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Консультация № 151544
23.11.2008, 16:58
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Здравствуйте! Выручайте, уважаемые эксперты!
Лодка длиной l=3 м и массой m=120 кг стоит на спокойной воде. На носу и корме находятся 2 рыбака массами m1=60 кг и m2=90 кг. На сколько сдвинется лодка относительно воды, если рыбаки поменяются местами?
Лодка длиной l=3 м и массой m=120 кг стоит на спокойной воде. На носу и корме находятся 2 рыбака массами m1=60 кг и m2=90 кг. На сколько сдвинется лодка относительно воды, если рыбаки поменяются местами?
Обсуждение
Неизвестный
24.11.2008, 15:40
общий
это ответ
Здравствуйте, Яровой Сергей Владимирович!
Здесь нужно применить закон сохранения количества движения.
Сначала рассмотрим перемещение первого рыбака, а потом перемещение второго.
1) Так как в начале лодка и рыбаки не двигались, то общий импульс системы равен нулю, тогда
(m(л) + m2)*v(л)= - m1*v2. (1)
Время движения первого рыбака совпадает с временем движения лодки, тогда в (1) v(л) можно заменить перемещением лодки l1 при перемещении первого рыбака (перемещение которого – l ). С учётом сказанного (1) перепишется в виде
(m(л) + m2)* l1= - m1* l. (2)
Откуда
l1 = - m1* l / (m(л) + m2)
Аналогично при перемещении второго рыбака
l2 = m2* l / (m(л) + m1)
l1 = -60 * 3 /(120 + 90) = - 6/7 (м)
l2 = 90* 3 / (120 + 60) = 3/2 (м)
Полное перемещение лодки
lп = l1 + l2 = 3/2 – 6/7 = 9/14 (м).
Здесь нужно применить закон сохранения количества движения.
Сначала рассмотрим перемещение первого рыбака, а потом перемещение второго.
1) Так как в начале лодка и рыбаки не двигались, то общий импульс системы равен нулю, тогда
(m(л) + m2)*v(л)= - m1*v2. (1)
Время движения первого рыбака совпадает с временем движения лодки, тогда в (1) v(л) можно заменить перемещением лодки l1 при перемещении первого рыбака (перемещение которого – l ). С учётом сказанного (1) перепишется в виде
(m(л) + m2)* l1= - m1* l. (2)
Откуда
l1 = - m1* l / (m(л) + m2)
Аналогично при перемещении второго рыбака
l2 = m2* l / (m(л) + m1)
l1 = -60 * 3 /(120 + 90) = - 6/7 (м)
l2 = 90* 3 / (120 + 60) = 3/2 (м)
Полное перемещение лодки
lп = l1 + l2 = 3/2 – 6/7 = 9/14 (м).
Неизвестный
24.11.2008, 23:47
общий
2Valeriy81: Такой вопрос: почему в импульсе лодки в обоих уравнениях учитывается лишь масса лодки и одного из рыбаков? Ведь скорость лодки, приобретаемая из-за взаимодействия с одним рыбаком, относится и к изменению скорости другого рыбака, который никуда с лодки не уходит, или я что-то неправильно понял? Объясните, пожалуйста, поподробней, как вы составляли уравнения импульсов тел?
Неизвестный
28.11.2008, 16:04
общий
Ошибочка-с. Можно следовать логике Valeriy81, но надо не забывать, что движение рыбака происходит относительно лодки, а относительно берега оно будет меньше, тоесть в уравнениях вместо l надо писать (l-l1) и (l-l2) соответственно или прислушатся к Andrekk и считать полные массы движущихся системм. В любом случае результат будет тот же и с ответом он не совпадает.
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