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Консультация № 108525
08.11.2007, 07:42
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Уважаемые эксперты, пожалуйста помогите решить задачки. Заранее большое спасибо. C уважение Роман Александрович.
1) Деревянный стержень массой m = 1 кг, и длинной l = 0,4 м. может вращаться около оси, проходящей через его середину перпендикулярно стержню. В конец стержня попадает пуля массой 0,01 кг, летящая перпендикулярно стержню со скоростью 200 м/с. Сколько оборотов в секунду будет делать стержень, если пуля застрянет в нём?
1) Деревянный стержень массой m = 1 кг, и длинной l = 0,4 м. может вращаться около оси, проходящей через его середину перпендикулярно стержню. В конец стержня попадает пуля массой 0,01 кг, летящая перпендикулярно стержню со скоростью 200 м/с. Сколько оборотов в секунду будет делать стержень, если пуля застрянет в нём?
Обсуждение
Неизвестный
09.11.2007, 00:21
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это ответ
Здравствуйте, Чурнов Роман Александрович!
Так как на систему стержень-пуля не действует крутящий момент внешних сил, то будет выполняться закон сохранения момента импульса:
J1*w1 = (J1 + J2)*w2
J1 = m*(L/2)^2 = 1/4*m*L^2 - момент инерции пули относительно оси вращения, m - масса пули, L/2 - расстояние от пули до оси вращения
J2 = 1/12*M*L^2 - момент инерции стержня относительно его середины.
w1 = v/(L/2) = 2*v/L - угловая скорость пули относительно оси в момент удара
w2 = w1*J1/(J1 + J2) = 2*v/L*1/4*m*L^2/(1/12*M*L^2 + 1/4*m*L^2) = (v/L)*6*m/(M + 3*m) = (200/0,4)*6*0,01/(1 + 0,03) = 30 рад/сек = 4,8 оборота/сек
Так как на систему стержень-пуля не действует крутящий момент внешних сил, то будет выполняться закон сохранения момента импульса:
J1*w1 = (J1 + J2)*w2
J1 = m*(L/2)^2 = 1/4*m*L^2 - момент инерции пули относительно оси вращения, m - масса пули, L/2 - расстояние от пули до оси вращения
J2 = 1/12*M*L^2 - момент инерции стержня относительно его середины.
w1 = v/(L/2) = 2*v/L - угловая скорость пули относительно оси в момент удара
w2 = w1*J1/(J1 + J2) = 2*v/L*1/4*m*L^2/(1/12*M*L^2 + 1/4*m*L^2) = (v/L)*6*m/(M + 3*m) = (200/0,4)*6*0,01/(1 + 0,03) = 30 рад/сек = 4,8 оборота/сек
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