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Консультация № 144930
Обсуждение
Неизвестный
25.09.2008, 17:43
общий
это ответ
Здравствуйте, Fibi4ka!
Запишем закон сохранения момента импульса (указанная вами формула):
I1*w1=I2*w2 (1)
где I1, I2 - момент инерции системы платформа-человек до и после перехода человека с края платформы к её центру, w1,w2 - соответствующие угловые скорости; момент инерции системы до перехода человека состоял из момента инерции платформы Iпл и момента инерции человека Iч; после же перехода человека к центру платформы его момент инерции относительно этой оси стал равен нулю:
I1=Iпл+Iч (2)
I2=Iпл (3)
Поскольку платформа представляет собой диск (цилиндр), а человек - материальную точку, их моменты инерции определяются как:
Iпл=M*R2/2 (4)
где M- искомая масса платформы
Iч=m*R2 (5)
где m=70 кг - масса человека
Подставляя (4) и (5) в (2) и (3) и подставляя получившиеся выражения для I1, I2 в (1) выражаем массу M платформы:
M=m*w12/(w22-w12) (6)
Поскольку угловая скорость связана с частотой n через постоянный множитель 2*pi
w=2*pi*n, в формуле (6) можно перейти к частоте:
M=m*n12/(n22-n12)=70*64/(100-64)=124,4 кг
Запишем закон сохранения момента импульса (указанная вами формула):
I1*w1=I2*w2 (1)
где I1, I2 - момент инерции системы платформа-человек до и после перехода человека с края платформы к её центру, w1,w2 - соответствующие угловые скорости; момент инерции системы до перехода человека состоял из момента инерции платформы Iпл и момента инерции человека Iч; после же перехода человека к центру платформы его момент инерции относительно этой оси стал равен нулю:
I1=Iпл+Iч (2)
I2=Iпл (3)
Поскольку платформа представляет собой диск (цилиндр), а человек - материальную точку, их моменты инерции определяются как:
Iпл=M*R2/2 (4)
где M- искомая масса платформы
Iч=m*R2 (5)
где m=70 кг - масса человека
Подставляя (4) и (5) в (2) и (3) и подставляя получившиеся выражения для I1, I2 в (1) выражаем массу M платформы:
M=m*w12/(w22-w12) (6)
Поскольку угловая скорость связана с частотой n через постоянный множитель 2*pi
w=2*pi*n, в формуле (6) можно перейти к частоте:
M=m*n12/(n22-n12)=70*64/(100-64)=124,4 кг
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