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Консультация № 201420
23.09.2021, 12:16
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Здравствуйте! Прошу помощи в следующем вопросе: Горизонтально расположенное тонкое однородное кольцо радиуса R=0,25 м, сделанное из свинцовой проволоки, вращается вокруг вертикальной оси, проходящей через центр кольца. При какой угловой скорости omega такое кольцо может разорваться, если для свинца предел прочности на разрыв, т. е. максимальная сила в расчёте на единицу площади поперечного сечения sigma=F/S=15*10^6 Па? Плотность свинца rho=11,3*10^3 кг/м^3.
Обсуждение
23.09.2021, 16:26
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Андрей Владимирович уже решил Вашу задачу на странице rfpro.ru/question/201273 (Ссылка)
23.09.2021, 20:27
общий
это ответ
Здраствуйте, Виталий Кочманюк
Предлагаю Вам следующее решение задачи. Оно приводилось здесь.
Дано:
м -- радиус тонкого однородного кольца, сделанного из свинцовой проволоки и вращающегося вокруг вертикальной оси, проходящей через его центр; 
Па -- допускаемое напряжение разрыва; 
кг/м3 -- плотность материала кольца (свинца).
Определить:
-- угловую скорость, при которой кольцо может разорваться.
В соответствии с формулой (8) отсюда: Ссылка >> условие прочности кольца имеет такой вид:
Тогда, чтобы кольцо не разорвалось, угловая скорость его вращения должна удовлетворять неравенству
что после подстановки числовых значений даёт
(рад/с).
Значит, кольцо разорвётся при
рад/с.
Ответ: кольцо разорвётся при рад/с.
Предлагаю Вам следующее решение задачи. Оно приводилось здесь.
Дано:
м -- радиус тонкого однородного кольца, сделанного из свинцовой проволоки и вращающегося вокруг вертикальной оси, проходящей через его центр; Па -- допускаемое напряжение разрыва; кг/м3 -- плотность материала кольца (свинца).Определить:
-- угловую скорость, при которой кольцо может разорваться.Решение
В соответствии с формулой (8) отсюда: Ссылка >> условие прочности кольца имеет такой вид:
Тогда, чтобы кольцо не разорвалось, угловая скорость его вращения должна удовлетворять неравенству
что после подстановки числовых значений даёт
(рад/с).Значит, кольцо разорвётся при
рад/с.Ответ: кольцо разорвётся при
рад/с.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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