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Консультация № 160037
09.02.2009, 19:49
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Доброго времени суток, Уважаемые эксперты.
Помогите в решении задачи, не могу понять как это выглядит и решается:
По касательной к шкиву маховика в виде диска диаметром 75 см и массой 40 кг приложена сила 1 кН. Определить угловое ускорение и частоту вращения маховика через 10 с после начала действия силы, если радиус шкива равен 12 см. Силой трения пренебречь.
Помогите в решении задачи, не могу понять как это выглядит и решается:
По касательной к шкиву маховика в виде диска диаметром 75 см и массой 40 кг приложена сила 1 кН. Определить угловое ускорение и частоту вращения маховика через 10 с после начала действия силы, если радиус шкива равен 12 см. Силой трения пренебречь.
Обсуждение
Неизвестный
09.02.2009, 22:03
общий
это ответ
Здравствуйте, Мария Романова!
Решение:
Дано: Rдиска = 37,5см = 0,375м; rшкива = 12см = 0,12м; F = 1кН = 10^3H.
Результирующий момент силы: М = F*r. (1)
Основной закон динамики вращательного движения: М = J*ε, (2)
где ε – угловое ускорение, J – момент инерции. Для диска (как цилиндра) момент инерции равен Jдиска= m*R^2/2. (3).
Сопоставляя (1) – (3) получим:
ε = М/Jдиска = (F*r)/(m*R^2/2)=(2*10^3H*0,12м)/(40кг*(0,375м)^2) = 42,66 с^-2.
Угловая скорость: ω = Инт(ε*dt) = ε*t = 426,6 с^-1.
Частота вращения n = ω/(2*pi) = 426,6/6,28 = 68 об/с
Ответ: Ускорение равно 42,66 с^-2. Частота вращения 68 об/с.
Решение:
Дано: Rдиска = 37,5см = 0,375м; rшкива = 12см = 0,12м; F = 1кН = 10^3H.
Результирующий момент силы: М = F*r. (1)
Основной закон динамики вращательного движения: М = J*ε, (2)
где ε – угловое ускорение, J – момент инерции. Для диска (как цилиндра) момент инерции равен Jдиска= m*R^2/2. (3).
Сопоставляя (1) – (3) получим:
ε = М/Jдиска = (F*r)/(m*R^2/2)=(2*10^3H*0,12м)/(40кг*(0,375м)^2) = 42,66 с^-2.
Угловая скорость: ω = Инт(ε*dt) = ε*t = 426,6 с^-1.
Частота вращения n = ω/(2*pi) = 426,6/6,28 = 68 об/с
Ответ: Ускорение равно 42,66 с^-2. Частота вращения 68 об/с.
Форма ответа
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