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Консультация № 201273
15.07.2021, 10:37
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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 W такое кольцо может разорваться, если для свинца предел
прочности на разрыв, т. е. максимальная сила в расчёте на единицу
площади поперечного сечения Q=F/S=15*10^6 Па? Плотность свинца считать известной и равной 11300 кг/м3.
R = 0,25 м , сделанное из свинцовой проволоки, вращается вокруг вертикальной оси, проходящей через центр кольца. При какой угловой
скорости W такое кольцо может разорваться, если для свинца предел
прочности на разрыв, т. е. максимальная сила в расчёте на единицу
площади поперечного сечения Q=F/S=15*10^6 Па? Плотность свинца считать известной и равной 11300 кг/м3.
Обсуждение
16.07.2021, 19:53
общий
это ответ
Здраствуйте, Dmitriy!
Предлагаю Вам следующее решение задачи.
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.
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.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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