Задача №27.65
Условие
Точка M массы m движется под действием силы тяжести по гладкой внутренней поверхности полого цилиндра радиуса r. В начальный момент угол φ0=π/2, а скорость точки равнялась нулю. Определить скорость точки M и реакцию поверхности цилиндра при угле φ=30°.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
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2.18
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2.20
2.21
2.22
2.23
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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
3.14
3.15
3.16
3.17
3.18
3.19
3.20
3.21
3.22
3.23
3.24
3.25
3.26
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3.31
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3.33
3.34
3.35
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3.38
4.1
4.2
4.3
4.4
4.5
4.6
4.7
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4.12
4.13
4.14
4.15
4.16
4.17
4.18
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4.20
4.21
4.22
4.23
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4.25
4.26
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4.29
4.30
4.31
4.32
4.33
4.34
4.35
4.36
4.37
4.38
4.39
4.40
4.41
4.42
4.43
4.44
4.45
4.46
4.47
4.49
4.50
4.51
4.52
4.53
4.54
4.55
4.56
4.57
4.58
4.59
4.61
4.62
4.63
4.64
4.65
4.66
4.67
4.68
4.69
4.70
4.71
4.72
4.73
4.74
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
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5.12
5.13
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5.21
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5.42
6.1
6.2
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6.6
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7.1
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8.1
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8.31
8.32
8.33
8.34
8.35
8.36
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8.38
8.39
8.40
8.41
8.42
8.43
9.1
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9.3
9.4
9.5
9.6
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9.13
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9.15
9.16
9.17
9.18
9.19
9.20
9.21
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9.26
9.27
10.1
10.2
10.3
10.4
10.5
10.6
10.7
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10.21
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10.23
11.1
11.2
11.3
11.4
11.5
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11.7
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12.1
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12.21
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12.26
12.27
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12.40
13.1
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14.1
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15.1
15.3
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16.1
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16.41
17.1
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18.1
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18.41
19.1
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20.1
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21.2
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22.1
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22.26
22.27
23.1
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23.31
23.32
23.33
23.34
23.35
23.36
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23.42
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23.44
23.45
23.46
23.47
23.48
23.49
23.50
23.51
23.52
23.53
23.54
23.55
23.56
23.57
23.58
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23.60
23.61
23.62
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23.64
23.65
23.66
23.67
23.68
23.69
23.70
23.71
24.1
24.2
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24.11
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24.26
24.27
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24.31
24.34
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25.1
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26.1
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26.26
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26.33
26.34
26.35
27.1
27.2
27.3
27.4
27.5
27.6
27.7
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27.10
27.11
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27.21
27.22
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27.24
27.25
27.26
27.27
27.28
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27.32
27.33
27.34
27.35
27.36
27.37
27.38
27.39
27.40
27.41
27.42
27.43
27.44
27.45
27.46
27.47
27.48
27.49
27.50
27.51
27.52
27.54
27.55
27.58
27.59
27.60
27.61
27.62
27.63
27.64
27.65
28.1
28.2
28.3
28.4
28.5
28.6
28.7
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28.11
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29.1
29.2
29.3
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29.5
29.6
29.7
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30.1
30.2
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30.4
30.5
30.6
30.7
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30.11
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30.26
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30.30
31.1
31.2
31.3
31.4
31.5
31.6
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31.9
31.11
31.13
31.14
31.15
31.16
31.17
31.18
31.19
31.20
31.21
31.22
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31.25
31.26
31.27
31.28
31.29
31.30
31.31
31.32
31.33
31.34
31.35
32.1
32.2
32.3
32.4
32.5
32.6
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32.8
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32.10
32.11
32.12
32.13
32.14
32.15
32.16
32.17
32.18
32.19
32.20
32.21
32.22
32.23
32.24
32.25
32.26
32.27
32.28
32.29
32.30
32.31
32.32
32.33
32.34
32.35
32.36
32.37
32.38
32.39
32.40
32.41
32.42
32.43
32.44
32.45
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
32.63
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
32.79
32.80
32.81
32.82
32.83
32.84
32.85
32.86
32.87
32.88
32.89
32.90
32.91
32.92
32.93
32.94
32.95
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
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33.6
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33.12
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33.16
33.17
33.18
33.19
33.20
33.21
33.22
34.1
34.2
34.3
34.4
34.5
34.6
34.7
34.8
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34.10
34.11
34.12
34.13
34.14
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34.16
34.17
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34.21
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34.27
34.28
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34.31
35.1
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35.21
36.1
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36.4
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36.13
36.14
37.1
37.2
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37.4
37.5
37.6
37.7
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37.11
37.12
37.13
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37.15
37.16
37.17
37.18
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37.25
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37.28
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37.31
37.32
37.33
37.34
37.35
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37.37
37.38
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37.41
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37.44
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37.48
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37.54
37.55
37.56
37.57
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37.59
38.1
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38.35
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38.38
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38.48
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38.53
39.1
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40.1
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41.1
41.2
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41.5
41.6
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41.16
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41.20
41.21
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41.23
42.1
42.2
42.3
42.4
42.5
42.6
42.7
42.8
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42.11
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42.18
43.1
43.2
43.3
43.4
43.6
43.7
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43.13
44.1
44.2
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45.3
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45.37
46.1
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47.1
47.2
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48.1
48.5
48.6
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48.34
48.35
48.38
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48.44
48.48
48.49
49.1
49.2
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49.11
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49.16
53.5
53.12
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54.1
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54.18
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54.32
54.33
54.35
55.2
55.3
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55.25
55.38
55.41
55.44
56.3
56.7
56.9