Задача №31.4
Условие
Путь, по которому движется вагонетка, скатываясь из точки A, образует разомкнутую петлю радиуса r, как показано на рисунке; ∠BOC=∠BOD=α. Найти, с какой высоты h должна скатываться вагонетка без начальной скорости, чтобы она могла пройти всю петлю, а также то значение угла α, при котором эта высота h наименьшая. Указание. На участке DC центр тяжести вагонетки совершает параболическое движение.Решение
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1.1
1.2
1.3
1.4
1.5
2.1
2.2
2.3
2.4
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3.1
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3.3
3.4
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4.1
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5.1
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9.1
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10.1
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12.1
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19.1
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24.1
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25.1
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26.1
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27.1
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27.34
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27.47
27.48
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27.55
27.58
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27.61
27.62
27.63
27.64
27.65
28.1
28.2
28.3
28.4
28.5
28.6
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29.1
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30.1
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31.1
31.2
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31.11
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31.35
32.1
32.2
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32.26
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32.29
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32.31
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32.34
32.35
32.36
32.37
32.38
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32.40
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32.42
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32.44
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32.46
32.47
32.48
32.49
32.50
32.51
32.52
32.53
32.54
32.55
32.56
32.57
32.58
32.59
32.60
32.61
32.62
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32.64
32.65
32.66
32.67
32.68
32.69
32.70
32.71
32.72
32.73
32.74
32.75
32.76
32.77
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32.81
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32.84
32.85
32.86
32.87
32.88
32.89
32.90
32.91
32.92
32.93
32.94
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32.96
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32.99
32.100
32.101
32.102
32.103
32.104
32.105
32.106
32.107
33.1
33.2
33.3
33.4
33.5
33.6
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33.22
34.1
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34.5
34.6
34.7
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34.31
35.1
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36.1
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37.1
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38.1
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39.1
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40.1
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41.1
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42.1
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43.1
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44.1
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45.3
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46.1
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47.1
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48.1
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49.1
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53.5
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54.1
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55.2
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56.3
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56.9