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Консультация № 167985
22.05.2009, 15:18
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Уважаемые эксперты помогите пожалуйста решить задачу следующего содержания (нуждаюсь в срочном ответе):
Тонкий однородный стержень длиной 9.8 м может свободно вращаться вокруг горизонтальной оси, проходящей через один из его концов. Стержень приводят в горизонтальное положение и отпускают. Найти максимальное значение угловой скорости.
Тонкий однородный стержень длиной 9.8 м может свободно вращаться вокруг горизонтальной оси, проходящей через один из его концов. Стержень приводят в горизонтальное положение и отпускают. Найти максимальное значение угловой скорости.
Обсуждение
Неизвестный
23.05.2009, 10:26
общий
это ответ
Здравствуйте, Саша Казаченко Ивановна!
Максимальная угловая скорость стержня будет достигнута им в момент пересечения отвесного положения, когда вся накопленная потенциальная энергия перейдёт в кинетическую. При поднятии стержня из отвесного в горизонтальное положение его центр тяжести поднялся на половину длины стержня, а изменение потенциальной энергии составило:
Wp=m*g*l/2 (1)
Кинетическая энергия вращающегося стержня записывается через его момент инерции I:
Wk=I*[$969$]2/2 (2)
Момент инерции стержня при прохождении оси вращения через один из его концов равен:
I=m*l2/3 (3)
Подставляя (3) в (2) и приравнивая (1) получаем:
g*l/2=l2*[$969$]2/6
откуда выражаем [$969$]:
[$969$]=[$8730$](3*g/l)=[$8730$](3)=1,73 рад/с
Максимальная угловая скорость стержня будет достигнута им в момент пересечения отвесного положения, когда вся накопленная потенциальная энергия перейдёт в кинетическую. При поднятии стержня из отвесного в горизонтальное положение его центр тяжести поднялся на половину длины стержня, а изменение потенциальной энергии составило:
Wp=m*g*l/2 (1)
Кинетическая энергия вращающегося стержня записывается через его момент инерции I:
Wk=I*[$969$]2/2 (2)
Момент инерции стержня при прохождении оси вращения через один из его концов равен:
I=m*l2/3 (3)
Подставляя (3) в (2) и приравнивая (1) получаем:
g*l/2=l2*[$969$]2/6
откуда выражаем [$969$]:
[$969$]=[$8730$](3*g/l)=[$8730$](3)=1,73 рад/с
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