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Уважаемые эксперты! Помогите, пожалуйста, решить две задачи и проверить ответ на вопрос из абитуриентской методички. Тема - Закон сохранения импульса.
№1. Шарики 1 и 2 висят: 1- на нити, 2 - на невесомом жестком стержне такой же длины, как и нить. После горизонтальных толчков шарики делают полные обороты в вертикальной плоскости. Найти отношение v1/v2 - минимальных начальных скоростей шариков. Варианты ответов (sqrt-корень квадратный): 1) 2, 2) 2/sqrt(3), 3) 2/sqrt(5), 4) sqrt(3)/2, 5) sqrt(5)/2.
№2. Брусок массы M=990г, скрепленный легкой пружиной жесткости k=10кн/м со стенкой удерживается на гладкой гориз. поверхности в положении, при котором пружина сжата на Δl1=6 см. В момент, когда брусок отпускают, в него попадает и застревает в нем пуля массы m=10 г, летевшая горизонтально с V=800 м/с. Пренебрегая смещением бруска во время движения в нем пули, найти: 1) скорость u бруска после застревания в нем пули, 2) работу Ac, совершенную силой сопротивления, действующей на пулю во время ее движения в бруске, 3) максимальное удлинение Δlmax пружины. В приложении - схематичный рисунок к задаче.
Хотя бы общие рекомендации. Заранее спасибо.
И еще 1 вопрос: Если тело массы m броили под углом a к горизонту со скоростью V0, то мощность N силы тяжести в момент удара о гориз. поверхность земли равна: 1) 0; 2) m*g*V0*cos(a), 3) -m*g*V0*cos(a), 4) m*g*V0*sin(a), 5) -m*g*V0*sin(a)
Приложение: ||_/\/\/\/\/\/\_|_|-----------------|_| - брусок, \/\/\ -пружина, --- - плоскость, брусок на ней лежит, а не висит...
Недостаток свободного времени не позволяет мне вплотную заняться Вашими задачами. А вот на вопрос попробую ответить: правильным будет ответ 4) m*g*V0*sin(a). Думаю, понятно, почему...
Здравствуйте, dark-saber! Вы можете посмотреть решение задачи 1 в приложении. Что касается задачи 2, то попробую решить, если будет время. Ясно, что для её решения нужно применить закон сохранения импульса... С уважением, Mr. Andy.
Приложение: Решение задачи 1.При минимальном натяжении нити шарик 1 будет иметь в верхней точке траектории скорость V1,отличную от v1 и определяемую из соотношений:m*g=m*V1^2/R,(m*v1^2)/2-(m*V1^2)/2=2*m*g*R.Тогда v1=sqrt (5*g*R).Для шарика 2 из закона сохранения энергии получаем:2*m*g*R=(m*v2^2)/2.Тогда v2=2*sqrt (g*R).Следовательно, v1/v2=(sqrt 5)/2.Ответ: (sqrt 5)/2.Заметим, что различие в значениях минимальных начальных скоростей обусловлены различным характером связей (нити и стержня). Для того, чтобы шарик 1 описал окружность, нить не должна провисать. Для шарика 2 траектория обусловлена длиной стержня, который жёсткий.
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Facta loquuntur.
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