Добавил:
ivanov666
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Теоретическая механика. Практикум. Учебное пособие
.pdf
Ɂɚɞɚɱɚ ʋ 3. Ʉɚɤɨɜɚ ɞɥɢɧɚ ɪɚɡɛɟɝɚ ɫɚɦɨɥɟɬɚ, ɜɟɫ ɤɨɬɨɪɨɝɨ Ɋ = 180 ɤɇ,
ɬɹɝɚ, ɪɚɡɜɢɜɚɟɦɚɹ ɞɜɢɝɚɬɟɥɟɦ
R = 10 ɤɇ, ɜɡɥɟɬɧɚɹ ɫɤɨɪɨɫɬɶ V = 216 ɤɦ/ɱ?
Ɂɚɞɚɱɚ ʋ 4. ɒɚɪɢɤ ɜɟɫɨɦ Ɋ = 0,3 ɇ ɜɥɨɠɟɧ ɜ ɜɟɪɬɢɤɚɥɶɧɨ ɩɨ-
ɫɬɚɜɥɟɧɧɵɣ ɫɚɦɨɫɬɪɟɥ, ɩɪɭɠɢɧɚ ɤɨɬɨɪɨɝɨ ɫɠɚɬɚ ɧɚ
ɰɢɟɧɬ ɠɟɫɬɤɨɫɬɢ ɩɪɭɠɢɧɵ
ɬɚɟɬ ɢɡ ɫɚɦɨɥɟɬɚ?
Ɂɚɞɚɱɚ ʋ 5. ɉɪɢ ɞɜɢɠɟɧɢɢ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ m = 5 ɤɝ ɩɨ ɝɨɪɢɡɨɧ-
ɬɚɥɶɧɨɣ ɲɟɪɨɯɨɜɚɬɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɟɺ ɫɤɨɪɨɫɬɶ ɢɡɦɟɧɢɥɚɫɶ ɫ
ɞɨ V = 8 ɦ/ɫ, ɧɚ ɬɨɱɤɭ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ F = 34,4 H, ɫɨɫɬɚɜɥɹɸɳɚɹ ɭɝɨɥ
α
= 45° ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɞɜɢɠɟɧɢɹ. Ɉɩɪɟɞɟɥɢɬɶ ɩɪɨɣɞɟɧɧɨɟ ɦɚɬɟɪɢ-
ɚɥɶɧɨɣ ɬɨɱɤɨɣ ɪɚɫɫɬɨɹɧɢɟ, ɟɫɥɢ ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ
Ɂɚɞɚɱɚ ʋ 6. Ɍɟɥɨ m = 5 ɤɝ ɩɨɞɧɢɦɚɟɬɫɹ ɜɜɟɪɯ ɫ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨ-
ɫɬɶɸ
V0 = 12 ɦ/ɫ ɩɨ ɝɥɚɞɤɨɣ ɧɚɤɥɨɧɧɨɣ ɩɥɨɫɤɨɫɬɢ, ɫɨɫɬɚɜɥɹɸɳɟɣ
ɭɝɨɥ
60° ɫ ɝɨɪɢɡɨɧɬɨɦ. Ʉɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ ɩɪɢɧɹɬɶ
f = 0,05. ɇɚ ɬɟɥɨ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ F = 100 ɇ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɜ ɫɬɨɪɨɧɭ
ɞɜɢɠɟɧɢɹ. Ɂɧɚɹ ɩɪɨɣɞɟɧɧɵɣ ɩɭɬɶ
ɪɨɫɬɶ.
Ɂɚɞɚɱɚ ʋ 7. ɉɪɢ ɞɜɢɠɟɧɢɢ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ m = 50 ɤɝ ɩɨ ɝɨ-
ɪɢɡɨɧɬɚɥɶɧɨɣ ɲɟɪɨɯɨɜɚɬɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɟɺ ɫɤɨɪɨɫɬɶ ɢɡɦɟɧɢɥɚɫɶ ɫ
V0 = 5 ɦ/ɫ ɞɨ V1 = 10 ɦ/ɫ. ɇɚ ɬɨɱɤɭ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ Ɋ = 100 ɇ, ɫɨɫɬɚɜ-
ɥɹɸɳɚɹ ɭɝɨɥ
ɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɨɣ ɪɚɫɫɬɨɹɧɢɟ, ɟɫɥɢ ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ
Ɂɚɞɚɱɚ ʋ 8. Ɍɟɥɨ m = 0,8 ɤɝ ɩɨɞɧɢɦɚɟɬɫɹ ɜɜɟɪɯ ɫ ɧɚɱɚɥɶɧɨɣ ɫɤɨ-
ɪɨɫɬɶɸ
ɭɝɨɥ
45° ɫ ɝɨɪɢɡɨɧɬɨɦ. Ʉɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ f = 0,2. ɇɚ ɬɟɥɨ ɞɟɣɫɬɜɭɟɬ
ɫɢɥɚ,
F = 7,6 ɇ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɜ ɫɬɨɪɨɧɭ ɞɜɢɠɟɧɢɹ. Ɂɧɚɹ ɩɪɨɣɞɟɧɧɵɣ
ɩɭɬɶ
S = 5 ɦ, ɨɩɪɟɞɟɥɢɬɶ ɤɨɧɟɱɧɭɸ ɫɤɨɪɨɫɬɶ.
Ɂɚɞɚɱɚ ʋ 9. ɉɪɢ ɞɜɢɠɟɧɢɢ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ m = 0,4 ɤɝ ɩɨ ɝɨ-
ɪɢɡɨɧɬɚɥɶɧɨɣ ɲɟɪɨɯɨɜɚɬɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɟɺ ɫɤɨɪɨɫɬɶ ɢɡɦɟɧɢɥɚɫɶ ɫ
V0 = 2 ɦ/ɫ ɞɨ V1 = 4 ɦ/ɫ. ɇɚ ɬɨɱɤɭ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ F = 1,36 ɇ, ɫɨɫɬɚɜ-
ɥɹɸɳɚɹ
ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɨɣ ɪɚɫɫɬɨɹɧɢɟ, ɟɫɥɢ ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ
30° ɧɚɩɪɚɜɥɟɧɢɟɦ ɞɜɢɠɟɧɢɹ. Ɉɩɪɟɞɟɥɢɬɶ ɩɪɨɣɞɟɧɧɨɟ ɦɚ-
V0 = 5 ɦ/ɫ ɩɨ ɝɥɚɞɤɨɣ ɧɚɤɥɨɧɧɨɣ ɩɥɨɫɤɨɫɬɢ, ɫɨɫɬɚɜɥɹɸɳɟɣ
α
= 150°, ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɞɜɢɠɟɧɢɹ. Ɉɩɪɟɞɟɥɢɬɶ ɩɪɨɣɞɟɧɧɨɟ
F = 40 ɤH, ɨɛɳɚɹ ɫɢɥɚ ɫɨɩɪɨɬɢɜɥɟɧɢɹ
h = 15 ɫɦ. Ʉɨɷɮɮɢ-
ɫ = 3 ɇ/ɫɦ. ɋ ɤɚɤɨɣ ɫɤɨɪɨɫɬɶɸ ɲɚɪɢɤ ɜɵɥɟ-
V0 = 4 ɦ/ɫ
f = 0,15.
S = 8 ɦ, Ɉɩɪɟɞɟɥɢɬɶ ɤɨɧɟɱɧɭɸ ɫɤɨ-
f = 0,1.
f = 0,1.
111
Ɂɚɞɚɱɚ ʋ 10. ɋɤɨɪɨɫɬɶ ɫɚɧɟɣ ɩɪɢ ɫɩɭɫɤɟ ɫ ɝɨɪɵ (α = 30°), ɢɡɦɟɧɹ-
ɟɬɫɹ ɨɬ 0 ɞɨ 8
ɥɢɬɶ ɜɵɫɨɬɭ ɝɨɪɵ.
Ɂɚɞɚɱɚ ʋ 11. Ƚɪɭɡ ɦɚɫɫɨɣ m = 5 ɤɝ ɩɟɪɟɦɟɳɚɸɬ ɧɚ ɪɚɫɫɬɨɹɧɢɟ
S = 4 ɦ ɫ ɩɨɦɨɳɶɸ ɬɪɨɫɚ. ɋɢɥɚ ɬɹɝɢ F = 3 ɇ ɢ ɫɨɫɬɚɜɥɹɟɬ ɫ ɝɨɪɢɡɨɧɬɨɦ
α
= 30°. Ɉɩɪɟɞɟɥɢɬɶ ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ ɝɪɭɡɚ ɨ ɩɨɜɟɪɯ-
ɧɨɫɬɶ, ɟɫɥɢ ɟɝɨ ɫɤɨɪɨɫɬɶ ɢɡɦɟɧɢɥɚɫɶ ɨɬ
Ɂɚɞɚɱɚ ʋ 12. ɉɨ ɧɚɤɥɨɧɧɨɣ ɩɥɨɫɤɨɫɬɢ (ɭɝɨɥ α = 45°) ɫɩɭɫɤɚɟɬɫɹ
ɛɟɡ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɬɹɠɟɥɨɟ ɬɟɥɨ. Ʉɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ
Ʉɚɤɭɸ ɫɤɨɪɨɫɬɶ ɛɭɞɟɬ ɢɦɟɬɶ ɬɟɥɨ, ɩɪɨɣɞɹ ɪɚɫɫɬɨɹɧɢɟ
Ɂɚɞɚɱɚ ʋ 13. ɉɨ ɧɚɤɥɨɧɧɨɣ ɩɥɨɫɤɨɫɬɢ (ɭɝɨɥ α = 45°) ɜɜɟɪɯ ɞɜɢ-
ɠɟɬɫɹ ɚɜɬɨɦɨɛɢɥɶ. ɉɪɨɞɟɥɚɜ ɩɭɬɶ
ɞɟɥɢɬɶ ɧɚɱɚɥɶɧɭɸ ɫɤɨɪɨɫɬɶ ɚɜɬɨɦɨɛɢɥɹ, ɟɫɥɢ ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ
f = 0,2.
Ɂɚɞɚɱɚ ʋ 14. ɉɪɢ ɞɜɢɠɟɧɢɢ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɢ m = 0,8 ɤɝ ɩɨ ɝɨ-
ɪɢɡɨɧɬɚɥɶɧɨɣ ɲɟɪɨɯɨɜɚɬɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɟɺ ɫɤɨɪɨɫɬɶ ɢɡɦɟɧɢɥɚɫɶ ɫ
V0 = 5 ɦ/ɫ ɞɨ V1 = 10 ɦ/ɫ. ɇɚ ɬɨɱɤɭ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ F = 1,9 ɇ, ɫɨɫɬɚɜ-
ɥɹɸɳɚɹ (ɭɝɨɥ
ɞɟɧɧɨɟ ɦɚɬɟɪɢɚɥɶɧɨɣ ɬɨɱɤɨɣ ɪɚɫɫɬɨɹɧɢɟ, ɟɫɥɢ ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ
f = 0,08.
Ɂɚɞɚɱɚ ʋ 15. Ƚɪɭɡ m = 6 ɤɝ ɫ ɩɨɦɨɳɶɸ ɬɪɨɫɚ ɩɟɪɟɦɟɳɚɸɬ ɩɨ ɝɨɪɢ-
ɡɨɧɬɚɥɶɧɨɣ ɩɨɜɟɪɯɧɨɫɬɢ. ȼ ɧɚɱɚɥɶɧɵɣ ɦɨɦɟɧɬ ɫɤɨɪɨɫɬɶ ɛɵɥɚ
ɚ ɱɟɪɟɡ
ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ
α
= 30° ɤ ɝɨɪɢɡɨɧɬɭ.
Ɂɚɞɚɱɚ ʋ 16. Ɍɟɥɨ m = 3 ɤɝ ɩɨɞɧɢɦɚɟɬɫɹ ɜɜɟɪɯ ɫ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨ-
ɫɬɶɸ
V0 = 2 ɦ/ɫ ɩɨ ɧɟɝɥɚɞɤɨɣ ɧɚɤɥɨɧɧɨɣ ɩɥɨɫɤɨɫɬɢ (ɭɝɨɥ α = 30°).
Ʉɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ
F = 39,6 ɇ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɜ ɫɬɨɪɨɧɭ ɞɜɢɠɟɧɢɹ. Ɂɧɚɹ ɩɪɨɣɞɟɧɧɵɣ ɩɭɬɶ
S = 2,5 ɦ, ɨɩɪɟɞɟɥɢɬɶ ɤɨɧɟɱɧɭɸ ɫɤɨɪɨɫɬɶ.
Ɂɚɞɚɱɚ ʋ 17. ɉɪɢ ɬɨɪɦɨɠɟɧɢɢ ɜɚɝɨɧ ɩɪɨɯɨɞɢɬ ɩɭɬɶ ɞɨ ɨɫɬɚɧɨɜɤɢ
S = 8
ɦ. Ɉɩɪɟɞɟɥɢɬɶ ɧɚɱɚɥɶɧɭɸ ɫɤɨɪɨɫɬɶ ɜɚɝɨɧɚ, ɟɫɥɢ ɤɨɷɮɮɢɰɢɟɧɬ
ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ
ɦ/ɫ. Ʉɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ f = 0,1. Ɉɩɪɟɞɟ-
0 ɞɨ 2 ɦ/ɫ.
f = 0,15.
S = 0,3 ɦ?
S = 8 ɦ, ɨɧ ɨɫɬɚɧɚɜɥɢɜɚɟɬɫɹ. Ɉɩɪɟ-
α
= 45
°
) ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɞɜɢɠɟɧɢɹ. Ɉɩɪɟɞɟɥɢɬɶ ɩɪɨɣ-
V0 = 2 ɦ/ɫ,
2 ɦ ɨɧɚ ɫɬɚɥɚ V1 = 4 ɦ/ɫ. Ɉɩɪɟɞɟɥɢɬɶ ɧɚɬɹɠɟɧɢɟ ɬɪɨɫɚ, ɟɫɥɢ
f = 0,1. Ɍɪɨɫ ɪɚɫɩɨɥɨɠɟɧ ɩɨɞ ɭɝɥɨɦ
f = 0,2. ɇɚ ɬɟɥɨ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ,
f = 0,75.
112
Ɂɚɞɚɱɚ ʋ 18. ɉɪɢ ɞɜɢɠɟɧɢɢ ɝɪɭɡɚ ɩɨ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɲɟɪɨɯɨɜɚ-
ɬɨɣ ɩɨɜɟɪɯɧɨɫɬɢ
V1 = 6 ɦ/ɫ. ɇɚ ɬɨɱɤɭ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ F = 2 ɇ, ɫɨɫɬɚɜɥɹɸɳɚɹ (ɭɝɨɥ α = 60°)
ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɞɜɢɠɟɧɢɹ. Ɉɩɪɟɞɟɥɢɬɶ ɩɪɨɣɞɟɧɧɵɣ ɩɭɬɶ, ɟɫɥɢ ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ
Ɂɚɞɚɱɚ ʋ 19. ȼɚɝɨɧɟɬɤɚ ɞɜɢɠɟɬɫɹ ɩɨ ɧɚɤɥɨɧɧɨɣ ɩɥɨɫɤɨɫɬɢ (ɭɝɨɥ
α
= 60°), ɫɤɨɪɨɫɬɶ ɟɺ ɢɡɦɟɧɹɟɬɫɹ ɨɬ V0 = 0 ɦ/ɫ ɞɨ V1 = 5 ɦ/ɫ. Ɉɩɪɟɞɟ-
ɥɢɬɶ ɩɪɨɣɞɟɧɧɵɣ ɩɭɬɶ, ɟɫɥɢ ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ
Ɂɚɞɚɱɚ ʋ 20. ɉɪɢ ɞɜɢɠɟɧɢɢ ɝɪɭɡɚ m = 1 ɤɝ ɩɨ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ
ɲɟɪɨɯɨɜɚɬɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɟɝɨ ɫɤɨɪɨɫɬɶ ɢɡɦɟɧɢɥɚɫɶ ɫ
V1 = 10 ɦ/ɫ. ɇɚ ɬɨɱɤɭ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ F = 10 ɇ, ɫɨɫɬɚɜɥɹɸɳɚɹ (ɭɝɨɥ
α
= 135°) ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɞɜɢɠɟɧɢɹ. Ɉɩɪɟɞɟɥɢɬɶ ɩɪɨɣɞɟɧɧɵɣ ɩɭɬɶ,
ɟɫɥɢ ɤɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ
Ɂɚɞɚɱɚ ʋ 21. Ɍɟɥɨ m = 0,8 ɤɝ ɩɨɞɧɢɦɚɟɬɫɹ ɜɜɟɪɯ ɫ ɧɚɱɚɥɶɧɨɣ ɫɤɨ-
ɪɨɫɬɶɸ
ɟɧɬ ɬɪɟɧɢɹ
ɫɬɨɪɨɧɭ ɞɜɢɠɟɧɢɹ. Ɂɧɚɹ ɩɪɨɣɞɟɧɧɵɣ ɩɭɬɶ
ɧɭɸ ɫɤɨɪɨɫɬɶ.
ɝɨɪɢɡɨɧɬɭ ɨɩɭɫɤɚɟɬɫɹ ɜɚɝɨɧɟɬɤɚ
ɧɚɬɚ ɩɪɢ ɬɨɪɦɨɠɟɧɢɢ ɜɚɝɨɧɟɬɤɢ ɜ ɤɨɧɰɟ ɫɩɭɫɤɚ, ɟɫɥɢ ɧɚɱɚɥɶɧɚɹ ɫɤɨɪɨɫɬɶ ɟɺ
ɥɟɫ ɜɚɝɨɧɟɬɤɢ ɨ ɞɨɪɨɝɭ
ɫ ɝɨɪɢɡɨɧɬɨɦ, ɫɩɭɫɤɚɟɬɫɹ ɛɟɡ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɬɹɠɟɥɨɟ ɬɟɥɨ. Ʉɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ
ɫɬɨɹɧɢɟ
ɫɬɶɸ
ɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ
ɥɟɧɧɚɹ ɜ ɫɬɨɪɨɧɭ ɞɜɢɠɟɧɢɹ. Ɂɧɚɹ ɩɪɨɣɞɟɧɧɵɣ ɩɭɬɶ
ɤɨɧɟɱɧɭɸ ɫɤɨɪɨɫɬɶ.
Ɂɚɞɚɱɚ ʋ 25. Ƚɪɭɡ ɫɩɭɫɤɚɟɬɫɹ ɩɨ ɧɚɤɥɨɧɧɨɣ ɩɥɨɫɤɨɫɬɢ (ɭɝɨɥ
α
ɫɤɨɪɨɫɬɶ ɛɭɞɟɬ ɢɦɟɬɶ ɝɪɭɡ, ɩɪɨɣɞɹ ɪɚɫɫɬɨɹɧɢɟ
V0 = 9 ɦ/ɫ ɩɨ ɧɚɤɥɨɧɧɨɣ ɩɥɨɫɤɨɫɬɢ (ɭɝɨɥ α = 60°). Ʉɨɷɮɮɢɰɢ-
Ɂɚɞɚɱɚ ʋ 22. ɉɨ ɤɚɧɚɬɧɨɣ ɠɟɥɟɡɧɨɣ ɞɨɪɨɝɟ ɫ ɭɤɥɨɧɨɦα = 30° ɤ
V0 = 2 ɦ/ɫ, ɩɪɨɣɞɟɧɧɵɣ ɩɭɬɶ S = 2 ɦ. Ʉɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɤɨ-
Ɂɚɞɚɱɚ ʋ 23. ɉɨ ɧɚɤɥɨɧɧɨɣ ɩɥɨɫɤɨɫɬɢ, ɫɨɫɬɚɜɥɹɸɳɟɣ ɭɝɨɥ α = 60°
S = 4 ɦ?
Ɂɚɞɚɱɚ ʋ 24. Ɍɟɥɨ m = 6 ɤɝ ɩɨɞɧɢɦɚɟɬɫɹ ɜɜɟɪɯ ɫ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨ-
V0 = 5 ɦ/ɫ ɩɨ ɧɟɝɥɚɞɤɨɣ ɧɚɤɥɨɧɧɨɣ ɩɥɨɫɤɨɫɬɢ (ɭɝɨɥ α = 45°). Ʉɨ-
= 45°) ɛɟɡ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ. Ʉɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ f = 0,5. Ʉɚɤɭɸ
m = 0,4 ɤɝ, ɫɤɨɪɨɫɬɶ ɟɝɨ ɢɡɦɟɧɢɥɚɫɶ ɫ V0 = 4 ɦ/ɫ ɞɨ
f = 0,1.
f = 0,1.
V0 = 6 ɦ/ɫ ɞɨ
f = 0,1.
f = 0,2. ɇɚ ɬɟɥɨ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ F = 16 ɇ, ɧɚɩɪɚɜɥɟɧɧɚɹ ɜ
S = 3 ɦ, ɨɩɪɟɞɟɥɢɬɶ ɤɨɧɟɱ-
m = 500 ɤɝ. Ɉɩɪɟɞɟɥɢɬɶ ɧɚɬɹɠɟɧɢɟ ɤɚ-
f = 0,01.
f = 0,1. Ʉɚɤɭɸ ɫɤɨɪɨɫɬɶ ɛɭɞɟɬ ɢɦɟɬɶ ɬɟɥɨ, ɩɪɨɣɞɹ ɪɚɫ-
f = 0,1. ɇɚ ɬɟɥɨ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ F = 20 ɇ, ɧɚɩɪɚɜ-
S = 2 ɦ, ɨɩɪɟɞɟɥɢɬɶ
S =2 ɦ?
113
x
Ɂɚɞɚɱɚ ʋ 26. ɒɚɪɢɤ ɜɟɫɨɦ Ɋ = 0,2 ɇ ɜɥɨɠɟɧ ɜ ɜɟɪɬɢɤɚɥɶɧɨ ɩɨ-
ɫɬɚɜɥɟɧɧɵɣ ɫɚɦɨɫɬɪɟɥ, ɩɪɭɠɢɧɚ ɤɨɬɨɪɨɝɨ ɫɠɚɬɚ ɧɚ
ɮɢɰɢɟɧɬ ɠɟɫɬɤɨɫɬɢ ɩɪɭɠɢɧɵ
ɜɵɥɟɬɢɬ ɢɡ ɫɚɦɨɫɬɪɟɥɚ?
Ɂɚɞɚɱɚ ʋ 27. ɉɪɢ ɬɨɪɦɨɠɟɧɢɢ ɚɜɬɨɦɨɛɢɥɶ ɞɨ ɨɫɬɚɧɨɜɤɢ ɩɪɨɯɨɞɢɬ
S = 25 ɦ. Ɉɩɪɟɞɟɥɢɬɶ ɧɚɱɚɥɶɧɭɸ ɫɤɨɪɨɫɬɶ ɚɜɬɨɦɨɛɢɥɹ, ɟɫɥɢ ɤɨ-
ɩɭɬɶ
ɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɤɨɥɟɫ ɨɛ ɚɫɮɚɥɶɬ ɩɪɢ ɬɨɪɦɨɠɟɧɢɢ
Ɂɚɞɚɱɚ ʋ 28. ɉɨ ɧɚɤɥɨɧɧɨɣ ɩɥɨɫɤɨɫɬɢ (ɭɝɨɥ α = 45°) ɫɩɭɫɤɚɟɬɫɹ
ɛɟɡ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɬɹɠɟɥɨɟ ɬɟɥɨ. Ʉɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ
Ʉɚɤɭɸ ɫɤɨɪɨɫɬɶ ɛɭɞɟɬ ɢɦɟɬɶ ɬɟɥɨ, ɩɪɨɣɞɹ ɪɚɫɫɬɨɹɧɢɟ S = 6 ɦ.
Ɂɚɞɚɱɚ ʋ 29. Ɍɟɥɨ m = 9 ɤɝ ɩɨɞɧɢɦɚɟɬɫɹ ɜɜɟɪɯ ɫ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨ-
V0 = 10 ɦ/ɫ, ɩɨ ɧɟɝɥɚɞɤɨɣ ɧɚɤɥɨɧɧɨɣ ɩɥɨɫɤɨɫɬɢ ɫɨɫɬɚɜɥɹɸɳɟɣ
ɫɬɶɸ
ɭɝɨɥ
α
= 60° ɫ ɝɨɪɢɡɨɧɬɨɦ. ɇɚ ɬɟɥɨ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ F = 180 ɇ, ɧɚɩɪɚɜ-
ɥɟɧɧɚɹ ɜ ɫɬɨɪɨɧɭ ɞɜɢɠɟɧɢɹ. Ɂɧɚɹ ɩɪɨɣɞɟɧɧɵɣ ɩɭɬɶ
ɥɢɬɶ ɤɨɧɟɱɧɭɸ ɫɤɨɪɨɫɬɶ. Ʉɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ
Ɂɚɞɚɱɚ ʋ 30. ɉɨ ɧɚɤɥɨɧɧɨɣ ɩɥɨɫɤɨɫɬɢ (ɭɝɨɥ α = 30°) ɫɩɭɫɤɚɟɬɫɹ
ɛɟɡ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ ɬɹɠɟɥɨɟ ɬɟɥɨ. Ʉɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ
Ʉɚɤɭɸ ɫɤɨɪɨɫɬɶ ɛɭɞɟɬ ɢɦɟɬɶ ɬɟɥɨ, ɩɪɨɣɞɹ ɪɚɫɫɬɨɹɧɢɟ S = 1 ɦ?
ɫ = 2 ɇ/ɫɦ. ɋ ɤɚɤɨɣ ɫɤɨɪɨɫɬɶɸ ɲɚɪɢɤ
f = 0,2 ɫɦ. Ʉɨɷɮ-
f = 0,2.
S = 10 ɦ, ɨɩɪɟɞɟ-
f = 0,3.
ɉɪɢɦɟɪ ʋ 7
Ɍɟɥɨ
y
F
ɬɪ
α
Ʉ ɝɪɭɡɭ ɩɪɢɥɨɠɟɧɵ ɫɥɟɞɭɸɳɢɟ ɫɢɥɵ: P – ɫɢɥɚ ɬɹɠɟɫɬɢ;
ɫɢɥɚ ɬɪɟɧɢɹ;
ɥɚ ɬɹɠɟɫɬɢ.
F
P
Ɋɢɫ. 43.
N
– ɧɨɪɦɚɥɶɧɚɹ ɪɟɚɤɰɢɹ ɧɚɤɥɨɧɧɨɣ ɩɥɨɫɤɨɫɬɢ; F – ɫɢ-
ɧɨɣ ɫɤɨɪɨɫɬɶɸ
ɫɬɢ (ɭɝɨɥ
ɇɚ ɬɟɥɨ ɞɟɣɫɬɜɭɟɬ ɫɢɥɚ
ɧɚɹ ɜ ɫɬɨɪɨɧɭ ɞɜɢɠɟɧɢɹ. Ɂɧɚɹ ɩɪɨɣɞɟɧɧɵɣ
ɩɭɬɶ
m = 4 ɤɝ ɩɨɞɧɢɦɚɟɬɫɹ ɜɜɟɪɯ ɫ ɧɚɱɚɥɶ-
VɈ =14 ɦ/ɫ ɩɨ ɧɟɝɥɚɞɤɨɣ ɩɥɨɫɤɨ-
α
= 45°) (ɪɢɫ. 43).
Ʉɨɷɮɮɢɰɢɟɧɬ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ
F = 80 ɇ, ɧɚɩɪɚɜɥɟɧ-
S = 5 ɦ, ɨɩɪɟɞɟɥɢɬɶ ɤɨɧɟɱɧɭɸ ɫɤɨɪɨɫɬɶ.
Ɋȿɒȿɇɂȿ
f = 0,04.
f = 0,33.
f = 0,5.
F –
ɬɪ
114
ɉɪɢɦɟɧɹɟɦ ɬɟɨɪɟɦɭ ɨɛ ɢɡɦɟɧɟɧɢɢ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɬɨɱɤɢ:
mv
2
0
1
=− (6)
2
.A
¦
K
2
2
mv
Ɋɚɛɨɬɚ
Ⱥ ɪɚɜɧɨɞɟɣɫɬɜɭɸɳɟɣ ɫɢɥ, ɩɪɢɥɨɠɟɧɧɵɯ ɤ ɬɟɥɭ, ɪɚɜɧɚ ɚɥ-
ɝɟɛɪɚɢɱɟɫɤɨɣ ɫɭɦɦɟ ɪɚɛɨɬ ɫɨɫɬɚɜɥɹɸɳɢɯ ɫɢɥ:
¦
+++= ).F(A)N(A)F(A)P(AA
(7)
ɬɪK
Ɍɚɤ ɤɚɤ ɪɟɚɤɰɢɹ N ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɚ ɩɟɪɟɦɟɳɟɧɢɸ, ɬɨ:
.0)N(A = (8)
Ɋɚɛɨɬɚ ɫɢɥɵ ɬɹɠɟɫɬɢ ɨɬɪɢɰɚɬɟɥɶɧɚ, ɬ. ɤ. ɝɪɭɡ ɩɨɞɧɢɦɚɟɬɫɹ ɜɜɟɪɯ,
ɪɚɜɧɚ:
,hP)P(A ⋅−= (9)
ɝɞɟ Ɋ = mq = 40 H.
h
S
5,37,0545sinSh45sin
=⋅=°⋅=→°= ɦ,
1405,340)P(A −=⋅−= (Ⱦɠ).
Ɋɚɛɨɬɚ ɫɢɥɵ ɬɪɟɧɢɹ ɨɬɪɢɰɚɬɟɥɶɧɚ, ɬ. ɤ. ɷɬɚ ɫɢɥɚ ɧɚɩɪɚɜɥɟɧɚ ɜ ɫɬɨɪɨɧɭ, ɩɪɨɬɢɜɨɩɨɥɨɠɧɭɸ ɧɚɩɪɚɜɥɟɧɢɸ ɞɜɢɠɟɧɢɹ ɝɪɭɡɚ, ɢ ɪɚɜɧɚ:
.SF)F(A
⋅−= (10)
ɬɪɬɪ
ɋɢɥɚ ɬɪɟɧɢɹ ɫɤɨɥɶɠɟɧɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɨɪɦɭɥɨɣ:
Fɬɪ = f ⋅ N. (11)
ɇɨɪɦɚɥɶɧɚɹ ɪɟɚɤɰɢɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɢɡ ɭɪɚɜɧɟɧɢɹ:
¦
Fiy = 0; N = P ⋅ cos 45° = 0 → ° N = P ⋅ cos 45°,
⋅
N = mq
cos 45° = 4 ⋅ 10 ⋅ 0,7 = 28 (H).
115
ɉɨɞɫɬɚɜɥɹɹ ɡɧɚɱɟɧɢɟ
F
ɬɪɟɧɢɹ:
N = 28 (H) ɜ ɮɨɪɦɭɥɭ (11), ɧɚɯɨɞɢɦ ɫɢɥɭ
Fɬɪ = 0,5 ⋅ 28 = 14 (ɇ).
ɉɨɞɫɬɚɜɥɹɹ ɡɧɚɱɟɧɢɟ
F ɜ ɮɨɪɦɭɥɭ (10), ɧɚɯɨɞɢɦ ɪɚɛɨɬɭ ɫɢɥɵ
ɬɪ
ɬɪɟɧɢɹ:
Ⱥ(
F ) = –14
ɬɪ
⋅
5 = –70 (Ⱦɠ). (12)
Ɋɚɛɨɬɚ ɫɢɥɵ F ɨɩɪɟɞɟɥɹɟɬɫɹ:
Ⱥ(
F ) = F
ɬɪ
Ⱥ(
) = 80
⋅
S,
⋅
5 = 400 (Ⱦɠ). (13)
ɉɨɞɫɬɚɜɥɹɹ ɡɧɚɱɟɧɢɹ (8), (9), (10), (11) ɜ ɮɨɪɦɭɥɭ (7), ɧɚɯɨɞɢɦ
ɫɭɦɦɭ ɪɚɛɨɬ ɫɢɥ, ɩɪɢɥɨɠɟɧɧɵɯ ɤ ɬɟɥɭ:
¦
Ⱥi = 0 – 140 – 70 + 400 = 190 (Ⱦɠ).
Ⱦɥɹ ɞɚɧɧɨɝɨ ɫɥɭɱɚɹ ɭɪɚɜɧɟɧɢɟ ɢɡɦɟɧɟɧɢɹ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ
ɩɪɢɧɢɦɚɟɬ ɜɢɞ:
2
v4
1
2
2
1
2
1
2
⋅
144
=
=
2
,190392v2
=−
,190392v2
+=
2
.582v2
=
1
,190
Ɉɬɤɭɞɚ ɨɩɪɟɞɟɥɹɟɦ ɤɨɧɟɱɧɭɸ ɫɤɨɪɨɫɬɶ:
17291v
1
≈= ɦ/ɫ.
Ɉɬɜɟɬ: v1 = 17 ɦ/ɫ.
116
ɋɉɂɋɈɄ ɊȿɄɈɆȿɇȾɍȿɆɈɃ ɅɂɌȿɊȺɌɍɊɕ
1. ȼɟɪɟɢɧɚ, Ʌ. ɂ. Ɍɟɯɧɢɱɟɫɤɚɹ ɦɟɯɚɧɢɤɚ: ɭɱɟɛɧɢɤ ɞɥɹ ɩɪɨɮ. ɨɛɪɚ-
ɡɨɜɚɧɢɹ / Ʌ. ɂ. ȼɟɪɟɢɧɚ. – 4-ɟ ɢɡɞ., ɫɬɟɪ. – Ɇ. : ɂɡɞɚɬɟɥɶɫɤɢɣ ɰɟɧɬɪ
«Ⱥɤɚɞɟɦɢɹ», 2007. – 224 ɫ.
2. Ɉɥɨɮɢɧɫɤɚɹ, ȼ. ɉ. Ʉɭɪɫ ɥɟɤɰɢɣ ɫ ɜɚɪɢɚɧɬɚɦɢ ɩɪɚɤɬɢɱɟɫɤɢɯ ɢ
ɬɟɫɬɨɜɵɯ ɡɚɞɚɧɢɣ: ɭɱɟɛ. ɩɨɫɨɛɢɟ. / ȼ. ɉ. Ɉɥɨɮɢɧɫɤɚɹ. – Ɇ. : ɎɈɊɍɆ:
ɂɇɎɊȺ-Ɇ, 2003. – 349 ɫ.: ɢɥ. – (ɋɟɪɢɹ «ɉɪɨɮɟɫɫɢɨɧɚɥɶɧɨɟ ɨɛɪɚɡɨɜɚɧɢɟ»).
3. ɗɪɞɟɞɢ,
ɚɥɨɜ: ɭɱɟɛ. ɩɨɫɨɛɢɟ ɞɥɹ ɬɟɯɧɢɤɭɦɨɜ / Ⱥ. Ⱥ. ɗɪɞɟɞɢ, ɇ. Ⱥ. ɗɪɞɟɞɢ, –
Ɇ. : ȼɵɫɲɚɹ ɲɤɨɥɚ: Ⱥɤɚɞɟɦɢɹ. 2001. – 318 ɫ.
4. Ⱥɪɤɭɲɚ, Ⱥ. ɂ. Ɍɟɯɧɢɱɟɫɤɚɹ ɦɟɯɚɧɢɤɚ. Ɍɟɨɪɟɬɢɱɟɫɤɚɹ ɦɟɯɚɧɢɤɚ
ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɬɟɪɢɚɥɨɜ: ɭɱɟɛ. ɩɨɫɨɛɢɟ ɞɥɹ ɫɪɟɞ. ɩɪɨɮ. ɭɱɟɛ. ɡɚɜɟɞɟɧɢɣ / Ⱥ. ɂ. Ⱥɪɤɭɲɚ. – Ɇ. : ȼɵɫɲɚɹ ɲɤɨɥɚ. 2005. – 352 ɫ.: ɢɥ.
5. Ⱥɪɤɭɲɚ, Ⱥ
ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɬɟɪɢɚɥɨɜ: ɭɱɟɛɧɢɤ ɞɥɹ ɫɪɟɞ. ɫɩɟɰ. ɭɱɟɛ. ɡɚɜɟɞɟɧɢɣ /
Ⱥ. ɂ. Ⱥɪɤɭɲɚ. – Ɇ. : ȼɵɫɲɚɹ ɲɤɨɥɚ, 2002. – 352 ɫ.: ɢɥ.
Ⱥ. Ⱥ. Ɍɟɨɪɟɬɢɱɟɫɤɚɹ ɦɟɯɚɧɢɤɚ. ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɦɚɬɟɪɢ-
. ɂ. Ɍɟɯɧɢɱɟɫɤɚɹ ɦɟɯɚɧɢɤɚ. Ɍɟɨɪɟɬɢɱɟɫɤɚɹ ɦɟɯɚɧɢɤɚ
117
ɉɊɂɅɈɀȿɇɂə
ɉɪɢɥɨɠɟɧɢɟ 1
ʋ
ɩ/ɩ
1 15 0,2588 0,9659
2 20 0,3420 0,9397
3 25 0,4226 0,9063
4 30 0,5000 0,8660
5 35 0,5736 0,8192
6 40 0,6428 0,7660
7 45 0,7071 0,7071
8 50 0,7660 0,6428
9 55 0,8192 0,5736
10 60 0,8660 0,5000
11 65 0,9063 0,4226
12 70 0,9397 0,3420
13 75 0,9659 0,2588
ɍɝɨɥ
ɜ ɝɪɚɞ.
sin cos
118
ɋɨɪɬɚɦɟɧɬ ɩɪɨɤɚɬɧɨɣ ɫɬɚɥɢ
b d ɭ
ɉɪɨɤɚɬɧɚɹ ɭɝɥɨɜɚɹ ɧɟɪɚɜɧɨɩɨɥɨɱɧɚɹ ɫɬɚɥɶ (ɩɨ ȽɈɋɌ 8510-86)
x
y
y
o
1
r
d
ɢ
ȼ
b
R
x
a
ɢ
y
b
o
x
r
o
y
x
d
1
ɉɪɢɥɨɠɟɧɢɟ 2
ʋ
ɩɪɨɮɢɥɹ
Ɋɚɡɦɟɪɵ,
ɦɦ
ȼ
Ʉɨɨɪɞɢɧɚɬɵ
ɰɟɧɬɪɚ ɬɹɠɟɫɬɢ
0
ɯ
0
ɉɥɨɳɚɞɶ
ɩɪɨɮɢɥɹ,
Ⱥ, ɫɦ
3,2/2 32 20 3 1,08 0,492 1,49
4/2,5 40 25 4 1,12 0,53 1,94
4,5/2,8 45 28 4 1,51 0,68 2,80
5/3,2 50 32 3 1,60 0,72 2,42
5,6/3,6 56 36 4 1,82 0,84 3,58
6,3/4,0 63 40 4 2,03 0,91 4,04
7/4,5 70 45 4,5 2,25 1,03 5,07
8,5 80 50 5 2,60 1,13 6,36
9/5,6 90 56 6 2,95 1,28 8,54
10/6,3 100 63 6 3,23 1,42 9,59
11/7 110 70 6,5 3,55 1,58 11,4
12,5/8 125 80 10 4,14 1,92 19,7
14/9 140 90 8 4,49 2,03 18
16/10 160 100 14 5,40 2,43 34,7
2
119
ɉɪɨɞɨɥɠɟɧɢɟ ɩɪɢɥɨɠɟɧɢɹ 2
b d
ɉɪɨɤɚɬɧɚɹ ɭɝɥɨɜɚɹ ɪɚɜɧɨɩɨɥɨɱɧɚɹ ɫɬɚɥɶ (ɩɨ ȽɈɋɌ 8509-86)
d
r
y
o
x
o
b
x
x
o
R
y
b
o
x
r
o
z
x
d
1
ʋ
ɩɪɨɮɢɥɹ
Ɋɚɡɦɟɪɵ,
ɦɦ
ɩɪɨɮɢɥɹ, Ⱥ, ɫɦ
ɉɥɨɳɚɞɶ
Z0,
2
ɫɦ
3,2 32 34 1,86 0,89
4 40 3 2,35 1,09
4,5 45 3 2,65 1,21
5,0 50 3 2,96 1,33
5,6 56 3,5 3,86 1,50
6,3 63 4 4,96 1,69
7 70 4,5 6,20 1,68
7,5 75 5 7,39 2,02
8 80 5,5 8,63 2,17
8 80 6 9,38 2,19
9 90 6 10,6 2,43
9 90 7 12,3 2,47
10 100 8 15,6 2,75
10 100 10 19,2 2,83
120
Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]