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Консультация № 193483
24.08.2018, 13:01
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
10-6. На горизонтальной плоскости лежит тонкий однородный стержень массы m =1 кг и длины l, который может вращаться вокруг вертикальной оси, проходящей через конец стержня О. Под углом альфа =30 градусов к стержню в той же плоскости движется маленький пластилиновый шарик такой же массы m со скоростью v = 1 м/с. Шарик прилипает к концу стержня, и система приобретает угловую скорость вращения omega. Найти угловую скорость вращения системы после удара, если l = 1 м. Сделать рисунок.
10-6. На горизонтальной плоскости лежит тонкий однородный стержень массы m =1 кг и длины l, который может вращаться вокруг вертикальной оси, проходящей через конец стержня О. Под углом альфа =30 градусов к стержню в той же плоскости движется маленький пластилиновый шарик такой же массы m со скоростью v = 1 м/с. Шарик прилипает к концу стержня, и система приобретает угловую скорость вращения omega. Найти угловую скорость вращения системы после удара, если l = 1 м. Сделать рисунок.
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Обсуждение
27.08.2018, 16:44
общий
это ответ
Здравствуйте, dar777!
До столкновения моменты количества движения стержня и шарика относительно точки O:
Lстержня = 0, Lшарика = mvl sin([$945$]) = mvl/2.
После столкновения:
Lстержня = J[$969$], Lшарика = ml2[$969$].
Здесь J - момент инерции стержня, J = ml2/3.
Система шарик + стержень изолирована, поэтому момент количества движения сохраняется:
mvl/2 = (ml2/3) [$969$] + (ml2) [$969$].
Отсюда находим [$969$] = (3/8)(v/l).
Подставляя численные значения, получим [$969$] = 3/8 рад/с.
До столкновения моменты количества движения стержня и шарика относительно точки O:
Lстержня = 0, Lшарика = mvl sin([$945$]) = mvl/2.
После столкновения:
Lстержня = J[$969$], Lшарика = ml2[$969$].
Здесь J - момент инерции стержня, J = ml2/3.
Система шарик + стержень изолирована, поэтому момент количества движения сохраняется:
mvl/2 = (ml2/3) [$969$] + (ml2) [$969$].
Отсюда находим [$969$] = (3/8)(v/l).
Подставляя численные значения, получим [$969$] = 3/8 рад/с.
5
У меня нет слов. Это просто чудо!
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