Задача №31.26
Условие
Точка M массы m=1 кг движется по гладкой поверхности круглого конуса, угол раствора которого 2α=90°, под влиянием силы отталкивания от вершины O, пропорциональной расстоянию: F=c*OM Н, где c=1 Н/м. В начальный момент точка M находится в точке A, расстояние OA равно a=2 м, начальная скорость v0=2 м/с и направлена параллельно основанию конуса. Определить движение точки M (силой тяжести пренебречь). Положение точки M определяем координатой z и полярными координатами r и φ в плоскости, перпендикулярной оси Oz; уравнение поверхности конуса r2-z2=0.Решение
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1.1
1.2
1.3
1.4
1.5
2.1
2.2
2.3
2.4
2.5
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3.1
3.2
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3.4
3.5
3.6
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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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11.1
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12.1
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13.1
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14.1
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17.1
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18.1
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19.1
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20.1
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21.2
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22.1
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23.1
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24.1
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24.34
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25.1
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26.1
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26.35
27.1
27.2
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27.26
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27.34
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27.48
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27.55
27.58
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27.64
27.65
28.1
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29.1
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30.1
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31.1
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31.34
31.35
32.1
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32.28
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32.31
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32.33
32.34
32.35
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32.37
32.38
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32.48
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32.50
32.51
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32.53
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32.55
32.56
32.57
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32.61
32.62
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32.64
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32.66
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32.72
32.73
32.74
32.75
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32.84
32.85
32.86
32.87
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32.89
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32.91
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32.100
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32.102
32.103
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32.105
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32.107
33.1
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34.1
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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
48.5
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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