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Консультация № 196408
19.09.2019, 19:35
0.00 руб.
1
3
2
Здравствуйте! У меня возникли сложности с таким вопросом:
Два концентрических колеса радиусами R = 50 см и r = 25 см вращаются в противоположные стороны с угловыми скоростями ω1 = 5 рад/с и ω2 = 10 рад/с соответственно. Между ними зажато третье колесо так, как показано на рисунке 1.41. Какова угловая скорость вращения этого колеса вокруг собственной оси? Проскальзывания нет.
Два концентрических колеса радиусами R = 50 см и r = 25 см вращаются в противоположные стороны с угловыми скоростями ω1 = 5 рад/с и ω2 = 10 рад/с соответственно. Между ними зажато третье колесо так, как показано на рисунке 1.41. Какова угловая скорость вращения этого колеса вокруг собственной оси? Проскальзывания нет.
Прикрепленные файлы:
Обсуждение
20.09.2019, 14:35
общий
это ответ
Здравствуйте, dar777!
В первую очередь надо убедиться, выполнимо ли Условие задачи "Проскальзывания нет" ?
Чтобы зажатое колесо3 вращалось м-ду большим (внешним) колесом1 и центральным колесом2 без проскальзывания, необходимо равенство линейных скоростей зажимающих колёс. Проверяем:
Линейная скорость большого колеса V1 = [$969$]1·R = 5·0,5 = 2,5 м/с
Линейная скорость малого, центрального колеса V2 = [$969$]2·r = 10·0,25 = 2,5 м/с
Скорости зажимающих колёс одинаковы. Значит, зажатое колесо3 может вращаться м-ду ними без проскальзывания с той же линейной скоростью V1 .
Диаметр зажатого колеса есть разница м-ду радиусами зажимающих колёс : D3 = R - r = 0,25 м.
Его радиус - вдвое меньше диаметра : R3 = D3/2 = 0,125 м.
Искомая угловая скорость зажатого колеса вокруг собственной оси [$969$]3 = V1/R3 = 20 рад/с .
В первую очередь надо убедиться, выполнимо ли Условие задачи "Проскальзывания нет" ?
Чтобы зажатое колесо3 вращалось м-ду большим (внешним) колесом1 и центральным колесом2 без проскальзывания, необходимо равенство линейных скоростей зажимающих колёс. Проверяем:
Линейная скорость большого колеса V1 = [$969$]1·R = 5·0,5 = 2,5 м/с
Линейная скорость малого, центрального колеса V2 = [$969$]2·r = 10·0,25 = 2,5 м/с
Скорости зажимающих колёс одинаковы. Значит, зажатое колесо3 может вращаться м-ду ними без проскальзывания с той же линейной скоростью V1 .
Диаметр зажатого колеса есть разница м-ду радиусами зажимающих колёс : D3 = R - r = 0,25 м.
Его радиус - вдвое меньше диаметра : R3 = D3/2 = 0,125 м.
Искомая угловая скорость зажатого колеса вокруг собственной оси [$969$]3 = V1/R3 = 20 рад/с .
5
Это самое лучшее решение!
20.09.2019, 16:31
общий
это ответ
Здравствуйте, dar777!
В прикреплённом файле находится решение этой задачи, которое я заимствовал здесь. В нём на рисунке показано распределение линейных скоростей точек третьего колеса. Отсутствующие в решении единицы измерения величин соответствуют СИ.
В прикреплённом файле находится решение этой задачи, которое я заимствовал здесь. В нём на рисунке показано распределение линейных скоростей точек третьего колеса. Отсутствующие в решении единицы измерения величин соответствуют СИ.
Прикрепленные файлы:
5
Это самое лучшее решение!
Об авторе:
Facta loquuntur.
Facta loquuntur.
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