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Консультация № 175114
10.12.2009, 22:01
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Здравствуйте!Помогите,пожалуйста,решить задачу:)
Космический корабль массой М=6,0 m,выбрасывает топливо с относительной скоростью U=3км/с.Масса корабля изменяется вследствие сгорания топлива с постоянной скоростью U=160кг/с.На сколько возрастает скорость за 30с работы двигателей?
Заранее благодарю за ответ:)
Космический корабль массой М=6,0 m,выбрасывает топливо с относительной скоростью U=3км/с.Масса корабля изменяется вследствие сгорания топлива с постоянной скоростью U=160кг/с.На сколько возрастает скорость за 30с работы двигателей?
Заранее благодарю за ответ:)
Обсуждение
Неизвестный
11.12.2009, 00:31
общий
это ответ
Здравствуйте, Сапогова Анжелика Вадимовна.
Запишем дифференциальное уравнения Мещерского для тела переменной массы:
M*dV/dt - U*dM/dt = 0
здесь dM - уменьшение массы корабля; U - относительная скорость выбрасываемого топлива; dV - увеличение скорости корабля;
dV = U*dM/M
Интегрируем: V = U*lnM + c
c находим из начальных условий(V=0; M=M0=6,0 m):
V = - U*ln(M0/M);
(знак минус означает, что скорость корабля V направлена в противоположную сторону относительно скорости топлива U)
Из условия M = M0 - u*t ; (u - уменьшение массы корабля в единицу времени)
V = - U*ln(M0/(M0 - u*t))
За первые 30с (∆t=t - 0=t) скорость корабля возрастет на:
∆V = U*ln(M0/(M0 - u*t)) = 3*ln(6000/(6000 - 160*30)) = 4.828 (км/с)
Запишем дифференциальное уравнения Мещерского для тела переменной массы:
M*dV/dt - U*dM/dt = 0
здесь dM - уменьшение массы корабля; U - относительная скорость выбрасываемого топлива; dV - увеличение скорости корабля;
dV = U*dM/M
Интегрируем: V = U*lnM + c
c находим из начальных условий(V=0; M=M0=6,0 m):
V = - U*ln(M0/M);
(знак минус означает, что скорость корабля V направлена в противоположную сторону относительно скорости топлива U)
Из условия M = M0 - u*t ; (u - уменьшение массы корабля в единицу времени)
V = - U*ln(M0/(M0 - u*t))
За первые 30с (∆t=t - 0=t) скорость корабля возрастет на:
∆V = U*ln(M0/(M0 - u*t)) = 3*ln(6000/(6000 - 160*30)) = 4.828 (км/с)
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