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Консультация № 196108
13.08.2019, 22:32
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Жёсткое тонкое кольцо массой m и радиусом R вращается с постоянной угловой скоростью ω вокруг оси, перпендикулярной плоскости кольца и проходящей через его центр. Определите силу упругости T, возникающую в кольце вследствие его вращения.
T = momega^2R/2pi
Жёсткое тонкое кольцо массой m и радиусом R вращается с постоянной угловой скоростью ω вокруг оси, перпендикулярной плоскости кольца и проходящей через его центр. Определите силу упругости T, возникающую в кольце вследствие его вращения.
T = momega^2R/2pi
Обсуждение
14.08.2019, 14:39
общий
это ответ
Здравствуйте, dar777!
В прикреплённом файле находится рисунок, иллюстрирующий решение задачи. Он заимствован мной здесь. Там же предложен и использованный мной "дифференциальный" подход к решению задачи.
Разобьём кольцо на малые элементы
каждый из которых имеет массу 
Запишем второй закон Ньютона для одного малого элемента кольца. Равнодействующая двух сил натяжения сообщает этому элементу нормальное ускорение, следовательно,
Поскольку при
также и 
постольку последнее уравнение можно переписать так:
-- искомая сила.
В прикреплённом файле находится рисунок, иллюстрирующий решение задачи. Он заимствован мной здесь. Там же предложен и использованный мной "дифференциальный" подход к решению задачи.
Разобьём кольцо на малые элементы
каждый из которых имеет массу Запишем второй закон Ньютона для одного малого элемента кольца. Равнодействующая двух сил натяжения сообщает этому элементу нормальное ускорение, следовательно,Поскольку при
также и постольку последнее уравнение можно переписать так:-- искомая сила.
Прикрепленные файлы:
5
Это самое лучшее решение!
Об авторе:
Facta loquuntur.
Facta loquuntur.
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