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Шахтные стационарные установки. Расчет и выбор оборудования подъемных установок. Учебное пособие

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ɋȺɋɟɥɢɜɪɚȼɋɄɨɥɨɦɢɟɰ
         
ɒȺɏɌɇɕȿɋɌȺɐɂɈɇȺɊɇɕȿɍɋɌȺɇɈȼɄɂ
ɊȺɋɑȿɌɂȼɕȻɈɊɈȻɈɊɍȾɈȼȺɇɂə
ɉɈȾɔȿɆɇɕɏɍɋɌȺɇɈȼɈɄ
ɍɱɟɛɧɨɟ ɩɨɫɨɛɢɟ
        
      
©ɂɧɮɪɚɂɧɠɟɧɟɪɢɹª


ɍȾɄ ȻȻɄ
ɋ
Ɋɟɰɟɧɡɟɧɬɵ:
ɞɨɤɬɨɪɬɟɯɧɢɱɟɫɤɢɯɧɚɭɤɩɪɨɮɟɫɫɨɪɡɚɜɤɚɮɟɞɪɨɣɝɨɪɧɨɣ
ɷɥɟɤɬɪɨɬɟɯɧɢɤɢɢɚɜɬɨɦɚɬɢɤɢɢɦɊɆɅɟɣɛɨɜɚɄ. ɇ. Ɇɚɪɟɧɢɱ;
ɤɚɧɞɢɞɚɬɬɟɯɧɢɱɟɫɤɢɯɧɚɭɤɚɤɚɞɟɦɢɤɆȺɇɗȻɡɚɦɝɟɧɟɪɚɥɶɧɨɝɨɞɢɪɟɤɬɨɪɚ
ɩɨɢɧɧɨɜɚɰɢɨɧɧɵɦɬɟɯɧɨɥɨɝɢɹɦɈɈɈ©Ⱦɨɧɛɚɫɫɭɝɥɟɚɜɬɨɦɚɬɢɤɚªȼ. Ɋ. Ȼɟɠɨɤ
    
  ɋɟɥɢɜɪɚɋȺ
ɋ   ɒɚɯɬɧɵɟ ɫɬɚɰɢɨɧɚɪɧɵɟ ɭɫɬɚɧɨɜɤɢ Ɋɚɫɱɟɬ ɢ ɜɵɛɨɪ ɨɛɨɪɭɞɨɜɚɧɢɹ
ɩɨɞɴɟɦɧɵɯɭɫɬɚɧɨɜɨɤɭɱɟɛɧɨɟɩɨɫɨɛɢɟɋȺɋɟɥɢɜɪɚȼɋɄɨɥɨɦɢɟɰí Ɇɨɫɤɜɚȼɨɥɨɝɞɚɂɧɮɪɚɂɧɠɟɧɟɪɢɹíɫɢɥɬɚɛɥ
,6%1 
Ɋɚɫɫɦɨɬɪɟɧɵɨɫɧɨɜɧɵɟɩɨɥɨɠɟɧɢɹɩɨɪɚɫɱɟɬɭɢɜɵɛɨɪɭɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟ ɫɤɨɝɨɨɛɨɪɭɞɨɜɚɧɢɹɩɨɞɴɟɦɧɵɯɭɫɬɚɧɨɜɨɤɞɥɹɝɨɪɧɵɯɩɪɟɞɩɪɢɹɬɢɣɉɪɢɜɟɞɟɧɵ ɩɪɢɦɟɪɵɪɚɫɱɟɬɚ ɢɜɵɛɨɪɚɨɛɨɪɭɞɨɜɚɧɢɹɫɩɪɚɜɨɱɧɵɟɦɚɬɟɪɢɚɥɵ ɚɬɚɤɠɟɨɩɢ ɫɚɧɵɩɪɢɧɰɢɩɵɪɚɛɨɬɵɨɫɧɨɜɧɵɯɭɡɥɨɜɢɫɢɫɬɟɦɩɨɞɴɟɦɧɨɣɭɫɬɚɧɨɜɤɢ
ȾɥɹɫɬɭɞɟɧɬɨɜɢɚɫɩɢɪɚɧɬɨɜɢɡɭɱɚɸɳɢɯɝɨɪɧɨɟɞɟɥɨɆɨɠɟɬɛɵɬɶɩɨɥɟɡɧɨ ɫɩɟɰɢɚɥɢɫɬɚɦɝɨɪɧɨɞɨɛɵɜɚɸɳɢɯɩɪɟɞɩɪɢɹɬɢɣ
ɍȾɄ
ȻȻɄ           
,6%1 ɋɟɥɢɜɪɚɋȺɄɨɥɨɦɢɟɰȼɋ
ɂɡɞɚɬɟɥɶɫɬɜɨ©ɂɧɮɪɚɂɧɠɟɧɟɪɢɹª  Ɉɮɨɪɦɥɟɧɢɟɂɡɞɚɬɟɥɶɫɬɜɨ©ɂɧɮɪɚɂɧɠɟɧɟɪɢɹª

ɋɈȾȿɊɀȺɇɂȿ
 ɉɪɟɞɢɫɥɨɜɢɟ Ɉɛɳɢɟɩɨɥɨɠɟɧɢɹ 
ȼɵɛɨɪɬɢɩɨɜɩɨɞɴɟɦɧɵɯɦɚɲɢɧ 
Ɋɚɫɱɟɬɫɤɢɩɨɜɨɣɨɞɧɨɤɚɧɚɬɧɨɣɞɜɭɯɤɨɧɰɟɜɨɣɩɨɞɴɟɦɧɨɣɭɫɬɚɧɨɜɤɢ 
ȼɵɛɨɪɫɤɢɩɚ  ȼɵɛɨɪɤɨɩɪɚ  Ɋɚɫɱɟɬɢɜɵɛɨɪɝɨɥɨɜɧɨɝɨɤɚɧɚɬɚ  ȼɵɛɨɪɩɨɞɴɟɦɧɨɣɦɚɲɢɧɵ ȼɵɛɨɪɤɨɩɪɨɜɵɯɲɤɢɜɨɜ  Ɋɚɫɩɨɥɨɠɟɧɢɟɩɨɞɴɟɦɧɨɣɦɚɲɢɧɵɨɬɧɨɫɢɬɟɥɶɧɨɭɫɬɶɹɫɬɜɨɥɚ  Ʉɢɧɟɦɚɬɢɤɚɩɨɞɴɟɦɧɨɣɭɫɬɚɧɨɜɤɢ 
ɉɨɫɬɪɨɟɧɢɟɞɢɚɝɪɚɦɦɵɭɫɢɥɢɣ Ɉɩɪɟɞɟɥɟɧɢɟɷɤɜɢɜɚɥɟɧɬɧɨɣɦɨɳɧɨɫɬɢɩɨɞɴɟɦɧɨɝɨɞɜɢɝɚɬɟɥɹ Ɋɚɫɱɟɬɷɤɨɧɨɦɢɱɟɫɤɢɯɩɨɤɚɡɚɬɟɥɟɣɩɪɢɧɹɬɵɯɪɟɲɟɧɢɣ
Ɋɚɫɱɟɬɫɤɢɩɨɜɨɣɦɧɨɝɨɤɚɧɚɬɧɨɣɩɨɞɴɟɦɧɨɣɭɫɬɚɧɨɜɤɢɫɞɜɭɦɹɫɨɫɭɞɚɦɢ
ȼɵɛɨɪɫɤɢɩɚ ȼɵɛɨɪɤɨɩɪɚ Ɋɚɫɱɟɬɢɜɵɛɨɪɝɨɥɨɜɧɵɯɢɭɪɚɜɧɨɜɟɲɢɜɚɸɳɢɯɤɚɧɚɬɨɜ ȼɵɛɨɪɩɨɞɴɟɦɧɨɣɦɚɲɢɧɵ Ʉɢɧɟɦɚɬɢɤɚɩɨɞɴɟɦɧɨɣɭɫɬɚɧɨɜɤɢ ɍɫɤɨɪɟɧɢɟɢɡɚɦɟɞɥɟɧɢɟ Ɋɚɫɱɟɬɞɢɚɝɪɚɦɦɵɫɤɨɪɨɫɬɢ ɉɨɫɬɪɨɟɧɢɟɞɢɚɝɪɚɦɦɭɫɢɥɢɣ ɗɤɜɢɜɚɥɟɧɬɧɚɹɦɨɳɧɨɫɬɶɩɨɞɴɟɦɧɨɝɨɞɜɢɝɚɬɟɥɹ Ɋɚɫɱɟɬɷɤɨɧɨɦɢɱɟɫɤɢɯɩɨɤɚɡɚɬɟɥɟɣ
Ɋɚɫɱɟɬɤɥɟɬɟɜɨɣɩɨɞɴɟɦɧɨɣɭɫɬɚɧɨɜɤɢ
Ɋɚɫɱɟɬɩɨɞɴɟɦɧɨɣɭɫɬɚɧɨɜɤɢɫɩɪɨɬɢɜɨɜɟɫɨɦ
ȼɵɛɨɪɢɪɚɫɱɟɬɬɨɪɦɨɡɧɨɝɨɭɫɬɪɨɣɫɬɜɚ
ȼɵɛɨɪɬɢɩɚɬɨɪɦɨɡɧɨɝɨɭɫɬɪɨɣɫɬɜɚ ɉɪɢɜɨɞɬɨɪɦɨɡɧɨɝɨɭɫɬɪɨɣɫɬɜɚɢɨɫɧɨɜɧɵɟɪɟɠɢɦɵɟɝɨɪɚɛɨɬɵ Ɉɩɪɟɞɟɥɟɧɢɟɪɚɫɱɟɬɧɵɯɡɧɚɱɟɧɢɣɬɨɪɦɨɡɧɵɯɦɨɦɟɧɬɨɜ ȼɵɛɨɪɪɚɫɱɟɬɧɨɝɨɬɨɪɦɨɡɧɨɝɨɦɨɦɟɧɬɚ Ɉɩɪɟɞɟɥɟɧɢɟɩɚɪɚɦɟɬɪɨɜɫɢɥɨɜɨɣɱɚɫɬɢɬɨɪɦɨɡɧɨɝɨɭɫɬɪɨɣɫɬɜɚ ɛɨɥɶɲɢɯɩɨɞɴɟɦɧɵɯɦɚɲɢɧɨɛɨɪɭɞɨɜɚɧɧɵɯɩɧɟɜɦɨɝɪɭɡɨɜɵɦɩɪɢɜɨɞɨɦ ɉȺɈɇɄɆɁ 
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Ɉɩɪɟɞɟɥɟɧɢɟɬɪɟɛɭɟɦɨɝɨɞɚɜɥɟɧɢɹ ɫɠɚɬɨɝɨɜɨɡɞɭɯɚɜɜɨɡɞɭɯɨɫɛɨɪɧɢɤɟ Ɉɩɪɟɞɟɥɟɧɢɟɜɟɥɢɱɢɧɵɡɚɦɟɞɥɟɧɢɹ ɩɪɢɩɪɟɞɨɯɪɚɧɢɬɟɥɶɧɨɦɬɨɪɦɨɠɟɧɢɢ Ɉɩɪɟɞɟɥɟɧɢɟɩɚɪɚɦɟɬɪɨɜɫɢɥɨɜɨɣɱɚɫɬɢɬɨɪɦɨɡɧɨɝɨɭɫɬɪɨɣɫɬɜɚɦɚɥɵɯ ɩɨɞɴɟɦɧɵɯɦɚɲɢɧɬɢɩɚɐɆɉȻ Ɉɩɪɟɞɟɥɟɧɢɟɩɚɪɚɦɟɬɪɨɜɫɢɥɨɜɨɣɱɚɫɬɢɬɨɪɦɨɡɧɨɝɨɭɫɬɪɨɣɫɬɜɚ ɦɧɨɝɨɤɚɧɚɬɧɵɯɩɨɞɴɟɦɧɵɯɦɚɲɢɧɬɢɩɚɐɒɆɉɆ
Ɋɚɫɱɟɬɪɨɬɨɪɧɵɯɫɨɩɪɨɬɢɜɥɟɧɢɣɞɜɢɝɚɬɟɥɹ
Ɉɩɪɟɞɟɥɟɧɢɟɩɭɫɤɨɜɵɯɦɨɦɟɧɬɨɜ ɉɨɫɬɪɨɟɧɢɟɦɟɯɚɧɢɱɟɫɤɢɯɯɚɪɚɤɬɟɪɢɫɬɢɤ ɉɨɫɬɪɨɟɧɢɟɟɫɬɟɫɬɜɟɧɧɨɣɯɚɪɚɤɬɟɪɢɫɬɢɤɢɩɨɞɴɟɦɧɨɝɨɞɜɢɝɚɬɟɥɹ Ɉɩɪɟɞɟɥɟɧɢɟɫɨɩɪɨɬɢɜɥɟɧɢɣɩɨɫɬɭɩɟɧɹɦ ȼɪɟɦɹɪɚɛɨɬɵɞɜɢɝɚɬɟɥɹɧɚɤɚɠɞɨɣɫɬɭɩɟɧɢ ȼɵɛɨɪɫɨɩɪɨɬɢɜɥɟɧɢɣɩɨɫɬɭɩɟɧɹɦ
ɉɪɢɦɟɪɵɪɚɫɱɟɬɚɢɜɵɛɨɪɚɝɥɚɜɧɨɣɩɨɞɴɟɦɧɨɣɭɫɬɚɧɨɜɤɢ
Ɋɚɫɱɟɬɫɤɢɩɨɜɨɣɨɞɧɨɤɚɧɚɬɧɨɣɞɜɭɯɤɨɧɰɟɜɨɣɩɨɞɴɟɦɧɨɣɭɫɬɚɧɨɜɤɢ Ɋɚɫɱɟɬɫɤɢɩɨɜɨɣɦɧɨɝɨɤɚɧɚɬɧɨɣɞɜɭɯɤɨɧɰɟɜɨɣɩɨɞɴɟɦɧɨɣɭɫɬɚɧɨɜɤɢ
ɋɩɢɫɨɤɢɫɩɨɥɶɡɨɜɚɧɧɵɯɢɫɬɨɱɧɢɤɨɜ ɉɪɢɥɨɠɟɧɢɹ


ɉɊȿȾɂɋɅɈȼɂȿ
ɉɨɞɡɟɦɧɚɹ ɞɨɛɵɱɚ ɥɸɛɨɝɨ ɬɜɟɪɞɨɝɨ ɩɨɥɟɡɧɨɝɨ ɢɫɤɨɩɚɟɦɨɝɨ ɫɜɹɡɚɧɚ ɫ
ɬɪɚɧɫɩɨɪɬɢɪɨɜɤɨɣɟɝɨɧɚɩɨɜɟɪɯɧɨɫɬɶ
Ⱦɥɹɲɚɯɬ Ⱦɨɧɛɚɫɫɚ ±ɷɬɨ ɭɝɨɥɶ ɹɜɥɹɸɳɢɣɫɹ ɧɟ ɬɨɥɶɤɨɢɫɬɨɱɧɢɤɨɦ ɷɧɟɪ ɝɢɢɧɨɢɜɚɠɧɟɣɲɢɦɫɵɪɶɟɦɞɥɹɦɟɬɚɥɥɭɪɝɢɱɟɫɤɨɣɯɢɦɢɱɟɫɤɨɣɢɪɹɞɚɞɪɭɝɢɯ ɨɬɪɚɫɥɟɣɩɪɨɦɵɲɥɟɧɧɨɫɬɢ
ɋɨɜɪɟɦɟɧɧɚɹ ɲɚɯɬɚ ± ɫɥɨɠɧɨɟ ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɨɟ ɩɪɟɞɩɪɢɹɬɢɟ ɧɚɫɵɳɟɧ ɧɨɟ ɪɚɡɧɨɨɛɪɚɡɧɵɦ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɦ ɨɛɨɪɭɞɨɜɚɧɢɟɦ ɪɚɡɦɟɳɟɧɧɵɦ ɤɚɤ ɩɨɞ ɡɟɦɥɟɣ ɬɚɤ ɢ ɧɚ ɩɨɜɟɪɯɧɨɫɬɢ ɚ ɞɥɹ Ⱦɨɧɟɰɤɨɝɨ ɛɚɫɫɟɣɧɚ ɷɬɨ ɟɳɟ ɢ ɛɨɥɶ ɲɚɹ±ɫɜɵɲɟ±ɦɝɥɭɛɢɧɚɪɚɡɪɚɛɨɬɨɤ
ɒɚɯɬɧɵɟ ɦɚɲɢɧɵ ɹɜɥɹɸɬɫɹ ɞɨɪɨɝɨɫɬɨɹɳɢɦɢ ɢɡɞɟɥɢɹɦɢ ɤɨɬɨɪɵɟ ɜ ɫɢɥɭ ɫɩɟɰɢɮɢɱɟɫɤɢɯɭɫɥɨɜɢɣɷɤɫɩɥɭɚɬɚɰɢɢɩɨɞɜɟɪɠɟɧɵɢɧɬɟɧɫɢɜɧɨɦɭɢɡɧɨɫɭ ɢ ɩɨ ɜɪɟɠɞɟɧɢɹɦȼ ɧɚɫɬɨɹɳɟɟɜɪɟɦɹɩɪɢɨɛɪɟɬɟɧɢɟɲɚɯɬɚɦɢɧɨɜɨɣɬɟɯɧɢɤɢɡɚɬɪɭɞ ɧɟɧɨ ɩɨɷɬɨɦɭ ɩɨɜɵɲɟɧɢɟ ɷɤɨɧɨɦɢɱɟɫɤɢɯ ɩɨɤɚɡɚɬɟɥɟɣ ɜɨɡɦɨɠɧɨ ɩɭɬɟɦ ɭɥɭɱ ɲɟɧɢɹɢɫɩɨɥɶɡɨɜɚɧɢɹɦɚɲɢɧɧɚɜɫɟɯɫɬɚɞɢɹɯɢɯɠɢɡɧɟɧɧɨɝɨɰɢɤɥɚ
ɒɚɯɬɧɚɹ ɩɨɞɴɟɦɧɚɹ ɭɫɬɚɧɨɜɤɚ ɹɜɥɹɟɬɫɹ ɨɫɧɨɜɧɵɦ ɫɜɹɡɵɜɚɸɳɢɦ ɡɜɟɧɨɦ ɩɨɞɡɟɦɧɵɯɜɵɪɚɛɨɬɨɤɫɩɨɜɟɪɯɧɨɫɬɶɸɢɨɬɟɟɫɨɫɬɨɹɧɢɹɡɚɜɢɫɢɬɠɢɡɧɟɞɟɹɬɟɥɶ ɧɨɫɬɶɩɪɟɞɩɪɢɹɬɢɹɉɨɞɝɨɬɨɜɤɚɫɩɟɰɢɚɥɢɫɬɨɜɞɥɹɩɪɨɟɤɬɢɪɨɜɚɧɢɹɬɟɯɧɢɱɟɫɤɨ ɝɨɨɛɫɥɭɠɢɜɚɧɢɹɪɟɦɨɧɬɚɢɷɤɫɩɥɭɚɬɚɰɢɢɫɬɚɰɢɨɧɚɪɧɨɝɨɨɛɨɪɭɞɨɜɚɧɢɹɲɚɯɬɤ ɤɨɬɨɪɨɦɭɨɬɧɨɫɹɬɫɹɢɩɨɞɴɟɦɧɵɟɭɫɬɚɧɨɜɤɢɹɜɥɹɟɬɫɹɨɞɧɨɣɢɡɩɟɪɜɨɨɱɟɪɟɞɧɵɯ ɡɚɞɚɱɭɱɟɛɧɵɯɡɚɜɟɞɟɧɢɣɝɨɪɧɨɝɨɩɪɨɮɢɥɹ
Ⱦɨɧɟɰɤɢɣɧɚɰɢɨɧɚɥɶɧɵɣ ɬɟɯɧɢɱɟɫɤɢɣɭɧɢɜɟɪɫɢɬɟɬ Ⱦɉɂɨɬɦɟɱɚɸɳɢɣɜ ɝɨɞɭɫɜɨɟɥɟɬɢɟɹɜɥɹɟɬɫɹɟɞɢɧɫɬɜɟɧɧɵɦɪɟɝɢɨɧɚɥɶɧɵɦɜɵɫɲɢɦɭɱɟɛ ɧɵɦ ɡɚɜɟɞɟɧɢɟɦ ɨɫɭɳɟɫɬɜɥɹɸɳɢɦ ɩɨɞɝɨɬɨɜɤɭ ɤɥɸɱɟɜɨɣ ɮɢɝɭɪɵ ɜ ɩɪɨɰɟɫɫɟ ɬɟɯɧɢɱɟɫɤɨɣ ɷɤɫɩɥɭɚɬɚɰɢɢ ɨɛɨɪɭɞɨɜɚɧɢɹ ɭɝɨɥɶɧɨɣ ɲɚɯɬɵ ± ɢɧɠɟɧɟɪɚ ɷɥɟɤɬɪɨɦɟɯɚɧɢɤɚɞɥɹ ɤɚɱɟɫɬɜɟɧɧɨɣɩɨɞɝɨɬɨɜɤɢ ɤɨɬɨɪɨɝɨɞɨɥɠɧɨ ɩɨɫɥɭɠɢɬɶɢ ɧɚɫɬɨɹɳɟɟɭɱɟɛɧɨɟɩɨɫɨɛɢɟ 

ɈȻɓɂȿɉɈɅɈɀȿɇɂə
Ɉɞɧɢɦɢɡ ɫɚɦɵɯ ɜɚɠɧɵɯɤɨɦɩɥɟɤɫɨɜɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ
ɪɭɞɧɢɤɨɜɢɲɚɯɬɹɜɥɹɸɬɫɹɩɨɞɴɟɦɧɵɟɭɫɬɚɧɨɜɤɢ
Ɍɪɚɧɫɩɨɪɬɧɵɟ ɨɩɟɪɚɰɢɢ ɜɵɩɨɥɧɹɟɦɵɟ ɩɨɞɴɟɦɧɵɦɢ ɭɫɬɚɧɨɜɤɚɦɢ ɨɛɟɫɩɟ ɱɢɜɚɸɬɧɨɪɦɚɥɶɧɨɟ ɮɭɧɤɰɢɨɧɢɪɨɜɚɧɢɟɲɚɯɬɵɤɚɤɝɨɪɧɨɝɨɩɪɟɞɩɪɢɹɬɢɹɩɨɷɬɨɦɭ ɤɧɚɞɟɠɧɨɫɬɢɩɨɞɴɟɦɨɜɩɪɟɞɴɹɜɥɹɸɬɫɹɩɨɜɵɲɟɧɧɵɟɬɪɟɛɨɜɚɧɢɹ
ɉɨɫɤɨɥɶɤɭ ɩɨɞɴɟɦɧɚɹ ɭɫɬɚɧɨɜɤɚ ɪɚɫɫɱɢɬɚɧɚ ɧɚ ɞɨɥɝɢɣ ɫɪɨɤ ɫɥɭɠɛɵɬɨ ɩɪɚɜɢɥɶɧɵɣɜɵɛɨɪɟɟ ɨɫɧɨɜɧɵɯ ɷɥɟɦɟɧɬɨɜ ɫɨɫɭɞɵ ɤɚɧɚɬɵɩɨɞɴɟɦɧɚɹɦɚɲɢɧɚ ɪɟɞɭɤɬɨɪ ɞɜɢɝɚɬɟɥɶ ɢ ɬ ɞ ɝɚɪɚɧɬɢɪɭɟɬ ɭɫɩɟɲɧɭɸ ɩɪɨɢɡɜɨɞɫɬɜɟɧɧɨɯɨɡɹɣɫ ɬɜɟɧɧɭɸɞɟɹɬɟɥɶɧɨɫɬɶɩɪɟɞɩɪɢɹɬɢɹ
ȼɷɬɨɦɭɱɟɛɧɨɦ ɩɨɫɨɛɢɢ ɩɪɟɞɥɚɝɚɟɬɫɹ ɦɚɬɟɪɢɚɥɧɟɨɛɯɨɞɢɦɵɣɞɥɹ ɫɬɭɞɟɧ ɬɨɜɩɪɢɜɵɩɨɥɧɟɧɢɢɞɢɩɥɨɦɧɨɝɨɩɪɨɟɤɬɚɤɭɪɫɨɜɨɣɢɪɚɫɱɟɬɧɨɣɪɚɛɨɬ ɩɨɜɵɛɨɪɭ ɩɨɞɴɟɦɧɨɣ ɭɫɬɚɧɨɜɤɢ ɫ ɧɨɜɟɣɲɢɦ ɝɨɪɧɨɲɚɯɬɧɵɦ ɨɛɨɪɭɞɨɜɚɧɢɟɦ ȼ ɩɨɫɨɛɢɢ ɩɪɢɜɟɞɟɧɵ ɩɪɨɟɤɬɧɵɟ ɪɚɫɱɟɬɵ ɩɨɞɴɟɦɧɵɯ ɭɫɬɚɧɨɜɨɤ ɲɚɯɬ ɫ ɰɢɥɢɧɞɪɢɱɟɫɤɢɦɢ ɛɚɪɚɛɚɧɧɵɦɢ ɢ ɦɧɨɝɨɤɚɧɚɬɧɵɦɢ ɩɨɞɴɟɦɧɵɦɢ ɦɚɲɢɧɚɦɢ ɚ ɬɚɤɠɟɞɚɧɵ ɧɟɨɛ ɯɨɞɢɦɵɟ ɫɩɪɚɜɨɱɧɵɟ ɦɚɬɟɪɢɚɥɵ ɨɫɧɨɜɧɨɝɨ ɨɛɨɪɭɞɨɜɚɧɢɹ ɫɨɜɪɟɦɟɧɧɵɯ ɩɨɞɴ ɟɦɨɜɂɡɥɨɠɟɧɧɵɟɜɭɱɟɛɧɨɦɩɨɫɨɛɢɢɫɜɟɞɟɧɢɹɦɨɝɭɬɛɵɬɶɩɨɥɟɡɧɵɝɨɪɧɵɦɢɧ ɠɟɧɟɪɚɦɦɟɯɚɧɢɤɚɦ ɨɛɫɥɭɠɢɜɚɸɳɢɦ ɩɨɞɴɟɦɧɨɟ ɨɛɨɪɭɞɨɜɚɧɢɟ ɲɚɯɬ ɢ ɪɭɞɧɢ ɤɨɜ

ȽɅȺȼȺȼɕȻɈɊɌɂɉɈȼɉɈȾɔȿɆɇɕɏɆȺɒɂɇ
ɉɨɞɴɟɦɧɵɟɦɚɲɢɧɵ ɫ ɰɢɥɢɧɞɪɢɱɟɫɤɢɦɢ ɛɚɪɚɛɚɧɚɦɢɤɚɤ ɩɪɚɜɢɥɨ ɩɪɢɧɢ ɦɚɸɬɫɹ ɞɥɹ ɨɫɧɚɳɟɧɢɹ ɜɟɪɬɢɤɚɥɶɧɵɯ ɩɨɞɴɟɦɨɜ ɲɚɯɬ ɝɥɭɛɢɧɨɣ ɞɨ ɦȿɫɥɢ ɝɥɭɛɢɧɚ ɲɚɯɬɵ ɛɨɥɟɟ  ɦ ɜ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɧɟɨɛɯɨɞɢɦɨ ɩɪɢɧɢɦɚɬɶ ɦɧɨɝɨɤɚɧɚɬɧɵɟɩɨɞɴɟɦɧɵɟɦɚɲɢɧɵ
Ɇɧɨɝɨɤɚɧɚɬɧɵɟɩɨɞɴɟɦɧɵɟɦɚɲɢɧɵɫɥɟɞɭɟɬɩɪɢɧɢɦɚɬɶɜ ɬɟɯ ɫɥɭɱɚɹɯɤɨ ɝɞɚ ɦɚɲɢɧɵ ɫ ɰɢɥɢɧɞɪɢɱɟɫɤɢɦɢ ɛɚɪɚɛɚɧɚɦɢ ɧɟ ɦɨɝɭɬ ɨɛɟɫɩɟɱɢɬɶ ɜɵɩɨɥɧɟɧɢɟ ɢɫɯɨɞɧɵɯɭɫɥɨɜɢɣɩɪɢɜɵɫɨɤɨɣɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢɢɷɤɨɧɨɦɢɱɧɨɫɬɢɪɚɛɨɬɵ
ɉɪɢɢɫɩɨɥɶɡɨɜɚɧɢɢɫɯɟɦɵɜɫɤɪɵɬɢɹɫɩɨɫɥɟɞɭɸɳɢɦɭɝɥɭɛɥɟɧɢɟɦɲɚɯɬɧɨ ɝɨɫɬɜɨɥɚɩɪɨɟɤɬɢɪɨɜɚɧɢɟɩɨɞɴɟɦɧɵɯɭɫɬɚɧɨɜɨɤɫɦɚɲɢɧɚɦɢɫɰɢɥɢɧɞɪɢɱɟɫɤɢ ɦɢɛɚɪɚɛɚɧɚɦɢɜɵɩɨɥɧɹɟɬɫɹɞɨ ɝɨɪɢɡɨɧɬɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɫɪɨɤɭ ɫɥɭɠɛɵɦɚ ɲɢɧɵ ɤɨɬɨɪɵɣ ɫɨɫɬɚɜɥɹɟɬ ± ɥɟɬ Ɇɧɨɝɨɤɚɧɚɬɧɵɟ ɩɨɞɴɟɦɧɵɟ ɭɫɬɚɧɨɜɤɢ ɩɪɨɟɤɬɢɪɭɸɬɫɹɧɚɦɚɤɫɢɦɚɥɶɧɭɸɤɨɧɟɱɧɭɸɝɥɭɛɢɧɭɫɬɜɨɥɚ
ȼɨɩɪɨɫɵ ɞɥɹ ɫɚɦɨɤɨɧɬɪɨɥɹ:
 ɉɪɢɜɟɞɢɬɟ ɢɫɯɨɞɧɵɟ ɭɫɥɨɜɢɹ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɩɨɞɴɟɦɧɵɯ ɦɚɲɢɧ ɫ ɰɢ
ɥɢɧɞɪɢɱɟɫɤɢɦɢɛɚɪɚɛɚɧɚɦɢɢɦɧɨɝɨɤɚɧɚɬɧɵɯ
 Ʉɚɤ ɩɪɢɧɢɦɚɬɶ ɩɨɞɴɟɦɧɭɸ ɦɚɲɢɧɭ ɜ ɭɫɥɨɜɢɹɯ ɲɚɯɬ ɫ ɩɨɫɥɟɞɭɸɳɟɣ ɭɝɥɭɛɤɨɣɲɚɯɬɧɨɝɨɫɬɜɨɥɚ"


ȽɅȺȼȺɊȺɋɑȿɌɋɄɂɉɈȼɈɃɈȾɇɈɄȺɇȺɌɇɈɃȾȼɍɏɄɈɇɐȿȼɈɃ
ɉɈȾɔȿɆɇɈɃɍɋɌȺɇɈȼɄɂ
ɂɫɯɨɞɧɵɦɢɞɚɧɧɵɦɢɞɥɹ ɩɪɨɟɤɬɢɪɨɜɚɧɢɹ ɩɨɞɴɟɦɧɵɯɭɫɬɚɧɨɜɨɤɹɜɥɹɸɬ ɫɹ
Ⱥ
±ɝɨɞɨɜɚɹɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶɲɚɯɬɵɬɵɫɬɨɧɧɜɝɨɞ
ɝɨɞ
ɇɲ ± ɝɥɭɛɢɧɚ ɲɚɯɬɵ ɦ ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɭɫɬɶɹ ɫɬɜɨɥɚ ɞɨ ɭɪɨɜɧɹ ɨɤɨɥɨ
ɫɬɜɨɥɶɧɨɝɨɞɜɨɪɚ
ȼɵɛɨɪɫɤɢɩɚ
ɋɤɢɩ ɜɵɛɢɪɚɟɬɫɹ ɧɚ ɨɫɧɨɜɟ ɪɚɰɢɨɧɚɥɶɧɨɣ ɝɪɭɡɨɩɨɞɴɟɦɧɨɫɬɢ ɤɨɬɨɪɭɸ ɨɩɪɟɞɟɥɹɸɬɩɨɮɨɪɦɭɥɟɩɪɨɮɟɫɫɨɪɚȿɥɚɧɱɢɤɚȽɆ
ɝɞɟ Ⱥ
ɱɚɫɪɚɰɝ
±ɱɚɫɨɜɚɹɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶɩɨɞɴɟɦɚɬɱ
ɱɚɫ.
ȺȺ
ɝɨɞɱɚɫ
tɇȺm
ɩɲ

ɤ
ɧ
tN


ɪ
ɝɞɟ ɤɧ.±ɤɨɷɮɮɢɰɢɟɧɬɧɟɪɚɜɧɨɦɟɪɧɨɫɬɢɪɚɛɨɬɵɢɪɟɡɟɪɜɚɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɢ
ɤɧ 
N±ɤɨɥɢɱɟɫɬɜɨɪɚɛɨɱɢɯɞɧɟɣɜɝɨɞɭN ɞɧɟɣɜɝɨɞɭ tp±ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶɪɚɛɨɬɵɩɨɞɴɟɦɚɜɞɟɧɶtɪ ɱɫɭɬ tn±ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶɩɚɭɡɵɩɪɟɞɜɚɪɢɬɟɥɶɧɨɩɪɢɧɢɦɚɟɬɫɹɪɚɜɧɨɣɫ
ɉɨm
ɩɪɢɧɢɦɚɟɬɫɹɫɬɚɧɞɚɪɬɧɵɣ ɫɤɢɩ ɫɪɚɡɝɪɭɡɤɨɣɱɟɪɟɡɞɧɨɫɫɟɤɬɨɪ
ɝ.ɪɚɰ
ɧɵɦɡɚɬɜɨɪɨɦɛɥɢɠɚɣɲɟɣɝɪɭɡɨɩɨɞɴɟɦɧɨɫɬɢɩɪɢɥȺɬɚɛɥȺ
ɏɚɪɚɤɬɟɪɢɫɬɢɤɚ ɫɤɢɩɚ
Ɍɢɩ
mɝ ±ɝɪɭɡɨɩɨɞɴɟɦɧɨɫɬɶɤɝ
mɫ ±ɦɚɫɫɚɫɨɫɭɞɚɫɤɢɩɤɝ
S0±ɪɚɫɫɬɨɹɧɢɟɦɟɠɞɭɨɫɹɦɢɫɤɢɩɨɜɜɫɬɜɨɥɟɦ
h '±ɩɪɟɜɵɲɟɧɢɟɪɚɦɵɫɤɢɩɚɧɚɞɛɭɧɤɟɪɨɦɜɨɜɪɟɦɹɪɚɡɝɪɭɡɤɢɦ
h0±ɞɥɢɧɚɪɚɡɝɪɭɡɨɱɧɨɝɨɭɱɚɫɬɤɚɩɭɬɢɦ
hc±ɜɵɫɨɬɚɫɤɢɩɚɦ
Q ±ɜɟɫɝɪɭɡɚɇ, Q = mɝ.Âg
G±ɜɟɫɫɨɫɭɞɚɫɤɢɩɚɇ.G = mɫ.Âg.

ȼɵɛɨɪɤɨɩɪɚ
J
V
V
Ʉɨɩɟɪ ɜɵɛɢɪɚɟɬɫɹ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɝɪɭɡɨɩɨɞɴɟɦɧɨɫɬɢ ɢ ɪɚɫɩɨɥɨɠɟɧɢɹ ɤɨɩɪɨɜɵɯ ɲɤɢɜɨɜ ɨɞɧɨɝɨ ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɪɭɝɨɝɨ ɧɚ ɨɞɧɨɣ ɨɫɢ ɢɥɢ ɜ ɨɞɧɨɣ ɩɥɨɫɤɨɫɬɢ
ɉɪɢ ɪɚɫɩɨɥɨɠɟɧɢɢ ɤɨɩɪɨɜɵɯ ɲɤɢɜɨɜ ɧɚ ɨɞɧɨɣ ɨɫɢ ɤɨɩɟɪ ɜɵɛɢɪɚɟɬɫɹ ɧɢɡɤɢɦɩɪɢɥȺɬɚɛɥȺ
Ɉɫɧɨɜɧɵɟɞɚɧɧɵɟɤɨɩɪɚ
ɇɤ – ɜɵɫɨɬɚɦ
hɛ –ɜɵɫɨɬɚɛɭɧɤɟɪɚɦ
Ɋɚɫɱɟɬɢɜɵɛɨɪɝɨɥɨɜɧɨɝɨɤɚɧɚɬɚ
ɋɭɳɟɫɬɜɭɸɬɫɥɟɞɭɸɳɢɟɜɚɪɢɚɧɬɵɪɚɫɱɟɬɚɢɜɵɛɨɪɚɝɨɥɨɜɧɨɝɨɤɚɧɚɬɚ
ɞɥɹɲɚɯɬɝɥɭɛɢɧɨɣɞɨɦɜɤɥɸɱɢɬɟɥɶɧɨɇɲ ɦ ɞɥɹɲɚɯɬɝɥɭɛɢɧɨɣɛɨɥɟɟɦɟɬɪɨɜɇɲ !ɦ
2.3.1. Ɋɚɫɱɟɬ ɢ ɜɵɛɨɪ ɝɨɥɨɜɧɨɝɨ ɤɚɧɚɬɚ ɞɥɹ ɲɚɯɬ ɝɥɭɛɢɧɨɣ ɞɨ 600 ɦ ɜɤɥɸɱɢɬɟɥɶɧɨ
Ʉɚɧɚɬ ɜɵɛɢɪɚɟɬɫɹ ɞɥɹ ɧɟɭɪɚɜɧɨɜɟɲɟɧɧɵɯ q ɢɭɪɚɜɧɨɜɟɲɟɧɧɵɯ
q pɤɩɨɞɴɟɦɨɜɝɞɟq, pɤ–ɜɟɫɫɨɨɬɜɟɬɫɬɜɟɧɧɨɨɞɧɨɝɨɦɟɬɪɚɭɪɚɜɧɨɜɟɲɢɜɚɸ ɳɟɝɨ ɢ ɝɨɥɨɜɧɨɝɨ ɤɚɧɚɬɨɜ ɤɝɦ ɩɨ ɪɚɫɱɟɬɧɨɣ ɦɚɫɫɟ ɨɞɧɨɝɨ ɦɟɬɪɚ ɝɨɥɨɜɧɨɝɨ ɤɚɧɚɬɚ
Ɋɚɫɱɟɬɧɚɹɦɚɫɫɚɨɞɧɨɝɨɦɟɬɪɚɝɨɥɨɜɧɨɝɨɤɚɧɚɬɚ

m
ɝɞɟ
±ɩɪɟɞɟɥɩɪɨɱɧɨɫɬɢɦɚɬɟɪɢɚɥɚɩɪɨɜɨɥɨɤɤɚɧɚɬɚɆɉɚ
ɜ
 ±Ɇɉɚ
ɜ
ɪɚɫɤ
ɜ
zmm
cɝ
 
JV
zH
Ȗ0 – ɭɫɥɨɜɧɵɣɨɛɴɟɦɧɵɣɜɟɫɦɚɬɟɪɢɚɥɚɤɚɧɚɬɚ Ɇɇ/ɦ3, Ȗ0 = 0,1 Ɇɇ/ɦ3 ɞɥɹɤɚɧɚɬɨɜɥɢɧɟɣɧɨɝɨɤɚɫɚɧɢɹ
=–ɫɬɚɬɢɱɟɫɤɢɣɡɚɩɚɫɩɪɨɱɧɨɫɬɢɞɥɹɫɤɢɩɨɜɵɯɩɨɞɴɟɦɨɜZ 
ɇ0 ±ɧɚɢɛɨɥɶɲɢɣɨɬɜɟɫɤɚɧɚɬɚɞɥɹɞɚɧɧɨɣɲɚɯɬɵɦ
ɋɨɨɬɧɨɲɟɧɢɟɜɟɫɚɢɦɚɫɫɵɨɞɧɨɝɨɦɟɬɪɚɤɚɧɚɬɚ
ɪɤ = mɤÂ g, ɇ

ɗɥɟɦɟɧɬɵɨɬɜɟɫɚɤɚɧɚɬɚɩɨɤɚɡɚɧɵɧɚɪɢɫɭɧɤɟ Ⱦɥɹɧɟɭɪɚɜɧɨɜɟɲɟɧɧɨɝɨɩɨɞɴɟɦɚ
ɇ
= ɇɲ + ɇɤ + hɭ 
ɨ
Ⱦɥɹɭɪɚɜɧɨɜɟɲɟɧɧɨɝɨɩɨɞɴɟɦɚ
ɇ
= ɇɲ + ɇɤ + hɭ + hn 
ɨ
ɝɞɟ hɭ ±ɜɵɫɨɬɚɭɝɥɭɛɤɢ, ɦ
hɭ ±ɦ hn– ɞɥɢɧɚɩɟɬɥɢɭɪɚɜɧɨɜɟɲɢɜɚɸɳɟɝɨɤɚɧɚɬɚɦ, hn –ɦ
ɍɪɚɜɧɨɜɟɲɢɜɚɧɢɟɫɤɢɩɨɜɵɯɩɨɞɴɟɦɨɜɪɚɰɢɨɧɚɥɶɧɨɢɫɩɨɥɶɡɨɜɚɬɶɧɚɲɚɯ
ɬɚɯɫɝɥɭɛɢɧɵɫɜɵɲɟɦ
Ⱦɥɹ ɷɤɫɩɥɭɚɬɚɰɢɢ ɩɨɞɴɟɦɨɜ ɩɪɢɧɢɦɚɸɬɫɹ ɤɚɧɚɬɵ ɬɢɩɚ ɅɄ ɩɨ ȽɈɋɌ
ɢȽɈɋɌɤɨɬɨɪɵɟɢɦɟɸɬıɜ––Ɇɉɚ
ɉɨ ɡɧɚɱɟɧɢɸ m
ɤ.ɪɚɫ.
ɢ ı
ɫɨɝɥɚɫɧɨ ȽɈɋɌ  ɜɵɛɢɪɚɟɬɫɹ ɤɚɧɚɬ ɪɚɜɧɨɝɨ ɢɥɢ
ɜ
ɛɥɢɠɚɣɲɟɝɨ ɛɨɥɶɲɟɝɨ ɡɧɚɱɟɧɢɹ ɦɚɫɫɵ ɨɞɧɨɝɨ ɦɟɬɪɚ ɞɥɢɧɵ ɤɚɧɚɬɚ ɩɪɢɥ Ⱥ ɬɚɛɥȺ
ɏɚɪɚɤɬɟɪɢɫɬɢɤɚ ɤɚɧɚɬɚ
ɌɢɩɜɫɨɨɬɜɟɬɫɬɜɢɢɫɩɪɢɧɹɬɵɦȽɈɋɌɨɦ
mɤ ±ɡɧɚɱɟɧɢɟɦɚɫɫɵɨɞɧɨɝɨɦɟɬɪɚɤɚɧɚɬɚɢɡɤɚɬɚɥɨɝɚɤɝɦ dɤ – ɞɢɚɦɟɬɪɤɚɧɚɬɚɦɦ F
±ɪɚɡɪɵɜɧɨɟɭɫɢɥɢɟɜɫɟɯɩɪɨɜɨɥɨɤɜɤɚɧɚɬɟɤɇ
ɪɚɡ
ɉɪɨɜɟɪɤɚɮɚɤɬɢɱɟɫɤɨɝɨɡɚɩɚɫɚɩɪɨɱɧɨɫɬɢɤɚɧɚɬɚɩɪɨɜɨɞɢɬɫɹɞɥɹɜɟɪɯɧɟɝɨ ɫɟɱɟɧɢɹɜɬɨɱɤɟɫɯɨɞɚɤɚɧɚɬɚɫɤɨɩɪɨɜɨɝɨɲɤɢɜɚɎɚɤɬɢɱɟɫɤɢɣɡɚɩɚɫɩɪɨɱɧɨɫɬɢ ɞɨɥɠɟɧ ɛɵɬɶ ɧɟ ɧɢɠɟ ɡɚɩɚɫɚ ɩɪɨɱɧɨɫɬɢ ɞɨɩɭɫɬɢɦɨɝɨ ɩɨ ɩɪɚɜɢɥɚɦ ɛɟɡɨɩɚɫɧɨ ɫɬɢ
F
z
ɮ
ɪɚɡ
z
t
 
ɇpGQ
ɤ
2.3.2. Ɋɚɫɱɟɬ ɢ ɜɵɛɨɪ ɝɨɥɨɜɧɨɝɨ ɤɚɧɚɬɚ ɞɥɹ ɲɚɯɬ ɫ ɝɥɭɛɢɧɨɣ ɛɨɥɟɟ 600 ɦ
ȼɷɬɨɦɫɥɭɱɚɟɤɚɧɚɬɪɚɫɫɱɢɬɵɜɚɟɬɫɹɩɨɤɨɧɟɱɧɨɣɧɚɝɪɭɡɤɟɞɥɹɫɟɱɟɧɢɹ ɜ ɦɟɫɬɟɤɪɟɩɥɟɧɢɹ ɫɨɫɭɞɚɤɤɚɧɚɬɭɬɟɛɟɡɭɱɟɬɚɜɟɫɚɨɬɜɟɫɚɤɚɧɚɬɚɧɢɠɧɟɟ ɫɟ ɱɟɧɢɟɤɚɧɚɬɚ

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