Задача №30.18
Условие
Две ненапряженные пружины AC и BC, расположенные по горизонтальной прямой Ax, прикреплены шарнирами к неподвижным точкам A и B, а в точке C — к гире массы 2 кг. Пружина AC сжимается на 1 см силой 20 Н, а пружина CB вытягивается на 1 см силой 40 Н. Расстояние AC=BC=10 см. Гире C сообщена скорость v0=2 м/с в таком направлении, что при последующем движении она проходит через точку D, координаты которой xD=8 см, yD=2 см, если за начало координат принять точку A и координатные оси направить, как указано на рисунке. Определить скорость гири в момент прохождения ее через точку D, лежащую в вертикальной плоскости xy.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
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
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2.20
2.21
2.22
2.23
2.24
2.25
2.26
2.27
2.28
2.29
2.30
2.31
2.32
2.33
2.34
2.35
2.36
2.37
2.38
2.39
2.40
2.41
2.42
2.43
2.44
2.45
2.46
2.47
2.48
2.49
2.50
2.51
2.52
2.53
2.54
2.55
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
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3.15
3.16
3.17
3.18
3.19
3.20
3.21
3.22
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3.24
3.25
3.26
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3.32
3.33
3.34
3.35
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4.1
4.2
4.3
4.4
4.5
4.6
4.7
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4.31
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4.44
4.45
4.46
4.47
4.49
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4.51
4.52
4.53
4.54
4.55
4.56
4.57
4.58
4.59
4.61
4.62
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4.64
4.65
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4.74
5.1
5.2
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5.4
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5.6
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6.1
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9.1
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9.4
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10.1
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11.1
11.2
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12.1
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13.1
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14.1
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15.1
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16.1
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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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23.71
24.1
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24.34
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25.1
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26.1
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26.33
26.34
26.35
27.1
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27.4
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27.32
27.33
27.34
27.35
27.36
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27.38
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27.40
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27.43
27.44
27.45
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27.47
27.48
27.49
27.50
27.51
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27.55
27.58
27.59
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27.61
27.62
27.63
27.64
27.65
28.1
28.2
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28.5
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29.1
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30.1
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30.6
30.7
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30.30
31.1
31.2
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31.25
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31.34
31.35
32.1
32.2
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32.4
32.5
32.6
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32.17
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32.20
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32.26
32.27
32.28
32.29
32.30
32.31
32.32
32.33
32.34
32.35
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32.37
32.38
32.39
32.40
32.41
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32.43
32.44
32.45
32.46
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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
32.63
32.64
32.65
32.66
32.67
32.68
32.69
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32.72
32.73
32.74
32.75
32.76
32.77
32.79
32.80
32.81
32.82
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32.84
32.85
32.86
32.87
32.88
32.89
32.90
32.91
32.92
32.93
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32.96
32.97
32.98
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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34.1
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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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38.53
39.1
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40.1
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41.1
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42.1
42.2
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42.4
42.5
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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
47.2
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48.1
48.5
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48.31
48.33
48.34
48.35
48.38
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48.44
48.48
48.49
49.1
49.2
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53.5
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54.1
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54.35
55.2
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55.38
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56.3
56.7
56.9