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Консультация № 200710
23.04.2021, 15:05
0.00 руб.
0
3
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Горизонтальная платформа массой 100 кг вращается вокруг вертикальной оси, проходящей через центр платформы, делая 10 об / мин. Человек массой 60 кг стоит при этом на краю платформы. С какой скоростью начнет вращаться платформа, если человек перейдет от края платформы к ее центру? Считать платформу круглым однородным диском, а человека - точечной массой.
Горизонтальная платформа массой 100 кг вращается вокруг вертикальной оси, проходящей через центр платформы, делая 10 об / мин. Человек массой 60 кг стоит при этом на краю платформы. С какой скоростью начнет вращаться платформа, если человек перейдет от края платформы к ее центру? Считать платформу круглым однородным диском, а человека - точечной массой.
Обсуждение
23.04.2021, 23:13
общий
это ответ
Дано:
mп=100 кг
mч=60 кг
[$969$]1=10 об/мин
Найти: [$969$]2
Решение:
Согласно закону сохранения момента импульса:
сумма моментов импульса платформы и человека на её краю равна моменту импульса платформы, когда человек перейдет и встанет в её центр, поскольку момент импульса материальной точки в центре вращения равен нулю.
То есть
(Jп+Jч)*[$969$]1=Jп*[$969$]2
- здесь
Jп=mп*R2/2 - момент инерции платформы;
Jч=mч*R2 - момент инерции человека на краю платформы.
Тогда
[$969$]2=[$969$]1*[2(mп/2 + mч)]/mп = [$969$]1*(1+2mч/mп)
[$969$]2 = 10 об/мин * (1+2*60/100) = 22 об/мин
*****
Удачи
mп=100 кг
mч=60 кг
[$969$]1=10 об/мин
Найти: [$969$]2
Решение:
Согласно закону сохранения момента импульса:
сумма моментов импульса платформы и человека на её краю равна моменту импульса платформы, когда человек перейдет и встанет в её центр, поскольку момент импульса материальной точки в центре вращения равен нулю.
То есть
(Jп+Jч)*[$969$]1=Jп*[$969$]2
- здесь
Jп=mп*R2/2 - момент инерции платформы;
Jч=mч*R2 - момент инерции человека на краю платформы.
Тогда
[$969$]2=[$969$]1*[2(mп/2 + mч)]/mп = [$969$]1*(1+2mч/mп)
[$969$]2 = 10 об/мин * (1+2*60/100) = 22 об/мин
*****
Удачи
Об авторе:
С уважением
shvetski
С уважением
shvetski
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