨɪɟɧɢɟ, 6) ɭɝɨɥ, ɫɨɫɬɚɜɥɹɟɦɵɣ ɧɚɩɪɚɜɥɟɧɢɟɦ ɩɨɥɧɨɝɨ ɭɫɤɨɪɟɧɢɹ ɫ ɪɚɞɢɭɫɨɦ ɤɨɥɟɫɚ. B
B
20
110.
Ʉɨɥɟɫɨ
ɜɪɚɳɚɟɬɫɹ
ɫ
ɩɨɫɬɨɹɧɧɵɦ
ɭɝɥɨɜɵɦ
ɭɫɤɨɪɟɧɢɟɦ
H = 2 ɪɚɞ/ɫ2. ɑɟɪɟɡ 0,5 ɫ ɩɨɫɥɟ ɧɚɱɚɥɚ ɞɜɢɠɟɧɢɹ ɩɨɥɧɨɟ ɭɫɤɨɪɟɧɢɟ ɤɨɥɟɫɚ
ɫɬɚɥɨ ɪɚɜɧɵɦ a = 0,136 ɦ/ɫ2. ɇɚɣɬɢ ɪɚɞɢɭɫ ɤɨɥɟɫɚ. 111. ɑɚɫɬɢɰɚ ɞɜɢɠɟɬɫɹ ɜɞɨɥɶ ɨɫɢ ɯ ɩɨ ɡɚɤɨɧɭ ɯ = Į t2 – ȕt3, ɝɞɟ Į ɢ ȕ – ɩɨɥɨɠɢɬɟɥɶɧɵɟ ɩɨɫɬɨɹɧɧɵɟ. ȼ ɦɨɦɟɧɬ t = 0 ɫɢɥɚ, ɞɟɣɫɬɜɭɸɳɚɹ ɧɚ ɱɚɫɬɢɰɭ, ɪɚɜɧɚ Fo. ɇɚɣɬɢ ɡɧɚɱɟɧɢɹ Fx ɫɢɥɵ ɜ ɬɨɱɤɚɯ ɩɨɜɨɪɨɬɚ ɢ ɜ ɦɨɦɟɧɬ, ɤɨɝɞɚ ɱɚɫɬɢɰɚ ɨɩɹɬɶ ɨɤɚɠɟɬɫɹ ɜ ɬɨɱɤɟ ɯ = 0. 112. Ⱦɜɚ ɤɚɦɧɹ ɩɚɞɚɸɬ ɜ ɲɚɯɬɭ. ȼɬɨɪɨɣ ɤɚɦɟɧɶ ɧɚɱɚɥ ɫɜɨɟ ɩɚɞɟɧɢɟ ɧɚ 1 ɫ ɩɨɡɠɟ ɩɟɪɜɨɝɨ. Ɉɩɪɟɞɟɥɢɬɶ ɞɜɢɠɟɧɢɟ ɩɟɪɜɨɝɨ ɤɚɦɧɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɬɨɪɨɝɨ. ɋɱɢɬɚɬɶ ɭɫɤɨɪɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ g = 9,8 ɦ/ɫ2. 113. ɉɚɪɚɲɸɬɢɫɬ, ɦɚɫɫɚ ɤɨɬɨɪɨɝɨ ɬ = 80 ɤɝ, ɫɨɜɟɪɲɚɟɬ ɡɚɬɹɠɧɨɣ ɩɪɵɠɨɤ. ɋɱɢɬɚɹ, ɱɬɨ ɫɢɥɚ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜɨɡɞɭɯɚ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɚ ɫɤɨɪɨɫɬɢ, ɨɩɪɟɞɟɥɢɬɶ, ɱɟɪɟɡ ɤɚɤɨɣ ɩɪɨɦɟɠɭɬɨɤ ɜɪɟɦɟɧɢ ǻt ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɩɚɪɚɲɸɬɢɫɬɚ ɛɭɞɟɬ ɪɚɜɧɚ 0,9 ɨɬ ɫɤɨɪɨɫɬɢ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɞɜɢɠɟɧɢɹ. Ʉɨɷɮɮɢɰɢɟɧɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ k = 10. ɇɚɱɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɩɚɪɚɲɸɬɢɫɬɚ ɪɚɜɧɚ ɧɭɥɸ. 114. ɇɚ ɝɥɚɞɤɨɣ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɧɚɯɨɞɹɬɫɹ ɞɜɚ ɛɪɭɫɤɚ ɦɚɫɫɨɣ m1 ɢ m2, ɤɨɬɨɪɵɟ ɫɨɟɞɢɧɟɧɵ ɧɢɬɶɸ. Ʉ ɛɪɭɫɤɚɦ ɜ ɦɨɦɟɧɬ t = 0 ɩɪɢɥɨɠɢɥɢ ɫɢɥɵ, ɩɪɨɬɢɜɨɩɨɥɨɠɧɨ ɧɚɩɪɚɜɥɟɧɧɵɟ ɢ ɡɚɜɢɫɹɳɢɟ ɨɬ ɜɪɟɦɟɧɢ ɤɚɤ F1 = Į1t ɢ F2 = ȕ2t. ɇɚɣɬɢ, ɱɟɪɟɡ ɫɤɨɥɶɤɨ ɜɪɟɦɟɧɢ ɧɢɬɶ ɩɨɪɜɟɬɫɹ, ɟɫɥɢ ɫɢɥɚ ɧɚɬɹɠɟɧɢɹ ɧɚ ɪɚɡɪɵɜ ɪɚɜɧɚ Fɩɪ. 115. Ⱦɜɚ ɛɪɭɫɤɚ, ɦɚɫɫɵ ɤɨɬɨɪɵɯ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɬ1 ɢ ɬ2, ɫɨɟɞɢɧɟɧɵ ɞɪɭɝ ɫ ɞɪɭɝɨɦ ɧɟɪɚɫɬɹɠɢɦɨɣ ɧɢɬɶɸ ɦɚɫɫɨɣ ɬ. Ȼɪɭɫɤɢ ɞɜɢɠɭɬɫɹ ɜ ɩɨɥɟ ɫɢɥɵ ɬɹɠɟɫɬɢ ɜɟɪɬɢɤɚɥɶɧɨ ɜɜɟɪɯ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɩɨɫɬɨɹɧɧɨɣ ɫɢɥɵ F, ɩɪɢɥɨɠɟɧɧɨɣ ɤ ɩɟɪɜɨɦɭ ɛɪɭɫɤɭ. ɇɚɣɬɢ: 1) ɭɫɤɨɪɟɧɢɟ ɫɢɫɬɟɦɵ; 2) ɫɢɥɵ ɧɚɬɹɠɟɧɢɹ ɧɢɬɢ ɜ ɬɨɱɤɚɯ ɤɚɫɚɧɢɹ ɛɪɭɫɤɨɜ. 116. ȼ ɤɚɤɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɢ ɫ ɤɚɤɨɣ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ ɞɨɥɠɟɧ ɥɟɬɟɬɶ ɜɞɨɥɶ ɷɤɜɚɬɨɪɚ ɫɚɦɨɥɟɬ, ɱɬɨɛɵ ɫɤɨɦɩɟɧɫɢɪɨɜɚɬɶ ɭɦɟɧɶɲɟɧɢɟ ɜɟɫɚ, ɨɛɭɫɥɨɜɥɟɧɧɨɟ ɜɪɚɳɟɧɢɟɦ Ɂɟɦɥɢ? 117. ȼ ɤɚɤɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɢ ɫ ɤɚɤɨɣ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ ɞɨɥɠɟɧ ɥɟɬɟɬɶ ɜɞɨɥɶ ɷɤɜɚɬɨɪɚ ɫɚɦɨɥɟɬ, ɱɬɨɛɵ ɫɤɨɦɩɟɧɫɢɪɨɜɚɬɶ ɭɦɟɧɶɲɟɧɢɟ ɜɟɫɚ, ɨɛɭɫɥɨɜɥɟɧɧɨɟ ɜɪɚɳɟɧɢɟɦ Ɂɟɦɥɢ? 118. Ʉ ɩɪɭɠɢɧɧɵɦ ɜɟɫɚɦ ɩɨɞɜɟɲɟɧ ɛɥɨɤ. ɑɟɪɟɡ ɛɥɨɤ ɩɟɪɟɤɢɧɭɬ ɲɧɭɪ, ɤ ɤɨɧɰɚɦ ɤɨɬɨɪɨɝɨ ɩɪɢɜɹɡɚɥɢ ɝɪɭɡɵ ɦɚɫɫɚɦɢ m1 = 1,5 ɤɝ ɢ m2 = 3 ɤɝ. Ʉɚɤɨɜɨ ɛɭɞɟɬ ɩɨɤɚɡɚɧɢɟ ɜɟɫɨɜ ɜɨ ɜɪɟɦɹ ɞɜɢɠɟɧɢɹ ɝɪɭɡɨɜ? Ɇɚɫɫɨɣ ɛɥɨɤɚ ɢ ɲɧɭɪɚ ɩɪɟɧɟɛɪɟɱɶ. 119. ɇɚ ɷɤɜɚɬɨɪɟ ɧɟɤɨɬɨɪɨɣ ɩɥɚɧɟɬɵ ɬɟɥɚ ɜɟɫɹɬ ɜɞɜɨɟ ɦɟɧɶɲɟ, ɱɟɦ ɧɚ ɩɨɥɸɫɟ. ɉɥɨɬɧɨɫɬɶ ɜɟɳɟɫɬɜɚ ɩɥɚɧɟɬɵ ȡ = 3·103 ɤɝ/ɦ3. Ɉɩɪɟɞɟɥɢɬɶ ɩɟɪɢɨɞ ɨɛɪɚɳɟɧɢɹ ɩɥɚɧɟɬɵ ɜɨɤɪɭɝ ɫɨɛɫɬɜɟɧɧɨɣ ɨɫɢ. 120. ɇɚ ɝɥɚɞɤɨɦ ɫɬɨɥɟ ɥɟɠɢɬ ɛɪɭɫɨɤ ɦɚɫɫɨɣ ɬ = 4 ɤɝ. Ʉ ɛɪɭɫɤɭ ɩɪɢɜɹɡɚɧɵ ɞɜɚ ɲɧɭɪɚ, ɩɟɪɟɤɢɧɭɬɵɟ ɱɟɪɟɡ ɧɟɩɨɞɜɢɠɧɵɟ ɛɥɨɤɢ, ɩɪɢɤɪɟɩɥɟɧɧɵɟ ɤ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɦ ɤɪɚɹɦ ɫɬɨɥɚ. Ʉ ɤɨɧɰɚɦ ɲɧɭɪɨɜ ɩɨɞɜɟɲɟɧɵ ɝɢɪɢ, ɦɚɫɫɵ ɤɨɬɨɪɵɯ ɬ1 = 1 ɤɝ ɢ ɬ2 = 2 ɤɝ. ɇɚɣɬɢ ɭɫɤɨɪɟɧɢɟ ɚ, 21
ɫ ɤɨɬɨɪɵɦ ɞɜɢɠɟɬɫɹ ɛɪɭɫɨɤ, ɢ ɫɢɥɭ ɧɚɬɹɠɟɧɢɹ Ɍ ɤɚɠɞɨɝɨ ɢɡ ɲɧɭɪɨɜ. Ɇɚɫɫɨɣ ɛɥɨɤɨɜ ɢ ɬɪɟɧɢɟɦ ɩɪɟɧɟɛɪɟɱɶ. 121. Ⱦɜɚ ɝɪɭɡɚ ɦɚɫɫɚɦɢ m1 = 3 ɤɝ ɢ m2 = 5 ɤɝ ɥɟɠɚɬ ɧɚ ɝɥɚɞɤɨɦ ɝɨɪɢɡɨɧɬɚɥɶɧɨɦ ɫɬɨɥɟ, ɫɜɹɡɚɧɧɵɟ ɲɧɭɪɨɦ, ɤɨɬɨɪɵɣ ɪɚɡɪɵɜɚɟɬɫɹ ɩɪɢ ɫɢɥɟ ɧɚɬɹɠɟɧɢɹ Ɍ = 24 ɇ. Ʉɚɤɭɸ ɦɚɤɫɢɦɚɥɶɧɭɸ ɫɢɥɭ F ɦɨɠɧɨ ɩɪɢɥɨɠɢɬɶ ɤ ɝɪɭɡɭ m1; ɤ ɝɪɭɡɭ m2, ɱɬɨɛɵ ɝɪɭɡ ɧɟ ɪɚɡɨɪɜɚɥɫɹ? Ʉɚɤ ɢɡɦɟɧɢɬɫɹ ɨɬɜɟɬ, ɟɫɥɢ ɭɱɟɫɬɶ ɬɪɟɧɢɟ? Ʉɨɷɮɮɢɰɢɟɧɬɵ ɬɪɟɧɢɹ ɝɪɭɡɨɜ ɨ ɫɬɨɥ ɨɞɢɧɚɤɨɜɵ. 122. Ɍɟɥɨ ɥɟɠɢɬ ɧɚ ɧɚɤɥɨɧɧɨɣ ɩɥɨɫɤɨɫɬɢ, ɫɨɫɬɚɜɥɹɸɳɟɣ ɫ ɝɨɪɢɡɨɧɬɨɦ ɭɝɨɥ ɚ = 4°. ɉɪɢ ɤɚɤɨɦ ɩɪɟɞɟɥɶɧɨɦ ɤɨɷɮɮɢɰɢɟɧɬɟ ɬɪɟɧɢɹ ɤ ɬɟɥɨ ɧɚɱɧɟɬ ɫɤɨɥɶɡɢɬɶ ɩɨ ɧɚɤɥɨɧɧɨɣ ɩɥɨɫɤɨɫɬɢ? ɋ ɤɚɤɢɦ ɭɫɤɨɪɟɧɢɟɦ ɚ ɛɭɞɟɬ ɫɤɨɥɶɡɢɬɶ ɬɟɥɨ ɩɨ ɩɥɨɫɤɨɫɬɢ, ɟɫɥɢ ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ k = 0,03? Ʉɚɤɨɟ ɜɪɟɦɹ t ɩɨɬɪɟɛɭɟɬɫɹ ɞɥɹ ɩɪɨɯɨɠɞɟɧɢɹ ɩɪɢ ɷɬɢɯ ɭɫɥɨɜɢɹɯ ɩɭɬɢ S = 100 ɦ? Ʉɚɤɭɸ ɫɤɨɪɨɫɬɶ v ɛɭɞɟɬ ɢɦɟɬɶ ɬɟɥɨ ɜ ɤɨɧɰɟ ɩɭɬɢ? 123. ɋɚɦɨɥɟɬ ɥɟɬɢɬ ɜ ɝɨɪɢɡɨɧɬɚɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɫ ɭɫɤɨɪɟɧɢɟɦ ɚ = 20 ɦ/ɫ2. Ʉɚɤɨɜɚ ɩɟɪɟɝɪɭɡɤɚ ɩɚɫɫɚɠɢɪɚ, ɧɚɯɨɞɹɳɟɝɨɫɹ ɜ ɫɚɦɨɥɟɬɟ? (ɉɟɪɟɝɪɭɡɤɨɣ ɧɚɡɵɜɚɟɬɫɹ ɨɬɧɨɲɟɧɢɟ ɫɢɥɵ F, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɩɚɫɫɚɠɢɪɚ, ɤ ɫɢɥɟ ɬɹɠɟɫɬɢ Ɋ.) 124. Ȼɪɭɫɨɤ ɦɚɫɫɨɣ m ɬɹɧɭɬ ɡɚ ɧɢɬɶ ɬɚɤ, ɱɬɨ ɨɧ ɞɜɢɠɟɬɫɹ ɫ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɶɸ ɩɨ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɫ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɬɪɟɧɢɹ k (ɪɢɫ.). ɇɚɣɬɢ ɭɝɨɥ D, ɩɪɢ ɤɨɬɨɪɨɦ ɧɚɬɹɠɟɧɢɟ ɧɢɬɢ ɦɢɧɢɦɚɥɶɧɨ. ɑɟɦɭ ɨɧɨ ɪɚɜɧɨ? 125. Ƚɥɚɞɤɢɣ ɫɬɟɪɠɟɧɶ Ⱥȼ ɞɥɢɧɨɣ l ɜɪɚɳɚɟɬɫɹ ɜ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɫ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ Ȧ ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɟɪɬɢɤɚɥɶɧɨɣ ɨɫɢ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɬɨɱɤɭ Ⱥ. ɇɚ ɫɬɟɪɠɧɟ ɧɚɯɨɞɢɬɫɹ ɫɤɨɥɶɡɹɳɚɹ ɦɭɮɬɚ ɦɚɫɫɨɣ ɬ. ȼ ɦɨɦɟɧɬ ɜɪɟɦɟɧɢ t0 = 0 ɦɭɮɬɚ ɧɚɱɢɧɚɟɬ ɞɜɢɝɚɬɶɫɹ ɢɡ ɬɨɱɤɢ Ⱥ ɫɨ ɫɤɨɪɨɫɬɶɸ v0. ɇɚɣɬɢ: 1) ɜɪɟɦɹ, ɱɟɪɟɡ ɤɨɬɨɪɨɟ ɦɭɮɬɚ ɞɨɫɬɢɝɧɟɬ ɬɨɱɤɢ ȼ; 2) ɫɢɥɭ ɪɟɚɤɰɢɢ ɫɬɟɪɠɧɹ ɤɚɤ ɮɭɧɤɰɢɸ ɪɚɫɫɬɨɹɧɢɹ ɨɬ ɬɨɱɤɢ Ⱥ. 126. ɇɚɤɥɨɧɧɚɹ ɩɥɨɫɤɨɫɬɶ, ɨɛɪɚɡɭɸɳɚɹ ɭɝɨɥ Į = 25° ɫ ɩɥɨɫɤɨɫɬɶɸ ɝɨɪɢɡɨɧɬɚ, ɢɦɟɟɬ ɞɥɢɧɭ l = 2 ɦ. Ɍɟɥɨ, ɞɜɢɝɚɹɫɶ ɪɚɜɧɨɭɫɤɨɪɟɧɧɨ, ɫɨɫɤɨɥɶɡɧɭɥɨ ɫ ɷɬɨɣ ɩɥɨɫɤɨɫɬɢ ɡɚ ɜɪɟɦɹ t = 2 ɫ. Ɉɩɪɟɞɟɥɢɬɶ ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ k ɬɟɥɚ ɨ ɩɥɨɫɤɨɫɬɶ. 127. ɉɪɢ ɜɵɜɨɞɟ ɫɩɭɬɧɢɤɚ ɧɚ ɤɪɭɝɨɜɭɸ ɨɪɛɢɬɭ, ɩɪɨɯɨɞɹɳɭɸ ɜɛɥɢɡɢ ɩɨɜɟɪɯɧɨɫɬɢ Ɂɟɦɥɢ, ɛɵɥɚ ɫɨɜɟɪɲɟɧɚ ɪɚɛɨɬɚ Ⱥ = 3,2·1010 Ⱦɠ. ɇɚɣɬɢ ɦɚɫɫɭ ɫɩɭɬɧɢɤɚ. Ɋɚɞɢɭɫ Ɂɟɦɥɢ R ɩɪɢɧɹɬɶ ɪɚɜɧɵɦ 6400 ɤɦ. 128. Ʉɚɦɟɲɟɤ ɫɤɨɥɶɡɢɬ ɫ ɧɚɢɜɵɫɲɟɣ ɬɨɱɤɢ ɤɭɩɨɥɚ, ɢɦɟɸɳɟɝɨ ɮɨɪɦɭ ɩɨɥɭɫɮɟɪɵ. Ʉɚɤɭɸ ɞɭɝɭ D ɨɩɢɲɟɬ ɤɚɦɟɲɟɤ, ɩɪɟɠɞɟ ɱɟɦ ɨɬɨɪɜɟɬɫɹ ɨɬ ɩɨɜɟɪɯɧɨɫɬɢ ɤɭɩɨɥɚ? Ɍɪɟɧɢɟɦ ɩɪɟɧɟɛɪɟɱɶ. 129. Ʉɚɤɨɜɚ ɩɟɪɜɚɹ ɤɨɫɦɢɱɟɫɤɚɹ ɫɤɨɪɨɫɬɶ ɞɥɹ ɩɥɚɧɟɬɵ, ɦɚɫɫɚ ɢ ɪɚɞɢɭɫ ɤɨɬɨɪɨɣ ɜ ɞɜɚ ɪɚɡɚ ɛɨɥɶɲɟ, ɱɟɦ ɭ Ɂɟɦɥɢ? 22
130. ɉɪɢ ɜɵɫɬɪɟɥɟ ɢɡ ɨɪɭɞɢɹ ɫɧɚɪɹɞ ɦɚɫɫɨɣ m1 = 10 ɤɝ ɩɨɥɭɱɚɟɬ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ E = 1,8 ɆȾɠ. Ɉɩɪɟɞɟɥɢɬɶ ɤɢɧɟɬɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ Ɍ2 ɫɬɜɨɥɚ ɨɪɭɞɢɹ ɜɫɥɟɞɫɬɜɢɟ ɨɬɞɚɱɢ, ɟɫɥɢ ɦɚɫɫɚ m2 ɫɬɜɨɥɚ ɨɪɭɞɢɹ ɪɚɜɧɚ 600 ɤɝ. 131. ɇɚɣɬɢ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɬɨɧɤɨɣ ɨɞɧɨɪɨɞɧɨɣ ɩɪɹɦɨɭɝɨɥɶɧɨɣ ɩɥɚɫɬɢɧɤɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɨɞɧɭ ɢɡ ɜɟɪɲɢɧ ɩɥɚɫɬɢɧɤɢ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɟɟ ɩɥɨɫɤɨɫɬɢ, ɟɫɥɢ ɫɬɨɪɨɧɵ ɩɥɚɫɬɢɧɤɢ ɪɚɜɧɵ a ɢ b, ɚ ɟɟ ɦɚɫɫɚ m. 132. Ɍɨɧɤɚɹ ɨɞɧɨɪɨɞɧɚɹ ɩɥɚɫɬɢɧɤɚ ɦɚɫɫɨɣ m = 0,6 ɤɝ ɢɦɟɟɬ ɮɨɪɦɭ ɪɚɜɧɨɛɟɞɪɟɧɧɨɝɨ ɩɪɹɦɨɭɝɨɥɶɧɨɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ. ɇɚɣɬɢ ɟɟ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ, ɫɨɜɩɚɞɚɸɳɟɣ ɫ ɨɞɧɢɦ ɢɡ ɤɚɬɟɬɨɜ, ɞɥɢɧɚ ɤɨɬɨɪɨɝɨ ɚ = 200 ɦɦ. 133. Ɍɨɧɤɢɣ ɨɞɧɨɪɨɞɧɵɣ ɫɬɟɪɠɟɧɶ ɞɥɢɧɨɣ l = 50 ɫɦ ɢ ɦɚɫɫɨɣ m = 400 ɝ ɜɪɚɳɚɟɬɫɹ ɫ ɭɝɥɨɜɵɦ ɭɫɤɨɪɟɧɢɟɦ İ = 3 ɪɚɞ/ɫ2 ɨɤɨɥɨ ɨɫɢ, ɩɪɨɯɨɞɹɳɟɣ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɫɬɟɪɠɧɸ ɱɟɪɟɡ ɟɝɨ ɫɟɪɟɞɢɧɭ. Ɉɩɪɟɞɟɥɢɬɶ ɜɪɚɳɚɸɳɢɣ ɦɨɦɟɧɬ Ɇ. 134. ɇɚ ɫɬɭɩɟɧɱɚɬɵɣ ɛɥɨɤ (ɪɢɫ.) ɧɚɦɨɬɚɧɵ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɯ ɧɚɩɪɚɜɥɟɧɢɹɯ ɞɜɟ ɧɢɬɢ. ɇɚ ɤɨɧɟɰ ɨɞɧɨɣ ɧɢɬɢ ɞɟɣɫɬɜɭɸɬ ɩɨɫɬɨɹɧɧɨɣ ɫɢɥɨɣ F, ɚ ɤ ɤɨɧɰɭ ɞɪɭɝɨɣ ɧɢɬɢ ɩɪɢɤɪɟɩɥɟɧ ɝɪɭɡ ɦɚɫɫɨɣ ɬ. ɂɡɜɟɫɬɧɵ ɪɚɞɢɭɫɵ R1 ɢ R2 ɛɥɨɤɚ ɢ ɟɝɨ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ I ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɜɪɚɳɟɧɢɹ. Ɍɪɟɧɢɹ ɧɟɬ. ɇɚɣɬɢ ɭɝɥɨɜɨɟ ɭɫɤɨɪɟɧɢɟ ɛɥɨɤɚ. 135. ɇɚɣɬɢ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɬɨɧɤɨɣ ɨɞɧɨɪɨɞɧɨɣ ɩɥɚɫɬɢɧɵ ɦɚɫɫɨɣ ɬ, ɢɦɟɸɳɟɣ ɮɨɪɦɭ ɪɚɜɧɨɫɬɨɪɨɧɧɟɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ ɫɨ ɫɬɨɪɨɧɨɣ ɚ, ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɞɧɨɣ ɢɡ ɟɝɨ ɫɬɨɪɨɧ. 136. ɑɟɥɨɜɟɤ ɫɬɨɢɬ ɜ ɰɟɧɬɪɟ ɫɤɚɦɶɢ ɀɭɤɨɜɫɤɨɝɨ ɢ ɜɦɟɫɬɟ ɫ ɧɟɣ ɜɪɚɳɚɟɬɫɹ, ɫɨɜɟɪɲɚɹ 30 ɨɛ/ɦɢɧ. Ɇɨɦɟɧɬ ɢɧɟɪɰɢɢ ɬɟɥɚ ɱɟɥɨɜɟɤɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ ɜɪɚɳɟɧɢɹ 1,2 ɤɝ · ɦ2. ȼ ɜɵɬɹɧɭɬɵɯ ɪɭɤɚɯ ɭ ɱɟɥɨɜɟɤɚ ɞɜɟ ɝɢɪɢ ɦɚɫɫɨɣ 3 ɤɝ ɤɚɠɞɚɹ. Ɋɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɝɢɪɹɦɢ 1,6 ɦ. ɇɚɣɬɢ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɱɟɥɨɜɟɤɚ ɫ ɝɢɪɹɦɢ. 137. ɋ ɤɚɤɨɣ ɫɤɨɪɨɫɬɶɸ ɦɟɬɚɥɥɢɱɟɫɤɢɣ ɲɚɪɢɤ ɞɨɫɬɢɝɚɟɬ ɞɧɚ ɫɨɫɭɞɚ ɜɵɫɨɬɨɣ 0,92 ɦ, ɧɚɩɨɥɧɟɧɧɨɝɨ ɠɢɞɤɨɫɬɶɸ, ɟɫɥɢ ɟɝɨ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɜ ɦɨɦɟɧɬ ɫɨɩɪɢɤɨɫɧɨɜɟɧɢɹ ɫ ɞɧɨɦ ɫɨɫɭɞɚ ɜ 2 ɪɚɡɚ ɦɟɧɶɲɟ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɠɢɞɤɨɫɬɢ? ȼɨ ɱɬɨ ɩɪɟɜɪɚɬɢɬɫɹ ɩɨɥɨɜɢɧɚ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɲɚɪɢɤɚ? 138. ȼɵɱɢɫɥɢɬɶ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ Jz ɦɨɥɟɤɭɥɵ NO2 ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ z, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɰɟɧɬɪ ɦɚɫɫ ɦɨɥɟɤɭɥɵ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɩɥɨɫɤɨɫɬɢ, ɫɨɞɟɪɠɚɳɟɣ ɹɞɪɚ ɚɬɨɦɨɜ. Ɇɟɠɴɹɞɟɪɧɨɟ ɪɚɫɫɬɨɹɧɢɟ d ɷɬɨɣ ɦɨɥɟɤɭɥɵ ɪɚɜɧɨ 0,118 ɧɦ, ɜɚɥɟɧɬɧɵɣ ɭɝɨɥ Į = 140°. 139. ɑɟɪɟɡ ɛɥɨɤ ɜ ɜɢɞɟ ɞɢɫɤɚ, ɢɦɟɸɳɢɣ ɦɚɫɫɭ ɬ = 80 ɝ, ɩɟɪɟɤɢɧɭɬɚ ɬɨɧɤɚɹ ɝɢɛɤɚɹ ɧɢɬɶ, ɤ ɤɨɧɰɚɦ ɤɨɬɨɪɨɣ ɩɨɞɜɟɲɟɧɵ ɝɪɭɡɵ ɦɚɫɫɚɦɢ
23
m1 = 100 ɝ ɢ ɬ2 = 200 ɝ. ɋ ɤɚɤɢɦ ɭɫɤɨɪɟɧɢɟɦ ɛɭɞɭɬ ɞɜɢɝɚɬɶɫɹ ɝɪɭɡɵ, ɟɫɥɢ ɢɯ ɩɪɟɞɨɫɬɚɜɢɬɶ ɫɚɦɢɦ ɫɟɛɟ? Ɍɪɟɧɢɟɦ ɩɪɟɧɟɛɪɟɱɶ. 140. Ɍɪɢ ɦɚɥɟɧɶɤɢɯ ɲɚɪɢɤɚ ɦɚɫɫɨɣ ɬ = 10 ɝ ɤɚɠɞɵɣ ɪɚɫɩɨɥɨɠɟɧɵ ɜ ɜɟɪɲɢɧɚɯ ɪɚɜɧɨɫɬɨɪɨɧɧɟɝɨ ɬɪɟɭɝɨɥɶɧɢɤɚ ɫɨ ɫɬɨɪɨɧɨɣ ɚ = 20 ɫɦ ɢ ɫɤɪɟɩɥɟɧɵ ɦɟɠɞɭ ɫɨɛɨɣ. Ɉɩɪɟɞɟɥɢɬɶ ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ J ɫɢɫɬɟɦɵ ɨɬɧɨɫɢɬɟɥɶɧɨ ɨɫɢ: 1) ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɣ ɩɥɨɫɤɨɫɬɢ ɬɪɟɭɝɨɥɶɧɢɤɚ ɢ ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɰɟɧɬɪ ɨɩɢɫɚɧɧɨɣ ɨɤɪɭɠɧɨɫɬɢ; 2) ɥɟɠɚɳɟɣ ɜ ɩɥɨɫɤɨɫɬɢ ɬɪɟɭɝɨɥɶɧɢɤɚ ɢ ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɰɟɧɬɪ ɨɩɢɫɚɧɧɨɣ ɨɤɪɭɠɧɨɫɬɢ ɢ ɨɞɧɭ ɢɡ ɜɟɪɲɢɧ ɬɪɟɭɝɨɥɶɧɢɤɚ. Ɇɚɫɫɨɣ ɫɬɟɪɠɧɟɣ, ɫɨɟɞɢɧɹɸɳɢɯ ɲɚɪɵ, ɩɪɟɧɟɛɪɟɱɶ. 141. ȼ ɞɧɟ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɫɨɫɭɞɚ ɢɦɟɟɬɫɹ ɤɪɭɝɥɨɟ ɨɬɜɟɪɫɬɢɟ ɞɢɚɦɟɬɪɨɦ d = 1 ɫɦ. Ⱦɢɚɦɟɬɪ ɫɨɫɭɞɚ D = 0,5 ɦ. ɇɚɣɬɢ: 1) ɡɚɜɢɫɢɦɨɫɬɶ ɫɤɨɪɨɫɬɢ v ɩɨɧɢɠɟɧɢɹ ɭɪɨɜɧɹ ɜɨɞɵ ɜ ɫɨɫɭɞɟ ɨɬ ɜɵɫɨɬɵ h ɷɬɨɝɨ ɭɪɨɜɧɹ; 2) ɱɢɫɥɨɜɨɟ ɡɧɚɱɟɧɢɟ ɷɬɨɣ ɫɤɨɪɨɫɬɢ ɞɥɹ ɜɵɫɨɬɵ h = 0,2 ɦ. 142. ȼɨɞɚ ɬɟɱɟɬ ɜ ɝɨɪɢɡɨɧɬɚɥɶɧɨ ɪɚɫɩɨɥɨɠɟɧɧɨɣ ɬɪɭɛɟ ɩɟɪɟɦɟɧɧɨɝɨ ɫɟɱɟɧɢɹ. ɋɤɨɪɨɫɬɶ v1 ɜɨɞɵ ɜ ɲɢɪɨɤɨɣ ɱɚɫɬɢ ɬɪɭɛɵ ɪɚɜɧɚ 20 ɫɦ/ɫ. Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ v2 ɜ ɭɡɤɨɣ ɱɚɫɬɢ ɬɪɭɛɵ, ɞɢɚɦɟɬɪ d2 ɤɨɬɨɪɨɣ ɜ 1,5 ɪɚɡɚ ɦɟɧɶɲɟ ɞɢɚɦɟɬɪɚ ɟɟ ɲɢɪɨɤɨɣ ɱɚɫɬɢ. 143. ȼ ɲɢɪɨɤɨɣ ɱɚɫɬɢ ɝɨɪɢɡɨɧɬɚɥɶɧɨ ɪɚɫɩɨɥɨɠɟɧɧɨɣ ɬɪɭɛɵ ɧɟɮɬɶ ɬɟɱɟɬ ɫɨ ɫɤɨɪɨɫɬɶɸ v1 = 2 ɦ/ɫ. Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ v2 ɧɟɮɬɢ ɜ ɭɡɤɨɣ ɱɚɫɬɢ ɬɪɭɛɵ, ɟɫɥɢ ɪɚɡɧɨɫɬɶ ǻɪ ɞɚɜɥɟɧɢɣ ɜ ɲɢɪɨɤɨɣ ɢ ɭɡɤɨɣ ɱɚɫɬɹɯ ɟɟ ɪɚɜɧɚ 6,65 ɤɉɚ. 144. ɇɚɣɬɢ ɫɤɨɪɨɫɬɶ ɬɟɱɟɧɢɹ ɩɨ ɬɪɭɛɟ ɭɝɥɟɤɢɫɥɨɝɨ ɝɚɡɚ, ɟɫɥɢ ɢɡɜɟɫɬɧɨ, ɱɬɨ ɡɚ ɩɨɥɱɚɫɚ ɱɟɪɟɡ ɩɨɩɟɪɟɱɧɨɟ ɫɟɱɟɧɢɟ ɬɪɭɛɵ ɩɪɨɬɟɤɚɟɬ 0,51 ɤɝ ɝɚɡɚ. ɉɥɨɬɧɨɫɬɶ ɝɚɡɚ ɩɪɢɧɹɬɶ ɪɚɜɧɨɣ 7,5 ɤɝ/ɦ3. Ⱦɢɚɦɟɬɪ ɬɪɭɛɵ 2 ɫɦ. 145. ȼ ɲɢɪɨɤɨɣ ɱɚɫɬɢ ɝɨɪɢɡɨɧɬɚɥɶɧɨ ɪɚɫɩɨɥɨɠɟɧɧɨɣ ɬɪɭɛɵ ɧɟɮɬɶ ɬɟɱɟɬ ɫɨ ɫɤɨɪɨɫɬɶɸ v1 = 2 ɦ/ɫ. Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ v2 ɧɟɮɬɢ ɜ ɭɡɤɨɣ ɱɚɫɬɢ ɬɪɭɛɵ, ɟɫɥɢ ɪɚɡɧɨɫɬɶ ǻɪ ɞɚɜɥɟɧɢɣ ɜ ɲɢɪɨɤɨɣ ɢ ɭɡɤɨɣ ɱɚɫɬɹɯ ɟɟ ɪɚɜɧɚ 6,65 ɤɉɚ. 146. ȼ ɝɨɪɢɡɨɧɬɚɥɶɧɨ ɪɚɫɩɨɥɨɠɟɧɧɨɣ ɬɪɭɛɟ ɫ ɩɥɨɳɚɞɶɸ S1 ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ, ɪɚɜɧɨɣ 20 ɫɦ2, ɬɟɱɟɬ ɠɢɞɤɨɫɬɶ. ȼ ɨɞɧɨɦ ɦɟɫɬɟ ɬɪɭɛɚ ɢɦɟɟɬ ɫɭɠɟɧɢɟ, ɜ ɤɨɬɨɪɨɦ ɩɥɨɳɚɞɶ S2 ɫɟɱɟɧɢɹ ɪɚɜɧɚ 12 ɫɦ2. Ɋɚɡɧɨɫɬɶ ǻh ɭɪɨɜɧɟɣ ɜ ɞɜɭɯ ɦɚɧɨɦɟɬɪɢɱɟɫɤɢɯ ɬɪɭɛɤɚɯ, ɭɫɬɚɧɨɜɥɟɧɧɵɯ ɜ ɲɢɪɨɤɨɣ ɢ ɭɡɤɨɣ ɱɚɫɬɹɯ ɬɪɭɛɵ, ɪɚɜɧɚ 8 ɫɦ. Ɉɩɪɟɞɟɥɢɬɶ ɨɛɴɟɦɧɵɣ ɪɚɫɯɨɞ Qv ɠɢɞɤɨɫɬɢ. 147. Ʉ ɩɨɪɲɧɸ ɫɩɪɢɧɰɨɜɤɢ, ɪɚɫɩɨɥɨɠɟɧɧɨɣ ɝɨɪɢɡɨɧɬɚɥɶɧɨ, ɩɪɢɥɨɠɟɧɚ ɫɢɥɚ F = 15 H. Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ v ɢɫɬɟɱɟɧɢɹ ɜɨɞɵ ɢɡ ɧɚɤɨɧɟɱɧɢɤɚ ɫɩɪɢɧɰɨɜɤɢ, ɟɫɥɢ ɩɥɨɳɚɞɶ S ɩɨɪɲɧɹ ɪɚɜɧɚ 12 ɫɦ2. 148. ȼ ɫɨɫɭɞ ɥɶɟɬɫɹ ɜɨɞɚ, ɩɪɢɱɟɦ ɡɚ 1 ɫ ɧɚɥɢɜɚɟɬɫɹ 0,2 ɥ ɜɨɞɵ. Ʉɚɤɨɜ ɞɨɥɠɟɧ ɛɵɬɶ ɞɢɚɦɟɬɪ d ɨɬɜɟɪɫɬɢɹ ɜ ɞɧɟ ɫɨɫɭɞɚ, ɱɬɨɛɵ ɜɨɞɚ ɜ ɧɟɦ ɞɟɪɠɚɥɚɫɶ ɧɚ ɩɨɫɬɨɹɧɧɨɦ ɭɪɨɜɧɟ h = 8,3 ɫɦ? 149. Ⱦɚɜɥɟɧɢɟ ɪ ɜɟɬɪɚ ɧɚ ɫɬɟɧɭ ɪɚɜɧɨ 200 ɉɚ. Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ v ɜɟɬɪɚ, ɟɫɥɢ ɨɧ ɞɭɟɬ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɫɬɟɧɟ. ɉɥɨɬɧɨɫɬɶ ɪ ɜɨɡɞɭɯɚ ɪɚɜɧɚ 1,29 ɤɝ/ɦ3. 24
150. ɋɬɪɭɹ ɜɨɞɵ ɞɢɚɦɟɬɪɨɦ d = 2 ɫɦ, ɞɜɢɠɭɳɚɹɫɹ ɫɨ ɫɤɨɪɨɫɬɶɸ v = 10 ɦ/ɫ, ɭɞɚɪɹɟɬɫɹ ɨ ɧɟɩɨɞɜɢɠɧɭɸ ɩɥɨɫɤɭɸ ɩɨɜɟɪɯɧɨɫɬɶ, ɩɨɫɬɚɜɥɟɧɧɭɸ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɫɬɪɭɟ. ɇɚɣɬɢ ɫɢɥɭ F ɞɚɜɥɟɧɢɹ ɫɬɪɭɢ ɧɚ ɩɨɜɟɪɯɧɨɫɬɶ, ɫɱɢɬɚɹ, ɱɬɨ ɩɨɫɥɟ ɭɞɚɪɚ ɨ ɩɨɜɟɪɯɧɨɫɬɶ ɫɤɨɪɨɫɬɶ ɱɚɫɬɢɰ ɜɨɞɵ ɪɚɜɧɚ ɧɭɥɸ. 151. Ɉɩɪɟɞɟɥɢɬɶ ɩɟɪɢɨɞ T, ɱɚɫɬɨɬɭ Q ɢ ɧɚɱɚɥɶɧɭɸ ɮɚɡɭ ij0 ɤɨɥɟɛɚɧɢɣ, ɡɚɞɚɧɧɵɯ ɭɪɚɜɧɟɧɢɟɦ ɯ = Ⱥ sinȦ(t+IJ), ɝɞɟ Ȧ = 2,5ʌɫ-1, IJ = 0,4 ɫ. 152. Ⱥɦɩɥɢɬɭɞɚ ɝɚɪɦɨɧɢɱɟɫɤɢɯ ɤɨɥɟɛɚɧɢɣ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ Ⱥ = 2 ɫɦ, ɩɨɥɧɚɹ ɷɧɟɪɝɢɹ ɤɨɥɟɛɚɧɢɣ W = 0,3 ɦɤȾɠ. ɉɪɢ ɤɚɤɨɦ ɫɦɟɳɟɧɢɢ ʌ ɨɬ ɩɨɥɨɠɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ ɧɚ ɤɨɥɟɛɥɸɳɭɸɫɹ ɬɨɱɤɭ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ F = 22,5 ɦɤɇ? 153. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɚɦɩɥɢɬɭɞɚ ɜɵɧɭɠɞɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɛɭɞɟɬ ɦɟɧɶɲɟ ɪɟɡɨɧɚɧɫɧɨɣ ɚɦɩɥɢɬɭɞɵ, ɟɫɥɢ ɱɚɫɬɨɬɚ ɢɡɦɟɧɟɧɢɹ ɜɵɧɭɠɞɚɸɳɟɣ ɫɢɥɵ ɛɭɞɟɬ ɛɨɥɶɲɟ ɪɟɡɨɧɚɧɫɧɨɣ ɱɚɫɬɨɬɵ: 1) ɧɚ 10 %? 2) ɜ ɞɜɚ ɪɚɡɚ? Ʉɨɷɮɮɢɰɢɟɧɬ ɡɚɬɭɯɚɧɢɹ į ɜ ɨɛɨɢɯ ɫɥɭɱɚɹɯ ɩɪɢɧɹɬɶ ɪɚɜɧɵɦ 0,1 Ȧ0 ( Ȧ0 – ɭɝɥɨɜɚɹ ɱɚɫɬɨɬɚ ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ). 154. Ⱦɜɚ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɦɚɹɬɧɢɤɚ, ɤɚɠɞɵɣ ɞɥɢɧɨɸ l = 50 ɫɦ ɢ ɦɚɫɫɨɣ ɬ = 45 ɝ, ɫɨɟɞɢɧɟɧɵ ɩɪɭɠɢɧɤɨɣ ɠɟɫɬɤɨɫɬɶɸ x = 0,66 ɇ/ɦ. ɉɪɢ ɪɚɜɧɨɜɟɫɢɢ ɦɚɹɬɧɢɤɢ ɡɚɧɢɦɚɸɬ ɜɟɪɬɢɤɚɥɶɧɨɟ ɩɨɥɨɠɟɧɢɟ. ɇɚɣɬɢ ɩɟɪɢɨɞ ɦɚɥɵɯ ɤɨɥɟɛɚɧɢɣ ɷɬɢɯ ɦɚɹɬɧɢɤɨɜ, ɟɫɥɢ ɢɯ ɤɨɥɟɛɚɧɢɹ ɩɪɨɢɫɯɨɞɹɬ ɜ ɜɟɪɬɢɤɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɵɟ ɫɬɨɪɨɧɵ (ɜ ɩɪɨɬɢɜɨɮɚɡɟ). 155. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɚɦɩɥɢɬɭɞɚ ɜɵɧɭɠɞɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ ɛɭɞɟɬ ɦɟɧɶɲɟ ɪɟɡɨɧɚɧɫɧɨɣ ɚɦɩɥɢɬɭɞɵ, ɟɫɥɢ ɱɚɫɬɨɬɚ ɢɡɦɟɧɟɧɢɹ ɜɵɧɭɠɞɚɸɳɟɣ ɫɢɥɵ ɛɭɞɟɬ ɛɨɥɶɲɟ ɪɟɡɨɧɚɧɫɧɨɣ ɱɚɫɬɨɬɵ: 1) ɧɚ 10 %? 2) ɜ ɞɜɚ ɪɚɡɚ? Ʉɨɷɮɮɢɰɢɟɧɬ ɡɚɬɭɯɚɧɢɹ į ɜ ɨɛɨɢɯ ɫɥɭɱɚɹɯ ɩɪɢɧɹɬɶ ɪɚɜɧɵɦ 0,1 Ȧ0 (Ȧ0 – ɭɝɥɨɜɚɹ ɱɚɫɬɨɬɚ ɫɨɛɫɬɜɟɧɧɵɯ ɤɨɥɟɛɚɧɢɣ). 156. Ƚɢɪɹ ɦɚɫɫɨɣ ɬ = 500 ɝ ɩɨɞɜɟɲɟɧɚ ɤ ɫɩɢɪɚɥɶɧɨɣ ɩɪɭɠɢɧɟ ɠɟɫɬɤɨɫɬɶɸ k = 20 ɇ/ɦ ɢ ɫɨɜɟɪɲɚɟɬ ɭɩɪɭɝɢɟ ɤɨɥɟɛɚɧɢɹ ɜ ɧɟɤɨɬɨɪɨɣ ɫɪɟɞɟ. Ʌɨɝɚɪɢɮɦɢɱɟɫɤɢɣ ɞɟɤɪɟɦɟɧɬ ɤɨɥɟɛɚɧɢɣ ș = 0,004. Ɉɩɪɟɞɟɥɢɬɶ ɱɢɫɥɨ N ɩɨɥɧɵɯ ɤɨɥɟɛɚɧɢɣ, ɤɨɬɨɪɵɟ ɞɨɥɠɧɚ ɫɨɜɟɪɲɢɬɶ ɝɢɪɹ, ɱɬɨɛɵ ɚɦɩɥɢɬɭɞɚ ɤɨɥɟɛɚɧɢɣ ɭɦɟɧɶɲɢɥɚɫɶ ɜ n = 2 ɪɚɡɚ. Ɂɚ ɤɚɤɨɟ ɜɪɟɦɹ t ɩɪɨɢɡɨɣɞɟɬ ɷɬɨ ɭɦɟɧɶɲɟɧɢɟ? 157. ɋɢɫɬɟɦɚ ɢɡ ɬɪɟɯ ɝɪɭɡɨɜ, ɫɨɟɞɢɧɟɧɧɵɯ ɫɬɟɪɠɧɹɦɢ ɞɥɢɧɨɣ l = 30 ɫɦ, ɤɨɥɟɛɥɟɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɨɫɢ, ɩɪɨɯɨɞɹɳɟɣ ɱɟɪɟɡ ɬɨɱɤɭ Ɉ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɩɥɨɫɤɨɫɬɢ ɱɟɪɬɟɠɚ. ɇɚɣɬɢ ɩɟɪɢɨɞ Ɍ ɤɨɥɟɛɚɧɢɣ ɫɢɫɬɟɦɵ. Ɇɚɫɫɚɦɢ ɫɬɟɪɠɧɟɣ ɩɪɟɧɟɛɪɟɱɶ, ɝɪɭɡɵ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɦɚɬɟɪɢɚɥɶɧɵɟ ɬɨɱɤɢ. 158. ɑɟɦɭ ɪɚɜɧɨ ɨɬɧɨɲɟɧɢɟ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɬɨɱɤɢ, ɫɨɜɟɪɲɚɸɳɟɣ ɝɚɪɦɨɧɢɱɟɫɤɨɟ ɤɨɥɟɛɚɧɢɟ, ɤ ɟɟ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɞɥɹ ɦɨɦɟɧɬɨɜ ɜɪɟɦɟɧɢ: 1) t = T/12, 2) t = T/8, 3) t = T/6? ɇɚɱɚɥɶɧɚɹ ɮɚɡɚ ɤɨɥɟɛɚɧɢɣ ɪɚɜɧɚ ʌ/6. 159. Ɍɨɱɤɚ ɭɱɚɫɬɜɭɟɬ ɨɞɧɨɜɪɟɦɟɧɧɨ ɜ ɞɜɭɯ ɤɨɥɟɛɚɧɢɹɯ ɨɞɧɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ: x1 = AcosȦt ɢ ɯ2 = Acos2Ȧt. ɇɚɣɬɢ ɦɚɤɫɢɦɚɥɶɧɭɸ ɫɤɨɪɨɫɬɶ ɬɨɱɤɢ. 25
160. ɇɚɣɬɢ ɩɟɪɢɨɞ ɦɚɥɵɯ ɩɨɩɟɪɟɱɧɵɯ ɤɨɥɟɛɚɧɢɣ ɲɚɪɢɤɚ ɦɚɫɫɨɣ m = 40 ɝ, ɭɤɪɟɩɥɟɧɧɨɝɨ ɧɚ ɫɟɪɟɞɢɧɟ ɧɚɬɹɧɭɬɨɣ ɫɬɪɭɧɵ ɞɥɢɧɵ l = 1,0 ɦ. ɋɢɥɭ ɧɚɬɹɠɟɧɢɹ ɫɬɪɭɧɵ ɫɱɢɬɚɬɶ ɩɨɫɬɨɹɧɧɨɣ ɢ ɪɚɜɧɨɣ F = 10 ɇ. Ɇɚɫɫɨɣ ɫɬɪɭɧɵ ɢ ɫɢɥɚɦɢ ɬɹɠɟɫɬɢ ɩɪɟɧɟɛɪɟɱɶ. 161. Ʉɚɤɨɟ ɤɨɥɢɱɟɫɬɜɨ ɫɬɨɥɤɧɨɜɟɧɢɣ ɢɫɩɵɬɵɜɚɟɬ ɡɚ 1 ɫ ɦɨɥɟɤɭɥɚ ɚɪɝɨɧɚ, ɟɫɥɢ ɞɚɜɥɟɧɢɟ ɝɚɡɚ ɪ = 1,3 10-3 ɉɚ, ɬɟɦɩɟɪɚɬɭɪɚ Ɍ = 290 Ʉ, ɚ ɷɮɮɟɤɬɢɜɧɵɣ ɞɢɚɦɟɬɪ ɦɨɥɟɤɭɥɵ ɚɪɝɨɧɚ d = 2,9 10-10 ɦ? 162. ȼ ɛɚɥɥɨɧɟ ɟɦɤɨɫɬɶɸ V = 15 ɥ ɧɚɯɨɞɢɬɫɹ ɫɦɟɫɶ, ɫɨɞɟɪɠɚɳɚɹ m1 = 10 ɝ ɜɨɞɨɪɨɞɚ, m2 = 54 ɝ ɜɨɞɹɧɨɝɨ ɩɚɪɚ ɢ m3 = 60 ɝ ɨɤɢɫɢ ɭɝɥɟɪɨɞɚ. Ɍɟɦɩɟɪɚɬɭɪɚ ɫɦɟɫɢ t = 27 0ɋ. Ɉɩɪɟɞɟɥɢɬɶ ɞɚɜɥɟɧɢɟ. 163. Ʉɚɤɨɣ ɨɛɴɟɦ V ɡɚɧɢɦɚɟɬ ɫɦɟɫɶ ɚɡɨɬɚ ɦɚɫɫɨɣ m1 = 1 ɤɝ ɢ ɝɟɥɢɹ m2 = 1 ɤɝ ɩɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ? 164. Ƚɚɡ ɩɪɢ ɞɚɜɥɟɧɢɢ 8 ɚɬɦ ɢ ɬɟɦɩɟɪɚɬɭɪɟ 12 0ɋ ɡɚɧɢɦɚɟɬ ɨɛɴɟɦ 855 ɥ. Ʉɚɤɨɜɨ ɛɭɞɟɬ ɞɚɜɥɟɧɢɟ, ɟɫɥɢ ɷɬɚ ɠɟ ɦɚɫɫɚ ɝɚɡɚ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ 47 0ɋ ɡɚɣɦɟɬ ɨɛɴɟɦ 800 ɥ? 165. Ⱦɜɚ ɨɞɢɧɚɤɨɜɵɯ ɫɨɫɭɞɚ ɫɨɟɞɢɧɟɧɵ ɬɪɭɛɤɨɣ, ɨɛɴɟɦɨɦ ɤɨɬɨɪɨɣ ɦɨɠɧɨ ɩɪɟɧɟɛɪɟɱɶ. ɋɢɫɬɟɦɚ ɧɚɩɨɥɧɟɧɚ ɝɚɡɨɦ ɢ ɧɚɯɨɞɢɬɫɹ ɩɪɢ ɚɛɫɨɥɸɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɟ Ɍ. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɢɡɦɟɧɢɬɫɹ ɞɚɜɥɟɧɢɟ ɜ ɬɚɤɨɣ ɫɢɫɬɟɦɟ, ɟɫɥɢ ɨɞɢɧ ɢɡ ɫɨɫɭɞɨɜ ɧɚɝɪɟɬɶ ɞɨ ɚɛɫɨɥɸɬɧɨɣ ɬɟɦɩɟɪɚɬɭɪɵ Ɍ1, ɚ ɞɪɭɝɨɣ ɩɨɞɞɟɪɠɢɜɚɬɶ ɩɪɢ ɩɪɟɠɧɟɣ ɬɟɦɩɟɪɚɬɭɪɟ Ɍ? 166. ɋɦɟɫɶ ɝɚɡɨɜ ɫɨɫɬɨɢɬ ɢɡ ɚɪɝɨɧɚ ɢ ɚɡɨɬɚ, ɜɡɹɬɵɯ ɩɪɢ ɨɞɢɧɚɤɨɜɵɯ ɭɫɥɨɜɢɹɯ ɢ ɜ ɨɞɢɧɚɤɨɜɵɯ ɨɛɴɟɦɚɯ. Ɉɩɪɟɞɟɥɢɬɶ ɩɨɤɚɡɚɬɟɥɶ ɚɞɢɚɛɚɬɵ Ȗ ɬɚɤɨɣ ɫɦɟɫɢ. 167. Ƚɟɥɢɣ, ɡɚɧɢɦɚɸɳɢɣ ɨɛɴɟɦ V = 1ɦ3 , ɧɚɯɨɞɢɬɫɹ ɩɨɞ ɞɚɜɥɟɧɢɟɦ ɪ = 102 ɉɚ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ Ɍ = 273 Ʉ. ɇɚɣɬɢ ɱɢɫɥɨ ɦɨɥɟɤɭɥ, ɤɨɬɨɪɵɟ ɜ ɬɟɱɟɧɢɟ 1 ɫ ɩɪɨɥɟɬɹɬ ɛɟɡ ɫɨɭɞɚɪɟɧɢɣ ɪɚɫɫɬɨɹɧɢɟ ɯ = 2·10-10 ɦ. ɗɮɮɟɤɬɢɜɧɵɣ ɞɢɚɦɟɬɪ ɦɨɥɟɤɭɥɵ ɝɟɥɢɹ d = 2,2·10-10 ɦ. 168. ȼ ɛɚɥɥɨɧɟ ɟɦɤɨɫɬɶɸ V = 15 ɥ ɧɚɯɨɞɢɬɫɹ ɫɦɟɫɶ, ɫɨɞɟɪɠɚɳɚɹ m1 = 10 ɝ ɜɨɞɨɪɨɞɚ, m2 = 54 ɝ ɜɨɞɹɧɨɝɨ ɩɚɪɚ ɢ m3 = 60 ɝ ɨɤɢɫɢ ɭɝɥɟɪɨɞɚ. Ɍɟɦɩɟɪɚɬɭɪɚ ɫɦɟɫɢ t = 27 0ɋ. Ɉɩɪɟɞɟɥɢɬɶ ɞɚɜɥɟɧɢɟ. 169. Ʉɚɤɨɟ ɤɨɥɢɱɟɫɬɜɨ ɫɬɨɥɤɧɨɜɟɧɢɣ ɢɫɩɵɬɵɜɚɟɬ ɡɚ 1 ɫ ɦɨɥɟɤɭɥɚ ɚɪɝɨɧɚ, ɟɫɥɢ ɞɚɜɥɟɧɢɟ ɝɚɡɚ ɪ = 1,3 10-3 ɉɚ, ɬɟɦɩɟɪɚɬɭɪɚ Ɍ = 290 Ʉ, ɚ ɷɮɮɟɤɬɢɜɧɵɣ ɞɢɚɦɟɬɪ ɦɨɥɟɤɭɥɵ ɚɪɝɨɧɚ d = 2,9 10-10 ɦ? 170. Ȼɚɥɥɨɧ ɜɦɟɫɬɢɦɨɫɬɶɸ V = 30 ɥ ɫɨɞɟɪɠɢɬ ɫɦɟɫɶ ɜɨɞɨɪɨɞɚ ɢ ɝɟɥɢɹ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ T = 300 Ʉ ɢ ɞɚɜɥɟɧɢɢ P = 828 ɤɉɚ. Ɇɚɫɫɚ ɬ ɫɦɟɫɢ ɪɚɜɧɚ 24 ɝ. Ɉɩɪɟɞɟɥɢɬɶ ɦɚɫɫɭ ɬ1 ɜɨɞɨɪɨɞɚ ɢ ɦɚɫɫɭ ɬ2 ɝɟɥɢɹ. 171. ɇɚɣɬɢ ɫɪɟɞɧɸɸ ɞɥɢɧɭ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɦɨɥɟɤɭɥɵ ɤɢɫɥɨɪɨɞɚ ɩɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ (ɷɮɮɟɤɬɢɜɧɵɣ ɞɢɚɦɟɬɪ ɦɨɥɟɤɭɥɵ ɤɢɫɥɨɪɨɞɚ 2,7 · 10-10 ɦ). 172. ȼɵɱɢɫɥɢɬɶ ɫɪɟɞɧɸɸ ɞɥɢɧɭ ɫɜɨɛɨɞɧɨɝɨ ɩɪɨɛɟɝɚ ɦɨɥɟɤɭɥ ɤɢɫɥɨɪɨɞɚ ɩɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ, ɟɫɥɢ ɢɡɜɟɫɬɧɨ, ɱɬɨ ɡɚ 1 ɫ ɤɚɠɞɚɹ ɦɨɥɟɤɭɥɚ ɫɬɚɥɤɢɜɚɟɬɫɹ ɫ ɞɪɭɝɢɦɢ ɜ ɫɪɟɞɧɟɦ 6,5 · 109 ɪɚɡ. 26
173. ɋɤɨɥɶɤɨ ɫɬɨɥɤɧɨɜɟɧɢɣ ɡɚ 1 ɫ ɢɫɩɵɬɵɜɚɟɬ ɦɨɥɟɤɭɥɚ ɧɟɨɧɚ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ 600 Ʉ ɢ ɞɚɜɥɟɧɢɢ 1 ɦɦ ɪɬ. ɫɬ. (ɷɮɮɟɤɬɢɜɧɵɣ ɞɢɚɦɟɬɪ ɦɨɥɟɤɭɥɵ ɧɟɨɧɚ 2,04 · 10-10 ɦ)? 174. ȼɨɞɚ ɩɪɢ ɫɨɛɥɸɞɟɧɢɢ ɧɟɨɛɯɨɞɢɦɵɯ ɩɪɟɞɨɫɬɨɪɨɠɧɨɫɬɟɣ ɦɨɠɟɬ ɛɵɬɶ ɩɟɪɟɨɯɥɚɠɞɟɧɚ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ t = –10 °ɋ. Ʉɚɤɚɹ ɦɚɫɫɚ ɥɶɞɚ ɬ ɨɛɪɚɡɭɟɬɫɹ ɢɡ M = 1 ɤɝ ɬɚɤɨɣ ɜɨɞɵ, ɟɫɥɢ ɛɪɨɫɢɬɶ ɜ ɧɟɟ ɤɭɫɨɱɟɤ ɥɶɞɚ ɢ ɬɟɦ ɜɵɡɜɚɬɶ ɡɚɦɟɪɡɚɧɢɟ? Ɍɟɩɥɨɟɦɤɨɫɬɶ ɩɟɪɟɨɯɥɚɠɞɟɧɧɨɣ ɜɨɞɵ ɫɱɢɬɚɬɶ ɧɟ ɡɚɜɢɫɹɳɟɣ ɨɬ ɬɟɦɩɟɪɚɬɭɪɵ ɢ ɪɚɜɧɨɣ ɬɟɩɥɨɟɦɤɨɫɬɢ ɨɛɵɱɧɨɣ ɜɨɞɵ. 175. Ɉɩɪɟɞɟɥɢɬɶ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɚ Q, ɜɵɞɟɥɹɸɳɟɟɫɹ ɩɪɢ ɢɡɨɬɟɪɦɢɱɟɫɤɨɦ ɫɠɚɬɢɢ ɬ = 7 ɝ ɚɡɨɬɚ, ɟɫɥɢ ɩɪɢ ɷɬɨɦ ɞɚɜɥɟɧɢɟ ɝɚɡɚ ɩɨɜɵɲɚɟɬɫɹ ɜ n = 50 ɪɚɡ. Ɉɩɪɟɞɟɥɢɬɶ ɬɚɤɠɟ ɪɚɛɨɬɭ Ⱥ, ɤɨɬɨɪɭɸ ɧɚɞɨ ɡɚɬɪɚɬɢɬɶ ɧɚ ɷɬɨ ɫɠɚɬɢɟ. Ɍɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ Ɍ = 27 °ɋ. 176. ɋɬɚɥɶɧɨɣ ɲɚɪɢɤ ɞɢɚɦɟɬɪɚ d = 3,0 ɦɦ ɨɩɭɫɤɚɟɬɫɹ ɫ ɧɭɥɟɜɨɣ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɶɸ ɜ ɩɪɨɜɚɧɫɤɨɦ ɦɚɫɥɟ, ɜɹɡɤɨɫɬɶ ɤɨɬɨɪɨɝɨ Ș = 90 ɦɉɚ·ɫ. ɑɟɪɟɡ ɫɤɨɥɶɤɨ ɜɪɟɦɟɧɢ ɩɨɫɥɟ ɧɚɱɚɥɚ ɞɜɢɠɟɧɢɹ ɫɤɨɪɨɫɬɶ ɲɚɪɢɤɚ ɛɭɞɟɬ ɨɬɥɢɱɚɬɶɫɹ ɨɬ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɡɧɚɱɟɧɢɹ ɧɚ n = 10 %? 177. ɇɚɣɬɢ ɱɢɫɥɨ ɯɨɞɨɜ ɩ ɩɨɪɲɧɹ, ɱɬɨɛɵ ɩɨɪɲɧɟɜɵɦ ɜɨɡɞɭɲɧɵɦ ɧɚɫɨɫɨɦ ɨɬɤɚɱɚɬɶ ɫɨɫɭɞ ɟɦɤɨɫɬɶɸ V ɨɬ ɞɚɜɥɟɧɢɹ Ɋ1 ɞɨ ɞɚɜɥɟɧɢɹ P2, ɟɫɥɢ ɟɦɤɨɫɬɶ ɯɨɞɚ ɩɨɪɲɧɹ ɪɚɜɧɚ V. ȼɪɟɞɧɵɦ ɩɪɨɫɬɪɚɧɫɬɜɨɦ ɩɪɟɧɟɛɪɟɱɶ. 178. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɫɤɨɪɨɫɬɶ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɡɜɭɤɚ ɜ ɜɨɡɞɭɯɟ ɥɟɬɨɦ (ɬɟɦɩɟɪɚɬɭɪɚ t = +27 ɨɋ) ɛɨɥɶɲɟ ɫɤɨɪɨɫɬɢ ɪɚɫɩɪɨɫɬɪɚɧɟɧɢɹ ɡɜɭɤɚ ɡɢɦɨɣ (ɬɟɦɩɟɪɚɬɭɪɚ t = –33 ɨɋ)? 179. Ɋɚɡɧɨɫɬɶ ɭɞɟɥɶɧɵɯ ɬɟɩɥɨɟɦɤɨɫɬɟɣ ɧɟɤɨɬɨɪɨɝɨ ɞɜɭɯɚɬɨɦɧɨɝɨ ɝɚɡɚ 260 Ⱦɠ/(ɤɝ · Ʉ). ɇɚɣɬɢ ɦɚɫɫɭ ɨɞɧɨɝɨ ɤɢɥɨɦɨɥɹ ɝɚɡɚ ɢ ɟɝɨ ɭɞɟɥɶɧɵɟ ɬɟɩɥɨɟɦɤɨɫɬɢ. 180. ɉɪɢ ɢɡɨɛɚɪɢɱɟɫɤɨɦ ɪɚɫɲɢɪɟɧɢɢ ɞɜɭɯɚɬɨɦɧɨɝɨ ɝɚɡɚ ɛɵɥɚ ɫɨɜɟɪɲɟɧɚ ɪɚɛɨɬɚ Ⱥ. Ʉɚɤɨɟ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ ɫɨɨɛɳɟɧɨ ɝɚɡɭ? 181. Ɇɚɫɫɚ m 2 ɝ ɚɡɨɬɚ, ɧɚɯɨɞɹɳɟɝɨɫɹ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ t = 0 0ɋ ɢ ɞɚɜɥɟɧɢɢ ɪ 0,2 Ɇɉɚ, ɢɡɨɬɟɪɦɢɱɟɫɤɢ ɪɚɫɲɢɪɹɟɬɫɹ ɡɚ ɫɱɟɬ ɩɨɥɭɱɟɧɧɨɝɨ ɢɡɜɧɟ ɬɟɩɥɚ ɞɨ ɨɛɴɟɦɚ V = 2 ɥ. ɇɚɣɬɢ: 1) ɪɚɛɨɬɭ, ɫɨɜɟɪɲɟɧɧɭɸ ɝɚɡɨɦ ɩɪɢ ɪɚɫɲɢɪɟɧɢɢ, 2) ɤɨɥɢɱɟɫɬɜɨ ɫɨɨɛɳɟɧɧɨɣ ɝɚɡɭ ɬɟɩɥɨɬɵ. 182. Ʉɚɤɨɟ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɚ Q ɩɨɬɪɟɛɭɟɬɫɹ ɧɚ ɧɚɝɪɟɜɚɧɢɟ 1 ɦ3 ɜɨɡɞɭɯɚ ɨɬ 0 ɞɨ 1 °ɋ ɩɪɢ ɩɨɫɬɨɹɧɧɨɦ ɨɛɴɟɦɟ ɢ ɧɚɱɚɥɶɧɨɦ ɞɚɜɥɟɧɢɢ ɪ = 760 ɦɦ ɪɬ. ɫɬ.? ɉɥɨɬɧɨɫɬɶ ɜɨɡɞɭɯɚ ɩɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ȡ0 = 0,00129 ɝ/ɫɦ3, ɫɊ = 0,237 ɤɚɥ/(ɝ°ɋ), Ȗ = cP/cv = 1,41. 183. ȼɟɪɬɢɤɚɥɶɧɚɹ ɤɚɩɢɥɥɹɪɧɚɹ ɫɬɟɤɥɹɧɧɚɹ ɬɪɭɛɤɚ ɩɨɞɜɟɲɟɧɚ ɤ ɤɨɪɨɦɵɫɥɭ ɜɟɫɨɜ ɢ ɭɪɚɜɧɨɜɟɲɟɧɚ ɝɢɪɹɦɢ. ɑɬɨ ɩɪɨɢɡɨɣɞɟɬ ɫ ɜɟɫɚɦɢ, ɟɫɥɢ ɩɨɞ ɤɚɩɢɥɥɹɪɧɭɸ ɬɪɭɛɤɭ ɨɫɬɨɪɨɠɧɨ ɩɨɞɧɟɫɬɢ ɫɨɫɭɞ ɫ ɜɨɞɨɣ ɬɚɤ, ɱɬɨɛɵ ɤɨɧɱɢɤ ɤɚɩɢɥɥɹɪɚ ɤɨɫɧɭɥɫɹ ɟɟ ɩɨɜɟɪɯɧɨɫɬɢ? 184. Ɇɚɫɫɚ m = 10 ɝ ɤɢɫɥɨɪɨɞɚ ɧɚɯɨɞɢɬɫɹ ɩɪɢ ɞɚɜɥɟɧɢɢ p = 0,3 Ɇɉɚ ɢ ɬɟɦɩɟɪɚɬɭɪɟ t = 10 °ɋ. ɉɨɫɥɟ ɧɚɝɪɟɜɚɧɢɹ ɩɪɢ ɪ- const ɝɚɡ ɡɚɧɹɥ ɨɛɴɟɦ V = 10 ɥ. ɇɚɣɬɢ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ Q, ɩɨɥɭɱɟɧɧɨɟ ɝɚɡɨɦ, ɢ ɷɧɟɪɝɢɸ ɬɟɩɥɨɜɨɝɨ ɞɜɢɠɟɧɢɹ ɦɨɥɟɤɭɥ ɝɚɡɚ W ɞɨ ɢ ɩɨɫɥɟ ɧɚɝɪɟɜɚɧɢɹ. 27
185. Ⱦɜɟ ɠɢɞɤɨɫɬɢ ɧɚɝɪɟɜɚɸɬɫɹ ɜ ɨɞɢɧɚɤɨɜɵɯ ɫɨɫɭɞɚɯ ɨɞɧɢɦ ɢ ɬɟɦ ɠɟ ɷɥɟɤɬɪɢɱɟɫɤɢɦ ɬɨɤɨɦ, ɞɥɹ ɱɟɝɨ ɜ ɤɚɠɞɵɣ ɫɨɫɭɞ ɜɫɬɚɜɥɟɧɵ ɨɞɢɧɚɤɨɜɵɟ ɩɪɨɜɨɥɨɱɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ. ȼ ɩɟɪɜɨɦ ɫɨɫɭɞɟ ɠɢɞɤɨɫɬɶ ɧɚɝɪɟɥɚɫɶ ɨɬ t0 ɞɨ t1. Ɇɚɫɫɚ ɠɢɞɤɨɫɬɢ ɜ ɩɟɪɜɨɦ ɫɨɫɭɞɟ ɬ, ɭɞɟɥɶɧɚɹ ɬɟɩɥɨɟɦɤɨɫɬɶ ɫ, ɩɨɥɧɚɹ ɬɟɩɥɨɟɦɤɨɫɬɶ ɩɟɪɜɨɝɨ ɫɨɫɭɞɚ ɋ1. Ɉɩɪɟɞɟɥɢɬɶ ɭɞɟɥɶɧɭɸ ɬɟɩɥɨɟɦɤɨɫɬɶ ɠɢɞɤɨɫɬɢ ɫ', ɧɚɥɢɬɨɣ ɜɨ ɜɬɨɪɨɣ ɫɨɫɭɞ, ɟɫɥɢ ɡɚ ɬɨ ɠɟ ɜɪɟɦɹ ɨɧɚ ɧɚɝɪɟɥɚɫɶ ɨɬ t' ɞɨ t’1. ɉɨɥɧɚɹ ɬɟɩɥɨɟɦɤɨɫɬɶ ɜɬɨɪɨɝɨ ɫɨɫɭɞɚ ɋ'1, ɚ ɦɚɫɫɚ ɠɢɞɤɨɫɬɢ ɜ ɧɟɦ ɬ'. 186. Ɉɩɪɟɞɟɥɢɬɶ ɭɞɟɥɶɧɵɟ ɬɟɩɥɨɟɦɤɨɫɬɢ cV ɢ ɫp ɫɦɟɫɢ, ɫɨɞɟɪɠɚɳɟɣ m1 = 3 ɤɝ ɚɡɨɬɚ ɢ m2 = 1 ɤɝ ɜɨɞɹɧɨɝɨ ɩɚɪɚ, ɩɪɢɧɢɦɚɹ ɷɬɢ ɝɚɡɵ ɡɚ ɢɞɟɚɥɶɧɵɟ. 187. ɂɞɟɚɥɶɧɚɹ ɬɟɩɥɨɜɚɹ ɦɚɲɢɧɚ ɪɚɛɨɬɚɟɬ ɩɨ ɰɢɤɥɭ Ʉɚɪɧɨ. ɉɪɢ ɷɬɨɦ 80 % ɬɟɩɥɚ, ɩɨɥɭɱɚɟɦɨɝɨ ɨɬ ɧɚɝɪɟɜɚɬɟɥɹ, ɩɟɪɟɞɚɟɬɫɹ ɨɯɥɚɞɢɬɟɥɸ. Ʉɨɥɢɱɟɫɬɜɨ ɬɟɩɥɚ, ɩɨɥɭɱɚɟɦɨɝɨ ɨɬ ɧɚɝɪɟɜɚɬɟɥɹ, ɪɚɜɧɨ 300 Ⱦɠ. ɇɚɣɬɢ: 1) ɤɨɷɮɮɢɰɢɟɧɬ ɩɨɥɟɡɧɨɝɨ ɞɟɣɫɬɜɢɹ (ɤ.ɩ.ɞ.) ɰɢɤɥɚ, 2) ɪɚɛɨɬɭ, ɫɨɜɟɪɲɟɧɧɭɸ ɩɪɢ ɩɨɥɧɨɦ ɰɢɤɥɟ. 188. Ʉɢɫɥɨɪɨɞ ɩɪɢ ɧɟɢɡɦɟɧɧɨɦ ɞɚɜɥɟɧɢɢ Ɋ = 0,08 Ɇɉɚ ɧɚɝɪɟɜɚɟɬɫɹ. ȿɝɨ ɨɛɴɟɦ ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɨɬ V1 = 1 ɦ3 ɞɨ V2 = 3 ɦ3. Ɉɩɪɟɞɟɥɢɬɶ ɢɡɦɟɧɟɧɢɟ ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ U ɤɢɫɥɨɪɨɞɚ, ɪɚɛɨɬɭ, ɫɨɜɟɪɲɟɧɧɭɸ ɢɦ ɩɪɢ ɪɚɫɲɢɪɟɧɢɢ, ɚ ɬɚɤɠɟ ɬɟɩɥɨɬɭ, ɫɨɨɛɳɟɧɧɭɸ ɝɚɡɨɦ. 189. ȼ ɫɨɫɭɞɟ ɜɦɟɫɬɢɦɨɫɬɶɸ V = 10 ɥ ɧɚɯɨɞɢɬɫɹ ɚɡɨɬ ɦɚɫɫɨɣ ɬ = 25 ɤɝ. Ɉɩɪɟɞɟɥɢɬɶ: 1) ɜɧɭɬɪɟɧɧɟɟ ɞɚɜɥɟɧɢɟ ɪ ɝɚɡɚ; 2) ɫɨɛɫɬɜɟɧɧɵɣ ɨɛɴɟɦ V ɦɨɥɟɤɭɥ. 190. ɂɞɟɚɥɶɧɵɣ ɝɚɡ ɫɨɜɟɪɲɚɟɬ ɰɢɤɥ Ʉɚɪɧɨ. Ɍɟɦɩɟɪɚɬɭɪɚ Ɍ1 ɧɚɝɪɟɜɚɬɟɥɹ ɜ ɱɟɬɵɪɟ ɪɚɡɚ ɜɵɲɟ ɬɟɦɩɟɪɚɬɭɪɵ Ɍ2 ɨɯɥɚɞɢɬɟɥɹ. Ʉɚɤɭɸ ɞɨɥɸ W ɤɨɥɢɱɟɫɬɜɚ ɬɟɩɥɨɬɵ, ɩɨɥɭɱɚɟɦɨɝɨ ɡɚ ɨɞɢɧ ɰɢɤɥ ɨɬ ɧɚɝɪɟɜɚɬɟɥɹ, ɝɚɡ ɨɬɞɚɟɬ ɨɯɥɚɞɢɬɟɥɸ? 191. ɂɞɟɚɥɶɧɵɣ ɝɚɡ, ɫɨɜɟɪɲɚɸɳɢɣ ɰɢɤɥ Ʉɚɪɧɨ, ɩɨɥɭɱɢɜ ɨɬ ɧɚɝɪɟɜɚɬɟɥɹ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ Q = 4,2 ɤȾɠ, ɫɨɜɟɪɲɢɥ ɪɚɛɨɬɭ Ⱥ = 590 Ⱦɠ. ɇɚɣɬɢ ɬɟɪɦɢɱɟɫɤɢɣ ɄɉȾ ɷɬɨɝɨ ɰɢɤɥɚ. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɬɟɦɩɟɪɚɬɭɪɚ Ɍ1 ɧɚɝɪɟɜɚɬɟɥɹ ɛɨɥɶɲɟ ɬɟɦɩɟɪɚɬɭɪɵ Ɍ2 ɨɯɥɚɞɢɬɟɥɹ? 192. Ɋɚɫɲɢɪɹɹɫɶ, ɜɨɞɨɪɨɞ ɫɨɜɟɪɲɢɥ ɪɚɛɨɬɭ Ⱥ = 6 ɤȾɠ. Ɉɩɪɟɞɟɥɢɬɶ ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ Q, ɩɨɞɜɟɞɟɧɧɨɟ ɤ ɝɚɡɭ, ɟɫɥɢ ɩɪɨɰɟɫɫ ɩɪɨɬɟɤɚɥ: 1) ɢɡɨɛɚɪɧɨ; 2) ɢɡɨɬɟɪɦɢɱɟɫɤɢ. 193. Ⱥɜɬɨɦɨɛɢɥɶɧɚɹ ɲɢɧɚ ɧɚɤɚɱɟɧɚ ɞɨ ɞɚɜɥɟɧɢɹ P = 220 ɤɉɚ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ Ɍ1 = 290 Ʉ. ȼɨ ɜɪɟɦɹ ɞɜɢɠɟɧɢɹ ɨɧɚ ɧɚɝɪɟɥɚɫɶ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ Ɍ2 = 330 Ʉ ɢ ɥɨɩɧɭɥɚ. ɋɱɢɬɚɹ ɩɪɨɰɟɫɫ, ɩɪɨɢɫɯɨɞɹɳɢɣ ɩɨɫɥɟ ɩɨɜɪɟɠɞɟɧɢɹ ɲɢɧɵ, ɚɞɢɚɛɚɬɧɵɦ, ɨɩɪɟɞɟɥɢɬɶ ɢɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ɜɵɲɟɞɲɟɝɨ ɢɡ ɧɟɟ ɜɨɡɞɭɯɚ. ȼɧɟɲɧɟɟ ɞɚɜɥɟɧɢɟ ɜɨɡɞɭɯɚ ɪɚɜɧɨ 100 ɤɉɚ. 194. ɉɪɢ ɚɞɢɚɛɚɬɧɨɦ ɪɚɫɲɢɪɟɧɢɢ ɤɢɫɥɨɪɨɞɚ ɫ ɧɚɱɚɥɶɧɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ T = 320 Ʉ ɜɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ ɭɦɟɧɶɲɢɥɚɫɶ ɧɚ 8,4 ɤȾɠ, ɚ ɟɝɨ ɨɛɴɟɦ ɭɜɟɥɢɱɢɥɫɹ ɜ 10 ɪɚɡ. Ɉɩɪɟɞɟɥɢɬɶ ɦɚɫɫɭ m ɤɢɫɥɨɪɨɞɚ. 195. ȼɨɞɨɪɨɞ ɩɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɢɦɟɥ ɨɛɴɟɦ V1 = 11,42 ɥ. Ɋɚɫɲɢɪɹɹɫɶ, ɜɨɞɨɪɨɞ ɫɨɜɟɪɲɢɥ ɪɚɛɨɬɭ Ⱥ = 6 ɤȾɠ. Ɉɩɪɟɞɟɥɢɬɶ ɤɨɥɢɱɟɫɬɜɨ 28
ɬɟɩɥɨɬɵ Q, ɩɨɞɜɟɞɟɧɧɨɟ ɤ ɝɚɡɭ, ɟɫɥɢ ɩɪɨɰɟɫɫ ɩɪɨɬɟɤɚɥ: 1) ɢɡɨɛɚɪɧɨ; 2) ɢɡɨɬɟɪɦɢɱɟɫɤɢ. 196. Ⱥɜɬɨɦɨɛɢɥɶɧɚɹ ɲɢɧɚ ɧɚɤɚɱɚɧɚ ɞɨ ɞɚɜɥɟɧɢɹ 220 ɤɉɚ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ 290 Ʉ. ȼɨ ɜɪɟɦɹ ɞɜɢɠɟɧɢɹ ɨɧɚ ɧɚɝɪɟɥɚɫɶ ɞɨ ɬɟɦɩɟɪɚɬɭɪɵ Ɍ2 = 330 Ʉ ɢ ɥɨɩɧɭɥɚ. ɋɱɢɬɚɹ ɩɪɨɰɟɫɫ, ɩɪɨɢɫɯɨɞɹɳɢɣ ɩɨɫɥɟ ɩɨɜɪɟɠɞɟɧɢɹ ɲɢɧɵ, ɚɞɢɚɛɚɬɧɵɦ, ɨɩɪɟɞɟɥɢɬɶ ɢɡɦɟɧɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ ǻT ɜɵɲɟɞɲɟɝɨ ɢɡ ɧɟɟ ɜɨɡɞɭɯɚ. ȼɧɟɲɧɟɟ ɞɚɜɥɟɧɢɟ ɪ0 ɜɨɡɞɭɯɚ ɪɚɜɧɨ 100 ɤɉɚ. 197. ɉɪɢ ɚɞɢɚɛɚɬɧɨɦ ɪɚɫɲɢɪɟɧɢɢ ɤɢɫɥɨɪɨɞɚ ɫ ɧɚɱɚɥɶɧɨɣ ɬɟɦɩɟɪɚɬɭɪɨɣ 320 Ʉ ɜɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ ɭɦɟɧɶɲɢɥɚɫɶ ɧɚ 8,4 ɤȾɠ, ɚ ɟɝɨ ɨɛɴɟɦ ɭɜɟɥɢɱɢɥɫɹ ɜ 10 ɪɚɡ. Ɉɩɪɟɞɟɥɢɬɶ ɦɚɫɫɭ m ɤɢɫɥɨɪɨɞɚ. 198. ȼɨɞɨɪɨɞ ɩɪɢ ɧɨɪɦɚɥɶɧɵɯ ɭɫɥɨɜɢɹɯ ɢɦɟɥ ɨɛɴɟɦ 100 ɦ3. ɇɚɣɬɢ ɢɡɦɟɧɟɧɢɟ ǻU ɜɧɭɬɪɟɧɧɟɣ ɷɧɟɪɝɢɢ ɝɚɡɚ ɩɪɢ ɟɝɨ ɚɞɢɚɛɚɬɧɨɦ ɪɚɫɲɢɪɟɧɢɢ ɞɨ ɨɛɴɟɦɚ 150 ɦ3. 199. ȼ ɰɢɥɢɧɞɪɟ ɩɨɞ ɩɨɪɲɧɟɦ ɧɚɯɨɞɢɬɫɹ ɜɨɞɨɪɨɞ ɦɚɫɫɨɣ m = 0,02 ɤɝ ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ 300 Ʉ. ȼɨɞɨɪɨɞ ɫɧɚɱɚɥɚ ɪɚɫɲɢɪɢɥɫɹ ɚɞɢɚɛɚɬɧɨ, ɭɜɟɥɢɱɢɜ ɫɜɨɣ ɨɛɴɟɦ ɜ ɩɹɬɶ ɪɚɡ, ɚ ɡɚɬɟɦ ɛɵɥ ɫɠɚɬ ɢɡɨɬɟɪɦɢɱɟɫɤɢ, ɩɪɢɱɟɦ ɨɛɴɟɦ ɝɚɡɚ ɭɦɟɧɶɲɢɥɫɹ ɜ ɩɹɬɶ ɪɚɡ. ɇɚɣɬɢ ɬɟɦɩɟɪɚɬɭɪɭ Ɍ2 ɜ ɤɨɧɰɟ ɚɞɢɚɛɚɬɧɨɝɨ ɪɚɫɲɢɪɟɧɢɹ ɢ ɩɨɥɧɭɸ ɪɚɛɨɬɭ A, ɫɨɜɟɪɲɟɧɧɭɸ ɝɚɡɨɦ. ɂɡɨɛɪɚɡɢɬɶ ɩɪɨɰɟɫɫ ɝɪɚɮɢɱɟɫɤɢ. 200. ɉɪɢ ɚɞɢɚɛɚɬɧɨɦ ɫɠɚɬɢɢ ɤɢɫɥɨɪɨɞɚ ɦɚɫɫɨɣ m = 20 ɝ ɟɝɨ ɜɧɭɬɪɟɧɧɹɹ ɷɧɟɪɝɢɹ ɭɜɟɥɢɱɢɥɚɫɶ ɧɚ ǻU = 8 ɤȾɠ ɢ ɬɟɦɩɟɪɚɬɭɪɚ ɩɨɜɵɫɢɥɚɫɶ ɞɨ Ɍ2 = 900 Ʉ. ɇɚɣɬɢ: 1) ɩɨɜɵɲɟɧɢɟ ɬɟɦɩɟɪɚɬɭɪɵ; 2) ɤɨɧɟɱɧɨɟ ɞɚɜɥɟɧɢɟ ɝɚɡɚ P2, ɟɫɥɢ ɧɚɱɚɥɶɧɨɟ ɞɚɜɥɟɧɢɟ P1 = 200 ɤɉɚ.
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ɍɱɟɛɧɨɟ ɢɡɞɚɧɢɟ
ɄɍɊɋ ɈȻɓȿɃ ɎɂɁɂɄɂ ɆȿɏȺɇɂɄȺ ɂ ɆɈɅȿɄɍɅəɊɇȺə ɎɂɁɂɄȺ ɑɚɫɬɶ 1 ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ ɞɥɹ ɜɭɡɨɜ ɋɨɫɬɚɜɢɬɟɥɢ: Ɋɨɝɚɡɢɧɫɤɚɹ Ɉɥɶɝɚ ȼɥɚɞɢɦɢɪɨɜɧɚ, ɉɥɚɤɫɢɰɤɢɣ Ⱥɧɞɪɟɣ Ȼɨɪɢɫɨɜɢɱ, Ɇɢɥɨɜɢɞɨɜɚ ɋɜɟɬɥɚɧɚ Ⱦɦɢɬɪɢɟɜɧɚ, ɋɢɞɨɪɤɢɧ Ⱥɧɞɪɟɣ Ⱥɥɟɤɫɚɧɞɪɨɜɢɱ Ɋɟɞɚɤɬɨɪ Ɉ.Ⱥ. ɂɫɚɟɜɚ
ɉɨɞɩɢɫɚɧɨ ɜ ɩɟɱɚɬɶ 06.09.07. Ɏɨɪɦɚɬ 60×84/16. ɍɫɥ. ɩɟɱ. ɥ. 1,74. Ɍɢɪɚɠ 50 ɷɤɡ. Ɂɚɤɚɡ 1824. ɂɡɞɚɬɟɥɶɫɤɨ-ɩɨɥɢɝɪɚɮɢɱɟɫɤɢɣ ɰɟɧɬɪ ȼɨɪɨɧɟɠɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ. 394000, ɝ. ȼɨɪɨɧɟɠ, ɩɥ. ɢɦ. Ʌɟɧɢɧɚ, 10. Ɍɟɥ. 208-298, 598-026 (ɮɚɤɫ) http://www.ppc.vsu.ru; e-mail:
[email protected] Ɉɬɩɟɱɚɬɚɧɨ ɜ ɬɢɩɨɝɪɚɮɢɢ ɂɡɞɚɬɟɥɶɫɤɨ-ɩɨɥɢɝɪɚɮɢɱɟɫɤɨɝɨ ɰɟɧɬɪɚ ȼɨɪɨɧɟɠɫɤɨɝɨ ɝɨɫɭɞɚɪɫɬɜɟɧɧɨɝɨ ɭɧɢɜɟɪɫɢɬɟɬɚ. 394000, ɝ. ȼɨɪɨɧɟɠ, ɭɥ. ɉɭɲɤɢɧɫɤɚɹ, 3. Ɍɟɥ. 204-133.
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